rgenoud/0000755000176200001440000000000012553121055011714 5ustar liggesusersrgenoud/inst/0000755000176200001440000000000012163254567012705 5ustar liggesusersrgenoud/inst/CITATION0000644000176200001440000000273211560203507014032 0ustar liggesuserscitHeader("To cite 'rgenoud' in publications use:") citEntry(entry = "Article", title = "Genetic Optimization Using Derivatives: The {rgenoud} Package for {R}", author = personList(person(c("Walter", "R."), "Mebane, Jr."), as.person("Jasjeet S. Sekhon")), journal = "Journal of Statistical Software", year = "2011", volume = "42", number = "11", pages = "1--26", url = "http://www.jstatsoft.org/v42/i11/", textVersion = paste("Walter R. Mebane, Jr., Jasjeet S. Sekhon (2011).", "Genetic Optimization Using Derivatives: The rgenoud Package for R.", "Journal of Statistical Software, 42(11), 1-26.", "URL http://www.jstatsoft.org/v42/i11/.") ) citEntry(header="To refer to the theory on which this package is based, also cite:", entry="Article", title = "Genetic Optimization Using Derivatives: Theory and Application to Nonlinear Models", author = personList(as.person("Jasjeet S. Sekhon"), person(c("Walter", "R."), "Mebane, Jr.")), journal = "Political Analysis", year = "1998", volume = "7", pages = "189--213", textVersion = paste("Jasjeet S. Sekhon, Walter R. Mebane, Jr. (1998).", "Genetic Optimization Using Derivatives: Theory and Application to Nonlinear Models", "Political Analysis, 7, 189-213.") ) citFooter("BibTeX entries for LaTeX users: use\n", sQuote('toBibtex(citation("rgenoud"))')) rgenoud/inst/doc/0000755000176200001440000000000012553042713013441 5ustar liggesusersrgenoud/inst/doc/Figures/0000755000176200001440000000000012142033214015033 5ustar liggesusersrgenoud/inst/doc/Figures/fig1.pdf0000644000176200001440000002366711762732324016411 0ustar liggesusers%PDF-1.5 % 1 0 obj << /Type /ObjStm /Length 425 /Filter /FlateDecode /N 11 /First 66 >> stream x]k0+޻>=J` l&BLJGwԉVA:}#!! $/"Jdyq@ $ RAH|sy ^5+1Rsiko nRyBGqgg]5TkZ8W1:խy︼8z!nMj F\s uőCе9ֺԝۚHq+ sZW'$jŵOj Z:n^٧Fp!7,[MxŪ>Ptp~ݺ$LPf hd: S2q qZYM"Y5:4qdlߝ^gxƾvt7OLѐV|endstream endobj 13 0 obj << /Subtype /XML /Type /Metadata /Length 1319 >> stream 2012-06-03T12:02:44-07:00 2012-06-03T12:02:44-07:00 UnknownApplication Untitled endstream endobj 14 0 obj << /Filter /FlateDecode /Length 7608 >> stream x|Ku9n;[F]@AcThAõu*6IHjI___y~;՟~ï_֏?Vd}>eԯAُX|LǗ9˳~qUUbH {VҒmrjqHs/k\PvR)9רmQЎYZ) {c3˞YcQy*%FN4F=55vʵfP4 ZdoCe!{(<8O[ikOh^yJT:H 4Ϟ4~V)_%"7c:j9VZTmU5{BBC,5"pm)-z~/rsQoZ>5gh^:=,eLi3JjNh %'}}ԙ3K2/\KPJ~,IYVWKVYU\o9[7r:)5۫'jeΑ֎\A q>e($c`+}o3!st(+ј)nUjhk?:hUe!/dRI!qL) %ʆ;MI;? jeHɻأ^%ZV!.Bb!G"!*-l zQYvzkAg*V=46QtghDÉj1, T1|`LS$ߺJCQaDo9kMc@-lm_m, N_hȲBDЯ!RN) mwQ AbANtgΛ>/{*ztzt#(I| IUˢKZ>/TS룅-ޒ;$ }fO&tkPtYA!蚯 <ƮsSl|}GvCH=)-n¶WiRap,(}o۬kAZK;Eњut{ˆ>5d'g0žxVa 65[ il<jkfG8e.7L68]Vy[kI9Gˠ;mZa_[Eev(ʠP/'tjlyS"RFj2(:֑y48L@PSIPXՒܛ|دd :-ԘS0UN{8|)0/DBa5'i=IRiЇσ߹$8,U8ФY}yȽS2?C`6xVѰ6 kT%iyR!wú&Z6R/Jny?liI/tN?`M]av'~`J|R; j Ծ J7 rOi+gQ5Zv+5M tZIt]-X:wL<}Y۶?tӡ看$∦N]nn(Q7IdZ&8G}J#n{'d iZY(O'ܠ$R֪TZٹ*z:kls,L|Qԩ M+;g+ڥwM 4jy[gfNujivW:+\nPQ76˳84 Jy:MrbS^O-=C?iZWN3Yٲ@i[ҳ&N[^X͝&[vYUuYBkNGjik ݴ608W*kv坲Z:ee=W<h6VH(8z?I~I<$ͱ^;s4t+mTŶ}3`rgh4le=Չt⧕&|+yKml1Ԟ%h̃ɲĦK6vӫ.hyجhvXX˶wYYFjŖM+b>[v33JV-ZYZ';v<'ɿig]N֦dؖ-PZP@[wS-#)tYcN,<(ZV5m^Ҁo&k`[DO^x~glֆzwIҶDc_jvRWnVbsMro=s}Ė&R_g=(TI+*:udWY̞ҴRFmzh95JPVmBԚCɠm͸M".$挢ii2bbt z9a44Zg'MVhgc<] ze=N;185]U*'xޤ  k J%Oק4 :A,lZMcC2qiaE/,&mBj7-,N'5ɽ_(-Z'+*.ZF]`<13an>ͻ;gypgqJɒ`_I)NxJOjWZ]9>V/IDckZ:}w|vr }WsCr®.giUhZD%:5ihTN8(iPNsnKgn>\VtEwOt8gw2uXSI=YCVu?.(SV=iU.{ߋ6?i/oAtZU7Iz7PAe%H7G?‡ѵNC>`yU!9@z,)jQhS<*wNe Z;'}Ѵw9ƃ L+hSWI4(ZԭQmN{zJsQ4Ԫɻ*AAP=//h_lݰwpk4!syL?s nޠF'+w,}*?~lHЙ-m#Hn-T{{fG{t:mb랼㘫nG,|J/k%l/J)4"yyR.-:M5Ӏ/M8sg86]8`5@NX Qtz&1)ُs 0O܄ [ZX& |ţ"C0F\}_ pODRԤuO[\=RϯIۺT\՗Ez =]0MC1><}y_G޴D8ɟgiăƸmLCbDQγaۄFn6*N֊4-7pǶZmIV2u,ent:<礱5Vi#C&b ^4w*0cjs}ΛbvxT>&#['ֳ(]WK@yeEA[z::YTڴdSMto:SS 7 ZK3UIv8HvnV8(ٶI;FLGS*}R g*#ns5k)xd^orILu竬CiH0p,ѩ({vx-[^裳;Ewt/].JwX&:IPիAJ'*c7{W6t.=c nmM4m=KZt M:Os}ZO&p+EdIԤ]r& >-?vj3P:K9RsCTn^|o86wSM ]X2wxxq^.C#~z+@AWێ(F5ʒU J;[Ȕ=mtI<iUFc1˗4 Q !1jotki"oҞ+8@FSu4[֥w8ElmUO.Tm!e}y׮ȌG/lgHahGDKzsksK$A󺌵&z-/jv\M'ϓz18c6=cdxPNut7,iau?:tcDv'K 8WۭvȺuDOZC}%7/@Ѻ;77d[y~ek8^P: ޜt޳_3xA1hq!./{vћ={׍W`s  7:sM>#/>I33tw}O@oA1B7ݸ{܎;A;O; !wxsAwQww Sw܃Txw <|Py>0owf;{w'4w Ko\;wڍK+n|@ݸy߾"wqoTEPq_1+"ÝJN8#0*ā~Ċ8o$<<~cMET w❓ƸnLP%ӌnύ +;]7.q}ܸG߸m7 Υ q{nLQДBs1IAD,.L޹xWB9n8)ToUмg_qVA+z-㰼/EGחv__[5KkKoE2nYЊ^4Gk溼ƶy?_#frn\\Њ^˸9jGkw}qy>2n/hů=V6z1k {c Cq-}U #V8Gsuxi{y}$yz1®= !&a|>]Qv&nO[ը"G OXk}ñ][퓷inPw#;Hb#nq;@F! 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pU)]ER3qf]WOWwZknODVMI^eytj&/ȝ2+_3^Z譭IZp+8]M;ЉZ1jZ{CoI[5߇"{QZjh{iݟ#UUg@O ne'V}k5R]%tsa?~ZMB,֋YpL$5_[~mnگrSVrWo^VCwWT;=w}@"JMN knlK$ob|BVVFگ:ZRM5tia)F-)]GhEj~IKXE6_LkUTip'0~Le؉qЪSm]mĖg*-%E/2%*;ei괹{<Ͷī~Ҍj7h=eV׶k٧Ɍ5ҷ6D'v{%$|YFVjԌLT▜,2IHQvV#$Ɍ%{bm;IĴ{gTںp2I?~:)Yzj,_oWѝsc}g*FTrN15l}%T~oiA6.X,DbnK E4Pi1F(Ɣ/7nlε(֣:RYۼbV,ʵVP~չPTc:榚^_jFcZU|O{}M@:~VqZ4ݧ%$.lZB5trQ֩O o'e>J|8IN1KW-('*zI&RRK}W:ʍ.W)(i 5 BN33%JhQVse̢FxZeNQoTҾ'Rq́p;@1zPvSX4k(Rn؜^&8hErQc ciQEѪ'$^&^yL+Zt0r:|NRU!ֱ4dbݒWl,V*th9:ZPrsOM֟8\ThuiIEEwL&&8IJqeY*F9TbqJtUiBnIvԜiSIF)N\4ШҍG$ٵҶ2qРԊRYEE=|MphH[DpԼNMo&Hʎ2rנԒne%$q5ba7k%odcK7FЕDe%+nUʥH7/(R\M&gbqtp֚{w9ӭ.u{^+,2RnтݕZZV 3wMsLO'is-k{wWD4pPyڕK]BjLF.T*4h\s4؆:Uӥ<RN9.v^h ^OORs}t#PmJi('LpЋqsy3<>.U+:55rK2g`t\i┚Ry_OC)_Dܚ]L!^#8yps˃O4)6ZLuONr}ǠR otaJjExT]"NU]+NWkr| N+R6 yZ%u$r=P8zWO_21yI+e SӍ=gzC?nV}0qRPI @8:/LMҍJ8UaYשOYfrʢey04TnZvӧ+{NtmgP-N>78DZR}ɾ_tSm?)8([F0RY`ԟ%m'T1Ro$c8VӇ3XYGEs]b%n@IrDoݣuONr}Fja(.ٓ媱S`wN-Mmm1©Q^:4q;p_JEiJ7gH3Jg/Dʰ]W3IbTu=e$6A7{y [zxF[$k/;GN)o*pq% TNaI&^*`ja MjR(Tԓ@8:Kۯ;HsˏNT5g)IۖH># G*y'4y5M+(qrRRe8Qha(C*kɽHԌ$#NY|/0BC].*jO%nN G Ӌ.ԥ&5UW*z͗3~vRNyI9˽Rji뙳: 5 Ӄ̕M]؊RSps(K#8(A(*.24wYGIG+wDhSiՌm:);m>Fy|(^1J8T8FhӡIS-4VM5tLj5HSwfmG=R^JmKʗG3%*RmG2،D+f]hmJ(Ӎ:qQUFε*uJXB[eʜ^f)9;ry#RY*II|FFճNNNܵ3FNRpk3dF)$\ M4fQ҆(ڞW{<NVvNT՞ %u%7z=OLt T/yo[~(̄R5de|cN,<($kSQa@Mg_VmR;_:O*SXaFN-Yܑ:4F5;Hgy+Dz- PB^O'rRn/8F?-b'T Pdֳ#gy+Dz- PB^O'rRn/8F?-b'T Pdֳ# endstream endobj 9 0 obj 36787 endobj 10 0 obj /DeviceGray endobj 11 0 obj << /Filter [ /DCTDecode ] /Width 106 /Height 106 /ColorSpace 10 0 R /BitsPerComponent 8 /Length 12 0 R >> stream JFIF++C  $" &0P40,,0bFJ:Ptfzxrfpnnpڢ| jj-!1QA"a2qRr#3?8B–^$j Z%sźupnxʺE#&d_R[j- w[4Fsg>xa\Znt+4fԓ%{^J}]hoW%mMOO܎<"U ;lI;iUg [kV]YU8t%y^Tm&s{Kgri/lo2&ؚ f&ک5OUiMWIֻrV 6ֵ_1M6ܛ&nME7niw my40)_,H9k[˦4.ֹmVƅ_U[o>i(8ѓ)/eG`f_U{A +WF|&vZft\ٸ9)\9֍6.k_h{x&.'n)KM;`Utٙ> endobj 16 0 obj 905 endobj 17 0 obj << /Title (lqdxmpl2B.pdf) /CreationDate (D:20120603155857) /ModDate (D:20120603155857) /Producer (ImageMagick 6.5.7-8 2012-04-30 Q16 http://www.imagemagick.org) >> endobj xref 0 18 0000000000 65535 f 0000000010 00000 n 0000000059 00000 n 0000000118 00000 n 0000000316 00000 n 0000000407 00000 n 0000000425 00000 n 0000000463 00000 n 0000000484 00000 n 0000037451 00000 n 0000037472 00000 n 0000037500 00000 n 0000038545 00000 n 0000038565 00000 n 0000038581 00000 n 0000038601 00000 n 0000038623 00000 n 0000038643 00000 n trailer << /Size 18 /Info 17 0 R /Root 1 0 R >> startxref 38823 %%EOF rgenoud/inst/doc/rgenoud.R0000644000176200001440000001317312553042713015234 0ustar liggesusers### R code from vignette source 'rgenoud.Rnw' ################################################### ### code chunk number 1: rgenoud.Rnw:488-495 ################################################### claw <- function(xx) { x <- xx[1] y <- (0.46*(dnorm(x,-1.0,2.0/3.0) + dnorm(x,1.0,2.0/3.0)) + (1.0/300.0)*(dnorm(x,-0.5,.01) + dnorm(x,-1.0,.01) + dnorm(x,-1.5,.01)) + (7.0/300.0)*(dnorm(x,0.5,.07) + dnorm(x,1.0,.07) + dnorm(x,1.5,.07))) return(y) } ################################################### ### code chunk number 2: rgenoud.Rnw:498-500 ################################################### library("rgenoud") claw1 <- genoud(claw, nvars=1, max=TRUE, pop.size=3000) ################################################### ### code chunk number 3: rgenoud.Rnw:855-877 (eval = FALSE) ################################################### ## source("supplemental.R") ## gradcheck <- rep(TRUE,23) ## gradcheck[6:7] <- FALSE ## sizeset <- c(5000,10000) ## genset <- c(30,100) ## nreps <- 50 ## gsarray <- array(NA, dim=c(length(sizeset), length(genset), 23, nreps)) ## asc <- function(x) { as.character(x) } ## dimnames(gsarray) <- list(asc(sizeset), asc(genset), NULL, NULL); ## for (gsize in sizeset) { ## for (ngens in genset) { ## for (i in 1:23) { ## for (j in 1:nreps) { ## gsarray[as.character(gsize), as.character(ngens),i,j] <- ## genoud(testfuncs[[i]], nvars=testNparms[i], pop.size=gsize, ## max.gen=ngens, hard.gen=TRUE, Domains=testbounds[[i]], ## solution.tol=1e-6, boundary=1, gradient.check=gradcheck[i], ## print=0)$value ## } ## } ## } ## } ################################################### ### code chunk number 4: rgenoud.Rnw:1020-1027 (eval = FALSE) ################################################### ## LQDxmpl <- function(b) { ## logistic <- function(x) { 1/(1+exp(-x)) } ## sIQR <- function(y, yhat, n) { ## IQR((y-yhat)/sqrt(yhat*(n-yhat)), na.rm=TRUE) ## } ## sIQR(y, m*logistic(x %*% b), m) ## } ################################################### ### code chunk number 5: rgenoud.Rnw:1032-1038 (eval = FALSE) ################################################### ## m <- 100 ## x <- cbind(1,rnorm(1000),rnorm(1000)) ## b1 <- c(.5, 1, -1) ## b2 <- c(0, -1, 1) ## logistic <- function(x) { 1/(1+exp(-x)) } ## y <- rbinom(1000, m, logistic(c(x[1:900,] %*% b1, x[901:1000,] %*% b2))) ################################################### ### code chunk number 6: rgenoud.Rnw:1047-1048 (eval = FALSE) ################################################### ## summary(glm1 <- glm(cbind(y,m-y) ~ x[,2] + x[,3], family="binomial")) ################################################### ### code chunk number 7: rgenoud.Rnw:1070-1073 (eval = FALSE) ################################################### ## suby <- y[1:900] ## subx <- x[1:900,] ## summary(glm2 <- glm(cbind(suby,m-suby) ~ subx[,2] + subx[,3], family="binomial")) ################################################### ### code chunk number 8: rgenoud.Rnw:1115-1132 (eval = FALSE) ################################################### ## dLQDxmpl <- function(b) { ## eps <- 1e-10 ## logistic <- function(x) { 1/(1+exp(-x)) } ## sIQR <- function(y, yhat, n) { ## IQR((y-yhat)/sqrt(yhat*(n-yhat)), na.rm=TRUE) ## } ## dsIQR <- vector() ## for (i in 1:length(b)) { ## beps <- b ## beps[i] <- b[i]+eps ## dsIQR <- ## c(dsIQR, ## (sIQR(y, m*logistic(x %*% beps), m)- ## sIQR(y, m*logistic(x %*% b), m))/eps) ## } ## return(dsIQR) ## } ################################################### ### code chunk number 9: rgenoud.Rnw:1136-1151 (eval = FALSE) ################################################### ## blen <- 3 ## lenbseq <- length(bseq <- seq(-2,2,length=200)) ## bseq3 <- seq(-1.2,-.9,length=200) ## bseq2 <- seq(.89,1.1,length=200) ## IQRarr <- IQRarrA <- array(NA, dim=c((1+blen), lenbseq, lenbseq)) ## dimnames(IQRarrA) <- list(NULL, as.character(bseq), as.character(bseq)) ## dimnames(IQRarr) <- list(NULL, as.character(bseq2), as.character(bseq3)) ## for (i in 1:lenbseq) { ## for (j in 1:lenbseq) { ## IQRarrA[1,i,j] <- LQDxmpl(c(.5, bseq[i], bseq[j])) ## IQRarrA[-1,i,j] <- dLQDxmpl(c(.5, bseq[i], bseq[j])) ## IQRarr[1,i,j] <- LQDxmpl(c(.5, bseq2[i], bseq3[j])) ## IQRarr[-1,i,j] <- dLQDxmpl(c(.5, bseq2[i], bseq3[j])) ## } ## } ################################################### ### code chunk number 10: rgenoud.Rnw:1154-1165 (eval = FALSE) ################################################### ## par(mfrow=c(2,2), lwd=.1) ## contour(bseq,bseq, IQRarrA[1,,], main="IQR", xlab="b[2]", ylab="b[3]") ## contour(bseq,bseq, IQRarrA[3,,], main="partial derivative w/r/t b[2]", ## xlab="b[2]", ylab="b[3]") ## loc2 <- (150:160)-5 ## loc3 <- (40:50)+5 ## contour(bseq[loc2],bseq[loc3], IQRarrA[3,loc2,loc3], ## main="partial derivative w/r/t b[2]", ## xlab="b[2]", ylab="b[3]") ## contour(bseq2,bseq3, IQRarr[3,,], main="partial derivative w/r/t b[2]", ## xlab="b[2]", ylab="b[3]") ################################################### ### code chunk number 11: rgenoud.Rnw:1221-1224 (eval = FALSE) ################################################### ## LQD1 <- ## genoud(LQDxmpl, nvars=3, max=FALSE, pop.size=2000, max.generations=300, ## wait.generations=100, gradient.check=FALSE, print=1) ################################################### ### code chunk number 12: rgenoud.Rnw:1292-1295 (eval = FALSE) ################################################### ## LQD1 <- ## genoud(LQDxmpl, nvars=3, max=FALSE, pop.size=10000, max.generations=1000, ## wait.generations=300, gradient.check=FALSE, print=1) rgenoud/inst/doc/rgenoud.bib0000644000176200001440000017213711552430730015573 0ustar liggesusers@string{aer = "American Economic Review"} @string{ajps= "American Journal of Political Science"} @string(apq = "American Politics Quarterly") @string{apsr= "American Political Science Review"} @string{ams = "Annals of Mathematical Statistics"} @string{aos = "Annals of Statistics"} @string{bjps= "British Journal of Political Science"} @string{ec = "Econometrica"} @string{ier = "International Economic Review"} @string{jasa= "Journal of the American Statistical Association"} @string{je = "Journal of Econometrics"} @string{jel = "Journal of Economic Literature"} @string{jep = "Journal of Economic Perspectives"} @string{jet = "Journal of Economic Theory"} @string{jmcb= "Journal of Money, Credit, and Banking"} @string{jme = "Journal of Monetary Economics"} @string{jpe = "Journal of Political Economy"} @string{jop = "Journal of Politics"} @string{jrsa= "Journal of the Royal Statistical Society, Series A"} @string{jrssb= "Journal of the Royal Statistical Society, Series B"} @string{lsq = "Legislative Studies Quarterly"} @string{pa = "Political Analysis"} @string{pm = "Political Methodology"} @string{pop = "Perspectives on Politics"} @string{ps = "PS: Political Science and Politics"} @string{qje = "Quarterly Journal of Economics"} @string{c-h = "Chapman \& Hall"} @string{cup = "Cambridge University Press"} @string{cornell.up = "Cornell University Press"} @string{hup = "Harvard University Press"} @string{mit = "MIT Press"} @string(pup = {Princeton University Press}) @string{s-v = "Springer-Verlag"} @string(sup = "Stanford University Press") @string{ucp = "University of California Press"} @string{uchp = "University of Chicago Press"} @string{ump = "University of Michigan Press"} @string{yup = "Yale University Press"} @string{cq = "Congressional Quarterly"} @string{aa = "Ann Arbor"} @string{berk= 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Sekhon}, title = {Genetic Optimization Using Derivatives: The \pkg{rgenoud} Package for \proglang{R}}, journal = {Journal of Statistical Software}, year = {2011}, note = {Forthcoming}, url = {http://www.jstatsoft.org/} } @article( mebane2000, author= {Mebane, Jr., Walter R.}, title= {Coordination, Moderation and Institutional Balancing in American Presidential and House Elections}, journal= apsr, volume=94, number = 1, pages= {37--57}, year= 2000 ) @Manual{MebaneSekhon1997, author = {Mebane, Jr., Walter R. and Jasjeet S. Sekhon}, title = {GENetic Optimization Using Derivatives (GENOUD)}, note = {Computer program available upon request}, year = {1997} } @article( MebaneSekhon2004, author= {Mebane, Jr., Walter R. and Jasjeet S. Sekhon}, title= {Robust Estimation and Outlier Detection for Overdispersed Multinomial Models of Count Data}, journal= ajps, volume=48, number = 2, pages= {391--410}, year= 2004 ) @Manual{MebaneSekhon.multinomRob, author = {Mebane, Jr., Walter R. and Jasjeet S. Sekhon}, title = {\pkg{multinomRob}: Robust Estimation of Overdispersed Multinomial Regression Models}, note = {\proglang{R}~package version~1.8-4}, url = {http://CRAN.R-project.org/package=multinomRob}, year = {2009}, } @article( MebaneSekhon2002, author= {Mebane, Jr., Walter R. and Jasjeet S. Sekhon}, title= {Coordination and Policy Moderation at Midterm}, journal= apsr, volume=96, number = 1, pages= {141--157}, year= 2002 ) @unpublished( MebaneSekhon1998, author= {Mebane, Jr., Walter R. and Jasjeet S. Sekhon}, title= {GENetic Optimization Using Derivatives (GENOUD)}, note = {Software Package. \url{http://sekhon.berkeley.edu/rgenoud/}}, year= 1998 ) @book( Michalewicz1992, author= {Michalewicz, Zbigniew}, title= {Genetic Algorithms + Data Structures = Evolution Programs}, publisher= s-v, address= {New York}, year= {1992} ) @unpublished( MichalewiczSwaminathanLogan1993, author= {Michalewicz, Zbigniew and Swarnalatha Swaminathan and Thomas D. 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A.}, title= {EDF Statistics for Goodness of Fit and Some Comparisons}, journal= jasa, volume=69, pages= {730--737}, year= 1974 ) @article( stokes2004, author= {Stokes, Houston}, title= {On the Advantage of Using Two or More Econometric Software Systems to Solve the Same Problem}, journal= {Journal of Economic and Social Measurement}, volume=29, number="1-3", pages= {307--320}, year= 2004 ) @Manual{synth2008, author = {Alexis Diamond and Jens Hainmueller}, title = {\pkg{Synth}: Synthetic Control Group Method for Comparative Case Studies}, note = {\proglang{R}~package version~0.1-6}, url = {http://CRAN.R-project.org/package=Synth}, year = {2008} } @incollection( vose1993, author= {Vose, Michael D.}, title= {Modeling Simple Genetic Algorithms}, booktitle= {Foundations of Genetic Algorithms 2}, editor= {L.~Darrell Whitley}, publisher= {Morgan Kaufmann}, address= {San Mateo, CA}, year= 1993 ) @Manual{WandKingLau2007, author = {Wand, Jonathan and Gary King and Olivia Lau}, title = {\pkg{Anchors}: Software for Anchoring Vignette Data}, note = {\proglang{R}~package version~2.0}, url = {http://wand.stanford.edu/anchors/}, year = {2008} } @book( wilcox1997, author= {Wilcox, Rand R.}, title= {Introduction to Robust Estimation}, publisher= {Academic Press}, address= {San Diego, CA}, year= 1997 ) @article( wilcoxon1945, author= {Wilcoxon, F}, title= {Individual Comparisons by Ranking Methods}, journal= {Biometrics}, volume=1, pages= {8083}, year= 1945 ) @article( WinshipMorgan1999, author= {Winship, Christopher and Stephen Morgan}, title= {The estimation of causal effects from observational data}, journal= "Annual Review of Sociology", volume=25, pages= "659--707", year= "1999" ) @article( wittman1989, author= {Wittman, Donald A}, title= {Why Democracies Produce Efficient Results}, journal= jpe, volume=97, pages= {1395--1424}, year= 1989 ) @article( yao.liu.lin1999, author= {Yao, Xin and Yong Liu and Guangming Lin}, title= {Evolutionary Programming Made Faster}, journal= {IEEE Transactions on Evolutionary Computation}, volume=3, month= {July}, number= 2, pages= {82--102}, year= 1999 ) @article( yule1899, author= {Yule, Undy G.}, title= {An Investigation into the Causes of Changes in Pauperism in England, Chiefly During the Last Two Intercensal Decades (Part I.)}, journal= {Journal of the Royal Statistical Society}, volume=62, number = 2, pages= {249--295}, year= 1899 ) @incollection( zaller2004, author= {Zaller, John R}, title= {Floating Voters in U.S.\ Presidential Elections, 1948--1996}, booktitle= {Studies in Public Opinion: Gauging Attitudes, Nonattitudes, Measurement Error and Change}, editor= {Willem Saris and Paul Sniderman}, publisher= pup, address= nj, year= "forthcoming" ) @book( zaller1992, author= {Zaller, John R}, title= {The Nature and Origins of Mass Opinion}, publisher= cup, address= ny, year= 1992 ) @unpublished( zaller1986, author= {Zaller, John R.}, title= {Analysis of Information Items in the 1985 NES Pilot Study}, note= {NES Pilot Study Report. Center for Political Studies, University of Michigan}, year= 1986 ) @unpublished( zaller1985, author= {Zaller, John R.}, title= {Proposal for the Measurement of Political Information}, note= {Report to the NES Board of Overseers. Center for Political Studies, University of Michigan}, year= 1985 ) @book( zakaria2003, author= {Zakaria, Fareed}, title= {The Future of Freedom: Illiberal Democracy at Home and Abroad}, publisher= {W. W. Norton}, address= {New York}, year= 2003 ) @article( zakaria1998, author= {Zakaria, Fareed}, title= {Doubts About Democracy}, journal= {Newsweek}, Month="January", day=5, year= 1998 ) @article( zakaria1997, author= {Zakaria, Fareed}, title= {The Rise of Illiberal Democracy}, journal= {Foreign Affairs}, volume=76, number=6, pages= {249--295}, year= 1997 ) @Article{Altman+McDonald:2011, author = {Micah Altman and Michael P. McDonald}, title = {\pkg{BARD}: Better Automated Redistricting}, journal = {Journal of Statistical Software}, year = {2011}, note = {Forthcoming}, url = {http://www.jstatsoft.org/} } @Article{Wand+King:2011, author = {Jonathan Wand and Gary King}, title = {\pkg{Anchors}: Software for Anchoring Vignette Data}, journal = {Journal of Statistical Software}, year = {2011}, note = {Forthcoming}, url = {http://www.jstatsoft.org/} } @Article{Sekhon:2011, author = {Jasjeet S. Sekhon}, title = {Multivariate and Propensity Score Matching Software with Automated Balance Optimization: The \pkg{Matching} Package for \proglang{R}}, journal = {Journal of Statistical Software}, year = {2011}, note = {Forthcoming}, url = {http://www.jstatsoft.org/} } @Manual{Rcore, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, } @Comment LocalWords: apsr booktitle Finifter Zaller NES Iyengar Shanto Brehm @Comment LocalWords: AlvarezBrehm ajps HorvitzThompson Horvitz jasa ny kunsch @Comment LocalWords: MannWhitney Psychometrika Biometrika rubinMI Stefanski @Comment LocalWords: Cantoni Elvezio Ronchetti CarrollPederson Pederson jssrb @Comment LocalWords: copas jrssb sekhon glmRob Probit Fearon Laitin's althaus @Comment LocalWords: Bartels's MebaneSekhon Keisuke Geert ec Allyson Berent @Comment LocalWords: Krosnick Visser Boninger Hausman Kosuke Rosenbaum Bon Ai @Comment LocalWords: Kornhauser Jamieson hersh url huntington Zakaria Fareed @Comment LocalWords: zakaria rustow Dankwart Lipset geddes MacKuen Brunell @Comment LocalWords: BrunellNiNardo DiNardo Reweighting AldrichMcKelvey rubin @Comment LocalWords: McKelvey imbens abadie incollection dominguez nguez jop @Comment LocalWords: Chappell Ordeshook Lupia fishkin Subclassification Jong @Comment LocalWords: CochranRubin BertsimasTsitsiklis Bertsimas Dimitris Yung @Comment LocalWords: Tsitsiklis Kaufmann Quantile Ellipsoidally Galiani Segal @Comment LocalWords: Gertler Schargrodsky GalianiGertlerSchargrodsky Diprete @Comment LocalWords: DipreteEngelhardt Engelhardt herbert Winship Jin PKfit @Comment LocalWords: WinshipMorgan BowersHansen Pharmacokinetics Vinod aer @Comment LocalWords: McCulloughVinod SchacharNalebuff Shachar Nalebuff Hsin @Comment LocalWords: AltmanGillMcDonald Braumoeller Jasjeet ivivc vitro vivo @Comment LocalWords: IVIVC Hainmueller Synth Mebane GENetic @Comment LocalWords: GENOUD DiceOptim Ginsbourger Roustant @Comment LocalWords: Kriging rgenoud/inst/doc/rgenoud.Rnw0000644000176200001440000021542711762766337015627 0ustar liggesusers\documentclass[nojss]{jss} \usepackage{amsmath} \usepackage{dcolumn} %%My declarations \newcommand{\hlink}{\htmladdnormallink} \newcommand{\MyPerp}{\perp \! \! \! \perp} \newcommand{\e}{\text{e-}} \newcolumntype{C}{>{$}c<{$}} \newcolumntype{L}{>{$}l<{$}} \newcolumntype{R}{>{$}r<{$}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% declarations for jss.cls %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% almost as usual \author{Walter R. Mebane, Jr. \\ University of Michigan \And Jasjeet S. Sekhon \\ UC Berkeley} %% for pretty printing and a nice hypersummary also set: \title{Genetic Optimization Using Derivatives: The \pkg{rgenoud} Package for \proglang{R}} \Plaintitle{Genetic Optimization Using Derivatives: The rgenoud Package for R} \Plainauthor{Walter R. Mebane, Jr., Jasjeet S. Sekhon} %% comma-separated \Shorttitle{\pkg{rgenoud}: Genetic Optimization Using Derivatives in \proglang{R}} %% an abstract and keywords \Abstract{ This introduction to the \proglang{R} package \pkg{rgenoud} is a modified version of \cite{MebaneJr.+Sekhon:2011}, published in the \textit{Journal of Statistical Software}. That version of the introduction contains higher resolution figures. \code{genoud} is an \proglang{R} function that combines evolutionary algorithm methods with a derivative-based (quasi-Newton) method to solve difficult optimization problems. \code{genoud} may also be used for optimization problems for which derivatives do not exist. \code{genoud} solves problems that are nonlinear or perhaps even discontinuous in the parameters of the function to be optimized. When the function to be optimized (for example, a log-likelihood) is nonlinear in the model's parameters, the function will generally not be globally concave and may have irregularities such as saddlepoints or discontinuities. Optimization methods that rely on derivatives of the objective function may be unable to find any optimum at all. Multiple local optima may exist, so that there is no guarantee that a derivative-based method will converge to the global optimum. On the other hand, algorithms that do not use derivative information (such as pure genetic algorithms) are for many problems needlessly poor at local hill climbing. Most statistical problems are regular in a neighborhood of the solution. Therefore, for some portion of the search space, derivative information is useful. The function supports parallel processing on multiple CPUs on a single machine or a cluster of computers.} \Keywords{genetic algorithm, evolutionary program, optimization, parallel computing, \proglang{R}} \Plainkeywords{genetic algorithm, evolutionary program, optimization, parallel computing, R} %% without formatting %% at least one keyword must be supplied %% publication information %% NOTE: This needs to filled out ONLY IF THE PAPER WAS ACCEPTED. %% If it was not (yet) accepted, leave them commented. \Volume{42} \Issue{11} %\Month{September} \Year{2011} \Submitdate{2007-02-11} \Acceptdate{2007-11-21} %% The address of (at least) one author should be given %% in the following format: \Address{ Walter R. Mebane, Jr.\\ % Professor\\ Department of Political Science\\ Department of Statistics\\ University of Michigan\\ Ann Arbor, MI 48109-1045\\ E-mail: \email{wmebane@umich.edu}\\ URL: \url{http://www.umich.edu/~wmebane} \\ [2ex] Jasjeet S. Sekhon\\ Department of Political Science\\ Department of Statistics\\ 210 Barrows Hall \#1950\\ UC Berkeley\\ Berkeley, CA 94720-1950\\ E-mail: \email{sekhon@berkeley.edu}\\ URL: \url{http://sekhon.berkeley.edu} } %% It is also possible to add a telephone and fax number %% before the e-mail in the following format: %% Telephone: +43/1/31336-5053 %% Fax: +43/1/31336-734 %% for those who use Sweave please include the following line (with % symbols): %% need no \usepackage{Sweave.sty} %% end of declarations %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \graphicspath{{Figures/}} \begin{document} \SweaveOpts{engine=R} %\VignetteIndexEntry{Using genoud} %\VignetteDepends{rgenoud} %\VignetteKeywords{rgenoud} %\VignettePackage{rgenoud} \section{Introduction} We developed the \proglang{R} package \pkg{rgenoud} to solve difficult optimization problems such as often arise when estimating nonlinear statistical models or solving complicated nonlinear, nonsmooth and even discontinuous functions.\footnote{The \pkg{rgenoud} software package is available from the Comprehensive \proglang{R} \citep{Rcore} Archive Network at \url{http://CRAN.R-project.org/package=rgenoud}.} Optimization difficulties often arise when the objective function (for instance, the log-likelihood) is a nonlinear function of the parameters. In such cases the function to be optimized is usually not globally concave. An objective function that is not globally concave may have multiple local optima, saddle points, boundary solutions or discontinuities. While the objective function for a statistical model is often concave in a neighborhood of the optimal solution, that neighborhood is often a small proportion of the parameter space of potential interest, and outside that neighborhood the function may be irregular. In such cases, methods of optimization that depend entirely on derivatives can be unreliable and often are virtually unusable. Newton-Raphson and quasi-Newton methods are among the commonly used optimization methods that rely completely on derivatives. Such methods work well when the function to be optimized is regular and smooth over the domain of parameter values that is of interest, but otherwise the methods often fail \citep{GillMurrayWright1981}. Even in models where such methods can be expected to work most of the time, resampling techniques such as the bootstrap \citep{EfronTibshirani1994} can generate resamples in which derivative-based optimization algorithms encounter severe difficulties. This is unfortunate because the methods most frequently used for optimization in problems of statistical estimation are entirely based on derivatives. The \pkg{rgenoud} package has been used by wide variety of users and developers. More than twelve \proglang{R} packages currently rely upon \pkg{rgenoud} including: \pkg{anchors} \citep[analyzing survey data with anchoring vignettes,][]{Wand+King:2011,WandKingLau2007,KingWand2007}; \pkg{BARD} \citep[automated redistricting,][]{Altman+McDonald:2011}; \pkg{boolean} \citep[boolean binary response models,][]{braumoeller2003,BraumoellerGoodrichKline2006}; \pkg{DiceOptim} \citep[kriging-based optimization for computer experiments,][]{DiceOptim}; \pkg{FAiR} \citep[factor analysis,][]{goodrich.fair}; \pkg{JOP} \citep[simultaneous optimization of multiple responses,][]{JOP}; \pkg{KrigInv} \citep[kriging-based inversion,][]{KrigInv}; \pkg{PKfit} \citep[data analysis in pharmacokinetics,][]{LeeLee2006}; \pkg{Matching} \citep[propensity score and multivariate matching,][]{SekhonMatching,Sekhon:2011}; \pkg{ivivc} \citep[in vitro-in vivo correlation modeling,][]{ivivc}; \pkg{multinomRob} \citep[robust multinomial models,][]{MebaneSekhon.multinomRob,MebaneSekhon2004}; and \pkg{Synth} \citep[synthetic control group method for comparative case studies,][]{AbadieGardeazabal2003,synth2008,Abadie+Diamond+Hainmueller:2011}. We present in Section \ref{sec:examples} an example using benchmark functions taken from \citet{yao.liu.lin1999}, followed by an example motivated by the \code{multinomRob} package. The benchmark suite includes functions that are high-dimensional, discontinuous or that have many local optima. The \code{multinomRob} package robustly estimates overdispersed multinomial regression models and uses \pkg{rgenoud} to solve a least quartile difference (LQD) generalized S-estimator \citep{MebaneSekhon2004}. The LQD is not a smooth function of the regression model parameters. The function is continuous, but the parameter space is finely partitioned by nondifferentiable boundaries. In another paper in this volume, the \pkg{Matching} package and its use of \pkg{rgenoud} are described in detail \citep{Sekhon:2011}. \pkg{Matching} provides functions for multivariate and propensity score matching and for finding optimal covariate balance based on a genetic search algorithm implemented in \pkg{rgenoud}. The search over optimal matches is discontinuous so no derivatives are used.\footnote{The \code{BFGS} option of \code{genoud} is set to \code{FALSE}, and the ninth operator which depends on derivatives is not used.} The search also involves lexical optimization which is a unique feature implemented in \pkg{rgenoud}.\footnote{Lexical optimization is useful when there are multiple fitness criteria; the parameters are chosen so as to maximize fitness values in lexical order---i.e., the second fit criterion is only considered if the parameters have the same fit for the first. See the \code{lexical} option and \citet{Sekhon:2011} for details. All of \code{genoud}'s options are described in the \proglang{R} help file for the function.} % If one wishes to use such a model, %significant optimization difficulties may need to be overcome. For %example, the estimating functions of all of the following models are %not in general globally concave: models with multivariate qualitative %variables, censoring or endogenous switching %\citep{maddala1983,amemiya1985}; linear covariance structures %\citep{bollen1989}; models for durations or transitions with %unobserved heterogeneity \citep{HeckmanSinger1985,lancaster1990}; %quasi-likelihood and extended quasi-likelihood models %\citep{McCullaghNelder1989} and systems based on such models %\citep{FahrmeirTutz1994}; and nonlinear simultaneous equation models %\citep{gallant1987}. For such models, optimization methods driven %entirely by derivatives are often unreliable. For some versions of %some of these models, algorithms such as EM that involve data %augmentation have been successfully applied to produce optimization %problems that derivative-based methods can solve %\citep[e.g.,][197]{lancaster1990}. The \pkg{rgenoud} package implements an updated and extended version of the \proglang{C} program \code{GENOUD} \citep{MebaneSekhon1997} described in \citep{SekhonMebane1998}. The many improvements include among other things the interface with \proglang{R}, which includes the ability to optimize functions written in \proglang{R}, options to optimize both floating point and integer-valued parameters, the ability to optimize loss functions which return multiple fitness values (lexical optimization), the ability to call \code{genoud} recursively, the ability to have the optimizer evaluate fits only for new parameter values, and the ability to use multiple computers, CPUs or cores to perform parallel computations. The \pkg{rgenoud} program combines an evolutionary algorithm with a quasi-Newton method. The quasi-Newton method is the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method \citep[][119]{GillMurrayWright1981} implemented in \proglang{R}'s \code{optim} function. When the BFGS is being used, our program offers the option of using either \pkg{rgenoud}'s built-in numerical derivatives (which are based on code taken from \citealt[][337--344]{GillMurrayWright1981}) or user-supplied analytical derivatives.\footnote{User supplied derivatives may be provides via the \code{gr} option.} Our program can also work without the BFGS, in which case no derivatives are needed and the optimizer will work even when the function is discontinuous. The primary benefit from using derivatives is that the algorithm will then quickly find a local optimum when a current set of trial solution parameter values is in a smooth neighborhood of the local optimum point. Appropriate use of the BFGS can make the algorithm converge to the global optimum much more quickly. But premature or excessive use of the BFGS can prevent convergence to the global optimum.\footnote{The user can control whether \code{genoud} uses the BFGS at all (via the \code{BFGS} option), and if operators that use the BFGS are used (via the \code{P9} option), how often they are used.} As always, it is hazardous to rely on an optimizer's default settings. Our program does not eliminate the need for judgment, testing and patience. As Gill, Murray and Wright observe, ``there is no guaranteed strategy that will resolve every difficulty'' \citep[285]{GillMurrayWright1981}. In this article, we very briefly review the theory of random search algorithms that supports the assertion that \pkg{rgenoud} has a high probability of finding the global optimum when such exists. And we present three examples of how to use the \code{genoud} function: to optimize a simple but fiendish scalar Normal mixture model; to minimize a suite of benchmark functions that have previously been used to test evolutionary programming optimization algorithms; and to optimize a version of the only intermittently differentiable LQD estimator. Additional details on both the theory and performance of \code{genoud} can be found in our article that describes \code{GENOUD} \citep{SekhonMebane1998}. \section{Background on Genetic Optimization} An evolutionary algorithm (EA) uses a collection of heuristic rules to modify a population of trial solutions in such a way that each generation of trial values tends to be, on average, better than its predecessor. The measure for whether one trial solution is better than another is the trial solution's fitness value. In statistical applications, the fitness is a function of the summary statistic being optimized (e.g., the log-likelihood). \pkg{rgenoud} works for cases in which a solution is a vector of floating-point or integer numbers that serve as the parameters of a function to be optimized. The search for a solution proceeds via a set of heuristic rules, or \textit{operators}, each of which acts on one or more trial solutions from the current population to produce one or more trial solutions to be included in the new population. EAs do not require derivatives to exist or the function to be continuous in order find the global optimum. The EA in \pkg{rgenoud} is fundamentally a genetic algorithm (GA) in which the code-strings are vectors of numbers rather than bit strings, and the GA operators take special forms tuned for the floating-point or integer vector representation. A GA uses a set of randomized genetic operators to evolve a finite population of finite code-strings over a series of generations \citep{holland1975,goldberg1989,GrefenstetteBaker1989}. The operators used in GA implementations vary \citep{davis1991,FilhoTreleavenAlippi1994}, but in an analytical sense the basic set of operators can be defined as reproduction, mutation, crossover and inversion. The variation in these operators across different GA implementations reflects the variety of codes best suited for different applications. Reproduction entails selecting a code-string with a probability that increases with the code-string's fitness value. Crossover and inversion use pairs or larger sets of the selected code-strings to create new code-strings. Mutation randomly changes the values of elements of a single selected code-string. Used in suitable combinations, the genetic operators tend to improve average fitness of each successive generation, though there is no guarantee that average fitness will improve between every pair of successive generations. Average fitness may well decline. But theorems exist to prove that parts of the trial solutions that have above average fitness values in the current population are sampled at an exponential rate for inclusion in the subsequent population \citep[][139--140]{holland1975}. Each generation's population contains a biased sample of code-strings, so that a substring's performance in that population is a biased estimate of its average performance over all possible populations \citep{dejong1993,grefenstette1993}. The long-run properties of a GA may be understood by thinking of the GA as a Markov chain. A state of the chain is a code-string population of the size used in the GA. For code-strings of finite length and GA populations of finite size, the state space is finite. If such a GA uses random reproduction and random mutation, all states always have a positive probability of occurring. A finite GA with random reproduction and mutation is therefore approximately a finite and irreducible Markov chain.\footnote{\citet[][372--419]{feller1970} and \citet[][107--142]{billingsley1986} review the relevant properties of Markov chains. The randomness in an actual GA depends on the performance of pseudorandom number generators. This and the limitations of floating point arithmetic mean it is not literally true that an actual GA has a positive probability of reaching any state from any other state, and some states may in fact not be reachable from a given set of initial conditions.} An irreducible, finite Markov chain converges at an exponential rate to a unique stationary distribution \citep[][128]{billingsley1986}. This means that the probability that each population occurs rapidly converges to a constant, positive value. \citet{NixVose1992} and \citet{vose1993} use a Markov chain model to show that in a GA where the probability that each code-string is selected to reproduce is proportional to its observed fitness, the stationary distribution strongly emphasizes populations that contain code-strings that have high fitness values. They show that asymptotic in the population size---i.e., in the limit for a series of GAs with successively larger populations---populations that have suboptimal average fitness have probabilities approaching zero in the stationary distribution, while the probability for the population that has optimal average fitness approaches one. If $k>1$ populations have optimal average fitness, then in the limiting stationary distribution the probability for each approaches $1/k$. The theoretical results of Nix and Vose imply that a GA's success as an optimizer depends on having a sufficiently large population of code-strings. If the GA population is not sufficiently large, then the Markov chain that the GA approximately implements is converging to a stationary distribution in which the probabilities of optimal and suboptimal states are not sharply distinguished. Suboptimal populations can be as likely to occur as optimal ones. If the stationary distribution is not favorable, the run time in terms of generations needed to produce an optimal code-string will be excessive. For all but trivially small state spaces, an unfavorable stationary distribution can easily imply an expected running time in the millions of generations. But if the stationary distribution strongly emphasizes optimal populations, relatively few generations may be needed to find an optimal code-string. In general, the probability of producing an optimum in a fixed number of generations tends to increase with the GA population size. \begin{table} \begin{center} \line(1,0){450} \end{center} \begin{enumerate} \item[\code{P1}] Cloning. Copy $\mathbf{X}_{t}$ into the next generation, $\mathbf{X}_{t+1}$. \item[\code{P2}] Uniform Mutation. At random choose $i\in\mathbf{N}$. Select a value $\tilde{x}_i \sim U(\underline{x}_i, \overline{x}_i)$. Set $X_i=\tilde{x}_i$. \item[\code{P3}] Boundary Mutation. At random choose $i\in\mathbf{N}$. Set either $X_i=\underline{x}_i$ or $X_i=\overline{x}_i$, with probability $1/2$ of using each value. \item[\code{P4}] Non-uniform Mutation. At random choose $i\in\mathbf{N}$. Compute $p = (1-t/T)^B u$, where $t$ is the current generation number, $T$ is the maximum number of generations, $B>0$ is a tuning parameter and $u \sim U(0,1)$. Set either $X_i=(1-p)x_i + p\underline{x}_i$ or $X_i=(1-p)x_i + p\overline{x}_i$, with probability $1/2$ of using each value. \item[\code{P5}] Polytope Crossover. Using $m=\max(2,n)$ vectors $\mathbf{x}$ from the current population and $m$ random numbers $p_j\in(0,1)$ such that $\sum_{j=1}^m p_j = 1$, set $\mathbf{X} = \sum_{j=1}^m p_j \mathbf{x}_j$. \item[\code{P6}] Simple Crossover. Choose a single integer $i$ from $\mathbf{N}$. Using two parameter vectors, $\mathbf{x}$ and $\mathbf{y}$, set $X_i = p x_i + (1-p) y_i$ and $Y_i = p y_i + (1-p) x_i$, where $p\in(0,1)$ is a fixed number. \item[\code{P7}] Whole Non-uniform Mutation. Do non-uniform mutation for all the elements of $\mathbf{X}$. \item[\code{P8}] Heuristic Crossover. Choose $p \sim U(0,1)$. Using two parameter vectors, $\mathbf{x}$ and $\mathbf{y}$, compute $\mathbf{z} = p(\mathbf{x} - \mathbf{y}) + \mathbf{x}$. If $\mathbf{z}$ satisfies all constraints, use it. Otherwise choose another $p$ value and repeat. Set $\mathbf{z}$ equal to the better of $\mathbf{x}$ and $\mathbf{y}$ if a satisfactory mixed $\mathbf{z}$ is not found by a preset number of attempts. In this fashion produce two $\mathbf{z}$ vectors. \item[\code{P9}] Local-minimum Crossover. Choose $p \sim U(0,1)$. Starting with $\mathbf{x}$, run BFGS optimization up to a preset number of iterations to produce $\mathbf{\tilde{x}}$. Compute $\mathbf{z} = p\mathbf{\tilde{x}} + (1-p)\mathbf{x}$. If $\mathbf{z}$ satisfies boundary constraints, use it. Otherwise shrink $p$ by setting $p = p/2$ and recompute $\mathbf{z}$. If a satisfactory $\mathbf{z}$ is not found by a preset number of attempts, return $\mathbf{x}$. This operators is extremely computationally intensive, use sparingly. \end{enumerate} \begin{flushleft} Notation: \\ [2ex] $\mathbf{X} =\begin{bmatrix}X_1,\dots,X_n\end{bmatrix}$ is the vector of $n$ parameters $X_i$. $\underline{x}_i$ is the lower bound and $\overline{x}_i$ is the upper bound on values for $X_i$. $x_i$ is the current value of $X_i$, and $\mathbf{x}$ is the current value of $\mathbf{X}$. $\mathbf{N} = \{1,\dots,n\}$. $p \sim U(0,1)$ means that $p$ is drawn from the uniform distribution on the $[0,1]$ interval. \end{flushleft} \caption{`genoud' Operators. Adapted from \citet{SekhonMebane1998}.} \label{tab:operators} \begin{center} \line(1,0){450} \end{center} \end{table} The evolutionary algorithm in \pkg{rgenoud} uses nine operators that are listed in Table~\ref{tab:operators}. The operators extend and modify a set of operators used in \code{GENOCOP} \citep{MichalewiczSwaminathanLogan1993, Michalewicz1992}. The operators are numbered using syntax matching that used to refer to them by \pkg{rgenoud}. The \textit{cloning} operator simply makes copies of the best trial solution in the current generation (independent of this operator, \pkg{rgenoud} always retains one instance of the best trial solution). The \textit{uniform mutation}, \textit{boundary mutation} and \textit{non-uniform mutation} operators act on a single trial solution. Uniform mutation changes one parameter in the trial solution to a random value uniformly distributed on the domain specified for the parameter. Boundary mutation replaces one parameter with one of the bounds of its domain. Non-uniform mutation shrinks one parameter toward one of the bounds, with the amount of shrinkage decreasing as the generation count approaches the specified maximum number of generations. \textit{Whole non-uniform mutation} does non-uniform mutation for all the parameters in the trial solution. \textit{Heuristic crossover} uses two trial solutions to produce a new trial solution located along a vector that starts at one trial solution and points away from the other one. \textit{Polytope crossover} (inspired by simplex search, \citealt[][94--95]{GillMurrayWright1981}) computes a trial solution that is a convex combination of as many trial solutions as there are parameters. \textit{Simple crossover} computes two trial solutions from two input trial solutions by swapping parameter values between the solutions after splitting the solutions at a randomly selected point. This operator can be especially effective if the ordering of the parameters in each trial solution is consequential. \textit{Local-minimum crossover} computes a new trial solution in two steps: first it does a preset number of BFGS iterations starting from the input trial solution; then it computes a convex combination of the input solutions and the BFGS iterate. \section{Examples} \label{sec:examples} The only function in the \pkg{rgenoud} package is \code{genoud}. The interface of this function is similar to that of the \code{optim} function in \proglang{R}. But the function has many additional arguments that control the behavior of the evolutionary algorithm. \subsection{Asymmetric Double Claw:} Our first example, which we also studied in \citet{SekhonMebane1998}, is a normal mixture called the Asymmetric Double Claw (ADC). We plot the function in Figure~\ref{fig:mixture1}. \begin{figure} \caption{Normal Mixture: Asymmetric Double Claw} \vspace{-.5in} \label{fig:mixture1} \begin{center} \includegraphics{fig1.pdf} \end{center} \vspace{-.7in} \end{figure} Mathematically, this mixture is defined as \begin{eqnarray} \label{eq:adclaw} f_{\mathrm{ADC}} & = \sum_{m=0}^{1} \frac{46}{100} \mathrm{N}\left(2m-1,\frac{2}{3}\right) + \sum_{m=1}^{3} \frac{1}{300} \mathrm{N}\left(\frac{-m}{2},\frac{1}{100}\right) + \sum_{m=1}^{3} \frac{7}{300} \mathrm{N}\left(\frac{m}{2},\frac{7}{100}\right), \end{eqnarray} where N is the normal density. The asymmetric double claw is difficult to maximize because there are many local solutions. There are five local maxima in Figure \ref{fig:mixture1}. Standard derivative-based optimizers would simply climb up the hill closest to the starting value. To optimize this normal mixture we must first create a function for it <>= claw <- function(xx) { x <- xx[1] y <- (0.46*(dnorm(x,-1.0,2.0/3.0) + dnorm(x,1.0,2.0/3.0)) + (1.0/300.0)*(dnorm(x,-0.5,.01) + dnorm(x,-1.0,.01) + dnorm(x,-1.5,.01)) + (7.0/300.0)*(dnorm(x,0.5,.07) + dnorm(x,1.0,.07) + dnorm(x,1.5,.07))) return(y) } @ And we now make a call to \pkg{rgenoud} using this function: <>= library("rgenoud") claw1 <- genoud(claw, nvars=1, max=TRUE, pop.size=3000) @ The first argument of \code{genoud} is the function to be optimized. The first argument of that function must be the vector of parameters over which optimizing is to occur. Generally, the function should return a scalar result.\footnote{The function to be optimized may return a vector if one wishes to do lexical optimization. Please see the \code{lexical} option to \code{genoud}.} The second argument of \code{genoud} in this example (\code{nvars}) is the number of variables the function to be optimized takes. The third argument, \code{max=TRUE}, tells \code{genoud} to maximize the function instead of its default behavior which is to minimize. The fourth option \code{pop.size} controls the most important part of the evolutionary algorithm, the population size. This is the number of individuals \code{genoud} uses to solve the optimization problem. As noted in the theoretical discussion, the theorems related to evolutionary algorithms are asymptotic in the population size so larger is generally better but obviously takes longer. The maximum solution of the double claw density is reliably found by \code{genoud} even using the default value of \code{pop.size=1000}. Reliability does increase as the \code{pop.size} is made larger. Unfortunately, because of the stochastic nature of the algorithm, it is impossible to generally answer the question of what is the best population size to use. Other options determine the maximum number of generations the evolutionary algorithm computes. These options are \code{max.generations}, \code{wait.generations} and \code{hard.generation.limit}. The specified termination point also affects how some of the operators perform: the two non-uniform mutation operators introduce smaller ranges of variation in the trial solutions as the generation count approaches the specified \code{max.generations} value. There are many more options that can be used to fine-tune the behavior of the algorithm. The output printed by \code{genoud} is controlled by a \code{print.level} argument. The default value, \code{print.level=2}, produces relatively verbose output that gives extensive information about the set of operators being used and the progress of the optimization. Normally \proglang{R} conventions would suggest setting the default to be \code{print.level=0}, which would suppress output to the screen, but because \code{genoud} runs may take a long time, it can be important for the user to receive some feedback to see the program has not died and to be able to see where the program got stuck if it eventually fails to make adequate progress. The output printed by the preceding invocation of \code{genoud}, which uses the default value for a \code{print.level} argument, is as follows. \begin{CodeChunk} \begin{CodeOutput} Fri Feb 9 19:33:42 2007 Domains: -1.000000e+01 <= X1 <= 1.000000e+01 Data Type: Floating Point Operators (code number, name, population) (1) Cloning........................... 372 (2) Uniform Mutation.................. 375 (3) Boundary Mutation................. 375 (4) Non-Uniform Mutation.............. 375 (5) Polytope Crossover................ 375 (6) Simple Crossover.................. 376 (7) Whole Non-Uniform Mutation........ 375 (8) Heuristic Crossover............... 376 (9) Local-Minimum Crossover........... 0 HARD Maximum Number of Generations: 100 Maximum Nonchanging Generations: 10 Population size : 3000 Convergence Tolerance: 1.000000e-03 Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation. Checking Gradients before Stopping. Using Out of Bounds Individuals. Maximization Problem. GENERATION: 0 (initializing the population) Fitness value... 4.112017e-01 mean............ 4.990165e-02 variance........ 9.708147e-03 #unique......... 3000, #Total UniqueCount: 3000 var 1: best............ 9.966758e-01 mean............ 3.453097e-02 variance........ 3.373681e+01 GENERATION: 1 Fitness value... 4.113123e-01 mean............ 2.237095e-01 variance........ 2.566140e-02 #unique......... 1858, #Total UniqueCount: 4858 var 1: best............ 9.995043e-01 mean............ 4.615946e-01 variance........ 7.447887e+00 [...] GENERATION: 10 Fitness value... 4.113123e-01 mean............ 2.953888e-01 variance........ 2.590842e-02 #unique......... 1831, #Total UniqueCount: 21708 var 1: best............ 9.995033e-01 mean............ 8.403935e-01 variance........ 5.363241e+00 GENERATION: 11 Fitness value... 4.113123e-01 mean............ 2.908561e-01 variance........ 2.733896e-02 #unique......... 1835, #Total UniqueCount: 23543 var 1: best............ 9.995033e-01 mean............ 8.084638e-01 variance........ 6.007372e+00 'wait.generations' limit reached. No significant improvement in 10 generations. Solution Fitness Value: 4.113123e-01 Parameters at the Solution (parameter, gradient): X[ 1] : 9.995033e-01 G[ 1] : -6.343841e-09 Solution Found Generation 1 Number of Generations Run 11 Fri Feb 9 19:33:45 2007 Total run time : 0 hours 0 minutes and 3 seconds \end{CodeOutput} \end{CodeChunk} %DESCRIBE OUTPUT After printing the date and time of the run, the program prints the domain of values it is allowing for each parameter of the function being optimized. In this case the default domain values are being used. Naturally it is important to specify domains wide enough to include the solution. In practice with highly nonlinear functions it is often better to specify domains that are relatively wide than to have domains that narrowly and perhaps even correctly bound the solution. This surprising behavior reflects the fact with a highly nonlinear function, a point that is close to the solution in the sense of simple numerical proximity may not be all that close in the sense of there being a short feasible path to get to the solution. Next the program prints the Data Type. This indicates whether the parameters of the function to be optimized are being treated as floating point numbers or integers. For more information about this, see the \code{data.type.int} argument. The program then displays the number of operators being used, followed by the values that describe the other characteristics set for this particular run: the maximum number of generations, the population size and the tolerance value to be used to determine when the parameter values will be deemed to have converged. The output then reports whether BFGS optimization will be applied to the best trial solution produced by the operators in each generation. For problems that are smooth and concave in a neighborhood of the global optimum, using the BFGS in this way can help \code{genoud} quickly converge once the best trial solution is in the correct neighborhood. This run of \code{genoud} will also compute the gradient at the best trial solution before stopping. In fact this gradient checking is used as a convergence check. The algorithm will not start counting its final set of generations (the \code{wait.generations}) until each element of the gradient is smaller in magnitude than the convergence tolerance. Gradients are never used and BFGS optimization is not used when the parameters of the function to be optimized are integers. The next message describes how strictly \code{genoud} is enforcing the boundary constraints specified by the domain values. By default (\code{boundary.enforcement=0}), the trial solutions are allowed to wander freely outside the boundaries. The boundaries are used only to define domains for those operators that use the boundary information. Other settings of the \code{boundary.enforcement} argument induce either more stringent or completely strict enforcement of the boundary constraints. Notice that the boundary constraints apply to the parameters one at a time. To enforce constraints that are defined by more complicated functional or data-dependent relationships, one can include an appropriate penalty function as part of the definition of the function to be optimized, letting that function define an extremely high (if minimizing) or low (if maximizing) value to be returned if the desired conditions are violated. After reporting whether it is solving a minimization or a maximization problem, \code{genoud} reports summary statistics that describe the distribution of the fitness value and the parameter values across the trial solutions at the end of each generation. In the default case where \code{genoud} is keeping track of all the distinct solutions considered over the whole course of the optimizing run, these generational reports also include a report of the number of unique trial solutions in the current population and the number of unique solutions ever considered. The benefit of keeping track of the solutions is to avoid repeatedly evaluating the function being optimized for the identical set of parameter values. This can be an important efficiency when function evaluations are expensive, as they can be in statistical applications where the data are extensive. This tracking behavior is controlled by the \code{MemoryMatrix} argument. Upon convergence, or when the hard maximum generation limit is reached, the program prints the fitness value at the best trial solution and that solution's parameter values. In this case the solution was found after one generation. While the Asymmetric Double Claw might present a difficult challenge for a gradient-based optimizer that uses only local hill climbing, it is an almost trivially simple problem for \code{genoud}. \subsection{Benchmark Functions:} The second example is a suite of 23 benchmark nonlinear functions used in \citet{yao.liu.lin1999} to study a pair of evolutionary programming optimization algorithms. Function definitions are in Table~\ref{tab:23funcs}. Because it includes a random component and so lacks a reproducible minimum value, we ignore the function numbered function 7 in their sequence.\footnote{The omitted function is $\sum_{i=1}^n ix_i^4 +U(0,1)$, where $U(0,1)$ is a uniformly distributed random variable on the unit interval that takes a new value whenever the function is evaluated. This stochastic aspect means that even given the set of parameters that minimize the nonstochastic component $\sum_{i=1}^n ix_i^4$, i.e., $x_i=0$, the value of the function virtually never attains the minimum possible value of zero. An optimizer that evaluated the function at $x_i=0$ would not in general obtain a function value smaller than the function value obtained for a wide range of different parameter values. Hence we do not consider this function to be a good test for function optimization algorithms.} Implementations of these functions are available in the supplemental \proglang{R} file provided with this article.\footnote{This supplemental file is available at \url{http://sekhon.berkeley.edu/rgenoud/func23.R}.} These \proglang{R} definitions include the values of the constants used in functions 14, 15 and 19 through 23. The function argument domains are restricted to the specific domains used by \citet{yao.liu.lin1999} via bounds that are stated in the list named \code{testbounds} in the supplemental file. \begin{table} \begin{center} \line(1,0){450} \end{center} \begin{tabular}{LLLL} \text{func.} & \text{definition} & n & \text{minimum}^a \\ 1 & \sum_{i=1}^n x_i^2 & 30 & 0 \\ 2 & \sum_{i=1}^n |x_i| + \prod_{i=1}^n |x_i| & 30 & 0 \\ 3 & \sum_{i=1}^n (\sum_{j=1}^i x_j)^2 & 30 & 0 \\ 4 & \max_i \{|x_i|, 1\leq i\leq n\} & 30 & 0 \\ 5 & \sum_{i=1}^{n-1} [100(x_{i+1}-x_i^2)^2 +(x_i-1)^2], & 30 & 0 \\ 6 & \sum_{i=1}^n (\lfloor x_i + 0.5\rfloor)^2 & 30 & 0 \\ 7 & \sum_{i=1}^n ix_i^4 +U(0,1) & 30 & 0 \\ 8 & \sum_{i=1}^n -x_i\sin(\sqrt{|x_i|}) & 30 & -12569.5 \\ 9 & \sum_{i=1}^n [x_i^2-10\cos(2\pi x_i)+10] & 30 & 0 \\ 10 & -20\exp\left(-0.2\sqrt{n^{-1}\sum_{i=1}^n x_i^2}\,\right) \\ & \qquad -\exp(n^{-1}\sum_{i=1}^n\cos 2\pi x_i)+20+e & 30 & 0 \\ 11 & (1/1000) \sum_{i=1}^n x_i^2 - \prod_{i=1}^n\cos\left(x_i/\sqrt{i}\right) + 1 & 30 & 0 \\ 12 & n^{-1}\pi \left\{10 \sin^2(\pi y_1)+\sum_{i=1}^{n-1}(y_i-1)^2 [1+10\sin^2(\pi y_{i+1})]+(y_n-1)^2\right\} \\ & \quad +\sum_{i=1}^n u(x_i,10,100,4), & 30 & 0 \\ & y_i=1+(x_i+1)/4, \quad u(x_i,a,k,m)=\begin{cases} k(x_i-a)^m, & x_i>a, \\ 0, & -a\leq x_i\leq a,\\ k(-x_i-a)^m, & x_i<-a, \end{cases} & \\ 13 & \left\{ \sin^2(3\pi x_1)+\sum_{i=1}^{n-1}(x_i-1)^2[1+\sin^2(3\pi x_{i+1})]\right\}/10 \\ & \quad +(x_n-1)[1+\sin^2(2\pi x_n)]/10 +\sum_{i=1}^n u(x_i,5,100,4) & 30 & 0 \\ 14 & \left\{1/500+ \sum_{j=1}^{25} 1/\left[j+\sum_{i=1}^2(x_i-a_{ij})^6\right]\right\}^{-1} & 2 & 1 \\ 15 & \sum_{i=1}^{11} [a_i-x_1(b_i^2+b_ix_2)/(b_i^2+b_ix_3+x_4)]^2 & 4 & 0.0003075 \\ 16 & 4x_1^2-2.1x_1^4+x_1^6/3+x_1x_2-4x_2^2+4x_2^4 & 2 & -1.0316285 \\ 17 & [x_2-5.1x_1^2/(4\pi^2) + 5x_1/\pi - 6]^2 + 10[1-1/(8\pi)]\cos(x_1) + 10 & 2 & 0.398 \\ 18 & [1+(x_1+x_2+1)^2(19-14 x_1+3 x_1^2-14 x_2+6 x_1 x_2+3 x_2^2)] \\ & \quad \times [30+(2 x_1-3 x_2)^2 (18-32 x_1+12 x_1^2+48 x_2-36 x_1 x_2+27 x_2^2)] & 2 & 3 \\ 19 & -\sum_{i=1}^4 c_i\exp\left[-\sum_{j=1}^4 a_{ij}(x_i-p_{ij})^2\right] & 4 & -3.86 \\ 20 & -\sum_{i=1}^4 c_i\exp\left[-\sum_{j=1}^6 a_{ij}(x_i-p_{ij})^2\right] & 6 & -3.32 \\ 21 & \sum_{i=1}^5 [(x-a_i)^{\prime}(x-a_i)+c_i]^{-1} & 4 & -10 \\ 22 & \sum_{i=1}^7 [(x-a_i)^{\prime}(x-a_i)+c_i]^{-1} & 4 & -10 \\ 23 & \sum_{i=1}^{10} [(x-a_i)^{\prime}(x-a_i)+c_i]^{-1} & 4 & -10 \end{tabular} \begin{flushleft} Notes: $^a$Minimum function value within specified bounds as given by \citet[85]{yao.liu.lin1999}. \end{flushleft} \vspace*{.1in} \caption{23 Benchmark Functions} \label{tab:23funcs} \begin{center} \line(1,0){450} \end{center} \end{table} As \citet{yao.liu.lin1999} describe, optimizing each of functions 1--13 presents a high-dimensional problem. These functions each have $n=30$ free parameters. Functions 1--5 are unimodal, with function 5 being a 30-dimensional version of the banana-shaped Rosenbrock function. Function 6 is a step function. Function 6 has one minimum value that occurs when all arguments are in the interval $x_i\in[0,.5)$, and the function is discontinuous. Functions 8--13 are multimodal, defined such that the number of local minima increases exponentially with the number of arguments. \citet[84]{yao.liu.lin1999} describe these functions as among ``the most difficult class of problems for many optimization algorithms (including [evolutionary programming]).'' Functions 14--23, which have between two and six free parameters each, each have only a few local minima. Nonetheless the evolutionary programming algorithms considered by \citet{yao.liu.lin1999} have trouble optimizing functions 21--23. Although \citet[85]{yao.liu.lin1999} state that each of these functions has a minimum value of $-10$, over 50 replications the two algorithms they consider achieve solutions averaging between $-5.52$ and $-9.10$ \citep[88, Table~IV]{yao.liu.lin1999}. We use these benchmark functions to illustrate not only how effective \code{genoud} can be with a range of difficult problems, but also to emphasize an important aspect of how one should think about trying to tune the optimizer's performance. Theory regarding genetic algorithms suggests that optimal solutions are more likely to appear as both the population size of candidate solutions and the number of generations increase. In \code{genoud} two arguments determine the number of generations. One is \code{max.generations}: if \code{hard.generation.limit=TRUE}, then the value specified for \code{max.generations} is a binding upper limit. The other is \code{wait.generations}, which determines when the algorithm terminates if \code{hard.generation.limit=FALSE}. But even if \code{hard.generation.limit=TRUE}, then \code{wait.generations} determines for how many generations the algorithm continues once the best parameter vector and the value of the function being optimized appear to have settled down. The fact that the current best solution is not changing should not be treated as decisive, because this solution may be merely a local optimum or a saddlepoint. If the population size is sufficient, the algorithm tends to build a population of trial solutions that contain parameters in neighborhoods of all the competitive local optima in the domain defined by the parameter boundaries. Even while the current best solution is stable, the algorithm is improving the solutions near other local optima. So having a higher \code{wait.generations} value never worsens the algorithm's efficacy. Increasing \code{max.generations} may or may not in itself improve optimization. The value of \code{max.generations} sets the value of $T$ used in the mutation operators---operators 4 and 7 in Table~\ref{tab:operators}. These mutation operators perform random search near a trial solution that has been selected for mutation only when the current generation count is an appreciable fraction of $T$. So increasing \code{max.generations} without changing \code{wait.generations} increases the period during which random search is occurring over a wider domain. For multimodal functions such a wider search may be helpful, but sometimes failing to search more densely near the current trial solutions is not good. We use \code{genoud} to minimize the 23 functions using two values for \code{pop.size} (5000 and 10000) and two values for \code{max.generations} (30 and 100). Following \citet{yao.liu.lin1999}, we replicate each optimization 50 times. The following code describes the computations. The list \code{testfuncs}, vector \code{testNparms} and list \code{testbounds} are defined in the supplemental \proglang{R} file, and it is assume that this file is loaded with the \code{source("supplemental.R")} command. The vector \code{gradcheck} is true for all elements except the ones corresponding to functions 6 and 7. <>= source("supplemental.R") gradcheck <- rep(TRUE,23) gradcheck[6:7] <- FALSE sizeset <- c(5000,10000) genset <- c(30,100) nreps <- 50 gsarray <- array(NA, dim=c(length(sizeset), length(genset), 23, nreps)) asc <- function(x) { as.character(x) } dimnames(gsarray) <- list(asc(sizeset), asc(genset), NULL, NULL); for (gsize in sizeset) { for (ngens in genset) { for (i in 1:23) { for (j in 1:nreps) { gsarray[as.character(gsize), as.character(ngens),i,j] <- genoud(testfuncs[[i]], nvars=testNparms[i], pop.size=gsize, max.gen=ngens, hard.gen=TRUE, Domains=testbounds[[i]], solution.tol=1e-6, boundary=1, gradient.check=gradcheck[i], print=0)$value } } } } @ Using \code{genoud} to minimize the benchmark functions produces excellent results, at least when the \code{pop.size} and \code{max.generations} arguments are sufficiently large. Table~\ref{tab:23mean} reports the mean function values for each configuration of the arguments. These values may be compared both to the true function minima given by \citet{yao.liu.lin1999} (see the rightmost column in Table~\ref{tab:23funcs}) and to the average minimum function values \citet{yao.liu.lin1999} report for their ``fast'' evolutionary programming (FEP) algorithm, which appear in the last column of Table~\ref{tab:23mean}. The \code{genoud} averages for the \code{max.gen=100} configurations equal or are close to the true minima for all the functions except function 13. One can reasonably argue that the average solutions for function 5 are not as close to zero as might be desired: these averages are close to $10^{-7}$, while the averages for other functions that have a true minimum of zero are $10^{-15}$ or smaller. And the averages for functions 6, 12 and 15 in the \code{pop.size=5000} case are off. The effect of increasing \code{pop.size} is apparent with respect to both those three functions and also functions 13 and 20--23: the average minima are smaller with \code{pop.size=10000} than with \code{pop.size=5000}. Except for functions 6 and 12 in the \code{pop.size=5000} case and function 13, all the \code{genoud} solution averages for \code{max.gen=100} are either slightly or substantially better than the corresponding FEP solution averages. The results in Table~\ref{tab:23mean} clearly illustrate the potential consequences of not allowing \code{genoud} to run for a sufficient number of generations. While some of the \code{genoud} solutions for \code{max.gen=30} have competitive means, several of the means are not good at all. \begin{table} \begin{center} \line(1,0){450} \end{center} \begin{tabular}{llllll} & \multicolumn{4}{c}{\code{genoud}} & \\ \cline{2-5} & \multicolumn{2}{c}{\code{pop.size=5000}$^a$} & \multicolumn{2}{c}{\code{pop.size=10000}$^a$} & \\ \text{func.} & \code{max=30} & \code{max=100} & \code{max=30} & \code{max=100} & \text{FEP}$^b$ \\ 1 & 1.453\e 32 & 1.658\e 32 & 2.416\e 32 & 6.134\e 32 & 5.7\e 4 \\ 2 & 6.55\e 16 & 7.212\e 16 & 9.652\e 16 & 1.043\e 15 & 8.1\e 3 \\ 3 & 4.633\e 18 & 3.918\e 18 & 3.787\e 18 & 4.032\e 18 & 1.6\e 2 \\ 4 & 6.203\e 17 & 6.542\e 17 & 9.453\e 17 & 7.85\e 17 & 0.3 \\ 5 & 0.07973 & 5.887\e 08 & 8.133\e 08 & 8.917\e 08 & 5.06 \\ 6 & 18.58 & 0.08 & 9.38 & 0 & 0 \\ % 7 & 0.1114 & 0.07473 & 0.1114 & 0.06466 & 7.6\e 3 \\ 8 & -12569.49 & -12569.49 & -12569.49 & -12569.49 & -12554.5 \\ 9 & 2.786 & 0 & 0.9353 & 0 & 4.6\e 2 \\ 10 & 2.849 & 3.997\e 15 & 2.199 & 3.997\e 15 & 1.8\e 2 \\ 11 & 7.994\e 17 & 7.105\e 17 & 9.548\e 17 & 6.439\e 17 & 1.6\e 2 \\ 12 & 5.371\e 19 & 0.004147 & 0.002073 & 1.178\e 19 & 9.2\e 6 \\ 13 & 0.02095 & 0.006543 & 0.006629 & 0.003011 & 1.6\e 4 \\ 14 & 0.998 & 0.998 & 0.998 & 0.998 & 1.22 \\ 15 & 0.0003441 & 0.0004746 & 0.0003807 & 0.0003807 & 5.0\e 4 \\ 16 & -1.0316285 & -1.0316285 & -1.0316285 & -1.0316285 & -1.03 \\ 17 & 0.3979 & 0.3979 & 0.3979 & 0.3979 & 0.398 \\ 18 & 3 & 3 & 3 & 3 & 3.02 \\ 19 & -3.863 & -3.863 & -3.863 & -3.863 & -3.86 \\ 20 & -3.274 & -3.277 & -3.279 & -3.286 & -3.27 \\ 21 & -9.85 & -9.444 & -9.95 & -10.05 & -5.52 \\ 22 & -9.771 & -10.09 & -10.19 & -10.3 & -5.52 \\ 23 & -10.1 & -9.997 & -10.32 & -10.21 & -6.57 \end{tabular} \begin{flushleft} Note: $^b$Average minimum function values (over 50 replications) obtained using \code{genoud}. $^a$Mean best function values (over 50 replications) reported for the ''fast'' evolutionary programming algorithm, from \citet[85 and 88, Tables II--IV]{yao.liu.lin1999}. \end{flushleft} \vspace*{.1in} \caption{Mean Values of 22 Optimized Functions} \label{tab:23mean} \begin{center} \line(1,0){450} \end{center} \end{table} The effect of increasing \code{pop.size} are even more clearly apparent in Table~\ref{tab:23sdev}, which reports the standard deviations of the respective minima across the 50 replications. With the exceptions of functions 6, 12, 13, 15 and 21 with \code{pop.size=5000}, the \code{genoud} solutions for \code{max.gen=100} vary much less than the corresponding FEP solutions. For those functions and also for functions 20, 22 and 23, the \code{max.gen=100} solutions with \code{pop.size=10000} vary noticeably less than the solutions with \code{pop.size=5000}. \begin{table} \begin{center} \line(1,0){450} \end{center} \begin{tabular}{llllll} & \multicolumn{4}{c}{\code{genoud}} & \\ \cline{2-5} & \multicolumn{2}{c}{\code{pop.size=5000}$^a$} & \multicolumn{2}{c}{\code{pop.size=10000}$^a$} & \\ \text{func.} & \code{max=30} & \code{max=100} & \code{max=30} & \code{max=100} & \text{FEP}$^b$ \\ 1 & 9.997\e 32 & 7.059\e 32 & 9.562\e 32 & 2.1\e 31 & 1.3\e 4 \\ 2 & 1.668\e 15 & 1.621\e 15 & 2.116\e 15 & 2.102\e 15 & 7.7\e 4 \\ 3 & 4.568\e 18 & 3.342\e 18 & 4.38\e 18 & 5.136\e 18 & 1.4\e 2 \\ 4 & 1.793\e 16 & 1.758\e 16 & 2.055\e 16 & 2.002\e 16 & 0.5 \\ 5 & 0.5638 & 4.921\e 08 & 5.573\e 08 & 4.955\e 08 & 5.87 \\ 6 & 5.65 & 0.274 & 3.528 & 0 & 0 \\ % 7 & 0.0837 & 0.05153 & 0.08042 & 0.04883 & 2.6\e 3 \\ 8 & 3.749\e 10 & 1.071\e 12 & 8.948\e 09 & 6.365\e 13 & 52.6 \\ 9 & 1.864 & 0 & 1.179 & 0 & 1.2\e 2 \\ 10 & 0.7146 & 0 & 0.702 & 0 & 2.1\e 3 \\ 11 & 1.209\e 16 & 1.582\e 16 & 1.289\e 16 & 8.713\e 17 & 2.2\e 2 \\ 12 & 2.336\e 18 & 0.02052 & 0.01466 & 7.423\e 19 & 3.6\e 6 \\ 13 & 0.03427 & 0.006867 & 0.006903 & 0.001508 & 7.3\e 5 \\ 14 & 5.638\e 12 & 8.894\e 11 & 1.029\e 12 & 4.35\e 12 & 0.56 \\ 15 & 0.0001813 & 0.0003546 & 0.000251 & 0.0002509 & 3.2\e 4 \\ 16 & 1.315\e 14 & 9.751\e 15 & 1.233\e 14 & 1.054\e 14 & 4.9\e 7 \\ 17 & 5.422\e 15 & 5.51\e 15 & 4.925\e 15 & 1.392\e 14 & 1.5\e 7 \\ 18 & 1.509\e 13 & 3.477\e 14 & 6.18\e 14 & 2.907\e 14 & 0.11 \\ 19 & 7.349\e 15 & 1.521\e 15 & 1.344\e 14 & 7.255\e 15 & 1.4\e 5 \\ 20 & 0.05884 & 0.0583 & 0.05765 & 0.05504 & 5.9\e 2 \\ 21 & 1.212 & 1.776 & 1.005 & 0.7145 & 1.59 \\ 22 & 1.937 & 1.269 & 1.052 & 0.7459 & 2.12 \\ 23 & 1.479 & 1.636 & 1.066 & 1.29 & 3.14 \end{tabular} \begin{flushleft} Note: $^a$Standard deviation of the minimum function values (over 50 replications) obtained using \code{genoud}. $^b$Standard deviation of the best function values (over 50 replications) reported for the ''fast'' evolutionary programming algorithm, from \citet[85 and 88, Tables II--IV]{yao.liu.lin1999}. \end{flushleft} \vspace*{.1in} \caption{Standard Deviations of Values of 22 Optimized Functions} \label{tab:23sdev} \begin{center} \line(1,0){450} \end{center} \end{table} \subsection{A Logistic Least Quartile Difference Estimator:} Our third example is a version of the LQD estimator used in \code{multinomRob}. Using the \proglang{R} function \code{IQR} to compute the interquartile range, the function to be minimized may be defined as follows.\footnote{The LQD problem solved in \code{multinomRob} is somewhat different. There the problem is to minimize the $\binom{h_{K}}{2}$ order statistic of the set of absolute differences among the standardized residuals, where $h_K$ is a function of the sample size and the number of unknown regression model coefficients \citep{MebaneSekhon2004}. The problem considered in the current example is simpler but exhibits similar estimation difficulties.} <>= LQDxmpl <- function(b) { logistic <- function(x) { 1/(1+exp(-x)) } sIQR <- function(y, yhat, n) { IQR((y-yhat)/sqrt(yhat*(n-yhat)), na.rm=TRUE) } sIQR(y, m*logistic(x %*% b), m) } @ For this example we define \code{LQDxmpl} after we compute the simulated data, so the data vector \code{y}, matrix \code{x} and scalar \code{m} are in scope to evaluate to have the values we simulate: <>= m <- 100 x <- cbind(1,rnorm(1000),rnorm(1000)) b1 <- c(.5, 1, -1) b2 <- c(0, -1, 1) logistic <- function(x) { 1/(1+exp(-x)) } y <- rbinom(1000, m, logistic(c(x[1:900,] %*% b1, x[901:1000,] %*% b2))) @ The data simulate substantial contamination. The first 900 observations are generated by one binomial regression model while the last 100 observations come from a very different model. Presuming we are interested in the model that generated the bulk of the data, ignoring the contamination in a generalized linear model with the binomial family produces very poor results: <>= summary(glm1 <- glm(cbind(y,m-y) ~ x[,2] + x[,3], family="binomial")) @ \begin{CodeChunk} \begin{CodeOutput} Call: glm(formula = cbind(y, m - y) ~ x[, 2] + x[, 3], family = "binomial") Deviance Residuals: Min 1Q Median 3Q Max -22.9168 -1.1693 0.3975 1.5895 24.6439 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 0.439492 0.007097 61.93 <2e-16 *** x[, 2] 0.679847 0.007985 85.14 <2e-16 *** x[, 3] -0.716963 0.007852 -91.31 <2e-16 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 \end{CodeOutput} \end{CodeChunk} Of course, if we knew which observations to omit the results would be much better: <>= suby <- y[1:900] subx <- x[1:900,] summary(glm2 <- glm(cbind(suby,m-suby) ~ subx[,2] + subx[,3], family="binomial")) @ \begin{CodeChunk} \begin{CodeOutput} Call: glm(formula = cbind(suby, m - suby) ~ subx[, 2] + subx[, 3], family = "binomial") Deviance Residuals: Min 1Q Median 3Q Max -3.21478 -0.71699 0.03528 0.67867 2.88314 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 0.501880 0.008036 62.46 <2e-16 *** subx[, 2] 1.003592 0.009779 102.63 <2e-16 *** subx[, 3] -0.984295 0.009437 -104.30 <2e-16 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 \end{CodeOutput} \end{CodeChunk} But in practical applications it is unknown apriori which observations should be treated as outliers. As the definition of \code{LQDxmpl} indicates, the LQD is based on minimizing the interquartile range (IQR) of the standardized residuals. Because the quartiles correspond to different data points for different values of the regression coefficients, the fitness function is not smooth, which is to say it is not everywhere differentiable. In general, at every point in the parameter space where the identity of the first or third quartile point changes, the function is not differentiable. Figure~\ref{fig:lqd1} illustrates this. A higher resolution version of this figure is available in \cite{MebaneJr.+Sekhon:2011}---also see \url{http://sekhon.berkeley.edu/papers/rgenoudJSS.pdf}. The IQR clearly has a minimum in the vicinity of the coefficient values used to generate most of the data. But contour plots for the numerically evaluated partial derivative with respect to the second coefficient parameter testify to the function's local irregularity. The function we use to evaluate this numerical derivative is defined as follows. <>= dLQDxmpl <- function(b) { eps <- 1e-10 logistic <- function(x) { 1/(1+exp(-x)) } sIQR <- function(y, yhat, n) { IQR((y-yhat)/sqrt(yhat*(n-yhat)), na.rm=TRUE) } dsIQR <- vector() for (i in 1:length(b)) { beps <- b beps[i] <- b[i]+eps dsIQR <- c(dsIQR, (sIQR(y, m*logistic(x %*% beps), m)- sIQR(y, m*logistic(x %*% b), m))/eps) } return(dsIQR) } @ Setting the intercept equal to 0.5, the code to generate the plotted values is % -rw-rw---- 1 wrm1 research 1878 Feb 10 2007 lqdxmpl2plotB.R <>= blen <- 3 lenbseq <- length(bseq <- seq(-2,2,length=200)) bseq3 <- seq(-1.2,-.9,length=200) bseq2 <- seq(.89,1.1,length=200) IQRarr <- IQRarrA <- array(NA, dim=c((1+blen), lenbseq, lenbseq)) dimnames(IQRarrA) <- list(NULL, as.character(bseq), as.character(bseq)) dimnames(IQRarr) <- list(NULL, as.character(bseq2), as.character(bseq3)) for (i in 1:lenbseq) { for (j in 1:lenbseq) { IQRarrA[1,i,j] <- LQDxmpl(c(.5, bseq[i], bseq[j])) IQRarrA[-1,i,j] <- dLQDxmpl(c(.5, bseq[i], bseq[j])) IQRarr[1,i,j] <- LQDxmpl(c(.5, bseq2[i], bseq3[j])) IQRarr[-1,i,j] <- dLQDxmpl(c(.5, bseq2[i], bseq3[j])) } } @ The following code produces the plots: <>= par(mfrow=c(2,2), lwd=.1) contour(bseq,bseq, IQRarrA[1,,], main="IQR", xlab="b[2]", ylab="b[3]") contour(bseq,bseq, IQRarrA[3,,], main="partial derivative w/r/t b[2]", xlab="b[2]", ylab="b[3]") loc2 <- (150:160)-5 loc3 <- (40:50)+5 contour(bseq[loc2],bseq[loc3], IQRarrA[3,loc2,loc3], main="partial derivative w/r/t b[2]", xlab="b[2]", ylab="b[3]") contour(bseq2,bseq3, IQRarr[3,,], main="partial derivative w/r/t b[2]", xlab="b[2]", ylab="b[3]") @ If the IQR function were smooth, we would see clearly separated, slightly curved contour lines, reflecting the nonlinearity of the \code{logistic} function, but there is nothing like that. Instead, looking over the domain $[-2,2]^2$ for the second and third regression coefficient parameters, with 200 points evaluated along each axis (the upper right plot), there is a splotchy cloud. This reflects the fact that the derivative changes sign very frequently over the domain: of the 40,000 points at which the derivative is evaluated, it is positive at 12,460 points and negative at 27,540 points. \begin{figure}[t] \caption{Contour Plots of the LQD Fitness Function and of its Partial Derivatives} \label{fig:lqd1} \begin{center} \includegraphics{lqdxmpl2B.pdf} % -rw-rw---- 1 wrm1 research 2745 Feb 10 23:15 lqdxmpl2plotB.Rout \end{center} \vspace{-.3in} \end{figure} The LQD fitness function is not appreciably smoother close to the true values. The bottom two plots show the partial derivatives with respect to the second coefficient parameter evaluated over the domain $[.89,1.1]\times[-1.2,-.9]$. The bottom left plot evaluates the derivatives at 11 points along each axis while the bottom right plot uses 200 points along each axis. In the left plot it is easier to see the intricacy of the partitioning of the parameter space as the identity of the first or third quartile point changes. The bottom right plot shows the intricacy in fact replicates at the finer grain of the more detailed evaluations (to see this it is probably necessary to magnify the plot while viewing online the \textit{Journal of Statistical Software} version of this documentation).\footnote{Please see \cite{MebaneJr.+Sekhon:2011} or \url{http://sekhon.berkeley.edu/papers/rgenoudJSS.pdf}.} Within this smaller domain the sign of the derivative changes even more frequently than it does over the domain $[-2,2]^2$: the derivative is positive at 18,098 points and negative at 21,902 points. While the LQD fitness function may be differentiable in a neighborhood of the global solution, that neighborhood, if it exists, is clearly not very big. As likely is that the global solution is located at a point where the function is not differentiable. Hence a numerically evaluated gradient is not meaningful for evaluating whether the solution has been found. At the true solution, numerical gradient values may differ substantially from zero. To use the LQD to estimate the binomial regression model parameters we use the following call to \code{genoud}. Because gradient information is of questionable relevance for this problem, we turn off the termination condition that the gradient at the solution be smaller than the value specified for the \code{solution.tolerance} argument. We retain the default setting \code{BFGS=TRUE} because, in principle, gradient-driven optimization may help in each of the many differentiable neighborhoods, even if it is useless across the nondifferentiable boundaries. Our experience optimizing the LQD \citep{MebaneSekhon2004} shows that using the BFGS in this way improves performance, even though the gradient is not useful for evaluating whether the solution has been found. <>= LQD1 <- genoud(LQDxmpl, nvars=3, max=FALSE, pop.size=2000, max.generations=300, wait.generations=100, gradient.check=FALSE, print=1) @ This invocation of the \code{LQDxmpl} function matches the behavior of \code{multinomRob} in that it produces an estimate for the intercept parameter along with the other coefficients. In a linear regression context, the interquartile range statistic contains no information about the intercept, so the LQD is not an estimator for that parameter. With a binomial regression model there is some information about the intercept due to the nonlinearity of the \code{logistic} function. The LQD estimate for the intercept should nonetheless be expected not to be very good. Results from the preceding estimation are as follows. % macht:/home/xchg/jss07/rgenoud: % -rw-rw---- 1 wrm1 research 5080 Aug 7 02:31 lqdxmpl1b.Rout \begin{CodeChunk} \begin{CodeOutput} Tue Aug 7 02:27:08 2007 Domains: -1.000000e+01 <= X1 <= 1.000000e+01 -1.000000e+01 <= X2 <= 1.000000e+01 -1.000000e+01 <= X3 <= 1.000000e+01 [...] HARD Maximum Number of Generations: 300 Maximum Nonchanging Generations: 100 Population size : 2000 Convergence Tolerance: 1.000000e-06 Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation. Not Checking Gradients before Stopping. Using Out of Bounds Individuals. Minimization Problem. Generation# Solution Value 0 4.951849e-01 56 1.298922e-01 57 1.298891e-01 59 1.298848e-01 60 1.298820e-01 61 1.298793e-01 62 1.298768e-01 63 1.298744e-01 'wait.generations' limit reached. No significant improvement in 100 generations. Solution Fitness Value: 1.298743e-01 Parameters at the Solution (parameter, gradient): X[ 1] : 8.130357e-02 G[ 1] : 9.616492e-03 X[ 2] : 8.889485e-01 G[ 2] : -1.167897e-01 X[ 3] : -9.327966e-01 G[ 3] : -3.090130e-02 Solution Found Generation 63 Number of Generations Run 164 Tue Aug 7 02:31:09 2007 Total run time : 0 hours 4 minutes and 1 seconds \end{CodeOutput} \end{CodeChunk} Recall that the gradient is not reliably informative at the solution. To check whether this solution is believable, we might try reestimating the model using a larger population and larger specified number of generations: <>= LQD1 <- genoud(LQDxmpl, nvars=3, max=FALSE, pop.size=10000, max.generations=1000, wait.generations=300, gradient.check=FALSE, print=1) @ At the price of a greatly increased running time (from four minutes up to one hour 53 minutes), the results are better than the first run (even though the summary measure of fit is slightly worse): % macht:/home/xchg/jss07/rgenoud: % -rw-rw---- 1 wrm1 research 5236 Aug 7 05:16 lqdxmpl1d.Rout \begin{CodeChunk} \begin{CodeOutput} Minimization Problem. Generation# Solution Value 0 2.238865e-01 2 1.301149e-01 3 1.300544e-01 4 1.300482e-01 6 1.300375e-01 7 1.300343e-01 8 1.300323e-01 134 1.299662e-01 135 1.299099e-01 136 1.298867e-01 137 1.298843e-01 138 1.298822e-01 139 1.298791e-01 141 1.298774e-01 'wait.generations' limit reached. No significant improvement in 300 generations. Solution Fitness Value: 1.298770e-01 Parameters at the Solution (parameter, gradient): X[ 1] : 2.013748e-01 G[ 1] : -7.394125e-02 X[ 2] : 9.526390e-01 G[ 2] : 7.807607e-02 X[ 3] : -9.642458e-01 G[ 3] : 3.834052e-02 Solution Found Generation 141 Number of Generations Run 442 Tue Aug 7 05:16:37 2007 Total run time : 1 hours 53 minutes and 45 seconds \end{CodeOutput} \end{CodeChunk} %$ This example demonstrates a key difficulty that arises when optimizing irregular functions in the absence of gradients. It is difficult to assess when or whether an optimum has been found. The estimated coefficient values are close to the ones used to generate most of the data, except as expected the estimate for the intercept is not good. The estimates are better than if we had ignored the possibility of contamination. But whether these are the best possible estimates is not clear. If we were to use an even larger population and specify that an even greater number of generations be run, perhaps a better solution would be found. %http://sekhon.berkeley.edu/rgenoud/R/genoud_cluster_manual.R %http://sekhon.berkeley.edu/rgenoud/R/genoud_cluster_manual_tunnel.R %\code{genoud} can be tricked into doing constrained optimization by %passing in a function which contains a penalty function. Even for less irregular problems convergence is difficult to determine. Nonlinear optimizers often report false convergence, and users should not simply trust whatever convergence criteria an optimizer uses. \citet{McCulloughVinod2003} offer four criteria for verifying the solution of a nonlinear solver. These criteria are meaningful only for problems that meet regularity conditions at the solution, notably differentiability, and as such are not useful for the LQD example offered above. The four criteria are: (1) making sure the gradients are zero; (2) inspecting the solution path (i.e., the trace) to make sure it follows the expected rate of convergence; (3) evaluating the Hessian to make sure it is well-conditioned;\footnote{Following an exchange with \citet{DrukkerWiggins2004}, \citet{McCulloughVinod2004b} modify their third suggestion to note that determining if the Hessian is well-conditioned in part depends on how the data are scaled. That is, a Hessian that appears to be ill-conditioned may be made well-conditioned by rescaling. So if an Hessian appears to be ill-conditioned, \citet{McCulloughVinod2004b} recommend that the analyst attempt to determine if rescaling the data can result in a well-conditioned Hessian.} and (4) profiling the likelihood to ascertain if a quadratic approximation is adequate. One may need to take the results from \code{genoud} and pass them to \code{optim} to conduct some of these diagnostic tests such as to profile the likelihood. It is also good practice to use more than one optimizer to verify the solution \citep{stokes2004}. Note that \code{genoud} uses its own random number seeds and internal pseudorandom number generators to insure backward compatibility with the original C version of the software and to make cluster behavior more predictable. These seeds are set by the \code{unif.seed} and \code{int.seed} options. The \proglang{R} \code{set.seed} command is ignored by \code{genoud}. %user supplied gradients and lexical search? \section{Conclusion} \label{sec:conclusion} The \code{genoud} function provides many more options than can be reviewed in this brief paper. These options are described in the \proglang{R} help file. The most important option influencing how well the evolutionary algorithm works is the \code{pop.size} argument. This argument controls the population size---i.e., it is the number of individuals \code{genoud} uses to solve the optimization problem. As noted above, the theorems proving that genetic algorithms find good solutions are asymptotic in both population size and the number of generations. It is therefore important that the \code{pop.size} value not be small. On the other hand, computational time is finite so obvious trade-offs must be made. As the LQD example illustrates, a larger population size is not necessarily demonstrably better. The most important options to ensure that a good solution is found, aside from \code{pop.size}, are \code{wait.generations}, \code{max.generations} and \code{hard.generation.limit}. Many statistical models have objective functions that are nonlinear functions of the parameters, and optimizing such functions is tricky business \citep{AltmanGillMcDonald2003}. Optimization difficulties often arise even for problems that are generally considered to be simple. For a cautionary tale on how optimization can be a difficult task even for such problems see Stokes' (\citeyear{stokes2004}) effort to replicate a probit model estimated by \citet[pp. 335]{maddala1992}. A recent controversy over estimating a nonlinear model estimated by maximum likelihood offers another cautionary tale \citep{DrukkerWiggins2004,McCulloughVinod2003,McCulloughVinod2004a,McCulloughVinod2004b,SchacharNalebuff2004}. End users are generally surprised to learn that such optimization issues can arise, and that results can substantially vary across optimizers and software implementations. The \pkg{rgenoud} package provides a powerful and flexible global optimizer. When compared with traditional derivative-based optimization methods, \pkg{rgenoud} performs well \citep{SekhonMebane1998}. Optimization of irregular functions is, however, as much of an art as science. And an optimizer cannot be used without thought even for simple surfaces, let alone spaces that require a genetic algorithm. We hope that the availability of a scalable global optimizer will allow users to work with difficult functions more effectively. \bibliography{rgenoud} \end{document} % LocalWords: optima GillMurrayWright EfronTibshirani GENOUD MebaneSekhon LQD % LocalWords: SekhonMebane multinomRob overdispersed nondifferentiable Broyden % LocalWords: Goldfarb Shanno BFGS optim genoud EA EAs GA holland goldberg GAs % LocalWords: GrefenstetteBaker davis FilhoTreleavenAlippi generation's dejong % LocalWords: substring's grefenstette billingsley Vose NixVose vose GA's ADC % LocalWords: GENOCOP MichalewiczSwaminathanLogan Michalewicz Polytope dnorm % LocalWords: nvars Nonchanging UniqueCount var MemoryMatrix IQR LQDxmpl exp % LocalWords: sIQR yhat na rm cbind rnorm rbinom Min Std Pr Signif suby subx % LocalWords: apriori Raphson saddlepoints fn Genoud's gr hessian unif int ssh % LocalWords: Tausworthe stdout tempdir polytope musil deckard makeSOCKcluster % LocalWords: usernames username PVM MPI peakgeneration parm UC Outlier seq mu % LocalWords: lapply xlab ylab col biclaw mNd ALTMAN rgenoud WandKingLau PKfit % LocalWords: KingWand braumoeller BraumoellerGoodrichKline pharmacokinetics % LocalWords: LeeLee pseudorandom pdf glm rw wrm lqdxmpl cl makeCluster probit % LocalWords: localhost clusterExport stopCluster AltmanGillMcDonald GENetic % LocalWords: McCulloughVinod SchacharNalebuff GenMatch GUI URL boolean Sekhon % LocalWords: CPUs nonlinearity FAiR goodrich SekhonMatching ivivc vitro vivo % LocalWords: multinomial Synth AbadieGardeazabal synth nonsmooth Rcore maxima % LocalWords: resampling resamples optimizer's eval nonstochastic testbounds % LocalWords: LLLL func ij unimodal Rosenbrock multimodal minima saddlepoint % LocalWords: testfuncs testNparms gradcheck sizeset genset nreps gsarray tol % LocalWords: gsize ngens FEP LLLLLL sqrt dLQDxmpl eps dsIQR beps blen lenbseq % LocalWords: bseq IQRarr IQRarrA dimnames mfrow lwd loc online DrukkerWiggins % LocalWords: maddala funcs sapply runif ifelse rbind crossprod byrow vXXi % LocalWords: interquartile rgenoud/inst/doc/rgenoud.pdf0000644000176200001440000166614212105141670015612 0ustar liggesusers%PDF-1.5 % 43 0 obj << /Length 3499 /Filter /FlateDecode >> stream xڝrF]_%D3\ڇTlV*N # eo%{%$K뛫Wo21UjMᒛduZ&5InVɇw̶~E^6a?kpo=9/A[ng½/\no7o_)MLU6M,TL[i _8eVY?sC/QIY_dBBefջTa֙&Y8d_ 㙁 ďw)%_}MۦME0yZ-3D'~kapl_;8q v;uӔiQîaHwܣ;2S&}v`g$d}͜@!؊q\+2 Sd[`myS'OIC>y_ݑW&iҦ%V5iTIѸ)}u+<"YH#D Si^o2{a9O@YT3@[գ]MҲ>Wň:-Rvt d(g:XX`aNLVE^.M8,NYQYkq ue?:w]%1rjlȤ8( d@+2#g͊ŝ ֙-3-8Vtr/'LԀτ[gp #U۶EV][Rjr^C&͍nf\>A#>*+g0\#ˣRțX o]v^{2gEm}b8O<*X.mܙ"p,@I!}R3uł',MͽN3v8(2/a}zw$1fN@"/Źe0Nǂ=!.g,}M@[ e;8lɅDҰ3 4^D{ M ;ՠ To{QaJru*M#Q"fUsƅ-B;KmS Wu_F37'5e~JߝDC/$\txU]"MCvlvjȑ!QA 4)7uLeXK ^7&t .yz=sھ8%[)>MzݫDKrKr^x'xGg/!iQ,Ե4IXDZw,Őw%{PSV#u],W0pɺ4煤;jx'QBB%7relwY\b&\P"04񅖴*?bn&:VU$(iFԋ* AW8_Oѱyӗ![ʇ 1Lf":.R?|D?pLc1!g fc`]7BK( Gr%p2^{ٯ;TyxdiCń%؎V Abv%UՑk0CٓJ)Jse$g\c{^bAH!y𴤯>d_nlcH?X#~Ϛ 9P%ZA7$>pt'ZB,UQB;PT]|"Ш Lm"i[l`cKwa]Wyu\D@%o{ӝJNhY9.??z4%jd0|"=A!5MDy7Ō*D:m* nCrӕEUMZ6Y6KV1^$  #s| )51vJEQ)ƙNo|H0:՝ pV;c:{~WD}!Z'5oiA.Nܻ@NvE- F|@êx'hj_ܜ7o%0S\&8ֵ- 0\]p`Zih;}! -+،n^yLU{=&W]5y,O(ʍWo\iS%K!˂Κ3Im6aP^e49u;mM`C/ xuL  'Fۑ'W&}36w"n.#+Fg;/g6)T cBTkÙ(hj)nuA*i⏣.|,gל}?#-N|LZf! 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Mebane, Jr., Jasjeet S. Sekhon)/Title(Genetic Optimization Using Derivatives: The rgenoud Package for R)/Subject()/Creator(LaTeX with hyperref package)/Producer(pdfTeX-1.40.13)/Keywords(genetic algorithm, evolutionary program, optimization, parallel computing, R) /CreationDate (D:20130208092200Z) /ModDate (D:20130208092200Z) /Trapped /False /PTEX.Fullbanner (This is pdfTeX, Version 3.1415926-2.4-1.40.13 (TeX Live 2012) kpathsea version 6.1.0) >> endobj 583 0 obj << /Type /ObjStm /N 44 /First 372 /Length 2103 /Filter /FlateDecode >> stream xڝY[s۶~ׯc=ʸDrė\`Ëן]ArD.ҌG @IH( B""` B?DQ "#pcDr"@RX7IB(`<`) hc@."Z1&28\1P"$ +(PRKT"D@xJ:* "x J %qC(!: )B@*q4 (L( ILXL&>9~7<&GzQ5(W48}|wr%F}feWy`H IQV']t5lrtM EYEa/>>|rߎFcO3/t(5_ǻ\'x^zyy=?o=&BЩ.^~~v1=!0;<xӭll >dAM99:k}Ѕ+HdUswPס#nGլl ʎ3L8!wcdGjXln9g7gH-aĖ?Wԍ6.ajs&,0> ڜVwơ[;|XdJ 58:Xxin, *5>9:W]HC~iZSٙ)ec-ikI2߫unĨk9BΒ<u7M+cu ~.Cuj:1}+5PMJM6ϫ,̔=<:2Ác[WRM2=ݯ&Asq/@ Kƻj`@0b$tvMO \Q;7*ɳ)ͪ"_3WWzy.V!f2S%K|_lz]oSS$Y>=ɳeZΘT|nMUXY^/RW'[r $g)1rfLHlz:)]. 4*^|?Kno Ѳ;ݭx㘹Y&Bs8K6Votmk X.VF 2BJirg:]8%iڪYOBJߧY׃h_MgyܜLB,<γdi" ?YQݙ&YSGiyv,MR,JaSy0&;N{LjM`uQǛ"Yo*8 avY3uV[*JC̠w?`|p Dsԟз|\uPNӼ^o>'Y-A0i4=}Z慁sW\Ģu-( :([K]-7P@67ƕc8i13nw25Px$m|SvC7"'/7ooTEvo9MouR`,>Rc:&OSX `-ѹ:yH~+ojSmkIH;=,|̪ L`?eqGiFTjSO nnu]4kֆD"{xD!{\h| LpiOD+A Zvb@'Xz<3|UQܗ`:'ŰIyl_K =" G!j5N y|ZkGMN)n^y| H9 (%~M'tIhO:)"\ܻ*Oܗ5,G9b1@{*4XXKᾤIquw9t[Gk>7};Z"Eߎ>98Ŝ;FFFGGE/9 v tfm`GSٓ=B׹! K̔%DW:C_T\H/Zksџy:ZRx]/ endstream endobj 611 0 obj << /Type /XRef /Index [0 612] /Size 612 /W [1 3 1] /Root 609 0 R /Info 610 0 R /ID [ ] /Length 1457 /Filter /FlateDecode >> stream x%KlWE_R(-Z*7A JiyFcW΍ DYh 9č0$&n\MpCt+rfs=;so!W, D 0@a ^dacn3207&U`ڲ:A5smdX6ͥj :˴n'У5Fv]Xuzim<΃;`\oݚVn'nsJ Tx.t` N] 8#(@8zA8 "C`Q08 ΀I0 8 9p\2X "X hZBp ̂ep yA=`0gLs2%@K{ @e0\%aupmpk9m}`)GVGVGVGVGVWZh*j&u= R;R;R;zz;z;¹^k;h^p4#0ܬ{L-}/#`t 1 ns&"\sHHHHHHH=^Oz vN jѝpr,oz[j9:k)1,3fY8N8SeNOinTPew:@~.Q!ml>:.`{4P@-ZtA旀΋%Pf h^ISdS- [9 :*`'h~_vvBt#&F=Z (8:,LN3$6w[=1+\AQy~ (bۿ8>h7]{Š]UtҊ_*VFѠt):e Y a+ suppressMessages(library(rgenoud)) > > #maximize the sin function > sin1 <- genoud(sin, nvars=1, max=TRUE, unif.seed=912821, int.seed=93058, print.level=0) > sin1$value <- signif(sin1$value,6) > sin1$par <- signif(sin1$par,6) > sin1$gradients <- signif(sin1$gradients,6) > print(sin1) $value [1] 1 $par [1] 7.85398 $gradients [1] -3.8465e-11 $generations [1] 11 $peakgeneration [1] 1 $popsize [1] 1000 $operators [1] 122 125 125 125 125 126 125 126 0 > > #minimize the sin function > sin2 <- genoud(sin, nvars=1, max=FALSE, unif.seed=912821, int.seed=93058, print.level=0) > sin2$value <- signif(sin2$value,6) > sin2$par <- signif(sin2$par,6) > sin2$gradients <- signif(sin2$gradients,6) > print(sin2) $value [1] -1 $par [1] -1.5708 $gradients [1] 5.94475e-11 $generations [1] 11 $peakgeneration [1] 1 $popsize [1] 1000 $operators [1] 122 125 125 125 125 126 125 126 0 > > #maximize a univariate normal mixture which looks like a claw > claw <- function(xx) { + x <- xx[1] + y <- (0.46*(dnorm(x,-1.0,2.0/3.0) + dnorm(x,1.0,2.0/3.0)) + + (1.0/300.0)*(dnorm(x,-0.5,.01) + dnorm(x,-1.0,.01) + dnorm(x,-1.5,.01)) + + (7.0/300.0)*(dnorm(x,0.5,.07) + dnorm(x,1.0,.07) + dnorm(x,1.5,.07))) + return(y) + } > claw1 <- genoud(claw, nvars=1,pop.size=3000,max=TRUE, unif.seed=912821, int.seed=93058, print.level=0) > claw1$value <- signif(claw1$value,6) > claw1$par <- signif(claw1$par,6) > claw1$gradients <- signif(claw1$gradients,6) > print(claw1) $value [1] 0.411312 $par [1] 0.999503 $gradients [1] -1.27716e-06 $generations [1] 11 $peakgeneration [1] 1 $popsize [1] 3000 $operators [1] 372 375 375 375 375 376 375 376 0 > > # Maximize a bivariate normal mixture which looks like a claw. > biclaw <- function(xx) { + mNd2 <- function(x1, x2, mu1, mu2, sigma1, sigma2, rho) + { + z1 <- (x1-mu1)/sigma1 + z2 <- (x2-mu2)/sigma2 + w <- (1.0/(2.0*pi*sigma1*sigma2*sqrt(1-rho*rho))) + w <- w*exp(-0.5*(z1*z1 - 2*rho*z1*z2 + z2*z2)/(1-rho*rho)) + return(w) + } + x1 <- xx[1]+1 + x2 <- xx[2]+1 + + y <- (0.5*mNd2(x1,x2,0.0,0.0,1.0,1.0,0.0) + + 0.1*(mNd2(x1,x2,-1.0,-1.0,0.1,0.1,0.0) + + mNd2(x1,x2,-0.5,-0.5,0.1,0.1,0.0) + + mNd2(x1,x2,0.0,0.0,0.1,0.1,0.0) + + mNd2(x1,x2,0.5,0.5,0.1,0.1,0.0) + + mNd2(x1,x2,1.0,1.0,0.1,0.1,0.0))) + + return(y) + } > biclaw1 <- genoud(biclaw, default.domains=20, nvars=2,pop.size=5000,max=TRUE, unif.seed=912821, int.seed=93058, print.level=0) > biclaw1$value <- signif(biclaw1$value,6) > biclaw1$par <- signif(biclaw1$par,6) > biclaw1$gradients <- signif(biclaw1$gradients,6) > print(biclaw1) $value [1] 1.67113 $par [1] -1 -1 $gradients [1] 2.49105e-08 -3.42757e-08 $generations [1] 12 $peakgeneration [1] 1 $popsize [1] 5000 $operators [1] 622 625 625 625 625 626 625 626 0 > > proc.time() user system elapsed 6.218 0.141 6.384 rgenoud/tests/tests.R0000644000176200001440000000376712163371233014362 0ustar liggesuserssuppressMessages(library(rgenoud)) #maximize the sin function sin1 <- genoud(sin, nvars=1, max=TRUE, unif.seed=912821, int.seed=93058, print.level=0) sin1$value <- signif(sin1$value,6) sin1$par <- signif(sin1$par,6) sin1$gradients <- signif(sin1$gradients,6) print(sin1) #minimize the sin function sin2 <- genoud(sin, nvars=1, max=FALSE, unif.seed=912821, int.seed=93058, print.level=0) sin2$value <- signif(sin2$value,6) sin2$par <- signif(sin2$par,6) sin2$gradients <- signif(sin2$gradients,6) print(sin2) #maximize a univariate normal mixture which looks like a claw claw <- function(xx) { x <- xx[1] y <- (0.46*(dnorm(x,-1.0,2.0/3.0) + dnorm(x,1.0,2.0/3.0)) + (1.0/300.0)*(dnorm(x,-0.5,.01) + dnorm(x,-1.0,.01) + dnorm(x,-1.5,.01)) + (7.0/300.0)*(dnorm(x,0.5,.07) + dnorm(x,1.0,.07) + dnorm(x,1.5,.07))) return(y) } claw1 <- genoud(claw, nvars=1,pop.size=3000,max=TRUE, unif.seed=912821, int.seed=93058, print.level=0) claw1$value <- signif(claw1$value,6) claw1$par <- signif(claw1$par,6) claw1$gradients <- signif(claw1$gradients,6) print(claw1) # Maximize a bivariate normal mixture which looks like a claw. biclaw <- function(xx) { mNd2 <- function(x1, x2, mu1, mu2, sigma1, sigma2, rho) { z1 <- (x1-mu1)/sigma1 z2 <- (x2-mu2)/sigma2 w <- (1.0/(2.0*pi*sigma1*sigma2*sqrt(1-rho*rho))) w <- w*exp(-0.5*(z1*z1 - 2*rho*z1*z2 + z2*z2)/(1-rho*rho)) return(w) } x1 <- xx[1]+1 x2 <- xx[2]+1 y <- (0.5*mNd2(x1,x2,0.0,0.0,1.0,1.0,0.0) + 0.1*(mNd2(x1,x2,-1.0,-1.0,0.1,0.1,0.0) + mNd2(x1,x2,-0.5,-0.5,0.1,0.1,0.0) + mNd2(x1,x2,0.0,0.0,0.1,0.1,0.0) + mNd2(x1,x2,0.5,0.5,0.1,0.1,0.0) + mNd2(x1,x2,1.0,1.0,0.1,0.1,0.0))) return(y) } biclaw1 <- genoud(biclaw, default.domains=20, nvars=2,pop.size=5000,max=TRUE, unif.seed=912821, int.seed=93058, print.level=0) biclaw1$value <- signif(biclaw1$value,6) biclaw1$par <- signif(biclaw1$par,6) biclaw1$gradients <- signif(biclaw1$gradients,6) print(biclaw1) rgenoud/src/0000755000176200001440000000000012553042713012506 5ustar liggesusersrgenoud/src/unif.h0000644000176200001440000000135212553042713013621 0ustar liggesusers/* RGENOUD Walter R. Mebane, Jr. Cornell University http://macht.arts.cornell.edu/wrm1 Jasjeet Singh Sekhon UC Berkeley http://sekhon.polisci.berkeley.edu $Header: /home/jsekhon/xchg/genoud/rgenoud.distribution/sources/RCS/unif.h,v 2.15 2005/10/29 06:14:44 jsekhon Exp jsekhon $ */ /* Tausworthe-Lewis-Payne generator */ #ifndef DEFTLPGEN typedef int integer; #define TLPAUXSIZE 1300 #define TLPDBSIZ 2000 #define ZEROI ((integer)0) #define TLPMOD 2147483647 void ruxorv (integer *, int, double *, integer *); void tlpseq (integer *, int, integer *, integer *); void tauint (integer *); void tlpcor (integer, int, integer *, integer *); #define DEFTLPGEN #endif rgenoud/src/print_format.cpp0000644000176200001440000001576312553042713015732 0ustar liggesusers/* RGENOUD Walter R. Mebane, Jr. Cornell University http://macht.arts.cornell.edu/wrm1 Jasjeet Singh Sekhon UC Berkeley http://sekhon.polisci.berkeley.edu June 3, 2012 */ #include "genoud.h" /********************************************************************************/ /* ReadPopulation(): */ /* */ /* This function reads in an old population file and initializes the */ /* newpopulation with it. */ /* */ /* */ /********************************************************************************/ long ReadPopulation(double **Data, long NewPopSize, long NewVars, FILE *fp, short PrintLevel) { char ctmp[MAXPATH]; int generation, PopSize, nvars, UsePopSize, FitVals; int i, j, ltmp, fint; double **OldData; short trip=0; /* This reads the "Generations:" name */ while(!(feof(fp))) { /* pos = ftell(fp); */ fint = fscanf(fp, "%s", ctmp); fint = fscanf(fp, " %d", &generation); if(PrintLevel>0) Rprintf( "Generation: %d\n", generation); /* This reads the "Population" name */ fint = fscanf(fp, "%s", ctmp); /* This reads the "Size:" name */ fint = fscanf(fp, "%s", ctmp); fint = fscanf(fp, " %d", &PopSize); if(PrintLevel>0 & trip==0) Rprintf( "Population Size: %d\n", PopSize); fint = fscanf(fp, "%s", ctmp); /* reads "Fit" */ fint = fscanf(fp, "%s", ctmp); /* reads "Values:" */ fint = fscanf(fp, "%d", &FitVals); /* reads number of fit values */ if(FitVals > 1) warning("Reading an existing population file is not supported for Fit Values != 1"); /* This reads the "Variables:" name */ fint = fscanf(fp, "%s", ctmp); fint = fscanf(fp, " %d", &nvars); if(PrintLevel>0 & trip==0) Rprintf( "Number of Variables: %d\n", nvars); if (trip==0) { if (nvars!=NewVars) return(0); OldData = JaMatrixAllocate(PopSize+2, nvars+2); trip++; } /* loop over the main data part */ for (i=1; i<=PopSize; i++) { fint = fscanf(fp,"%d",<mp); for (j=0; j<=nvars; j++) { fint = fscanf(fp,"%lf", &OldData[i][j]); } } } /* Map OldData to Data */ if (NewPopSize < PopSize) UsePopSize = NewPopSize; else UsePopSize=PopSize; for (i=1; i<=UsePopSize; i++) { Data[i][nvars+1] = 0.0; for (j=0; j<=nvars; j++) { Data[i][j] = OldData[i][j]; } } /* let's print the population file */ if(PrintLevel>1) { Rprintf( "\nRead in Population. Used Population Size: %d\n", UsePopSize); for (i=1; i<=UsePopSize; i++) { Rprintf( "%d \t", i); for (j=0; j<=nvars; j++) { Rprintf( "%e \t", Data[i][j]); } Rprintf( "\n"); } Rprintf( "\n"); /* fflush(output); */ } JaMatrixFree(OldData, PopSize); return(PopSize); } /* end Read Population */ /********************************************************************************/ /* */ /* FUNCTION NAME : print_domains() */ /* */ /* SYNOPSIS : void print_domains(equal,t_equ) */ /* */ /* DESCRIPTION : This function prints the matrix passed, on to*/ /* the standard output, in the format of */ /* domains. */ /* */ /* FUNCTIONS CALLED : None */ /* */ /* CALLING FUNCITONS : main() */ /* */ /* */ /* REV DATE BY DESCRIPTION */ /* --- ---- -- ----------- */ /* */ /* */ /********************************************************************************/ void print_domains(MATRIX equal, int t_equ, short DataType) /* MATRIX equal; the domains matrix, with the upper and lower limits int t_equ; *the total number of domains */ { int i,j; Rprintf("Domains:\n"); //Integer if (DataType==1) { for(i=1; i<=t_equ; i++) { for(j=1; j<=3; j++) { if(j == 2) Rprintf(" <= X%-2d <= ",(int)equal[i][j]); else Rprintf(" %d ",(int) equal[i][j]); } Rprintf("\n"); } } else { for(i=1; i<=t_equ; i++) { for(j=1; j<=3; j++) { if(j == 2) Rprintf(" <= X%-2d <= ",(int)equal[i][j]); else Rprintf(" %e ",equal[i][j]); } Rprintf("\n"); } } } /********************************************************************************/ /* */ /* FUNCTION NAME : print_population() */ /* */ /********************************************************************************/ void print_population(int popsize, int nvars, int generation, int lexical, double **foo, FILE *out) { int i,j; if (lexical < 2) { fprintf(out,"Generation: %d \t Population Size: %d \t Fit Values: 1 \t Variables: %d\n\n", generation, popsize, nvars); for(i = 1; i <= popsize; i++) { fprintf(out,"%d \t %e \t",i, foo[i][0]); for (j = 1; j <= nvars; j++) { fprintf(out,"%e \t ",foo[i][j]); } fprintf(out,"\n"); } fprintf(out,"\n\n"); } else { long lexical_end = lexical-1+nvars+2; fprintf(out,"Generation: %d \t Population Size: %d \t Fit Values: %d \t Variables: %d\n\n", generation, popsize, lexical, nvars); for(i = 1; i <= popsize; i++) { fprintf(out,"%d \t ", i); /* print lexical fit values */ fprintf(out,"%e \t ",foo[i][0]); for(j=(nvars+2);j Jasjeet Singh Sekhon UC Berkeley http://sekhon.polisci.berkeley.edu June 3, 2012 */ #include "genoud.h" #include "unif.h" /* unif.h integer definition */ int NewUnifSeed[MAXTHREADS]; int RandIntSeed[MAXTHREADS]; int ThreadNumber; extern double func4g(double *X); void genoud(struct GND_IOstructure *Structure) { extern int NewUnifSeed[MAXTHREADS]; extern int RandIntSeed[MAXTHREADS]; extern int ThreadNumber; MATRIX domains, /*Matrix for Domains*/ final_mat; /*The final Domain*/ VECTOR LowerBounds, UpperBounds, X; /*Initial values for the variables*/ INDEX fin; /*Size of final matrix*/ int i, /*Counter variable*/ nvars; /*Remaining variables after p-variables were eliminated*/ time_t start_time, stop_time; double delta_time; long hours, minutes, seconds; char time_str[27]; static long BaseNewUnifSeed=81282, BaseRandIntSeed=53058; static short firsttime=1; /* FILE *output; */ /* Lamarck Child Test Variables */ // char LVMchar[1000]; long LVMreturn; /********************************************************************************/ LVMreturn=0; time(&start_time); strcpy(time_str, ctime(&start_time)); /* Fault Tolerant MinMax */ if (Structure->MinMax > 0) Structure->MinMax=1; else Structure->MinMax=0; if (Structure->OutputType!=0) { error("output path/type must be the 'R' default"); } /* else { output=stdout; } */ if(Structure->PrintLevel>0) Rprintf("\n\n%s",time_str); ThreadNumber=Structure->ThreadNumber; if (ThreadNumber > MAXTHREADS) { error("No more than %d threads allowed\n\n", MAXTHREADS); } if (Structure->ProvideSeeds == 1) { /* Only toggle the instance number if we have threads! */ NewUnifSeed[ThreadNumber] = Structure->UnifSeed; RandIntSeed[ThreadNumber] = Structure->IntSeed; } else { /* If a Seed is NOT provided, use the base random number and run from that base! In other words, might as well the ThreadNumber equal to 0 */ if (firsttime==1) { NewUnifSeed[0] = BaseNewUnifSeed; RandIntSeed[0] = BaseRandIntSeed; firsttime=0; } ThreadNumber = 0; } fin.r = Structure->nvars; /*total number of inequalities + domains*/ fin.c = Structure->nvars+2; /*x2 variables + lower limits + upper limits*/ nvars = Structure->nvars; /*Allocating memory for all the vectors and matrices*/ final_mat = matrix(1,fin.r,1,fin.c); domains = matrix(1,nvars,1,3); LowerBounds = Gvector(1, nvars); UpperBounds = Gvector(1, nvars); X = Gvector(1,nvars); /* SETUP DOMAINS */ /* alter the domains when we are using integers because of the "open set" problem. We only extend the UPPER domain bound */ if (Structure->DataType==1) { for(i=0; invars; i++) Structure->Domains[i][1] = Structure->Domains[i][1] + 0.99999; } for(i=1; i<=Structure->nvars; i++) { domains[i][1] = Structure->Domains[i-1][0]; domains[i][2] = (double) i; domains[i][3] = Structure->Domains[i-1][1]; } for (i=1; i<=nvars; i++) { LowerBounds[i] = domains[i][1]; UpperBounds[i] = domains[i][3]; } /*Initialization*/ if(Structure->PrintLevel>0) print_domains(domains,nvars,Structure->DataType); if (Structure->DataType==1) { JaIntegerOptimization(Structure, X, domains); } else { optimization(Structure, X, domains); } /* free memory */ free_matrix(final_mat,1,fin.r,1); free_matrix(domains, 1, nvars, 1); free_vector(LowerBounds,1); free_vector(UpperBounds,1); free_vector(X,1); /* print final numbers and the time this has taken */ if(Structure->PrintLevel>0) { Rprintf( "\n"); Rprintf( "Solution Found Generation %d\n", Structure->oPeakGeneration); Rprintf( "Number of Generations Run %d\n", Structure->oGenerations); } time(&stop_time); strcpy(time_str, ctime(&stop_time)); if(Structure->PrintLevel>0) Rprintf("\n%s",time_str); delta_time = difftime(stop_time, start_time); hours = (int) (delta_time/3600); minutes = (int) (delta_time - (hours*3600))/60; seconds = (int) delta_time - (hours*3600) - (minutes*60); if(Structure->PrintLevel>0) { Rprintf("Total run time : %d hours %d minutes and %d seconds\n", hours, minutes, seconds); /* fflush(output); */ } /* no longer allowed */ /* if (Structure->OutputType==1) fclose(output); */ } rgenoud/src/frange_ran.cpp0000644000176200001440000000356212553042713015322 0ustar liggesusers/* RGENOUD Walter R. Mebane, Jr. Cornell University http://macht.arts.cornell.edu/wrm1 Jasjeet Singh Sekhon UC Berkeley http://sekhon.polisci.berkeley.edu $Header: /home/jsekhon/xchg/genoud/rgenoud.distribution/sources/RCS/frange_ran.cpp,v 2.15 2005/10/29 06:14:44 jsekhon Exp jsekhon $ */ #include "genoud.h" /* replacements for random number functions in GENOCOP's frange_ran.c */ #include "unif.h" #include "urans.h" double newunif(void) { extern int NewUnifSeed[MAXTHREADS]; extern int ThreadNumber; /* static integer aux[TLPAUXSIZE], iseed = NEWUNIFSEED ;*/ static integer aux[TLPAUXSIZE]; double wrkout; double wrk; /* get a random uniform double on (0,1] */ ruxorv (&NewUnifSeed[ThreadNumber], 1, &wrk, aux); wrkout = (double) wrk; return(wrkout); } double frange_ran(double llim, double ulim) /* double ulim; double llim; */ { /*llim, ulim: The upper and lower limits between which the random number is to be generated*/ double num1, diff = ulim - llim; if (diff == 0) return(llim); else if(diff < 0.0001) return((flip() == TAIL) ? llim : ulim); do { // printf("num1: %lf, ulim: %lf, llim: %lf\n",num1,ulim,llim); // fflush(stdout); num1 = llim + newunif()*(ulim-llim) ; } while((num1ulim)); // printf("fr2\n"); // fflush(stdout); return(num1); } unsigned int randint (void) { extern int RandIntSeed[MAXTHREADS]; extern int ThreadNumber; /* static integer aux[TLPAUXSIZE], iseed = RANDINTSEED ; */ static integer aux[TLPAUXSIZE]; integer wrk; int num; /* get a signed 32-bit number from the TLP generator */ tlpseq (&RandIntSeed[ThreadNumber], 1, &wrk, aux); /* truncate to 16 bits */ num = wrk%65535; return (num); } unsigned int newrand (void) { return (randint()); } rgenoud/src/evaluate.cpp0000644000176200001440000037365312553042713015041 0ustar liggesusers/* RGENOUD Walter R. Mebane, Jr. University of Michigan http://www-personal.umich.edu/~wmebane Jasjeet Singh Sekhon UC Berkeley http://sekhon.berkeley.edu June 27, 2013 */ #include "genoud.h" #include "gradient.h" extern "C" { double genoud_optim(SEXP fn_optim, SEXP rho, double *X, long parameters); void RlexicalSort(SEXP fnLexicalSort, SEXP rho, double **population, short int MinMax, long pop_size, long nvars, long lexical_end, short int type); long RmemoryMatrixEvaluate(SEXP fnMemoryMatrixEvaluate, SEXP rho, double **Memory, double **population, short int MinMax, long pop_size, long UniqueCount, long nvars, long lexical, long lexical_end); void userGradientfn(SEXP fnGR, SEXP rho, double *parms, double *grad, long nvars); } long Gnvars[MAXINSTANCES]; struct GND_IOstructure *ExternStructure; int JaIntegerCMP(double **a, double **b) { extern long Gnvars[MAXINSTANCES]; extern struct GND_IOstructure *ExternStructure; long i = 0; long nvars; nvars=Gnvars[ExternStructure->InstanceNumber]; for (i=1; i<=nvars; i++) { if ( (int) a[0][i] != (int) b[0][i]) break; } if ( (int) a[0][i] > (int) b[0][i]) i = 1; else if ( (int) a[0][i] < (int) b[0][i]) i = -1; return i; } /* end of JaIntegerCMP */ int JaDoubleCMP(double **a, double **b) { extern long Gnvars[MAXINSTANCES]; extern struct GND_IOstructure *ExternStructure; long i = 0; long nvars; nvars=Gnvars[ExternStructure->InstanceNumber]; for (i=1; i<=nvars; i++) { if ( a[0][i] != b[0][i]) break; } if ( a[0][i] > b[0][i]) i = 1; else if ( a[0][i] < b[0][i]) i = -1; return i; } /* end of JaCMP */ /* Cummulative probability on crossover */ /* Random probability on mutation */ /* NO multiple hits per agent possible */ /********************************************************************************/ /* */ /* FUNCTION NAME : optimization() */ /* */ /* SYNOPSIS : double optimization(X,x1,x2,fin_mat,rc,tot_eq) */ /* */ /* DESCRIPTION : This procedure initializes the population */ /* with the values X passed from main, and */ /* evaluates them. After assigning weight */ /* for each member of the populaiton, a group */ /* of them are chosen to reproduce and a group */ /* is chosen to die. Genetic operators are */ /* applied and a new generation is produced */ /* to replace the members that died. This */ /* cycle continues for the number of times, */ /* user specifies in the input file */ /* */ /* FUNCTIONS CALLED : assign_probab(), */ /* evaluate(), */ /* find_cum_probab(), */ /* find_live_die(), */ /* find_parent(), */ /* ivector(), */ /* matrix(), */ /* oper1(), */ /* oper2(), */ /* oper3(), */ /* oper4(), */ /* oper5(), */ /* oper6(), */ /* print_population(), */ /* sort(), */ /* Gvector() was vector(). */ /* */ /* CALLING FUNCITONS : main() */ /* */ /* */ /********************************************************************************/ void optimization(struct GND_IOstructure *Structure, VECTOR X, MATRIX domains) { extern struct GND_IOstructure *ExternStructure; MATRIX new_genera, /*Temporary storage for the new generation*/ population, /*Population of x2 variables*/ temp; VECTOR probab, /*Probability of agents to die or live*/ cum_probab, /*Cumilative probability of agents*/ t_vec; IVECTOR live; /* for oper4 */ IVECTOR parents; long count_gener= 1; /*Counter to keep track of the number of generations*/ unsigned long peak_cnt; int /*Total number of agents chosen to reproduce*/ j1, j2, j3, j4, j5, j6, j7, j8, oper, ocnt, B, /*Parameter for the 3rd operator - nonuniform mutation*/ STEP, /*Parameter for the 5th operator - simple arithmetical crossover*/ first_live=0, /*Index of the two parents for crossover parents*/ second_live=0, first_die, /*Index of the two parents for crossover death*/ second_die, die_now; /*index of agent to replace in current operation*/ long i,j, s, k; /* for oper 4 */ int p2use; double Q; /*Probability of the best agent*/ FLAG same; double **Jnew; double bfgsfit; double *grad, *evalX, *finalhessin, *bfgsoutX; int nochange_gen=0; double oldfitvalue=0; int IncreaseGenerations; short int GradientTrigger=0; short int BoundaryTrigger; long InstanceNumber; long nvars, MaxGenerations, WaitGenerations, count; long pop_size, P, P0, P1, P2, P3, P4, P5, P6, P7, P8; short int MinMax, GradientCheck, BoundaryEnforcement, UseBFGS, HardMaximumNumber=0; double SolutionTolerance, *Results, *Gradients; short PrintLevel, HardGenerationLimit; /* Old variables which may change when SetRunTimeParameters is run during a run! */ long pop_size_old; /* Summary Statistics (mean, variance etc) */ /* double popmean, popvar, popwrk, popstat; */ /* Population Print population*/ FILE *popout; long *tobs, nnull; double *mean, *var, *skew, *kur; /* Stuff for the Unique Stuff (how's that for an informative comment! */ /* A big Matrix which remembers all of our past evaluations. It's maximum memory is set in genoud.h */ extern long Gnvars[MAXINSTANCES]; double **Memory; long MemorySize=0, UniqueCount=0, OldUniqueCount=0; /* fine two unique parents count */ long SameCount, UniquePairs; ExternStructure=Structure; Results=Structure->oResults; Gradients=Structure->oGradients; /* Structure Done */ SetRunTimeParameters(Structure, 1, &pop_size, &nvars, &MaxGenerations, &WaitGenerations, &MinMax, &GradientCheck, &BoundaryEnforcement, &UseBFGS, &SolutionTolerance, &InstanceNumber, &P, &P0, &P1, &P2, &P3, &P4, &P5, &P6, &P7, &P8, &PrintLevel, &HardGenerationLimit); /*Space allocation for all the vectors and matrices involved*/ long lexical_end = (Structure->Lexical-1)+nvars+2; /* population[][0] = fitness value (first) population[][1:nvars] = parameter values population[][nvars+1] = flag for fitting population[][(nvars+2):((Structure->Lexical-1)+nvars+2)] = other fitness for Lexical fitting */ population = JaMatrixAllocate(pop_size+2, lexical_end); new_genera = JaMatrixAllocate(pop_size+2, lexical_end); /* reset population to get rid of odd things being passed to R */ for(i=1; i<=pop_size; i++) { for(j=0; jLexical > 1 || Structure->Transform == 1) { LexicalReturn = (double *) malloc(Structure->Lexical*sizeof(double)); oldfitvalueVEC = (double *) malloc(Structure->Lexical*sizeof(double)); } temp = matrix(0,nvars+1,0,nvars); probab = Gvector(1,pop_size); t_vec = Gvector(1,nvars); cum_probab = Gvector(1,pop_size); live = ivector(1,pop_size); /*for oper4 Find max(2,nvars) parents for crossover operator 4*/ p2use = nvars > 2 ? nvars : 2; parents = ivector(1,p2use); Gnvars[Structure->InstanceNumber]=nvars; if (Structure->MemoryUsage==1) { if (HardGenerationLimit==0) MemorySize=3*(MaxGenerations+1)*pop_size+1+pop_size; else MemorySize=(MaxGenerations+1)*pop_size+1+pop_size; Memory = JaMatrixAllocate(MemorySize, lexical_end); } grad = (double *) malloc((nvars)*sizeof(double)); evalX = (double *) malloc((nvars)*sizeof(double)); finalhessin = (double *) malloc(((nvars*nvars)+(nvars))*sizeof(double)); bfgsoutX = (double *) malloc((nvars+1)*sizeof(double)); /* populationstats variables */ mean = (double *) malloc((nvars+1)*sizeof(double)); var = (double *) malloc((nvars+1)*sizeof(double)); skew = (double *) malloc((nvars+1)*sizeof(double)); kur = (double *) malloc((nvars+1)*sizeof(double)); tobs = (long *) malloc((nvars+1)*sizeof(long)); Q=0.5; B=6; STEP=10; if(PrintLevel>0) { switch(MinMax) { case 0: Rprintf("Minimization Problem.\n"); break; case 1: Rprintf("Maximization Problem.\n"); break; } } /* if (PrintLevel>2) { Rprintf("Parameter B (hardcoded): %d\n", B); Rprintf("Parameter Q (hardcoded): %f\n", Q); } */ peak_cnt = 0; pop_size_old=0; if (Structure->ShareType == 1 || Structure->ShareType == 3) { if(PrintLevel>0) Rprintf( "Using old population file to initialize new population.\n"); if((popout = fopen(Structure->ProjectPath, "r")) == NULL) { Rprintf(" Generating new population\n"); warning("Unable to open the old project file: %s", Structure->ProjectPath); } else { pop_size_old=ReadPopulation(population, pop_size, nvars, popout, PrintLevel); fclose(popout); if (pop_size_old<2) { warning("The old population file appears to be from a different genoud specification."); pop_size_old=0; } } if (PrintLevel>1) { if((popout = fopen(Structure->ProjectPath, "a")) == NULL) { warning("Unable to open the project file: %s", Structure->ProjectPath); /* free populationstats stuff */ free(mean); free(var); free(skew); free(kur); free(tobs); free(bfgsoutX); free(finalhessin); free(evalX); free(grad); /* free numeric.c allocations */ if (Structure->MemoryUsage==1) JaMatrixFree(Memory, MemorySize); JaMatrixFree(population, pop_size+2); JaMatrixFree(new_genera, pop_size+2); free_matrix(temp, 0, nvars+1, 0); free_vector(probab, 1); free_vector(t_vec, 1); free_vector(cum_probab, 1); free_ivector(live, 1); free_ivector(parents, 1); if(Structure->Lexical > 1 || Structure->Transform == 1) { free(LexicalReturn); free(oldfitvalueVEC); } error("Fatal Error. See output for diagnostic information."); } fclose(popout); } } /* end of ShareType 0 */ else { if (PrintLevel>1) { if((popout = fopen(Structure->ProjectPath, "w")) == NULL) { Rprintf("Unable to open the project file: %s", Structure->ProjectPath); /* free populationstats stuff */ free(mean); free(var); free(skew); free(kur); free(tobs); free(bfgsoutX); free(finalhessin); free(evalX); free(grad); /* free numeric.c allocations */ if (Structure->MemoryUsage==1) JaMatrixFree(Memory, MemorySize); JaMatrixFree(population, pop_size+2); JaMatrixFree(new_genera, pop_size+2); free_matrix(temp, 0, nvars+1, 0); free_vector(probab, 1); free_vector(t_vec, 1); free_vector(cum_probab, 1); free_ivector(live, 1); free_ivector(parents, 1); if(Structure->Lexical > 1 || Structure->Transform == 1) { free(LexicalReturn); free(oldfitvalueVEC); } error("Fatal Error. See output for diagnostic information."); } fclose(popout); } } /* The new initial value matrix: setting a new initial value for every individual */ if (ExternStructure->nStartingValues > 0) { /* Adjust old starting values (from ReadPopulation) so we have enough room for our starting.values */ pop_size_old = pop_size_old-ExternStructure->nStartingValues-1; if (pop_size_old < 0) pop_size_old = 0; // seed the starting values until we run out of population or starting values! j = pop_size_old; for(s=0; snStartingValues; s++) { j++; for(i=1; i<=nvars; i++) { population[j][i] = ExternStructure->StartingValues[s][i-1]; population[j][nvars+1] = -1.0; } } // end of for loop pop_size_old = j; // randomly add on people if we still have population left over! for(j=pop_size_old+1; j<=pop_size; j++) { for(i=1; i<=nvars; i++) { population[j][i] = frange_ran(domains[i][1], domains[i][3]); population[j][nvars+1] = -1.0; } } } // end of we have starting values! else { for(j=pop_size_old+1; j<=pop_size; j++) { for(i=1; i<=nvars; i++) { population[j][i] = frange_ran(domains[i][1], domains[i][3]); population[j][nvars+1] = -1.0; } } } // end of else if (Structure->MemoryUsage==1) { OldUniqueCount=UniqueCount; if (UniqueCount==0) UniqueCount = 1; UniqueCount = RmemoryMatrixEvaluate(Structure->fnMemoryMatrixEvaluate, Structure->rho, Memory, population, MinMax, pop_size, UniqueCount, nvars, Structure->Lexical, lexical_end); if ( (UniqueCount+pop_size) >= MemorySize ) { Structure->MemoryUsage=0; warning("Turned Off MemoryMatrix because memory usage was too great."); } /* end of if */ } // end of Memory based evaluation else { for (i=1; i<=pop_size; i++) { if (population[i][nvars+1]==-1.0 || population[i][nvars+1]==11.0) { for(j=1; j<=nvars; j++) X[j] = population[i][j]; if (Structure->whichFUN == 1) // neither Lexical, nor Transform { population[i][0] = evaluate(Structure->fn, Structure->rho, X, nvars, MinMax); } else if(Structure->whichFUN == 2) // Lexical but not Transform { EvaluateLexical(Structure->fn, Structure->rho, X, nvars, Structure->Lexical, MinMax, LexicalReturn); population[i][0] = LexicalReturn[0]; count = 0; for(j=(nvars+2);jfn, Structure->rho, X, nvars, Structure->Lexical, MinMax, LexicalReturn); population[i][0] = LexicalReturn[0]; count = 0; if(Structure->Lexical > 1) for(j=(nvars+2);j0) { Rprintf( "\nNOTE: Transformed individual below lower bound.\n"); Rprintf("NOTE: Generation: %d \t Parameter: %d \t Value: %e \t Bound: %e\n\n", count_gener, j, X[j], domains[j][1]); } warning("Transformed individual below lower bound. Generation: %d; Parameter: %d; Value: %e; Bound: %e", count_gener, j, X[j], domains[j][1]); } if(X[j] > domains[j][3]) { if(PrintLevel>0) { Rprintf( "\nNOTE: Transformed individual above upper bound.\n"); Rprintf("NOTE: Generation: %d \t Parameter: %d \t Value: %e \t Bound: %e\n\n", count_gener, j, X[j], domains[j][3]); } warning("Transformed individual above upper bound. Generation: %d; Parameter: %d; Value: %e; Bound: %e", count_gener, j, X[j], domains[j][3]); } population[i][j] = X[j]; // put the transformation in anyway }//end for }//end Transform } } //end of i loop } // end of default evaluation if(Structure->MemoryUsage!=1) { /*Sort the initial individuals based on their evaluation function*/ if (Structure->Lexical < 2) { sort(MinMax,population,pop_size,0); } else { /* in eval.cpp because it is like the EvaluateLexical() function */ RlexicalSort(Structure->fnLexicalSort, Structure->rho, population, MinMax, pop_size, nvars, lexical_end, 1); } } peak_cnt = count_gener; /* since we are on generation 0 */ oldfitvalue=population[1][0]; if(Structure->Lexical > 1) { oldfitvalueVEC[0]=population[1][0]; k = 1; for (i=(nvars+2);i0) { Rprintf("\nThe best initial individual is:\n"); print_vector(population[1],1,nvars,output); if (Structure->Lexical > 1) { Rprintf("\nbest (lexical) fitness:\n"); Rprintf("%e ", population[1][0]); for(j=(nvars+2);jLexical > 1) { Rprintf("The worst (lexical) fitness is:\n"); Rprintf("%e ", population[pop_size][0]); for(j=(nvars+2);jLexical > 1) { Rprintf("\n\nGeneration#\t Solution Values (lexical)\n"); Rprintf("\n%7d \t%e ", 0, population[1][0]); for(j=(nvars+2);j1) { Rprintf("GENERATION: 0 (initializing the population)\n"); populationstats(population, pop_size, nvars, mean, var, skew, kur, tobs); if(Structure->Lexical > 1) { Rprintf( "Lexical Fit..... %e ", population[1][0]); for(j=(nvars+2);j 0) Rprintf( "#null........... %d\n", nnull); if(Structure->MemoryUsage==1) Rprintf( "#unique......... %d, #Total UniqueCount: %d\n", UniqueCount-OldUniqueCount, UniqueCount); /* Rprintf( "tobs............ %d\n", tobs[i]); */ for (i=1; i<=nvars; i++) { Rprintf( "var %d:\n", i); Rprintf( "best............ %e\n", population[1][i]); Rprintf( "mean............ %e\n", mean[i]); Rprintf( "variance........ %e\n", var[i]); /* Rprintf( "skewness........ %e\n", skew[i]); Rprintf( "kurtosis........ %e\n", kur[i]); */ nnull = pop_size-tobs[i]; if(nnull > 0) Rprintf( "#null........... %d\n", nnull); /* Rprintf( "tobs............ %d\n", tobs[i]); */ } } /* end of printlevel if */ /* if(PrintLevel>0) fflush(output); */ /* Print the population file */ if ( PrintLevel == 1 ) { if((popout = fopen(Structure->ProjectPath, "w")) == NULL) { Rprintf("Unable to open the project file: %s", Structure->ProjectPath); /* free populationstats stuff */ free(mean); free(var); free(skew); free(kur); free(tobs); free(bfgsoutX); free(finalhessin); free(evalX); free(grad); /* free numeric.c allocations */ if (Structure->MemoryUsage==1) JaMatrixFree(Memory, MemorySize); JaMatrixFree(population, pop_size+2); JaMatrixFree(new_genera, pop_size+2); free_matrix(temp, 0, nvars+1, 0); free_vector(probab, 1); free_vector(t_vec, 1); free_vector(cum_probab, 1); free_ivector(live, 1); free_ivector(parents, 1); if(Structure->Lexical > 1 || Structure->Transform == 1) { free(LexicalReturn); free(oldfitvalueVEC); } error("Fatal Error. See output for diagnostic information."); } print_population((int) pop_size, (int) nvars, 0, (int) Structure->Lexical, population, popout); fclose(popout); } /* end of PrintLevel if */ if ( PrintLevel>1 ) { if((popout = fopen(Structure->ProjectPath, "a")) == NULL) { Rprintf("Unable to open the project file: %s", Structure->ProjectPath); /* free populationstats stuff */ free(mean); free(var); free(skew); free(kur); free(tobs); free(bfgsoutX); free(finalhessin); free(evalX); free(grad); /* free numeric.c allocations */ if (Structure->MemoryUsage==1) JaMatrixFree(Memory, MemorySize); JaMatrixFree(population, pop_size+2); JaMatrixFree(new_genera, pop_size+2); free_matrix(temp, 0, nvars+1, 0); free_vector(probab, 1); free_vector(t_vec, 1); free_vector(cum_probab, 1); free_ivector(live, 1); free_ivector(parents, 1); if(Structure->Lexical > 1 || Structure->Transform == 1) { free(LexicalReturn); free(oldfitvalueVEC); } error("Fatal Error. See output for diagnostic information."); } print_population((int) pop_size, (int) nvars, 0, (int) Structure->Lexical, population, popout); fflush(popout); fclose(popout); } /* Interrupt setup. Let's print a nice message to recover the best solution so far if at least generation 0 has been run */ if (PrintLevel > 0 & (strcmp(Structure->ProjectPath, "/dev/null")!=0)) setVar(install("interrupted"), ScalarLogical(1), Structure->rho); /*Assigning probability of survival for each of the agent, with the*/ /*probability provided by the user for the best agent*/ assign_probab(probab,pop_size,Q); /*Finding the cumulative probability of the agents*/ find_cum_probab(cum_probab,probab,pop_size); /*Reproducing and evaluating for the total number of generations times*/ do { /*Initializing the live vector*/ for(j=1; j<=pop_size; j++) { live[j] = 0; for(i=0; i0; ocnt--) oper1(t_vec,domains,nvars); for(i=1; i<=nvars; i++) new_genera[die_now][i] = t_vec[i]; die_now--; j1++; } break; case 2: /* JS Description: Boundary Mutation */ /*Applying the second operator, boundary mutation*/ if (j2 < P2) { /*Find one parent for mutation operator 2*/ first_live = find_parent(live,pop_size); live[first_live]--; /* check that agent to replace is in range */ if (die_now < 2) { error( "No agents to be replaced\n"); } new_genera[die_now][nvars+1] = 2.0; for(i=1; i<=nvars; i++) t_vec[i] = population[first_live][i]; oper2(t_vec,domains,nvars); for(i=1; i<=nvars; i++) new_genera[die_now][i] = t_vec[i]; die_now--; j2++; } break; case 3: /* JS Description: Non-uniform Mutation */ /*Applying the third operator, non-uniform mutation*/ if (j3 < P3) { /*Find one parent for mutation operator 3*/ first_live = find_parent(live,pop_size); live[first_live]--; /* check that agent to replace is in range */ if (die_now < 2) { error( "No agents to be replaced\n"); } new_genera[die_now][nvars+1] = 3.0; for(i=1; i<=nvars; i++) t_vec[i] = population[first_live][i]; for (ocnt = irange_ran(1,nvars); ocnt>0; ocnt--) oper3(t_vec,domains,nvars,MaxGenerations,count_gener,B); for(i=1; i<=nvars; i++) new_genera[die_now][i] = t_vec[i]; die_now--; j3++; } break; case 4: /*Applying the fourth operator, GENOUD Polytope Crossover */ if (j4 < (int) P4) { /*Find max(2,nvars) parents for crossover operator 4*/ for (i=1; i= (UniquePairs) ) break; for(i=1; i<=nvars; i++) { if (population[first_live][i] != population[second_live][i]) { same = FALSE; break; } } } /* end of while same==TRUE loop */ /* check that agents to replace are in range */ if (die_now < 3) { error("Not enough agents to be replaced\n"); } live[first_live]--; live[second_live]--; first_die = die_now-- ; second_die = die_now-- ; new_genera[first_die][nvars+1] = 5.0; new_genera[second_die][nvars+1] = 5.0; if (!same) { for(i=1; i<=nvars; i++) { temp[1][i] = population[first_live][i]; temp[2][i] = population[second_live][i]; } oper5(temp[1],temp[2],STEP,domains,nvars); for(i=1; i<=nvars; i++) { new_genera[first_die][i] = temp[1][i]; new_genera[second_die][i] = temp[2][i]; } } else { /* copy agent chosen twice into two new indivs */ for(i=1; i<=nvars; i++) { new_genera[first_die][i] = population[first_live][i]; new_genera[second_die][i] = population[second_live][i]; } } j5++; } break; case 6: /* JS Description: Whole Non-uniform Mutation */ /*Applying the sixth operator, whole non-uniform mutation*/ if (j6 < P6) { /*Find one parent for mutation operator 6*/ first_live = find_parent(live,pop_size); live[first_live]--; /* check that agent to replace is in range */ if (die_now < 2) { error( "No agents to be replaced\n"); } new_genera[die_now][nvars+1] = 6.0; for(i=1; i<=nvars; i++) t_vec[i] = population[first_live][i]; oper6(t_vec,domains,nvars,MaxGenerations,count_gener,B); for(i=1; i<=nvars; i++) new_genera[die_now][i] = t_vec[i]; die_now--; j6++; } break; case 7: /* JS Description: Heuristic Crossover */ /*Applying the seventh operator*/ if (j7 < (int) P7/2) { /*Find two distinct parents for operator 7*/ same = TRUE; SameCount=0; while (same==TRUE) { SameCount++; first_live = find_parent(live,pop_size); second_live = find_parent(live,pop_size); if (SameCount >= (UniquePairs) ) break; for(i=1; i<=nvars; i++) { if (population[first_live][i] != population[second_live][i]) { same = FALSE; break; } } } /* end of while same==TRUE loop */ /* check that agents to replace are in range */ if (die_now < 3) { error("Not enough agents to be replaced\n"); } live[first_live]--; live[second_live]--; first_die = die_now-- ; second_die = die_now-- ; new_genera[first_die][nvars+1] = 7.0; new_genera[second_die][nvars+1] = 7.0; if (!same) { if (first_live < second_live) /* first agent is better agent */ for(i=1; i<=nvars; i++) { temp[2][i] = population[first_live][i]; temp[1][i] = population[second_live][i]; } else /* second agent is better agent */ for(i=1; i<=nvars; i++) { temp[2][i] = population[second_live][i]; temp[1][i] = population[first_live][i]; } oper7(temp[1],temp[2],domains,nvars); for(i=1; i<=nvars; i++) new_genera[first_die][i] = temp[1][i]; if (first_live < second_live) /* first agent is better agent */ for(i=1; i<=nvars; i++) { temp[2][i] = population[first_live][i]; temp[1][i] = population[second_live][i]; } else /* second agent is better agent */ for(i=1; i<=nvars; i++) { temp[2][i] = population[second_live][i]; temp[1][i] = population[first_live][i]; } oper7(temp[1],temp[2],domains,nvars); for(i=1; i<=nvars; i++) new_genera[second_die][i] = temp[1][i]; } else { /* copy agent chosen twice into two new indivs */ for(i=1; i<=nvars; i++) { new_genera[first_die][i] = population[first_live][i]; new_genera[second_die][i] = population[second_live][i]; } } j7++; } case 8: /* JS Description: Local-Minimum Crossover */ /*Applying the eighth operator, homotopy (BFGS) */ if (j8 < P8 & (Structure->BFGSburnin >= 0) & (count_gener > Structure->BFGSburnin)) { /*Find one parent for BFGS operator 1*/ first_live = find_parent(live,pop_size); live[first_live]--; /* check that agent to replace is in range */ if (die_now < 2) { error( "No agents to be replaced\n"); } new_genera[die_now][nvars+1] = 8.0; for(i=1; i<=nvars; i++) t_vec[i] = population[first_live][i]; oper8(Structure->fn_optim, Structure->rho, t_vec, domains, SolutionTolerance, nvars, BoundaryEnforcement, PrintLevel, Structure->P9mix); for(i=1; i<=nvars; i++) new_genera[die_now][i] = t_vec[i]; die_now--; j8++; } break; } } /*Replace the population with the new generation */ Jnew = new_genera; new_genera = population; population = Jnew; if (Structure->MemoryUsage==1) { OldUniqueCount=UniqueCount; UniqueCount = RmemoryMatrixEvaluate(Structure->fnMemoryMatrixEvaluate, Structure->rho, Memory, population, MinMax, pop_size, UniqueCount, nvars, Structure->Lexical, lexical_end); if ( (UniqueCount+pop_size) >= MemorySize ) { Structure->MemoryUsage=0; warning("Turned Off MemoryMatrix because memory usage was too great."); } /* end of if */ } // end of MemoryUsage==1 else { for (i=1; i<=pop_size; i++) { if (population[i][nvars+1]!=0) { for(j=1; j<=nvars; j++) X[j] = population[i][j]; if (Structure->whichFUN == 1) // neither Lexical, nor Transform { population[i][0] = evaluate(Structure->fn, Structure->rho, X, nvars, MinMax); } else if(Structure->whichFUN == 2) // Lexical but not Transform { EvaluateLexical(Structure->fn, Structure->rho, X, nvars, Structure->Lexical, MinMax, LexicalReturn); population[i][0] = LexicalReturn[0]; count = 0; for(j=(nvars+2);jfn, Structure->rho, X, nvars, Structure->Lexical, MinMax, LexicalReturn); population[i][0] = LexicalReturn[0]; count = 0; if(Structure->Lexical > 1) for(j=(nvars+2);jMemoryUsage!=1) { /*Sort the new population based on their evaluation function*/ if (Structure->Lexical < 2) { sort(MinMax,population,pop_size,0); } else { /* in eval.cpp because it is like the EvaluateLexical() function */ RlexicalSort(Structure->fnLexicalSort, Structure->rho, population, MinMax, pop_size, nvars, lexical_end, 1); } } /* apply the bfgs to the best individual */ if (UseBFGS != 0 & (Structure->BFGSburnin >= 0) & (count_gener > Structure->BFGSburnin)) { for (i=1; i<=nvars; i++) { bfgsoutX[i-1]=population[1][i]; } bfgsfit = genoud_optim(Structure->fn_optim, Structure->rho, bfgsoutX, nvars); if (Structure->whichFUN == 1) // neither Lexical, nor Transform { switch(MinMax) { case 0: if (population[1][0] > bfgsfit) /* minimize */ { /* is the BFGS individual in the bounds? */ BoundaryTrigger=0; /* outside of bounds ? */ for (i=0; i1) { Rprintf( "\nNOTE: BFGS hit on best individual produced Out of Boundary individual.\n"); Rprintf("NOTE: Generation: %d \t Parameter: %d \t Value: %e\n\n", count_gener, i+1, bfgsoutX[i]); Rprintf("NOTE: Fit: %e\n\n", bfgsfit); } warning("BFGS hit on best individual produced Out of Boundary individual."); } if (bfgsoutX[i] > domains[j][3]) { BoundaryTrigger=1; if (PrintLevel>1) { Rprintf( "\nNOTE: BFGS hit on best individual produced Out of Boundary individual.\n"); Rprintf("NOTE: Generation: %d \t Parameter: %d \t Value: %e\n", count_gener, i+1, bfgsoutX[i]); Rprintf("NOTE: Fit: %e\n\n", bfgsfit); } warning("BFGS hit on best individual produced Out of Boundary individual."); } } /* end for loop */ /* if we use out of bounds individuals then proceed */ /* 0=anything goes, 1: regular; 2: no trespassing! */ if (BoundaryEnforcement==0) { for(i=1;i<=nvars;i++) { population[1][i]=bfgsoutX[i-1]; } population[1][0]=bfgsfit; } else if (BoundaryTrigger==0) { for(i=1;i<=nvars;i++) { population[1][i]=bfgsoutX[i-1]; } population[1][0]=bfgsfit; } } /* end if (population[1][0] > bfgs) */ case 1: if (population[1][0] < bfgsfit) /* maximize */ { /* is the BFGS individual in the bounds? */ BoundaryTrigger=0; /* outside of bounds ? */ for (i=0; i1) { Rprintf( "\nNOTE: BFGS hit on best individual produced Out of Boundary individual.\n"); Rprintf("NOTE: Generation: %d \t Parameter: %d \t Value: %e\n\n", count_gener, i+1, bfgsoutX[i]); } warning("BFGS hit on best individual produced Out of Boundary individual."); } if (bfgsoutX[i] > domains[j][3]) { BoundaryTrigger=1; if (PrintLevel>1) { Rprintf( "\nNOTE: BFGS hit on best individual produced Out of Boundary individual.\n"); Rprintf("NOTE: Generation: %d \t Parameter: %d \t Value: %e\n\n", count_gener, i+1, bfgsoutX[i]); } warning("BFGS hit on best individual produced Out of Boundary individual."); } } /* end for loop */ /* if we we use out of bounds individuals then proceed */ /* 0=anything goes, 1: regular; 2: no trespassing! */ if (BoundaryEnforcement==0) { for(i=1;i<=nvars;i++) { population[1][i]=bfgsoutX[i-1]; } population[1][0]=bfgsfit; } else if (BoundaryTrigger==0) { for(i=1;i<=nvars;i++) { population[1][i]=bfgsoutX[i-1]; } population[1][0]=bfgsfit; } } /* end if (population[1][0] < bfgsfit) */ } /* end switch */ }/*end of NOT lexical bfgs hit */ else if(Structure->whichFUN == 2) // Lexical but not Transform { /* is the BFGS individual in the bounds? */ BoundaryTrigger=0; /* outside of bounds ? */ for (i=0; i1) { Rprintf( "\nNOTE: BFGS hit on best individual produced Out of Boundary individual.\n"); Rprintf("NOTE: Generation: %d \t Parameter: %d \t Value: %e\n\n", count_gener, i+1, bfgsoutX[i]); Rprintf("NOTE: Fit: %e\n\n", bfgsfit); } warning("BFGS hit on best individual produced Out of Boundary individual."); } if (bfgsoutX[i] > domains[j][3]) { BoundaryTrigger=1; if (PrintLevel>1) { Rprintf( "\nNOTE: BFGS hit on best individual produced Out of Boundary individual.\n"); Rprintf("NOTE: Generation: %d \t Parameter: %d \t Value: %e\n", count_gener, i+1, bfgsoutX[i]); Rprintf("NOTE: Fit: %e\n\n", bfgsfit); } warning("BFGS hit on best individual produced Out of Boundary individual."); } } /* end for loop */ /* if we use out of bounds individuals then proceed */ /* 0=anything goes, 1: regular; 2: no trespassing! */ /* Add new individual to the END because we are doing lexical stuff */ if (BoundaryEnforcement==0) { for(i=1;i<=nvars;i++) { population[(pop_size-1)][i]=bfgsoutX[i-1]; X[i] = bfgsoutX[i-1]; } EvaluateLexical(Structure->fn, Structure->rho, X, nvars, Structure->Lexical, MinMax, LexicalReturn); population[(pop_size-1)][0] = LexicalReturn[0]; count = 0; for(i=(nvars+2);ifnLexicalSort, Structure->rho, population, MinMax, pop_size, nvars, lexical_end, 1); } else if (BoundaryTrigger==0) { for(i=1;i<=nvars;i++) { population[(pop_size-1)][i]=bfgsoutX[i-1]; X[i] = bfgsoutX[i-1]; } EvaluateLexical(Structure->fn, Structure->rho, X, nvars, Structure->Lexical, MinMax, LexicalReturn); population[(pop_size-1)][0] = LexicalReturn[0]; count = 0; for(i=(nvars+2);ifnLexicalSort, Structure->rho, population, MinMax, pop_size, nvars, lexical_end, 1); } } /*end of LEXICAL bfgs hit */ else // Transform { for(j=1; j<=nvars; j++) { X[j] = bfgsoutX[(j-1)]; } // Call EvaluateTransform now to transform X EvaluateTransform(Structure->fn, Structure->rho, X, nvars, Structure->Lexical, MinMax, LexicalReturn); /* is the BFGS individual in the bounds? */ BoundaryTrigger=0; /* outside of bounds ? */ for (j=1; i<=nvars; i++) { if (X[j] < domains[j][1]) { BoundaryTrigger=1; if (PrintLevel>1) { Rprintf( "\nNOTE: BFGS hit on best individual produced Out of Boundary individual.\n"); Rprintf("NOTE: Generation: %d \t Parameter: %d \t Value: %e\n\n", count_gener, j, X[j]); Rprintf("NOTE: Fit: %e\n\n", bfgsfit); } warning("BFGS hit on best individual produced Out of Boundary individual."); } if (X[j] > domains[j][3]) { BoundaryTrigger=1; if (PrintLevel>1) { Rprintf( "\nNOTE: BFGS hit on best individual produced Out of Boundary individual.\n"); Rprintf("NOTE: Generation: %d \t Parameter: %d \t Value: %e\n", count_gener, j, X[j]); Rprintf("NOTE: Fit: %e\n\n", bfgsfit); } warning("BFGS hit on best individual produced Out of Boundary individual."); } } /* end for loop */ /* if we use out of bounds individuals then proceed */ /* 0=anything goes, 1: regular; 2: no trespassing! */ /* Figure out why BoundaryEnforcement==0 and BoundaryTrigerr==0 are separate above */ if (BoundaryEnforcement == 0 || BoundaryTrigger == 0) { if(Structure->Lexical < 2) // Transform but not Lexical { for(i=1; i<=nvars; i++) { population[1][i] = X[i]; } population[1][0] = LexicalReturn[0]; // from ~45 lines above } else /* Add new individual to the END because we are doing Transform and Lexical */ { for(i=1;i<=nvars;i++) { population[(pop_size-1)][i] = X[i]; } population[(pop_size-1)][0] = LexicalReturn[0]; // from ~55 lines above count = 0; for(i=(nvars+2);ifnLexicalSort, Structure->rho, population, MinMax, pop_size, nvars, lexical_end, 1); } } /* end of boundary enforcment */ } /*end of TRANSFORM bfgs hit */ } /* end of UseBFGS */ /* check to see if fit is improving */ if(Structure->Lexical < 2) { switch(MinMax) { case 0: if ( (oldfitvalue - SolutionTolerance) > population[1][0]) { nochange_gen=0; oldfitvalue=population[1][0]; peak_cnt = count_gener; } else nochange_gen++; break; case 1: if ( (oldfitvalue + SolutionTolerance) < population[1][0]) { nochange_gen=0; oldfitvalue=population[1][0]; peak_cnt = count_gener; } else nochange_gen++; break; } } /* if(Structure->Lexical < 2) */ else { switch(MinMax) { case 0: LexicalFitsImproving = 0; if ( (oldfitvalue - SolutionTolerance) > population[1][0]) { LexicalFitsImproving = 1; } else { k=1; for (i=(nvars+2);i population[1][i] ) { LexicalFitsImproving = 1; break; } /* (oldfitvalueVEC[k] - SolutionTolerance) > population[1][i] ) */ k++; } /* for (i=(nvars+2);i population[1][0]) */ if (LexicalFitsImproving) { nochange_gen = 0; peak_cnt = count_gener; oldfitvalue=population[1][0]; oldfitvalueVEC[0]=population[1][0]; k = 1; for (i=(nvars+2);i population[1][i] ) */ k++; } /* for (i=(nvars+2);i population[1][0]) */ if (LexicalFitsImproving) { nochange_gen = 0; peak_cnt = count_gener; oldfitvalue=population[1][0]; oldfitvalueVEC[0]=population[1][0]; k = 1; for (i=(nvars+2);iLexical > 2) */ if(PrintLevel==1) { if( nochange_gen==0 ) { if(Structure->Lexical > 1) { Rprintf("\n%7d \t%e ", count_gener, population[1][0]); for(j=(nvars+2);j1) { Rprintf("\nGENERATION: %d\n", count_gener); populationstats(population, pop_size, nvars, mean, var, skew, kur, tobs); if(Structure->Lexical > 1) { Rprintf( "Lexical Fit..... %e ", population[1][0]); for(j=(nvars+2);j 0) Rprintf( "#null........... %d\n", nnull); if(Structure->MemoryUsage==1) Rprintf( "#unique......... %d, #Total UniqueCount: %d\n", UniqueCount-OldUniqueCount, UniqueCount); /* Rprintf( "tobs............ %d\n", tobs[i]); */ for (i=1; i<=nvars; i++) { Rprintf( "var %d:\n", i); Rprintf( "best............ %e\n", population[1][i]); Rprintf( "mean............ %e\n", mean[i]); Rprintf( "variance........ %e\n", var[i]); /* Rprintf( "skewness........ %e\n", skew[i]); Rprintf( "kurtosis........ %e\n", kur[i]); */ nnull = pop_size-tobs[i]; if(nnull > 0) Rprintf( "#null........... %d\n", nnull); /* Rprintf( "tobs............ %d\n", tobs[i]); */ } } /* end of printlevel if */ /* if (PrintLevel>0) fflush(output); */ /* Print the population file */ if ( PrintLevel == 1 ) { if((popout = fopen(Structure->ProjectPath, "w")) == NULL) { Rprintf("Unable to open the project file: %s", Structure->ProjectPath); /* free populationstats stuff */ free(mean); free(var); free(skew); free(kur); free(tobs); free(bfgsoutX); free(finalhessin); free(evalX); free(grad); /* free numeric.c allocations */ if (Structure->MemoryUsage==1) JaMatrixFree(Memory, MemorySize); JaMatrixFree(population, pop_size+2); JaMatrixFree(new_genera, pop_size+2); free_matrix(temp, 0, nvars+1, 0); free_vector(probab, 1); free_vector(t_vec, 1); free_vector(cum_probab, 1); free_ivector(live, 1); free_ivector(parents, 1); if(Structure->Lexical > 1 || Structure->Transform == 1) { free(LexicalReturn); free(oldfitvalueVEC); } error("Fatal Error. See output for diagnostic information."); } print_population((int) pop_size, (int) nvars, (int) count_gener, (int) Structure->Lexical, population, popout); fclose(popout); } /* end of PrintLevel if */ if ( PrintLevel>1) { if((popout = fopen(Structure->ProjectPath, "a")) == NULL) { Rprintf("Unable to open the project file: %s", Structure->ProjectPath); /* free populationstats stuff */ free(mean); free(var); free(skew); free(kur); free(tobs); free(bfgsoutX); free(finalhessin); free(evalX); free(grad); /* free numeric.c allocations */ if (Structure->MemoryUsage==1) JaMatrixFree(Memory, MemorySize); JaMatrixFree(population, pop_size+2); JaMatrixFree(new_genera, pop_size+2); free_matrix(temp, 0, nvars+1, 0); free_vector(probab, 1); free_vector(t_vec, 1); free_vector(cum_probab, 1); free_ivector(live, 1); free_ivector(parents, 1); if(Structure->Lexical > 1 || Structure->Transform == 1) { free(LexicalReturn); free(oldfitvalueVEC); } error("Fatal Error. See output for diagnostic information."); } print_population((int) pop_size, (int) nvars, (int) count_gener, (int) Structure->Lexical, population, popout); fflush(popout); fclose(popout); } if (nochange_gen > (WaitGenerations)) { /* increase the number of WaitGenerations if the gradients are NOT zero! */ if (GradientCheck==0) { if(PrintLevel>0) { Rprintf("\n'wait.generations' limit reached.\n"); Rprintf("No significant improvement in %d generations.\n", nochange_gen-1); /* fflush(output); */ } MaxGenerations = 0; nochange_gen=0; } else { for (i=1; i<=nvars; i++) { bfgsoutX[i-1]=population[1][i]; } if(Structure->UserGradient==0) { gradient(Structure->fn, Structure->rho, bfgsoutX, grad, nvars, MinMax, BoundaryEnforcement, domains); } else { userGradientfn(Structure->fnGR, Structure->rho, bfgsoutX, grad, nvars); } GradientTrigger = 0; for (i=0; i SolutionTolerance) { GradientTrigger = 1; break; } } /* end for loop */ if (GradientTrigger==1) { IncreaseGenerations = WaitGenerations; WaitGenerations += IncreaseGenerations; if(Structure->BFGSburnin < 0) Structure->BFGSburnin = 0; if(PrintLevel>0) { Rprintf( "\nDoubling 'wait.generations' limit to %d (from %d) ", WaitGenerations, IncreaseGenerations); Rprintf("because at least one gradient is too large.\n"); Rprintf("G[%d]: %e\t Solution Tolerance: %e\n\n", i+1, grad[i], SolutionTolerance); } } else { if(PrintLevel>0) { Rprintf("\n'wait.generations' limit reached.\n"); Rprintf("No significant improvement in %d generations.\n", nochange_gen-1); /* fflush(output); */ } MaxGenerations = 0; nochange_gen=0; } }/* end else loop */ } /* end of if (nochange_gen > (WaitGenerations)) { */ if ( (count_gener == MaxGenerations) && (GradientTrigger==1) ) { if (HardGenerationLimit==0) { IncreaseGenerations = MaxGenerations; MaxGenerations += IncreaseGenerations; if(PrintLevel>0) { Rprintf( "\nIncreasing 'max.generations' limit by %d generations to %d ", IncreaseGenerations, MaxGenerations); Rprintf("because at least one gradient is too large.\n\n"); } } // if (Structure->HardGenerationLimit==0) else { HardMaximumNumber = 1; warning("Stopped because hard maximum generation limit was hit.\nAt least one gradient is too large."); if(PrintLevel>0) { Rprintf("\nNOTE: HARD MAXIMUM GENERATION LIMIT HIT\n"); Rprintf(" At least one gradient is too large\n"); } } // else } // if ( (count_gener == MaxGenerations) && (GradientTrigger==1) ) /* increase the number of generations if fitness has been improving */ if ( (count_gener == MaxGenerations) && (nochange_gen < WaitGenerations) ) { if (HardGenerationLimit==0) { if (WaitGenerations > MaxGenerations) { IncreaseGenerations = WaitGenerations; MaxGenerations += (int) (IncreaseGenerations); if(PrintLevel>0) { Rprintf( "\nIncreasing 'max.generations' limit by %d generations to %d ", IncreaseGenerations, MaxGenerations); Rprintf("because the fitness is still impoving.\n\n"); } } else { IncreaseGenerations = MaxGenerations; MaxGenerations += (int) (IncreaseGenerations); if(PrintLevel>0) { Rprintf( "\nIncreasing 'max.generations' limit by %d generations to %d ", IncreaseGenerations, MaxGenerations); Rprintf("because the fitness is still improving.\n\n"); } } } // if (Structure->HardGenerationLimit==0) else { if (HardMaximumNumber==0) { warning("Stopped because hard maximum generation limit was hit."); if(PrintLevel>0) { Rprintf("\nNOTE: HARD MAXIMUM GENERATION LIMIT HIT\n"); } } /* end of if HardMax */ } } // if ( (count_gener == MaxGenerations) && (nochange_gen < WaitGenerations) ) /* if(PrintLevel>0) fflush(output); */ } /* end of do loop */ /*Increment iteration count and test whether all generations are done*/ while (++count_gener <= MaxGenerations); if(PrintLevel>0) { if(Structure->Lexical > 1) { Rprintf("\nSolution Lexical Fitness Value:\n"); Rprintf("%e ", population[1][0]); for(j=(nvars+2);joPeakGeneration=peak_cnt; Structure->oGenerations=count_gener-1; /* obtain gradients */ /* print best solution */ if (GradientCheck==0 && UseBFGS==0) { for(j = 1; j <= nvars; j++) { i = j-1; if(PrintLevel>0) Rprintf(" X[%2d] :\t%e\n",j,population[1][j]); grad[i] = -1.0; Results[i] = population[1][j]; Gradients[i] = grad[i]; } } /* end of if (GradientCheck==0 && UseBFGS==0) */ else { for (i=1; i<=nvars; i++) { bfgsoutX[i-1]=population[1][i]; } if(Structure->UserGradient==0) { gradient(Structure->fn, Structure->rho, bfgsoutX, grad, nvars, MinMax, BoundaryEnforcement, domains); } else { userGradientfn(Structure->fnGR, Structure->rho, bfgsoutX, grad, nvars); } for(j = 1; j <= nvars; j++) { i = j-1; if(PrintLevel>0) Rprintf(" X[%2d] :\t%e\tG[%2d] :\t%e\n",j,population[1][j],j,grad[i]); Results[i] = population[1][j]; Gradients[i] = grad[i]; } } /* end of else (GradientCheck==0 && UseBFGS==0) */ Structure->oFitValues[0]=population[1][0]; if (Structure->Lexical > 1) { k = 1; for (i=(nvars+2);ioFitValues[k]=population[1][i]; k++; } } /* free memory */ /* free populationstats stuff */ free(mean); free(var); free(skew); free(kur); free(tobs); free(bfgsoutX); free(finalhessin); free(evalX); free(grad); if (Structure->MemoryUsage==1) JaMatrixFree(Memory, MemorySize); JaMatrixFree(population, pop_size+2); JaMatrixFree(new_genera, pop_size+2); free_matrix(temp, 0, nvars+1, 0); free_vector(probab, 1); free_vector(t_vec, 1); free_vector(cum_probab, 1); free_ivector(live, 1); free_ivector(parents, 1); if(Structure->Lexical > 1 || Structure->Transform == 1) { free(LexicalReturn); free(oldfitvalueVEC); } } /* end optimiztion function */ /********************************************************************************/ /* */ /* FUNCTION NAME : sort() */ /* */ /* SYNOPSIS : void sort(MinMax, population,pop_size, */ /* variable) */ /* */ /* DESCRIPTION : This function sorts the population, in the */ /* ascending or the descending order of the */ /* evaluation function, depending on whether */ /* it is a maximization or a minimization */ /* function, respectively. */ /* */ /* As an alternative, the sortq function below */ /* can be used, That sorting function uses */ /* the quicksort algorithm. */ /* */ /* */ /* FUNCTIONS CALLED : swap() */ /* */ /* CALLING FUNCITONS : optimization() */ /* */ /********************************************************************************/ void sort(short int MinMax, MATRIX population, int pop_size, long nvar) /* short int MinMax; Tells whether it is a maximizaiton or a minimization function int pop_size; Population size MATRIX population; Array of population */ { int i,j; /*If MinMax is 0 sorts in the descending order, and*/ /*if it is 1 sorts in the ascending order*/ /*Sorted in ascending or descending order, based on*/ /*the evaluated values of each of the agents*/ switch(MinMax) { case 0 : for(i=1; i<=pop_size; i++) for(j=i+1; j<=pop_size; j++) if(population[i][nvar] > population[j][nvar]) swap(&population[i],&population[j]); break; case 1 : for(i=1; i<=pop_size; i++) for(j=i+1; j<=pop_size; j++) if(population[i][nvar] < population[j][nvar]) swap(&population[i],&population[j]); break; } } /********************************************************************************/ /* */ /* FUNCTION NAME : swap() */ /* */ /* SYNOPSIS : void swap(x,y) */ /* */ /* DESCRIPTION : This function interchanges the values of */ /* x and y. */ /* */ /* FUNCTIONS CALLED : None */ /* */ /* CALLING FUNCITONS : sort() */ /* */ /* */ /********************************************************************************/ void swap(double **x, double **y) /* double **x,**y; */ { double *temp; temp = *x; *x = *y; *y = temp; } /********************************************************************************/ /* */ /* FUNCTION NAME : find_parent() */ /* */ /* SYNOPSIS : int find_parent(live,pop_size) */ /* */ /* DESCRIPTION : This function returns the index of the */ /* agent in the population, which is to be */ /* chosen for reproduction. */ /* */ /* FUNCTIONS CALLED : irange_ran() */ /* */ /* CALLING FUNCITONS : optimization() */ /* */ /* */ /********************************************************************************/ int find_parent(IVECTOR live, int pop_size) /* int pop_size; Population size IVECTOR live; Vector containing the number of times each agent is going to reproduce */ { int i,temp,t1=0,tot=0; /*Finding the total number of parents to reproduce*/ for(i=1; i<=pop_size; i++) tot = tot + live[i]; if(tot==0) { error("No agents to select"); } /*Choosing one of them randomly*/ temp = irange_ran(1,tot); tot = 0; i = 1; do{ if(live[i]!=0) t1 = i; tot = tot + live[i++]; }while(tot cum_probab[i]) && (i< pop_size)); /*Chosing the parent with that probability to reproduce*/ if(count < P) { live[i]++; count++; } }while(count < P); } /********************************************************************************/ /* */ /* FUNCTION NAME : find_die() */ /* */ /* SYNOPSIS : void find_die(cum_probab,die,pop_size,P4+P5) */ /* */ /* DESCRIPTION : This function finds the agents from the */ /* population, who are going to die. */ /* */ /* FUNCTIONS CALLED : frange_ran() */ /* */ /* CALLING FUNCITONS : optimization() */ /* */ /* */ /* */ /********************************************************************************/ int find_die(VECTOR cum_probab, IVECTOR die, int pop_size) /* VECTOR cum_probab; Cumulative probability IVECTOR die; Agents that are going to die int pop_size; Population size */ { double random; int i; int done = FALSE; do { /*Choosing a random cumulative probability*/ random = frange_ran(0.0,1.0); i=0; /*Finding the agent with the chosen cumulative probability*/ do{ i++; } while((random > cum_probab[i]) && (i< pop_size)); /*Chosing the agent to die*/ if ((die[pop_size+1-i] == 0) && (i < pop_size)) done = TRUE; } while(!done); return(pop_size+1-i); } void SetRunTimeParameters(struct GND_IOstructure *Structure, short FirstTime, long *PopSize, long *nvars, long *MaxGenerations, long *WaitGenerations, short *MinMax, short *GradientCheck, short *BoundaryEnforcement, short *UseBFGS, double *SolutionTolerance, long *InstanceNumber, long *P, long *P0, long *P1, long *P2, long *P3, long *P4, long *P5, long *P6, long *P7, long *P8, short *PrintLevel, short *HardGenerationLimit) { double tP; int i; *PopSize=Structure->PopSize; *nvars=Structure->nvars; *MaxGenerations=Structure->MaxGenerations; *WaitGenerations=Structure->WaitGenerations; if (FirstTime==1) *HardGenerationLimit=Structure->HardGenerationLimit; *MinMax=Structure->MinMax; *GradientCheck=Structure->GradientCheck; *BoundaryEnforcement=Structure->BoundaryEnforcement; *UseBFGS=Structure->UseBFGS; *InstanceNumber=Structure->InstanceNumber; *SolutionTolerance=Structure->SolutionTolerance; *PrintLevel=Structure->PrintLevel; /* Check to make sure that all operators are positve numbers! */ if (Structure->P[0] < 0 ) { warning("Operator 1 (Cloning) was Assigned an Illegal Value: %d.", Structure->P[0]); Structure->P[0]=0.0; } if (Structure->P[1] < 0 ) { warning("Operator 1 (Uniform Mutation) was Assigned an Illegal Value: %d.", Structure->P[1]); Structure->P[1]=0.0; } if (Structure->P[2] < 0 ) { warning("Operator 3 (Boundary Mutation) was Assigned an Illegal Value: %d.", Structure->P[2]); Structure->P[2]=0; } if (Structure->P[3] < 0 ) { warning("Operator 4 (Non-Uniform Mutation) was Assigned an Illegal Value: %d.", Structure->P[3]); Structure->P[3]=0; } if (Structure->P[4] < 0 ) { warning("Operator 5 (Polytope Crossover) was Assigned an Illegal Value: %d.", Structure->P[4]); Structure->P[4]=0; } if (Structure->P[5] < 0 ) { warning("Operator 6 (Simple Crossover) was Assigned an Illegal Value: %d.", Structure->P[5]); Structure->P[5]=0; } if (Structure->P[6] < 0 ) { warning("Operator 7 (Whole Non-Uniform Mutation) was Assigned an Illegal Value: %d.", Structure->P[6]); Structure->P[6]=0; } if (Structure->P[7] < 0 ) { warning("Operator 8 (Heuristic Crossover) was Assigned an Illegal Value: %d.", Structure->P[7]); Structure->P[7]=0; } /* if DataType==1 (i.e., integer) we are not giong to use any gradient information etc. */ if (Structure->DataType==1) { *UseBFGS=0; *GradientCheck=0; if (Structure->P[8] > 0) { warning("Operator 9 (Local-Minimum Crossover) was Assigned an Illegal Value: %d\nThis is an illegal value because we are working with integer data.", Structure->P[8]); Structure->P[8]=0; } /* end of if */ } else { if (Structure->P[8] < 0 ) { warning("Operator 9 (Local-Minimum Crossover) was Assigned an Illegal Value: %d.", Structure->P[8]); Structure->P[8]=0; } } /* end of else */ /* Let's figure out the number of operators we need. Move stuff to absolute space */ tP = 0; for (i=0; i<9; i++) { tP = tP + Structure->P[i] ; } if (tP > 0) { *P0 = Iround( (Structure->P[0] / tP) * (double) (*PopSize-2) ); *P1 = Iround( (Structure->P[1] / tP) * (*PopSize-2) ); *P2 = Iround( (Structure->P[2] / tP) * (*PopSize-2) ); *P3 = Iround( (Structure->P[3] / tP) * (*PopSize-2) ); *P4 = Iround( (Structure->P[4] / tP) * (*PopSize-2) ); *P5 = Iround( (Structure->P[5] / tP) * (*PopSize-2) ); *P6 = Iround( (Structure->P[6] / tP) * (*PopSize-2) ); *P7 = Iround( (Structure->P[7] / tP) * (*PopSize-2) ); *P8 = Iround( (Structure->P[8] / tP) * (*PopSize-2) ); } else { *P0 = 0; *P1 = 0; *P2 = 0; *P3 = 0; *P4 = 0; *P5 = 0; *P6 = 0; *P7 = 0; *P8 = 0; } /* Check to make sure that all operators (i.e., 5, 7) which have to be even numbers are */ if (fmod((long double) *P5, (long double) 2) > 0.0) { if(Structure->PrintLevel>2) { Rprintf("\nNOTE: Operator 6 (Simple Crossover) may only be started\n"); Rprintf("NOTE: an even number of times. I am increasing this operator by one.\n"); } *P5=*P5+1; } if (fmod((long double) *P7, (long double) 2) > 0.0) { if(Structure->PrintLevel>2) { Rprintf("\nNOTE: Operator 8 (Heuristic Crossover) may only be started\n"); Rprintf("NOTE: an even number of times. I am increasing this operator by one.\n"); } *P7=*P7+1; } /*P is the total number of parents needed for applying all the operators*/ *P = *P1 + *P2 + *P3 + *P4 + *P5 + *P6 + *P7 + *P8; if(*P > *PopSize) { if(Structure->PrintLevel>0) { Rprintf("\nNOTE: The total number of operators greater than population size\n"); } if (fmod((long double) *P+1, (long double) 2) > 0.0) { *PopSize = *P+2; if(Structure->PrintLevel>0) { Rprintf("NOTE: I'm increasing the population size to %d (operators+2).\n", *PopSize); } } else { *PopSize = *P+1; if(Structure->PrintLevel>0) { Rprintf("NOTE: I'm increasing the population size to %d (operators+1).\n", *PopSize); } } } else if ( *P== *PopSize) { if(Structure->PrintLevel>0) { Rprintf("\nNOTE: The total number of operators equal to the population size\n"); } if (fmod( (long double) *P+1, (long double) 2) > 0.0) { *PopSize = *P+2; if(Structure->PrintLevel>0) { Rprintf("NOTE: I'm increasing the population size to %d (operators+2).\n", *PopSize); } } else { *PopSize = *P+1; if(Structure->PrintLevel>0) { Rprintf("NOTE: I'm increasing the population size to %d (operators+1).\n", *PopSize); } } } if (fmod( (long double) *PopSize, (long double) 2) > 0.0) { if(Structure->PrintLevel>0) { Rprintf("NOTE: population size is not an even number\n"); Rprintf(" increasing population size by 1\n"); } *PopSize=*PopSize+1; } /* return PopSize and P values to the return data structure */ *P0 = *PopSize-*P-1; Structure->oP[0]=*P0; Structure->oP[1]=*P1; Structure->oP[2]=*P2; Structure->oP[3]=*P3; Structure->oP[4]=*P4; Structure->oP[5]=*P5; Structure->oP[6]=*P6; Structure->oP[7]=*P7; Structure->oP[8]=*P8; Structure->oPopSize=*PopSize; if(Structure->PrintLevel>0) { Rprintf( "\n"); if (Structure->DataType==1) Rprintf( "Data Type: Integer\n"); else Rprintf( "Data Type: Floating Point\n"); Rprintf("Operators (code number, name, population) \n"); Rprintf("\t(1) Cloning........................... \t%d\n", *P0); Rprintf("\t(2) Uniform Mutation.................. \t%d\n", *P1); Rprintf("\t(3) Boundary Mutation................. \t%d\n", *P2); Rprintf("\t(4) Non-Uniform Mutation.............. \t%d\n", *P3); Rprintf("\t(5) Polytope Crossover................ \t%d\n", *P4); Rprintf("\t(6) Simple Crossover.................. \t%d\n", *P5); Rprintf("\t(7) Whole Non-Uniform Mutation........ \t%d\n", *P6); Rprintf("\t(8) Heuristic Crossover............... \t%d\n", *P7); Rprintf("\t(9) Local-Minimum Crossover........... \t%d\n\n", *P8); if (*HardGenerationLimit==0) Rprintf("SOFT Maximum Number of Generations: %lu\n", *MaxGenerations); else Rprintf("HARD Maximum Number of Generations: %lu\n", *MaxGenerations); Rprintf("Maximum Nonchanging Generations: %lu\n", *WaitGenerations); Rprintf("Population size : %d\n", *PopSize); Rprintf("Convergence Tolerance: %e\n", *SolutionTolerance); Rprintf( "\n"); if (*UseBFGS !=0) { Rprintf( "Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation.\n"); } else { Rprintf( "Not Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation.\n"); } if (*GradientCheck==0) Rprintf("Not Checking Gradients before Stopping.\n"); else Rprintf("Checking Gradients before Stopping.\n"); if (*BoundaryEnforcement==0) Rprintf("Using Out of Bounds Individuals.\n\n"); else if (*BoundaryEnforcement==1) Rprintf("Not Using Out of Bounds Individuals But Allowing Trespassing.\n\n"); else if (*BoundaryEnforcement==2) Rprintf("Not Using Out of Bounds Individuals and Not Allowing Trespassing.\n\n"); } /* if(Structure->PrintLevel>0) fflush(output); */ } /* End SetOperators */ /********************************************************************************/ /* JaIntegerOptimization: */ /* */ /* This function assumes that the X variables are integers. */ /* */ /* The cross over operators are different! */ /* */ /********************************************************************************/ void JaIntegerOptimization(struct GND_IOstructure *Structure, VECTOR X, MATRIX domains) { extern struct GND_IOstructure *ExternStructure; MATRIX new_genera, /*Temporary storage for the new generation*/ population, /*Population of x2 variables*/ temp; VECTOR probab, /*Probability of agents to die or live*/ cum_probab, /*Cumilative probability of agents*/ t_vec; IVECTOR live; /* for oper4 */ IVECTOR parents; long count_gener= 1; /*Counter to keep track of the number of generations*/ unsigned long peak_cnt; int /*Total number of agents chosen to reproduce*/ j1, j2, j3, j4, j5, j6, j7, j8, oper, ocnt, B, /*Parameter for the 3rd operator - nonuniform mutation*/ STEP, /*Parameter for the 5th operator - simple arithmetical crossover*/ first_live=0, /*Index of the two parents for crossover parents*/ second_live=0, first_die, /*Index of the two parents for crossover death*/ second_die, die_now; /*index of agent to replace in current operation*/ long i,j, s, k; /* for oper 4 */ int p2use; double Q; /*Probability of the best agent*/ FLAG same; double **Jnew; double *grad, *evalX, *finalhessin, *bfgsoutX; int nochange_gen=0; double oldfitvalue=0; int IncreaseGenerations; short int GradientTrigger=0; long InstanceNumber; long nvars, MaxGenerations, WaitGenerations, count; long pop_size, P, P0, P1, P2, P3, P4, P5, P6, P7, P8; short int MinMax, GradientCheck, BoundaryEnforcement, UseBFGS, HardMaximumNumber=0; double SolutionTolerance, *Results, *Gradients; short PrintLevel, HardGenerationLimit; /* Old variables which may change when SetRunTimeParameters is run during a run! */ long pop_size_old; /* Summary Statistics (mean, variance etc) */ /* double popmean, popvar, popwrk, popstat; */ /* Population Print population*/ FILE *popout; long *tobs, nnull; double *mean, *var, *skew, *kur; /* Stuff for the Unique Stuff (how's that for an informative comment! */ /* A big Matrix which remembers all of our past evaluations. It's maximum memory is set in genoud.h */ extern long Gnvars[MAXINSTANCES]; double **Memory; long MemorySize=0, UniqueCount=0, OldUniqueCount=0; /* fine two unique parents count */ long SameCount, UniquePairs; ExternStructure=Structure; Results=Structure->oResults; Gradients=Structure->oGradients; /* Structure Done */ SetRunTimeParameters(Structure, 1, &pop_size, &nvars, &MaxGenerations, &WaitGenerations, &MinMax, &GradientCheck, &BoundaryEnforcement, &UseBFGS, &SolutionTolerance, &InstanceNumber, &P, &P0, &P1, &P2, &P3, &P4, &P5, &P6, &P7, &P8, &PrintLevel, &HardGenerationLimit); /*Space allocation for all the vectors and matrices involved*/ long lexical_end = (Structure->Lexical-1)+nvars+2; /* population[][0] = fitness value (first) population[][1:nvars] = parameter values population[][nvars+1] = flag for fitting population[][(nvars+2):((Structure->Lexical-1)+nvars+2)] = other fitness for Lexical fitting */ population = JaMatrixAllocate(pop_size+2, lexical_end); new_genera = JaMatrixAllocate(pop_size+2, lexical_end); /* reset population to get rid of odd things being passed to R */ for(i=1; i<=pop_size; i++) { for(j=0; jLexical > 1) { LexicalReturn = (double *) malloc(Structure->Lexical*sizeof(double)); oldfitvalueVEC = (double *) malloc(Structure->Lexical*sizeof(double)); } temp = matrix(0,nvars+1,0,nvars); probab = Gvector(1,pop_size); t_vec = Gvector(1,nvars); cum_probab = Gvector(1,pop_size); live = ivector(1,pop_size); /*for oper4 Find max(2,nvars) parents for crossover operator 4*/ p2use = nvars > 2 ? nvars : 2; parents = ivector(1,p2use); Gnvars[Structure->InstanceNumber]=nvars; if (Structure->MemoryUsage==1) { if (HardGenerationLimit==0) MemorySize=3*(MaxGenerations+1)*pop_size+1+pop_size; else MemorySize=(MaxGenerations+1)*pop_size+1+pop_size; Memory = JaMatrixAllocate(MemorySize, lexical_end); } grad = (double *) malloc((nvars)*sizeof(double)); evalX = (double *) malloc((nvars)*sizeof(double)); finalhessin = (double *) malloc(((nvars*nvars)+(nvars))*sizeof(double)); bfgsoutX = (double *) malloc((nvars+1)*sizeof(double)); /* populationstats variables */ mean = (double *) malloc((nvars+1)*sizeof(double)); var = (double *) malloc((nvars+1)*sizeof(double)); skew = (double *) malloc((nvars+1)*sizeof(double)); kur = (double *) malloc((nvars+1)*sizeof(double)); tobs = (long *) malloc((nvars+1)*sizeof(long)); /* JS: Integer Q was different, why? Q=0.2; */ Q=0.5; B=6; STEP=10; if(PrintLevel>0) { switch(MinMax) { case 0: Rprintf("Minimization Problem.\n"); break; case 1: Rprintf("Maximization Problem.\n"); break; } } /* if (PrintLevel>2) { Rprintf("Parameter B (hardcoded): %d\n", B); Rprintf("Parameter Q (hardcoded): %f\n", Q); } */ peak_cnt = 0; pop_size_old=0; if (Structure->ShareType == 1 || Structure->ShareType == 3) { if(PrintLevel>0) Rprintf( "Using old population file to initialize new population\n"); if((popout = fopen(Structure->ProjectPath, "r")) == NULL) { Rprintf(" Generating new population\n"); warning("Unable to open the old project file: %s", Structure->ProjectPath); } else { pop_size_old=ReadPopulation(population, pop_size, nvars, popout, PrintLevel); fclose(popout); for (i=1; i<=pop_size; i++) { for (j=1; j<=nvars; j++) { population[i][j] = (int) population[i][j]; } } if (pop_size_old<2) { warning("The old population file appears to be from a different genoud specification."); pop_size_old=0; } } if (PrintLevel>1) { if((popout = fopen(Structure->ProjectPath, "a")) == NULL) { warning("Unable to open the project file: %s", Structure->ProjectPath); /* free populationstats stuff */ free(mean); free(var); free(skew); free(kur); free(tobs); free(bfgsoutX); free(finalhessin); free(evalX); free(grad); /* free numeric.c allocations */ if (Structure->MemoryUsage==1) JaMatrixFree(Memory, MemorySize); JaMatrixFree(population, pop_size+2); JaMatrixFree(new_genera, pop_size+2); free_matrix(temp, 0, nvars+1, 0); free_vector(probab, 1); free_vector(t_vec, 1); free_vector(cum_probab, 1); free_ivector(live, 1); free_ivector(parents, 1); if(Structure->Lexical > 1) { free(LexicalReturn); free(oldfitvalueVEC); } error("Fatal Error. See output for diagnostic information."); } fclose(popout); } } /* end of ShareType 0 */ else { if (PrintLevel>1) { if((popout = fopen(Structure->ProjectPath, "w")) == NULL) { warning("Unable to open the project file: %s", Structure->ProjectPath); /* free populationstats stuff */ free(mean); free(var); free(skew); free(kur); free(tobs); free(bfgsoutX); free(finalhessin); free(evalX); free(grad); /* free numeric.c allocations */ if (Structure->MemoryUsage==1) JaMatrixFree(Memory, MemorySize); JaMatrixFree(population, pop_size+2); JaMatrixFree(new_genera, pop_size+2); free_matrix(temp, 0, nvars+1, 0); free_vector(probab, 1); free_vector(t_vec, 1); free_vector(cum_probab, 1); free_ivector(live, 1); free_ivector(parents, 1); if(Structure->Lexical > 1) { free(LexicalReturn); free(oldfitvalueVEC); } error("Fatal Error. See output for diagnostic information."); } fclose(popout); } } /* The new initial value matrix: setting a new initial value for every individual */ if (ExternStructure->nStartingValues > 0) { /* Adjust old starting values (from ReadPopulation) so we have enough room for our starting.values */ pop_size_old = pop_size_old-ExternStructure->nStartingValues-1; if (pop_size_old < 0) pop_size_old = 0; // seed the starting values until we run out of population or starting values! j = pop_size_old; for(s=0; snStartingValues; s++) { j++; for(i=1; i<=nvars; i++) { population[j][i] = (int) ExternStructure->StartingValues[s][i-1]; population[j][nvars+1] = -1.0; } } // end of for loop pop_size_old = j; // randomly add on people if we still have population left over! for(j=pop_size_old+1; j<=pop_size; j++) { for(i=1; i<=nvars; i++) { population[j][i] = (int) frange_ran(domains[i][1], domains[i][3]); population[j][nvars+1] = -1.0; } } } // end of we have starting values! else { for(j=pop_size_old+1; j<=pop_size; j++) { for(i=1; i<=nvars; i++) { population[j][i] = (int) frange_ran(domains[i][1], domains[i][3]); population[j][nvars+1] = -1.0; } } } // end of else if (Structure->MemoryUsage==1) { OldUniqueCount=UniqueCount; if (UniqueCount==0) UniqueCount = 1; UniqueCount = RmemoryMatrixEvaluate(Structure->fnMemoryMatrixEvaluate, Structure->rho, Memory, population, MinMax, pop_size, UniqueCount, nvars, Structure->Lexical, lexical_end); if ( (UniqueCount+pop_size) >= MemorySize ) { Structure->MemoryUsage=0; warning("Turned Off MemoryMatrix because memory usage was too great."); } /* end of if */ } // end of Memory based evaluation else { for (i=1; i<=pop_size; i++) { if (population[i][nvars+1]==-1.0 || population[i][nvars+1]==11.0) { for(j=1; j<=nvars; j++) X[j] = population[i][j]; if (Structure->Lexical < 2) { population[i][0] = evaluate(Structure->fn, Structure->rho, X, nvars, MinMax); } else { EvaluateLexical(Structure->fn, Structure->rho, X, nvars, Structure->Lexical, MinMax, LexicalReturn); population[i][0] = LexicalReturn[0]; count = 0; for(j=(nvars+2);jMemoryUsage!=1) { /*Sort the initial individuals based on their evaluation function*/ if (Structure->Lexical < 2) { sort(MinMax,population,pop_size,0); } else { /* in eval.cpp because it is like the EvaluateLexical() function */ RlexicalSort(Structure->fnLexicalSort, Structure->rho, population, MinMax, pop_size, nvars, lexical_end, 1); } } peak_cnt = count_gener; /* since we are on generation 0 */ oldfitvalue=population[1][0]; if(Structure->Lexical > 1) { oldfitvalueVEC[0]=population[1][0]; k = 1; for (i=(nvars+2);i0) { Rprintf("\nThe best initial individual is:\n"); print_vector(population[1],1,nvars,output); if (Structure->Lexical > 1) { Rprintf("\nbest (lexical) fitness:\n"); Rprintf("%e ", population[1][0]); for(j=(nvars+2);jLexical > 1) { Rprintf("The worst (lexical) fitness is:\n"); Rprintf("%e ", population[pop_size][0]); for(j=(nvars+2);jLexical > 1) { Rprintf("\n\nGeneration#\t Solution Values (lexical)\n"); Rprintf("\n%7d \t%e ", 0, population[1][0]); for(j=(nvars+2);j1) { Rprintf("GENERATION: 0 (initializing the population)\n"); populationstats(population, pop_size, nvars, mean, var, skew, kur, tobs); if(Structure->Lexical > 1) { Rprintf( "Lexical Fit..... %e ", population[1][0]); for(j=(nvars+2);j 0) Rprintf( "#null........... %d\n", nnull); if(Structure->MemoryUsage==1) Rprintf( "#unique......... %d, #Total UniqueCount: %d\n", UniqueCount-OldUniqueCount, UniqueCount); /* Rprintf( "tobs............ %d\n", tobs[i]); */ for (i=1; i<=nvars; i++) { Rprintf( "var %d:\n", i); Rprintf( "best............ %e\n", population[1][i]); Rprintf( "mean............ %e\n", mean[i]); Rprintf( "variance........ %e\n", var[i]); /* Rprintf( "skewness........ %e\n", skew[i]); Rprintf( "kurtosis........ %e\n", kur[i]); */ nnull = pop_size-tobs[i]; if(nnull > 0) Rprintf( "#null........... %d\n", nnull); /* Rprintf( "tobs............ %d\n", tobs[i]); */ } } /* end of printlevel if */ /* if(PrintLevel>0) fflush(output); */ /* Print the population file */ if ( PrintLevel == 1 ) { if((popout = fopen(Structure->ProjectPath, "w")) == NULL) { Rprintf("Unable to open the project file: %s", Structure->ProjectPath); /* free populationstats stuff */ free(mean); free(var); free(skew); free(kur); free(tobs); free(bfgsoutX); free(finalhessin); free(evalX); free(grad); /* free numeric.c allocations */ if (Structure->MemoryUsage==1) JaMatrixFree(Memory, MemorySize); JaMatrixFree(population, pop_size+2); JaMatrixFree(new_genera, pop_size+2); free_matrix(temp, 0, nvars+1, 0); free_vector(probab, 1); free_vector(t_vec, 1); free_vector(cum_probab, 1); free_ivector(live, 1); free_ivector(parents, 1); if(Structure->Lexical > 1) { free(LexicalReturn); free(oldfitvalueVEC); } error("Fatal Error. See output for diagnostic information."); } print_population((int) pop_size, (int) nvars, 0, (int) Structure->Lexical, population, popout); fclose(popout); } /* end of PrintLevel if */ if ( PrintLevel>1) { if((popout = fopen(Structure->ProjectPath, "a")) == NULL) { Rprintf("Unable to open the project file: %s", Structure->ProjectPath); /* free populationstats stuff */ free(mean); free(var); free(skew); free(kur); free(tobs); free(bfgsoutX); free(finalhessin); free(evalX); free(grad); /* free numeric.c allocations */ if (Structure->MemoryUsage==1) JaMatrixFree(Memory, MemorySize); JaMatrixFree(population, pop_size+2); JaMatrixFree(new_genera, pop_size+2); free_matrix(temp, 0, nvars+1, 0); free_vector(probab, 1); free_vector(t_vec, 1); free_vector(cum_probab, 1); free_ivector(live, 1); free_ivector(parents, 1); if(Structure->Lexical > 1) { free(LexicalReturn); free(oldfitvalueVEC); } error("Fatal Error. See output for diagnostic information."); } print_population((int) pop_size, (int) nvars, 0, (int) Structure->Lexical, population, popout); fflush(popout); fclose(popout); } /* Interrupt setup. Let's print a nice message to recover the best solution so far if at least generation 0 has been run */ if (PrintLevel > 0 & (strcmp(Structure->ProjectPath, "/dev/null")!=0)) setVar(install("interrupted"), ScalarLogical(1), Structure->rho); /*Assigning probability of survival for each of the agent, with the*/ /*probability provided by the user for the best agent*/ assign_probab(probab,pop_size,Q); /*Finding the cumulative probability of the agents*/ find_cum_probab(cum_probab,probab,pop_size); /*Reproducing and evaluating for the total number of generations times*/ do { /*Initializing the live vector*/ for(j=1; j<=pop_size; j++) { live[j] = 0; for(i=0; i0; ocnt--) JaIntegerOper1(t_vec,domains,nvars); for(i=1; i<=nvars; i++) new_genera[die_now][i] = t_vec[i]; die_now--; j1++; } break; case 2: /* JS Description: Boundary Mutation */ /*Applying the second operator, boundary mutation*/ if (j2 < P2) { /*Find one parent for mutation operator 2*/ first_live = find_parent(live,pop_size); live[first_live]--; /* check that agent to replace is in range */ if (die_now < 2) { error( "No agents to be replaced\n"); } new_genera[die_now][nvars+1] = 2.0; for(i=1; i<=nvars; i++) t_vec[i] = population[first_live][i]; JaIntegerOper2(t_vec,domains,nvars); for(i=1; i<=nvars; i++) new_genera[die_now][i] = t_vec[i]; die_now--; j2++; } break; case 3: /* JS Description: Non-uniform Mutation */ /*Applying the third operator, non-uniform mutation*/ if (j3 < P3) { /*Find one parent for mutation operator 3*/ first_live = find_parent(live,pop_size); live[first_live]--; /* check that agent to replace is in range */ if (die_now < 2) { error( "No agents to be replaced\n"); } new_genera[die_now][nvars+1] = 3.0; for(i=1; i<=nvars; i++) t_vec[i] = population[first_live][i]; for (ocnt = irange_ran(1,nvars); ocnt>0; ocnt--) JaIntegerOper3(t_vec,domains,nvars,MaxGenerations,count_gener,B); for(i=1; i<=nvars; i++) new_genera[die_now][i] = t_vec[i]; die_now--; j3++; } break; case 4: /*Applying the fourth operator, GENOUD Polytope Crossover */ if (j4 < (int) P4) { /*Find max(2,nvars) parents for crossover operator 4*/ for (i=1; i= (UniquePairs) ) break; for(i=1; i<=nvars; i++) { if ((int) population[first_live][i] != (int) population[second_live][i]) { same = FALSE; break; } } } /* end of while same==TRUE loop */ /* check that agents to replace are in range */ if (die_now < 3) { error("Not enough agents to be replaced\n"); } live[first_live]--; live[second_live]--; first_die = die_now-- ; second_die = die_now-- ; new_genera[first_die][nvars+1] = 5.0; new_genera[second_die][nvars+1] = 5.0; if (!same) { for(i=1; i<=nvars; i++) { temp[1][i] = population[first_live][i]; temp[2][i] = population[second_live][i]; } JaIntegerOper5(temp[1],temp[2],STEP,domains,nvars); for(i=1; i<=nvars; i++) { new_genera[first_die][i] = temp[1][i]; new_genera[second_die][i] = temp[2][i]; } } else { /* copy agent chosen twice into two new indivs */ for(i=1; i<=nvars; i++) { new_genera[first_die][i] = population[first_live][i]; new_genera[second_die][i] = population[second_live][i]; } } j5++; } break; case 6: /* JS Description: Whole Non-uniform Mutation */ /*Applying the sixth operator, whole non-uniform mutation*/ if (j6 < P6) { /*Find one parent for mutation operator 6*/ first_live = find_parent(live,pop_size); live[first_live]--; /* check that agent to replace is in range */ if (die_now < 2) { error( "No agents to be replaced\n"); } new_genera[die_now][nvars+1] = 6.0; for(i=1; i<=nvars; i++) t_vec[i] = population[first_live][i]; JaIntegerOper6(t_vec,domains,nvars,MaxGenerations,count_gener,B); for(i=1; i<=nvars; i++) new_genera[die_now][i] = t_vec[i]; die_now--; j6++; } break; case 7: /* JS Description: Heuristic Crossover */ /*Applying the seventh operator*/ if (j7 < (int) P7/2) { /*Find two distinct parents for operator 7*/ same = TRUE; SameCount=0; while (same==TRUE) { SameCount++; first_live = find_parent(live,pop_size); second_live = find_parent(live,pop_size); if (SameCount >= (UniquePairs) ) break; for(i=1; i<=nvars; i++) { if ((int) population[first_live][i] != (int) population[second_live][i]) { same = FALSE; break; } } } /* end of while same==TRUE loop */ /* check that agents to replace are in range */ if (die_now < 3) { error("Not enough agents to be replaced\n"); } live[first_live]--; live[second_live]--; first_die = die_now-- ; second_die = die_now-- ; new_genera[first_die][nvars+1] = 7.0; new_genera[second_die][nvars+1] = 7.0; if (!same) { if (first_live < second_live) /* first agent is better agent */ for(i=1; i<=nvars; i++) { temp[2][i] = population[first_live][i]; temp[1][i] = population[second_live][i]; } else /* second agent is better agent */ for(i=1; i<=nvars; i++) { temp[2][i] = population[second_live][i]; temp[1][i] = population[first_live][i]; } JaIntegerOper7(temp[1],temp[2],domains,nvars); for(i=1; i<=nvars; i++) new_genera[first_die][i] = temp[1][i]; if (first_live < second_live) /* first agent is better agent */ for(i=1; i<=nvars; i++) { temp[2][i] = population[first_live][i]; temp[1][i] = population[second_live][i]; } else /* second agent is better agent */ for(i=1; i<=nvars; i++) { temp[2][i] = population[second_live][i]; temp[1][i] = population[first_live][i]; } JaIntegerOper7(temp[1],temp[2],domains,nvars); for(i=1; i<=nvars; i++) new_genera[second_die][i] = temp[1][i]; } else { /* copy agent chosen twice into two new indivs */ for(i=1; i<=nvars; i++) { new_genera[first_die][i] = population[first_live][i]; new_genera[second_die][i] = population[second_live][i]; } } j7++; } } } /*Replace the population with the new generation */ Jnew = new_genera; new_genera = population; population = Jnew; if (Structure->MemoryUsage==1) { OldUniqueCount=UniqueCount; UniqueCount = RmemoryMatrixEvaluate(Structure->fnMemoryMatrixEvaluate, Structure->rho, Memory, population, MinMax, pop_size, UniqueCount, nvars, Structure->Lexical, lexical_end); if ( (UniqueCount+pop_size) >= MemorySize ) { Structure->MemoryUsage=0; warning("Turned Off MemoryMatrix because memory usage was too great."); } /* end of if */ } // end of MemoryUsage==1 else { for (i=1; i<=pop_size; i++) { if (population[i][nvars+1]!=0) { for(j=1; j<=nvars; j++) X[j] = population[i][j]; if (Structure->Lexical < 2) { population[i][0] = evaluate(Structure->fn, Structure->rho, X, nvars, MinMax); } else { EvaluateLexical(Structure->fn, Structure->rho, X, nvars, Structure->Lexical, MinMax, LexicalReturn); population[i][0] = LexicalReturn[0]; count = 0; for(j=(nvars+2);jMemoryUsage!=1) { /*Sort the new population based on their evaluation function*/ if (Structure->Lexical < 2) { sort(MinMax,population,pop_size,0); } else { /* in eval.cpp because it is like the EvaluateLexical() function */ RlexicalSort(Structure->fnLexicalSort, Structure->rho, population, MinMax, pop_size, nvars, lexical_end, 1); } } /* check to see if fit is improving */ if(Structure->Lexical < 2) { switch(MinMax) { case 0: if ( (oldfitvalue - SolutionTolerance) > population[1][0]) { nochange_gen=0; oldfitvalue=population[1][0]; peak_cnt = count_gener; } else nochange_gen++; break; case 1: if ( (oldfitvalue + SolutionTolerance) < population[1][0]) { nochange_gen=0; oldfitvalue=population[1][0]; peak_cnt = count_gener; } else nochange_gen++; break; } } /* if(Structure->Lexical < 2) */ else { switch(MinMax) { case 0: LexicalFitsImproving = 0; if ( (oldfitvalue - SolutionTolerance) > population[1][0]) { LexicalFitsImproving = 1; } else { k=1; for (i=(nvars+2);i population[1][i] ) { LexicalFitsImproving = 1; break; } /* (oldfitvalueVEC[k] - SolutionTolerance) > population[1][i] ) */ k++; } /* for (i=(nvars+2);i population[1][0]) */ if (LexicalFitsImproving) { nochange_gen = 0; peak_cnt = count_gener; oldfitvalue=population[1][0]; oldfitvalueVEC[0]=population[1][0]; k=1; for (i=(nvars+2);i population[1][i] ) */ k++; } /* for (i=(nvars+2);i population[1][0]) */ if (LexicalFitsImproving) { nochange_gen = 0; peak_cnt = count_gener; oldfitvalue=population[1][0]; oldfitvalueVEC[0]=population[1][0]; k=1; for (i=(nvars+2);iLexical > 2) */ if(PrintLevel==1) { if( nochange_gen==0 ) { if(Structure->Lexical > 1) { Rprintf("\n%7d \t%e ", count_gener, population[1][0]); for(j=(nvars+2);j1) { Rprintf("\nGENERATION: %d\n", count_gener); populationstats(population, pop_size, nvars, mean, var, skew, kur, tobs); if(Structure->Lexical > 1) { Rprintf( "Lexical Fit..... %e ", population[1][0]); for(j=(nvars+2);j 0) Rprintf( "#null........... %d\n", nnull); if(Structure->MemoryUsage==1) Rprintf( "#unique......... %d, #Total UniqueCount: %d\n", UniqueCount-OldUniqueCount, UniqueCount); /* Rprintf( "tobs............ %d\n", tobs[i]); */ for (i=1; i<=nvars; i++) { Rprintf( "var %d:\n", i); Rprintf( "best............ %e\n", population[1][i]); Rprintf( "mean............ %e\n", mean[i]); Rprintf( "variance........ %e\n", var[i]); /* Rprintf( "skewness........ %e\n", skew[i]); Rprintf( "kurtosis........ %e\n", kur[i]); */ nnull = pop_size-tobs[i]; if(nnull > 0) Rprintf( "#null........... %d\n", nnull); /* Rprintf( "tobs............ %d\n", tobs[i]); */ } } /* end of printlevel if */ /* if (PrintLevel>0) fflush(output); */ /* Print the population file */ if ( PrintLevel == 1 ) { if((popout = fopen(Structure->ProjectPath, "w")) == NULL) { Rprintf("Unable to open the project file: %s", Structure->ProjectPath); /* free populationstats stuff */ free(mean); free(var); free(skew); free(kur); free(tobs); free(bfgsoutX); free(finalhessin); free(evalX); free(grad); /* free numeric.c allocations */ if (Structure->MemoryUsage==1) JaMatrixFree(Memory, MemorySize); JaMatrixFree(population, pop_size+2); JaMatrixFree(new_genera, pop_size+2); free_matrix(temp, 0, nvars+1, 0); free_vector(probab, 1); free_vector(t_vec, 1); free_vector(cum_probab, 1); free_ivector(live, 1); free_ivector(parents, 1); if(Structure->Lexical > 1) { free(LexicalReturn); free(oldfitvalueVEC); } error("Fatal Error. See output for diagnostic information."); } print_population((int) pop_size, (int) nvars, (int) count_gener, (int) Structure->Lexical, population, popout); fclose(popout); } /* end of PrintLevel if */ if ( PrintLevel>1) { if((popout = fopen(Structure->ProjectPath, "a")) == NULL) { Rprintf("Unable to open the project file: %s", Structure->ProjectPath); /* free populationstats stuff */ free(mean); free(var); free(skew); free(kur); free(tobs); free(bfgsoutX); free(finalhessin); free(evalX); free(grad); /* free numeric.c allocations */ if (Structure->MemoryUsage==1) JaMatrixFree(Memory, MemorySize); JaMatrixFree(population, pop_size+2); JaMatrixFree(new_genera, pop_size+2); free_matrix(temp, 0, nvars+1, 0); free_vector(probab, 1); free_vector(t_vec, 1); free_vector(cum_probab, 1); free_ivector(live, 1); free_ivector(parents, 1); if(Structure->Lexical > 1) { free(LexicalReturn); free(oldfitvalueVEC); } error("Fatal Error. See output for diagnostic information."); } print_population((int) pop_size, (int) nvars, (int) count_gener, (int) Structure->Lexical, population, popout); fflush(popout); fclose(popout); } if (nochange_gen > (WaitGenerations)) { /* increase the number of WaitGenerations if the gradients are NOT zero! */ if (GradientCheck==0) { if(PrintLevel>0) { Rprintf("\n'wait.generations' limit reached.\n"); Rprintf("No significant improvement in %d generations.\n", nochange_gen-1); /* fflush(output); */ } MaxGenerations = 0; nochange_gen=0; } else { for (i=1; i<=nvars; i++) { bfgsoutX[i-1]=population[1][i]; } if(Structure->UserGradient==0) { gradient(Structure->fn, Structure->rho, bfgsoutX, grad, nvars, MinMax, BoundaryEnforcement, domains); } else { userGradientfn(Structure->fnGR, Structure->rho, bfgsoutX, grad, nvars); } GradientTrigger = 0; for (i=0; i SolutionTolerance) { GradientTrigger = 1; break; } } /* end for loop */ if (GradientTrigger==1) { IncreaseGenerations = WaitGenerations; WaitGenerations += IncreaseGenerations; if(PrintLevel>0) { Rprintf( "\nDoubling 'wait.generations' limit to %d (from %d) ", WaitGenerations, IncreaseGenerations); Rprintf("because at least one gradient is too large.\n"); Rprintf("G[%d]: %e\t Solution Tolerance: %e\n\n", i+1, grad[i], SolutionTolerance); } } else { if(PrintLevel>0) { Rprintf("\n'wait.generations' limit reached.\n"); Rprintf("No significant improvement in %d generations.\n", nochange_gen-1); /* fflush(output); */ } MaxGenerations = 0; nochange_gen=0; } }/* end else loop */ } /* end of if (nochange_gen > (WaitGenerations)) { */ if ( (count_gener == MaxGenerations) && (GradientTrigger==1) ) { if (HardGenerationLimit==0) { IncreaseGenerations = MaxGenerations; MaxGenerations += IncreaseGenerations; if(PrintLevel>0) { Rprintf( "\nIncreasing 'max.generations' limit by %d generations to %d ", IncreaseGenerations, MaxGenerations); Rprintf("because at least one gradient is too large.\n\n"); } } // if (Structure->HardGenerationLimit==0) else { HardMaximumNumber = 1; warning("Stopped because hard maximum generation limit was hit.\nAt least one gradient is too large."); if(PrintLevel>0) { Rprintf("\nNOTE: HARD MAXIMUM GENERATION LIMIT HIT\n"); Rprintf(" At least one gradient is too large\n"); } } // else } // if ( (count_gener == MaxGenerations) && (GradientTrigger==1) ) /* increase the number of generations if fitness has been improving */ if ( (count_gener == MaxGenerations) && (nochange_gen < WaitGenerations) ) { if (HardGenerationLimit==0) { if (WaitGenerations > MaxGenerations) { IncreaseGenerations = WaitGenerations; MaxGenerations += (int) (IncreaseGenerations); if(PrintLevel>0) { Rprintf( "\nIncreasing 'max.generations' limit by %d generations to %d ", IncreaseGenerations, MaxGenerations); Rprintf("because the fitness is still impoving.\n\n"); } } else { IncreaseGenerations = MaxGenerations; MaxGenerations += (int) (IncreaseGenerations); if(PrintLevel>0) { Rprintf( "\nIncreasing 'max.generations' limit by %d generations to %d ", IncreaseGenerations, MaxGenerations); Rprintf("because the fitness is still improving.\n\n"); } } } // if (Structure->HardGenerationLimit==0) else { if (HardMaximumNumber==0) { warning("Stopped because hard maximum generation limit was hit."); if(PrintLevel>0) { Rprintf("\nNOTE: HARD MAXIMUM GENERATION LIMIT HIT\n"); } } /* end of if HardMax */ } } // if ( (count_gener == MaxGenerations) && (nochange_gen < WaitGenerations) ) /* if(PrintLevel>0) fflush(output); */ } /* end of do loop */ /*Increment iteration count and test whether all generations are done*/ while (++count_gener <= MaxGenerations); if(PrintLevel>0) { if(Structure->Lexical > 1) { Rprintf("\nSolution Lexical Fitness Value:\n"); Rprintf("%e ", population[1][0]); for(j=(nvars+2);joPeakGeneration=peak_cnt; Structure->oGenerations=count_gener-1; /* obtain gradients */ /* print best solution */ if (GradientCheck==0 && UseBFGS==0) { for(j = 1; j <= nvars; j++) { i = j-1; if(PrintLevel>0) Rprintf(" X[%2d] :\t%e\n",j,population[1][j]); grad[i] = -1.0; Results[i] = population[1][j]; Gradients[i] = grad[i]; } } /* end of if (GradientCheck==0 && UseBFGS==0) */ else { for (i=1; i<=nvars; i++) { bfgsoutX[i-1]=population[1][i]; } if(Structure->UserGradient==0) { gradient(Structure->fn, Structure->rho, bfgsoutX, grad, nvars, MinMax, BoundaryEnforcement, domains); } else { userGradientfn(Structure->fnGR, Structure->rho, bfgsoutX, grad, nvars); } for(j = 1; j <= nvars; j++) { i = j-1; if(PrintLevel>0) Rprintf(" X[%2d] :\t%e\tG[%2d] :\t%e\n",j,population[1][j],j,grad[i]); Results[i] = population[1][j]; Gradients[i] = grad[i]; } } /* end of else (GradientCheck==0 && UseBFGS==0) */ Structure->oFitValues[0]=population[1][0]; if (Structure->Lexical > 1) { k = 1; for (i=(nvars+2);ioFitValues[k]=population[1][i]; k++; } } /* free memory */ /* free populationstats stuff */ free(mean); free(var); free(skew); free(kur); free(tobs); free(bfgsoutX); free(finalhessin); free(evalX); free(grad); if (Structure->MemoryUsage==1) JaMatrixFree(Memory, MemorySize); JaMatrixFree(population, pop_size+2); JaMatrixFree(new_genera, pop_size+2); free_matrix(temp, 0, nvars+1, 0); free_vector(probab, 1); free_vector(t_vec, 1); free_vector(cum_probab, 1); free_ivector(live, 1); free_ivector(parents, 1); if(Structure->Lexical > 1) { free(LexicalReturn); free(oldfitvalueVEC); } } /* end JaIntegerOptimization */ /********************************************************************************/ /* JaIntegerSort(): */ /* */ /* This function sorts a double** on an integer basis. */ /* The function also assumes that the double** is indexed from 1 in its rows */ /* and from zero in its columns. */ /* */ /********************************************************************************/ void JaIntegerSort(double **InMatrix, long n, long k) { /* extern int JaIntegerCMP(); */ long i, j; double **Tmp; extern long Gnvars[MAXINSTANCES]; long nvars; Tmp = JaMatrixAllocate(n, k); nvars=Gnvars[ExternStructure->InstanceNumber]; for (i=1; i<=n; i++) { for (j=0; jInstanceNumber]; for (i=1; i<=n; i++) { for (j=0; j Jasjeet Singh Sekhon UC Berkeley http://sekhon.polisci.berkeley.edu August 3, 2009 */ #include "genoud.h" void genoud(struct GND_IOstructure *Structure); extern "C" { // mkanswer SEXP mkans(double *oFitValues, double *oResults, double *oGradients, long *oP, long oGenerations, long oPeakGeneration, long oPopSize, long nvars, long lexical) { SEXP ans; long length, i, indx, operators; operators=9; length= lexical + (nvars*2) + 3 + operators; PROTECT(ans=allocVector(REALSXP,length)); REAL(ans)[0] = (double) oGenerations; REAL(ans)[1] = (double) oPeakGeneration; REAL(ans)[2] = (double) oPopSize; indx = 2; // include fit values for (i=0; i 0) { /* need to free a matrix of StaringValues below */ StartingValues = (double **) malloc(nStartingValues*sizeof(double)); for (i=0; ifn=fn; MainStructure->rho=rho; MainStructure->fnLexicalSort=fnLexicalSort; MainStructure->fnMemoryMatrixEvaluate=fnMemoryMatrixEvaluate; MainStructure->fnGR=fnGR; MainStructure->fn_optim=fn_optim; MainStructure->Lexical=asInteger(lexical); MainStructure->UserGradient=asInteger(RuserGradient); MainStructure->nvars=parameters; MainStructure->PopSize=asInteger(pop_size); MainStructure->MaxGenerations=asInteger(max_generations); MainStructure->WaitGenerations=asInteger(wait_generations); MainStructure->HardGenerationLimit=asInteger(hard_generation_limit); MainStructure->nStartingValues=nStartingValues; MainStructure->StartingValues=StartingValues; MainStructure->P[0]=REAL(P)[0]; MainStructure->P[1]=REAL(P)[1]; MainStructure->P[2]=REAL(P)[2]; MainStructure->P[3]=REAL(P)[3]; MainStructure->P[4]=REAL(P)[4]; MainStructure->P[5]=REAL(P)[5]; MainStructure->P[6]=REAL(P)[6]; MainStructure->P[7]=REAL(P)[7]; MainStructure->P[8]=REAL(P)[8]; MainStructure->Domains=domains; MainStructure->MinMax=asInteger(max); MainStructure->GradientCheck=asInteger(gradient_check); MainStructure->BoundaryEnforcement=asInteger(boundary_enforcement); MainStructure->SolutionTolerance=asReal(solution_tolerance); MainStructure->UseBFGS=asInteger(BFGS); MainStructure->MemoryUsage=asInteger(MemoryMatrix); MainStructure->Debug=asInteger(Debug); MainStructure->InstanceNumber=asInteger(instance_number); MainStructure->ProvideSeeds=asInteger(provide_seeds); MainStructure->UnifSeed=asInteger(unif_seed); MainStructure->IntSeed=asInteger(int_seed); MainStructure->PrintLevel=asInteger(print_level); MainStructure->DataType=asInteger(data_type_int); /* Share Type: (0) no reading of the existing project file and no looking at the public population file (1) reading of any existing project file, but no examining of public population file (2) NO reading of any existing project file but examination of public population file (3) BOTH reading of any existing project file AND examination of public population file */ MainStructure->ShareType=asInteger(share_type); //Paths char OutputPath[1000], ProjectPath[1000]; strcpy(OutputPath,STRING_VALUE(output_path)); strcpy(ProjectPath,STRING_VALUE(project_path)); MainStructure->OutputPath=OutputPath; MainStructure->ProjectPath=ProjectPath; MainStructure->OutputType=asInteger(output_type); /* output data structures */ FitValues = (double *) malloc(MainStructure->Lexical*sizeof(double)); Results = (double *) malloc(parameters*sizeof(double)); Gradients = (double *) malloc(parameters*sizeof(double)); MainStructure->oFitValues=FitValues; MainStructure->oResults=Results; MainStructure->oGradients=Gradients; /* from setupGenoud */ /* output data structures */ MainStructure->oGenerations=0; MainStructure->oPeakGeneration=0; MainStructure->oPopSize=0; MainStructure->ThreadNumber=0; /* Operator Options */ MainStructure->P9mix=asReal(RP9mix); MainStructure->BFGSburnin=asInteger(BFGSburnin); /* Transform Related Variables */ /* whichFUN == 3 implies EvaluateTransform should be called */ /* whichFUN == 2 implies EvaluateLexical should be called */ /* whichFUN == 1 implies evaluate should be called */ MainStructure->Transform=asInteger(transform); if(MainStructure->Transform == 1) MainStructure->whichFUN = 3; else if(MainStructure->Lexical > 1) MainStructure->whichFUN = 2; else MainStructure->whichFUN = 1; genoud(MainStructure); ret = mkans(MainStructure->oFitValues, MainStructure->oResults, MainStructure->oGradients, MainStructure->oP, MainStructure->oGenerations, MainStructure->oPeakGeneration, MainStructure->oPopSize, MainStructure->nvars, MainStructure->Lexical); // Free memory free(MainStructure); for (i=0; i 0) { for (i=0; i Jasjeet Singh Sekhon UC Berkeley http://sekhon.berkeley.edu August 3, 2009 */ #include #include #include #include "genoud.h" extern "C" { double evaluate(SEXP fn, SEXP rho, double *X, long nvars, short int MinMax) { SEXP R_fcall, Rx; double fit; long i; int isFinite=0; PROTECT(Rx = allocVector(REALSXP, nvars)); for (i=0; i 1) { k=0; for(j=0; j Jasjeet Singh Sekhon UC Berkeley http://sekhon.polisci.berkeley.edu June 2, 2012 */ #include "genoud.h" double **JaMatrixAllocate(long nobs, long nvars) { long i; double **M; M= (double **) malloc(nobs*sizeof(double *)); for (i=0; i=nrl;i--) free((double*) (m[i]+ncl)); free((double*) (m+nrl)); } } void free_imatrix(int **m, int nrl, int nrh, int ncl) { int i; if (m == NULL) return; else { for(i=nrh;i>=nrl;i--) free((unsigned int*) (m[i]+ncl)); free((unsigned int*) (m+nrl)); } } rgenoud/src/gradient.h0000644000176200001440000000764712553042713014472 0ustar liggesusers/* RGENOUD Walter R. Mebane, Jr. Cornell University http://macht.arts.cornell.edu/wrm1 Jasjeet Singh Sekhon UC Berkeley http://sekhon.polisci.berkeley.edu $Header: /home/jsekhon/xchg/genoud/rgenoud.distribution/sources/RCS/gradient.h,v 2.15 2005/10/29 06:14:44 jsekhon Exp jsekhon $ */ #define EPS 0.000000000000001 /* machine precision */ void gradient(SEXP fn, SEXP rho, double *p, double *g, long nparms, short MinMax, short BoundaryEnforcement, double **Domains); double func4g(SEXP fn, SEXP rho, double *X, long nvars, short MinMax, short BoundaryEnforcement, double **Domains); void numgrad(SEXP fn, SEXP rho, double *epsacc, double *optint, int nparms, double *invals, double *grads, double *wrk, double (*func)(SEXP fn, SEXP rho, double *X, int nvars, short int MinMax), short MinMax); void numgradc(SEXP fn, SEXP rho, double *epsacc, double *optint, int nparms, double *invals, double *grads, double *wrk, double (*func)(SEXP fn, SEXP rho, double *X, long nvars, short MinMax, short BoundaryEnforcement, double **Domains), short MinMax, short BoundaryEnforcement, double **Domains); extern double *numopgc(double *epsacc, double *optint, int nparms, int nobs, double *invals, double *opg, double *wrk, int (*func)(double *X, double *outvec)); double **eaccuracy(SEXP fn, SEXP rho, int nparms, int ndiffs, double h, double *invals, double *wrk, double (*func)(SEXP fn, SEXP rho, double *X, long nvars, short MinMax, short BoundaryEnforcement, double **Domains), short MinMax, short BoundaryEnforcement, double **Domains); struct estints { int nparms; int *errors; /* 0 == OK, >=1 == error */ double *hf, /* interval */ *phi, /* f' (first derivative) */ *phic, /* f' (first derivative, central-difference) */ *phi2, /* f'' (second derivative) */ *ef, /* error bound */ *hessian; /* hessian matrix (lower triangle) */ }; struct estints *algfd(SEXP fn, SEXP rho, int nparms, double *eps, double *invals, double *wrk, double (*func)(SEXP fn, SEXP rho, double *X, long nvars, short MinMax, short BoundaryEnforcement, double **Domains), short MinMax, short BoundaryEnforcement, double **Domains); void fdestimates(SEXP fn, SEXP rho, int parm, double fvalue, double *invals, double *wrk, double eps, double h, double *fplus, double *fminus, double *phif, double *phib, double *phic, double *phi2, double *cf, double *cb, double *c2, double (*func)(SEXP fn, SEXP rho, double *X, long nvars, short MinMax, short BoundaryEnforcement, double **Domains), int nparms, short MinMax, short BoundaryEnforcement, double **Domains); struct estints *numhessian(struct estints *instruc, double *invals, double *wrk, double (*func)(double *)); struct estints *numhessianc(SEXP fn, SEXP rho, struct estints *instruc, double *invals, double *wrk, double (*func)(SEXP fn, SEXP rho, double *X, long nvars, short MinMax, short BoundaryEnforcement, double **Domains), short MinMax, short BoundaryEnforcement, double **Domains); void estoptint(SEXP fn, SEXP rho, double *epsacc, double *optint, int nparms, int ndiffs, int pflag, double *invals, double (*func)(SEXP fn, SEXP rho, double *X, long nvars, short MinMax, short BoundaryEnforcement, double **Domains), short MinMax, short BoundaryEnforcement, double **Domains); void dohessians(SEXP fn, SEXP rho, double *epsacc, int nparms, int nobs, int ndiffs, double *invals, double (*func)(SEXP fn, SEXP rho, double *X, long nvars, short MinMax, short BoundaryEnforcment, double **Domains), double (*funco)(double *, double *), short MinMax, short BoundaryEnforcement, double **Domains); rgenoud/src/unif.cpp0000644000176200001440000000734412553042713014163 0ustar liggesusers/* RGENOUD Walter R. Mebane, Jr. Cornell University http://macht.arts.cornell.edu/wrm1 Jasjeet Singh Sekhon UC Berkeley http://sekhon.polisci.berkeley.edu $Header: /home/jsekhon/xchg/genoud/rgenoud.distribution/sources/RCS/unif.cpp,v 2.15 2005/10/29 06:14:44 jsekhon Exp jsekhon $ */ #include #include "unif.h" void ruxorv (integer *iseed, int n, double *rvec, integer *aux) { /* the double precision random uniforms in rvec have only 31 random bits set *iseed!=0 to reinitialize the sequence, else use *iseed==0 *iseed always equals 0 on return aux points to an integer vector of length > 1279+3 */ int i, ibloc, nw; static integer wrk[TLPDBSIZ]; double fk = 1.0/((double) TLPMOD) ; /* if n==0, initialize the TLP seed vector in aux[] and return */ if (n == 0) { /* initialize only if *iseed > 0 */ if (*iseed != 0) tlpseq (iseed, 0, wrk, aux); } else { nw = n; ibloc = 0; while (nw > TLPDBSIZ) { tlpseq (iseed, TLPDBSIZ, wrk, aux); if (ibloc > 0) { for (i=0; i 0) { tlpseq (iseed, nw, wrk, aux); if (ibloc > 0) { for (i=0; i k+3 */ /* initialize aux if nonzero *iseed is supplied or if aux[k+2] is not set to the magic value */ if (*iseed != ZEROI || aux[k+2] != k) { if (*iseed < ZEROI) *iseed = -(*iseed); seedw = (*iseed != seed) ? (*iseed ^ seed) : seed ; *iseed = ZEROI; for (i=0; i 0) tlpcor (k, n, rvec, aux); } /* Tausworthe-Lewis-Payne generator, core recursion. assumes aux is valid see Bratley, Fox and Schrage (1983, 190) and Bright and Enison (1979) */ void tlpcor (integer k, int n, integer *rvec, integer *aux) { /* aux is a vector of length k+2 */ int ii; integer i, j, inew; /* get the recursion location indexes out of AUX */ i = aux[k]; j = aux[k+1]; for (ii=0; ii Jasjeet Singh Sekhon UC Berkeley http://sekhon.polisci.berkeley.edu June 3, 2012 */ #include "genoud.h" void add(double *in1, double *in2, double *out, int row, int col) { int i, j, idx; for (i=0;i DOUBLEMAX) { tobs[j]=tobs[j]-1; } if (popdata[i][j] < -1*DOUBLEMAX) { tobs[j]=tobs[j]-1; } else sum[0] += popdata[i][j]; } dinobs = 1.0/tobs[j]; sum[0] *= dinobs; sum[1] = 0.0; sum[2] = 0.0; sum[3] = 0.0; for (i=1; i<=nobs; i++) { if ( (popdata[i][j] < DOUBLEMAX) && (popdata[i][j] > -1*DOUBLEMAX) ) { x1 = popdata[i][j] - sum[0]; x2 = x1*x1; sum[1] += x2; x2 *= x1; sum[2] += x2; x2 *= x1; sum[3] += x2; } /* end of if */ } /* end of i loop */ mean[j] = sum[0]; rvar[j] = sum[1] * dinobs; rskew[j] = sum[2] * dinobs; rkur[j] = sum[3] * dinobs; } /* end of j loop */ for (j=0; j<=nvars; j++) { x1 = rvar[j] ; var[j] = x1; x2 = 1.0 / (x1*x1) ; kur[j] = rkur[j] * x2; skew[j] = rskew[j] * sqrt(x2/x1); } /* free data and work storage */ free(rkur); free(rskew); free(rvar); } rgenoud/src/genoud.h0000644000176200001440000002363112553042713014145 0ustar liggesusers/* RGENOUD Walter R. Mebane, Jr. Cornell University http://macht.arts.cornell.edu/wrm1 Jasjeet Singh Sekhon UC Berkeley http://sekhon.polisci.berkeley.edu June 3, 2012 */ #include #include #include #include #include #include #include #include extern "C" { /* function definitions */ double evaluate(SEXP fn, SEXP rho, double *X, long nvars, short int MinMax); void EvaluateLexical(SEXP fn, SEXP rho, double *X, long nvars, long lexical, short int MinMax, double *ret); void EvaluateTransform(SEXP fn, SEXP rho, double *X, long nvars, long lexical, short int MinMax, double *ret); } /*end of extern C */ #define M(ROW,COL,NCOLS) (((ROW)*(NCOLS))+(COL)) #define EVALUATE -645271937 #define DOUBLEMAX DOUBLE_XMAX #define MAXPATH 1000 #define MAXTHREADS 20 #define MAXINSTANCES 20 #define ERROR_CODE -99999 #define MAX_OPER_UNIQUE_TRY 1000 #define TRUE 1 #define FALSE 0 #define DOS_SYS FALSE /* set to true for dos, false for unix */ #define UNIX_SYS TRUE /* set to true for unix, false for dos */ #define flip() ((int) ((newrand()*(long)2)/(long) 65535)) #define MIN -32768 #define MAX 32768 #define HEAD 1 #define TAIL 0 #define TRIES 1000 #define MULT 25173 #define INCR 13849 #define MOD ((long int) 65536) #define SHUFFLE 256 /* size of random number shuffle array */ #define EST_OFFSET 0 /* offset in hours from Eastern Standard Time zone) */ #define NOTDONE_ADD 0.25 /* number of generations with no changes to be treated as convergence at generation limit */ #define NOTDONE_LIM 50 typedef double **MATRIX; typedef double *VECTOR; typedef int **IMATRIX; typedef int *IVECTOR; typedef int FLAG; typedef int TOSS; typedef struct {int r; int c;}INDEX; struct GND_IOstructure { /* --- Basic Input Parameters ---- */ SEXP fn; SEXP rho; SEXP fnLexicalSort; SEXP fnMemoryMatrixEvaluate; SEXP fnGR; SEXP fn_optim; long nvars; long PopSize; long MaxGenerations; long WaitGenerations; double P[9]; /* Operators */ double **Domains; short MinMax; short GradientCheck; short BoundaryEnforcement; /* 0=anything goes, 1: regular; 2: no trespassing! */ double SolutionTolerance; long ThreadNumber; /* indexed from zero */ long InstanceNumber; /* indexed from zero, the number of parallel runs */ short UseBFGS; /* Use BFGS on the Best Individual 1= True, 0=False */ short DataType; /* 1== integer, everything else equals float */ short MemoryUsage; /* 0=minimize, 1=normal */ short Debug; /* T, F */ short HardGenerationLimit; // T, F /* Starting Values (if we want to provide any) */ double **StartingValues; /* a matrix of starting values (each set consists of a row) */ long nStartingValues; /* number of starting values */ /* Random Number Stuff */ short ProvideSeeds; /* 0: no, 1: yes */ long UnifSeed; long IntSeed; /* --- Ouput Diagnostics --- */ double *oFitValues; double *oResults; double *oGradients; long oP[9]; /* operators used */ long oGenerations; long oPeakGeneration; long oPopSize; /* Output Files */ char* OutputPath; char* ProjectPath; /* I/O types */ short OutputType; short PrintLevel; /* Parallel Processing Stuff */ short ShareType; /* lexical sorting */ long Lexical; short int UserGradient; /* Operator Options */ double P9mix; int BFGSburnin; /* Transform Related Variables */ short int whichFUN; /* 1, 2, or 3 corresponding to which evaluate function to call */ short int Transform; /* 0 or 1 indicating whether transformed parameters are returned */ }; /* bfgs.c */ void dfgsmin(SEXP fn, SEXP rho, double *p, int n, double gtol, int *iter, double *fret, double *hessian, short int MinMax, short int BoundaryEnforcement, long InstanceNumber, double **Domains, short PrintLevel, FILE *output); /* change_order.c file */ void get_var_order(IVECTOR tot, IVECTOR cart, IMATRIX var_order); void find_x1_x2(int tot, IMATRIX var_order, IVECTOR x1, IVECTOR x2); void find_ac1_ac2(int t1, int t2, int t3, IVECTOR x1, IVECTOR x2, MATRIX mat, MATRIX ac1, MATRIX ac2); void find_lu1_lu2(IVECTOR tot, IVECTOR x1, IVECTOR x2, VECTOR dom, VECTOR dom1, VECTOR dom2); void find_limits(int tot, MATRIX domains, VECTOR llim, VECTOR ulim); void find_new_in_eq(VECTOR a1b, MATRIX a1a2, VECTOR ll, VECTOR ul, INDEX rc, MATRIX newin); void find_org_in_eq(VECTOR a1_b, MATRIX a1_a2, VECTOR vec_d, MATRIX c1, MATRIX c2, int c1row, INDEX a1a2, MATRIX org_ineq); void initialize(MATRIX mat, INDEX rc); void find_final_mat1(VECTOR l2, VECTOR u2, MATRIX finmat, int row, int col); void find_final_mat2(MATRIX newin, int r, int c, int finr, MATRIX finmat); void find_final_mat3(MATRIX orgin, int r, int c, int finr, MATRIX finmat); /* evaluate.c */ void optimization(struct GND_IOstructure *Structure, VECTOR X, MATRIX domains); void sort(short int MinMax, MATRIX population, int pop_size, long nvar); void swap(double **x, double **y); int find_parent(IVECTOR live, int pop_size); void assign_probab(VECTOR probab, int pop_size, double Q); double x_pow_y(double x, int y); void find_cum_probab(VECTOR cum_probab, VECTOR probab, int pop_size); void find_live(VECTOR cum_probab, IVECTOR live, int pop_size, int P); int find_die(VECTOR cum_probab, IVECTOR die, int pop_size); void SetRunTimeParameters(struct GND_IOstructure *Structure, short FirstTime, long *PopSize, long *nvars, long *MaxGenerations, long *WaitGenerations, short *MinMax, short *GradientCheck, short *BoundaryEnforcement, short *UseBFGS, double *SolutionTolerance, long *InstanceNumber, long *P, long *P0, long *P1, long *P2, long *P3, long *P4, long *P5, long *P6, long *P7, long *P8, short *PrintLevel, short *HardGenerationLimit); void JaIntegerOptimization(struct GND_IOstructure *Structure, VECTOR X, MATRIX domains); void JaIntegerSort(double **InMatrix, long n, long k); int JaIntegerCMP(double **a, double **b) ; void JaDoubleSort(double **InMatrix, long n, long k); int JaDoubleCMP(double **a, double **b) ; /* frange_ran.c */ double newunif(void); double frange_ran(double llim, double ulim); unsigned int randint(void); unsigned int newrand(void); /* math.c */ /* Not needed here. In here for completeness! */ void add(double *in1, double *in2, double *out, int row, int col); void copy(double *in, double *target, int row, int col); void multi(double *in1, double *in2, double *out, int row1, int col1, int row2, int col2, int outrowcol[2]); void scalarmulti(double scalar, double *in1, double *out, int row, int col) ; void scalarmultioffdiag(double scalar, double *in1, double *out, int row, int col) ; void subtract(double *in1, double *in2, double *out, int row, int col); double trace(double *a, int n); void transpose(double *orig_matrix, double *t_matrix, int orig_rows, int orig_columns); void copy_matrix(MATRIX mat1, MATRIX mat2, int lr, int ur, int lc, int uc); int Iround(double in); void samplestats(double **obsdata, int numobsv, int novarsv, int weightflag, double *weightdata); void populationstats(double **popdata, int numobsv, int novarsv, double *mean, double *var, double *skew, double *kur, long *tobs); /* multiply.c */ void mmprod(int m, int nm, int n, MATRIX mul_cm, MATRIX mul_am, MATRIX mul_bm); void mvprod(int m, int nm, VECTOR cm, MATRIX am, VECTOR bm); /* numerics.c */ double **JaMatrixAllocate(long n, long k); void JaMatrixFree(double **M, long k); short **JaShortMatrixAllocate(long nobs, long nvars); void JaShortMatrixFree(double **M, long nobs); MATRIX matrix(int nrl, int nrh, int ncl, int nch); void nrerror(char error_text[]); double *Gvector(int nl, int nh); int **imatrix(int nrl, int nrh, int ncl, int nch); int *ivector(int nl, int nh); void free_vector(double *v, int nl); void free_ivector(int *v, int nl); void free_matrix(double **m, int nrl, int nrh, int ncl); void free_imatrix(int **m, int nrl, int nrh, int ncl); /* operators.c file */ void oper1(VECTOR parent, double **domains, int nvars); void oper2(VECTOR parent, double **domains, int nvars); void oper3(VECTOR parent, double **domains, int nvars, int T, int t, int B); void oper4(MATRIX p, int p2use, int nvars); void oper5(VECTOR p1, VECTOR p2, int STEP, double **domains, int nvars); void oper6(VECTOR parent, double **domains, int nvars, int T, int t, int B); void oper7(VECTOR p1, VECTOR p2, double **domains, int nvars); void oper8(SEXP fn, SEXP rho, VECTOR parent, MATRIX domains, double SolutionTolerance, long nvars, short BoundaryEnforcement, short PrintLevel, double mix); void find_range(double *llim, double *ulim, int comp, double **domains, int nvars, VECTOR parent); void find_rangeInt(int *llim, int *ulim, int comp, double **domains, int nvars, VECTOR parent); int irange_ran(int llim, int ulim); double get_F(int T, int t, double y, int B); void JaIntegerOper1(VECTOR parent, double **domains, int nvars); void JaIntegerOper2(VECTOR parent, double **domains, int nvars); void JaIntegerOper3(VECTOR parent, double **domains, int nvars, int T, int t, int B); void JaIntegeroper4(MATRIX p, int p2use, int nvars, double **domains); void JaIntegerOper5(VECTOR p1, VECTOR p2, int STEP, double **domains, int nvars); void JaIntegerOper6(VECTOR parent, double **domains, int nvars, int T, int t, int B); void JaIntegerOper7(VECTOR p1, VECTOR p2, double **domains, int nvars); FLAG InBounds(VECTOR child, double **domains, int nvars); /*print_format.c */ long ReadPopulation(double **Data, long NewPopSize, long NewVars, FILE *fp, short PrintLevel); void print_domains(MATRIX equal, int t_equ, short DataType); void print_population(int popsize, int nvars, int generation, int lexical, double **foo, FILE *out); rgenoud/src/urans.h0000644000176200001440000000077212553042713014015 0ustar liggesusers/* RGENOUD Walter R. Mebane, Jr. Cornell University http://macht.arts.cornell.edu/wrm1 Jasjeet Singh Sekhon UC Berkeley http://sekhon.polisci.berkeley.edu $Header: /home/jsekhon/xchg/genoud/rgenoud.distribution/sources/RCS/urans.h,v 2.15 2005/10/29 06:14:44 jsekhon Exp jsekhon $ */ /* set seeds for the random number generators */ #ifndef DEFURANS #define NEWUNIFSEED 81345 #define RANDINTSEED 98711 #define DEFURANS #endif rgenoud/src/change_order.cpp0000644000176200001440000005464712553042713015652 0ustar liggesusers/* RGENOUD Walter R. Mebane, Jr. Cornell University http://macht.arts.cornell.edu/wrm1 Jasjeet Singh Sekhon UC Berkeley http://sekhon.polisci.berkeley.edu $Header: /home/jsekhon/xchg/genoud/rgenoud.distribution/sources/RCS/change_order.cpp,v 2.15 2005/10/29 06:14:44 jsekhon Exp jsekhon $ */ #include "genoud.h" void get_var_order(IVECTOR tot, IVECTOR cart, IMATRIX var_order) /* IVECTOR tot, array with total number of variables and equalities cart; array with the subscript of the variables to be eliminated IMATRIX var_order; matrix with the variables in one column and a tag in the other to identify as to whether it is to be eliminated or not */ { int i; for(i=1; i<=tot[0]; i++) { var_order[i][1] = i; var_order[i][2] = 0; } for(i=1; i<=tot[1]; i++) var_order[cart[i]][2] = 1; } /********************************************************************************/ /* */ /* FUNCTION NAME : find_x1_x2() */ /* */ /* SYNOPSIS : void find_x1_x2(tot,var_order,eq_co,x1,x2) */ /* */ /* DESCRIPTION : This function splits the original vector of */ /* variables into x1 and x2, where x1 consists */ /* of the 'p' variables to be eliminated and */ /* x2 consists of the remaining variables */ /* */ /* FUNCTIONS CALLED : None */ /* */ /* CALLING FUNCITONS : main() */ /* */ /* */ /* REV DATE BY DESCRIPTION */ /* --- ---- -- ----------- */ /* */ /* */ /********************************************************************************/ void find_x1_x2(int tot, IMATRIX var_order, IVECTOR x1, IVECTOR x2) /* int tot; total number of variables IMATRIX var_order; array of variables with tag identifying them to be eliminated IVECTOR x1, array of variables to be eliminated x2; array of remaining variables */ { int i,j=1,k=1; for(i=1; i<=tot; i++) { if(var_order[i][2] == 1) x1[j++] = var_order[i][1]; else x2[k++] = var_order[i][1]; } } /********************************************************************************/ /* */ /* FUNCTION NAME : find_ac1_ac2() */ /* */ /* SYNOPSIS : void find_ac1_ac2(t1,t2,t3,x1,x2,mat,ac1,ac2)*/ /* */ /* DESCRIPTION : This function splits the original equality */ /* or the inequality matrix into two matrices; */ /* the p-equalities or the inequalities and the*/ /* remaining part of the matrix */ /* */ /* FUNCTIONS CALLED : None */ /* */ /* CALLING FUNCITONS : main() */ /* */ /* */ /* */ /* REV DATE BY DESCRIPTION */ /* --- ---- -- ----------- */ /* */ /* */ /********************************************************************************/ void find_ac1_ac2(int t1, int t2, int t3, IVECTOR x1, IVECTOR x2, MATRIX mat, MATRIX ac1, MATRIX ac2) /* int t1,t2,t3; IVECTOR x1,x2; the variables corresponding to the split matrices MATRIX mat, the original matrix to be split ac1,ac2; the split matrices */ { int i,j; for(i=1; i<=t1; i++) for(j=1; j<=t2; j++) ac1[j][i] = mat[j][x1[i]]; for(i=1; i<=t3; i++) for(j=1; j<=t2; j++) ac2[j][i] = mat[j][x2[i]]; } /********************************************************************************/ /* */ /* FUNCTION NAME : find_lu1_lu2() */ /* */ /* SYNOPSIS : void find_lu1_lu2_(tot,x1,x2,dom,dom1,dom2) */ /* */ /* DESCRIPTION : This function splits the lower or the upper */ /* bounds of the total domain constraints into */ /* two groups, one with the domain constraints */ /* for the variables to be eliminated and the */ /* other one for the remaining variables */ /* */ /* FUNCTIONS CALLED : None */ /* */ /* CALLING FUNCITONS : main() */ /* */ /* */ /* REV DATE BY DESCRIPTION */ /* --- ---- -- ----------- */ /* */ /* */ /********************************************************************************/ void find_lu1_lu2(IVECTOR tot, IVECTOR x1, IVECTOR x2, VECTOR dom, VECTOR dom1, VECTOR dom2) /* IVECTOR tot,x1,x2; VECTOR dom, the original array of the lower or the upper bounds dom1,dom2; the original bounds split in to two groups */ { int i; for(i=1; i<=tot[1]; i++) dom1[i] = dom[x1[i]]; for(i=1; i<=tot[0]-tot[1]; i++) dom2[i] = dom[x2[i]]; } /********************************************************************************/ /* */ /* FUNCTION NAME : find_limits() */ /* */ /* SYNOPSIS : void find_limits(tot,domains,llim,ulim) */ /* */ /* DESCRIPTION : This function forms seperate arrays for the */ /* lower and upper limits of the domains from */ /* the original domain constraints read already*/ /* from the input file */ /* */ /* FUNCTIONS CALLED : None */ /* */ /* CALLING FUNCITONS : main() */ /* */ /* */ /* REV DATE BY DESCRIPTION */ /* --- ---- -- ----------- */ /* */ /* */ /********************************************************************************/ void find_limits(int tot, MATRIX domains, VECTOR llim, VECTOR ulim) /* int tot; MATRIX domains; matrix containing the domain variables and the limits VECTOR llim,ulim; vectors of lower and upper limits */ { int i; for(i=1; i<=tot; i++) { llim[i] = domains[i][1]; ulim[i] = domains[i][3]; } } /********************************************************************************/ /* */ /* FUNCTION NAME : find_new_in_eq() */ /* */ /* SYNOPSIS : void find_new_in_eq(a1b.a1a2,ll,ul,rc,newin) */ /* */ /* DESCRIPTION : This function converts the original */ /* equality constraints into domain */ /* constraints eliminating the p-equalities */ /* */ /* FUNCTIONS CALLED : None */ /* */ /* CALLING FUNCITONS : main() */ /* */ /* */ /* REV DATE BY DESCRIPTION */ /* --- ---- -- ----------- */ /* */ /* */ /********************************************************************************/ void find_new_in_eq(VECTOR a1b, MATRIX a1a2, VECTOR ll, VECTOR ul, INDEX rc, MATRIX newin) /* VECTOR a1b, the product of a-inverse and b ll,ul; upper and lower limits of the domain constraints MATRIX a1a2, the products of a-inverse and matrix a2 newin; the final matrix with domain constraints INDEX rc; */ { int i,j; for(i=1; i<=rc.r; i++) for(j=1; j<=rc.c; j++) if(j==1) newin[i][j] = ll[i] - a1b[i];/*eliminating the constrants from the*/ else if(j==rc.c) /*equations in the domain constraints*/ newin[i][j] = ul[i] - a1b[i]; else newin[i][j] = 0 - a1a2[i][j-1]; } /********************************************************************************/ /* */ /* FUNCTION NAME : find_org_in_eq() */ /* */ /* SYNOPSIS : void find_org_in_eq(a1_b,a1_a2,vec_d,c1,c2, */ /* c1row,a1a2,org_ineq)*/ /* */ /* DESCRIPTION : This function converts the original */ /* inequality constraints into domain */ /* constraints, with the variables other than */ /* the p-variables eliminated */ /* */ /* FUNCTIONS CALLED : matrix(). */ /* mmprod(), */ /* mvprod(), */ /* Gvector(), */ /* */ /* CALLING FUNCITONS : main() */ /* */ /* REV DATE BY DESCRIPTION */ /* --- ---- -- ----------- */ /* */ /* */ /********************************************************************************/ void find_org_in_eq(VECTOR a1_b, MATRIX a1_a2, VECTOR vec_d, MATRIX c1, MATRIX c2, int c1row, INDEX a1a2, MATRIX org_ineq) /* VECTOR vec_d, the RHS constant vector a1_b; product of a1-inverse and b MATRIX a1_a2, product of a1-inverse and a2 org_ineq, the converted inequalities into domains c1,c2; p_inequalities and the remaining inequalities int c1row; INDEX a1a2; rows and columns of the matrices */ { int i,j; VECTOR temp; MATRIX mat; temp = Gvector(1,c1row); mat = matrix(1,c1row,1,a1a2.c-1); mvprod(c1row,a1a2.r,temp,c1,a1_b);/*matrix, vector product C1.invA1.b*/ mmprod(c1row,a1a2.r,a1a2.c-1,mat,c1,a1_a2);/*matrix, matrix product*/ for(i=1; i<=c1row; i++) for(j=1; j<=a1a2.c; j++) { if (j==a1a2.c) org_ineq[i][j] = vec_d[i] - temp[i]; else org_ineq[i][j] = c2[i][j] - mat[i][j]; } free_vector(temp,1); free_matrix(mat,1,c1row,1); } /********************************************************************************/ /* */ /* FUNCTION NAME : initialize() */ /* */ /* SYNOPSIS : void initialize(mat,rc) */ /* */ /* DESCRIPTION : This function initializes all the components */ /* of the given matrix to zero */ /* */ /* FUNCTIONS CALLED : None */ /* */ /* CALLING FUNCITONS : main() */ /* */ /* REV DATE BY DESCRIPTION */ /* --- ---- -- ----------- */ /* */ /* */ /********************************************************************************/ void initialize(MATRIX mat, INDEX rc) /* MATRIX mat; INDEX rc; */ { int i,j; for(i=1; i<=rc.r; i++) for(j=1; j<=rc.c; j++) mat[i][j] = 0.0; } /********************************************************************************/ /* */ /* FUNCTION NAME : find_final_mat1() */ /* */ /* SYNOPSIS : void find_final_mat1(x2,l2,u2,finmat,row,col)*/ /* */ /* DESCRIPTION : This function copies the remaining original */ /* domain constraints on to the final matrix */ /* to be printed */ /* */ /* FUNCTIONS CALLED : None */ /* */ /* CALLING FUNCITONS : main() */ /* */ /* */ /* REV DATE BY DESCRIPTION */ /* --- ---- -- ----------- */ /* */ /* */ /********************************************************************************/ void find_final_mat1(VECTOR l2, VECTOR u2, MATRIX finmat, int row, int col) /* MATRIX finmat; VECTOR l2,u2; int row,col; */ { int i,j=2; for(i=1; i<=row; i++) { finmat[i][1] = l2[i]; finmat[i][col] = u2[i]; finmat[i][j++] = 1.0; } } /********************************************************************************/ /* */ /* FUNCTION NAME : find_final_mat2() */ /* */ /* SYNOPSIS : void find_final_mat2(newin,r,c,finr,finmat) */ /* */ /* DESCRIPTION : This function appends the new inequalities */ /* got from the original equalities, on to the */ /* final matrix to be printed */ /* */ /* FUNCTIONS CALLED : None */ /* */ /* CALLING FUNCITONS : main() */ /* */ /* */ /* REV DATE BY DESCRIPTION */ /* --- ---- -- ----------- */ /* */ /* */ /********************************************************************************/ void find_final_mat2(MATRIX newin, int r, int c, int finr, MATRIX finmat) /* MATRIX newin,finmat; int r,c,finr; */ { int i,j; for(i=1; i<=r; i++) { for(j=1; j<=c; j++) finmat[finr][j] = newin[i][j]; finr++; } } /********************************************************************************/ /* */ /* FUNCTION NAME : find_final_mat3() */ /* */ /* SYNOPSIS : void find_final_mat3(orgin,r,c,finr,finmat) */ /* */ /* DESCRIPTION : This function appends the inequalities, which*/ /* were converted into domain constraints, on */ /* to the final matrix to be printed */ /* */ /* FUNCTIONS CALLED : None */ /* */ /* CALLING FUNCITONS : main() */ /* */ /* */ /* */ /* REV DATE BY DESCRIPTION */ /* --- ---- -- ----------- */ /* */ /* */ /********************************************************************************/ void find_final_mat3(MATRIX orgin, int r, int c, int finr, MATRIX finmat) /* MATRIX orgin,finmat; int r,c,finr; */ { int i,j; for(i=1; i<=r; i++) { finmat[finr][1] = MIN; for(j=1; j<=c; j++) finmat[finr][j+1] = orgin[i][j]; finr++; } } rgenoud/src/gradient.cpp0000644000176200001440000006023412553042713015014 0ustar liggesusers/* RGENOUD Walter R. Mebane, Jr. Cornell University http://macht.arts.cornell.edu/wrm1 Jasjeet Singh Sekhon UC Berkeley http://sekhon.polisci.berkeley.edu June 2, 2012 */ #include "genoud.h" #include "gradient.h" double GammaLN(double xx) { double cof[6] = { 76.18009173, -86.50532033, 24.01409822, -1.231739516, 0.12085003E-2, -0.536382E-5, }; double stp = 2.50662827465; double x, tmp, ser; int j; x = xx - 1.0; tmp = x + 5.5; tmp = (x + 0.5) * log(tmp) - tmp; ser = 1.0; for (j = 0; j < 6; j++) { x += 1.0; ser += cof[j] / x; } return tmp + log(stp * ser); } double VMgamma(double xx) { #define PI2 3.141592654 if (xx > 0) return exp(GammaLN(xx)); else if (xx < 0) return PI2 / exp(GammaLN(1 - xx)) / sin( PI2 * (1 - xx)); else return 0; } /* func4g is required by the gradient code. It takes what is in evaluate() and increments it down by 1 NOTE: funco() (which not used here) does not increment evaluate() down by 1. The code internal to the function does this. */ double func4g(SEXP fn, SEXP rho, double *X, long nvars, short MinMax, short BoundaryEnforcement, double **Domains) { double fit; short BoundaryTrigger=0; long i; if (BoundaryEnforcement==2) { for (i=0; i Domains[(i+1)][3]){ BoundaryTrigger=1; break; } } if (BoundaryTrigger > 0) { // *Status=-3; // min if (MinMax==0) return(-1*DOUBLEMAX); //max else return(DOUBLEMAX); } } if (MinMax==0) fit=evaluate(fn, rho, X-1, nvars, MinMax); else fit = -1*evaluate(fn, rho, X-1, nvars, MinMax); return(fit); } /* replace gradient() body with analytical gradient code, if desired. by default, numerical gradients with the intervals in *optint are used arguments (must be identical in any replacement code): *p, vector of parameters, p[0] is the first parameter; *g, vector that will hold the gradient, allocated by caller, g[0] is the derivative for the first parameter; nparms, the number of parameters, p[nparms-1] is the last parameter. */ void gradient(SEXP fn, SEXP rho, double *p, double *g, long nparms, short MinMax, short BoundaryEnforcement, double **Domains) { double *wrk; int ndiffs; /* formally declared global in graddata.h */ // double *epsacc, *optint, *ihessians; double *epsacc, *optint; optint = (double *) malloc(nparms*sizeof(double)); epsacc = (double *) malloc(nparms*sizeof(double)); wrk = (double *) malloc(nparms*sizeof(double)); ndiffs = 9; /* order of differences for num grad optimal interval calcs */ estoptint(fn, rho, epsacc, optint, nparms, ndiffs, 2, p, func4g, MinMax, BoundaryEnforcement, Domains); /* numgradc: numerical gradient, central-difference */ numgradc(fn, rho, epsacc, optint, nparms, p, g, wrk, func4g, MinMax, BoundaryEnforcement, Domains); free(wrk); free(epsacc); free(optint); return; } /* numerical gradient, forward-difference */ /* see Gill, Murray and Wright, 1981, "Practical Optimization," p. 342 */ /* invals, grads, wrk should point to double w[nparms+1] arrays; func is the function whose gradient is to be evaluated */ void numgrad(SEXP fn, SEXP rho, double *epsacc, double *optint, int nparms, double *invals, double *grads, double *wrk, double (*func)(SEXP fn, SEXP rho, double *X, int nvars, short int MinMax), short MinMax) { int i; // double u, rf, fplus, fminus; double u, fplus, fminus; double epsuse; double duse; /* evaluate func at the input point */ u = func(fn, rho, invals, nparms, MinMax); /* copy the parameter values for point at which to evaluate the gradient */ for (i=0; i 0.1) { /* switch to central-diff */ duse = pow(duse, 2.0/3.0); /* see GMW p 131 */ wrk[i] = invals[i] + duse; fplus = func(fn, rho, wrk, nparms, MinMax); wrk[i] = invals[i] - duse; fminus = func(fn, rho, wrk, nparms, MinMax); grads[i] = (fplus-fminus) * 0.5 / duse ; } wrk[i] = invals[i]; } } /* numerical gradient, central-difference */ /* see Gill, Murray and Wright, 1981, "Practical Optimization," p. 342 */ /* invals, grads, wrk should point to double w[nparms+1] arrays; func is the function whose gradient is to be evaluated */ void numgradc(SEXP fn, SEXP rho, double *epsacc, double *optint, int nparms, double *invals, double *grads, double *wrk, double (*func)(SEXP fn, SEXP rho, double *X, long nvars, short MinMax, short BoundaryEnforcement, double **Domains), short MinMax, short BoundaryEnforcement, double **Domains) { int i; // double u, rf, fplus, fminus; double u, fplus, fminus; double epsuse; double duse; /* evaluate func at the input point */ u = func(fn, rho, invals, nparms, MinMax, BoundaryEnforcement, Domains); /* copy the parameter values for point at which to evaluate the gradient */ for (i=0; iEPS*scale) { while (huse > v/scale) huse *= 0.1; } for (j=1; jerrors = (int *) calloc(nparms, sizeof(int)); outstruc->hf = (double *) calloc(nparms, sizeof(double)); outstruc->phi = (double *) calloc(nparms, sizeof(double)); outstruc->phic = (double *) calloc(nparms, sizeof(double)); outstruc->phi2 = (double *) calloc(nparms, sizeof(double)); outstruc->ef = (double *) calloc(nparms, sizeof(double)); outstruc->nparms = nparms; /* evaluate func at the input point */ u = func(fn, rho, invals, nparms, MinMax, BoundaryEnforcement, Domains); /* copy the parameter values for point at which to evaluate the gradient */ for (i=0; icb ? cf : cb) <= 0.1) hs = hk; if (0.001 <= c2 && c2 <= 0.1) { hphi = hk; goto FD5; } if (0.001 > c2) goto FD4; FD3: do { k++; hk *= 10.0; fdestimates(fn, rho, i, u, invals, wrk, eps[i], hk, &fplus, &fminus, &phif, &phib, &phic, &phi2, &cf, &cb, &c2, func, nparms, MinMax, BoundaryEnforcement, Domains); if (hs<0 && ((cf>cb ? cf : cb) <= 0.1)) hs = hk; if (c2 <= 0.1) { hphi = hk; goto FD5; } } while (k 0.1) { hphi = hk * 10.0; goto FD5; } if ((cf>cb ? cf : cb) <= 0.1) hs = hk; if (0.001 <= c2 && c2 <= 0.1) { hphi = hk; goto FD5; } } while (khf[i] = hf; outstruc->phi[i] = phi; outstruc->phic[i] = phic; outstruc->phi2[i] = phi2; outstruc->ef[i] = ef; if ((ef>ebar ? ef : ebar) <= 0.5*fabs(phi)) { outstruc->errors[i] = 0; } else outstruc->errors[i] = 1; continue; FD6: if (hs<0) { hf = hbar; phi = phi2 = ef = 0.0; errval = 2; } else if (hs > 0 && c2 > 0.1) { hf = hs; wrk[i] = invals[i] + hf; fplus = func(fn, rho, wrk, nparms, MinMax, BoundaryEnforcement, Domains); wrk[i] = invals[i]; phi = (fplus-u)/hf; phi2 = 0.0; ef = 2.0*eps[i]/hf ; errval = 3; } else { hf = hk; wrk[i] = invals[i] + hf; fplus = func(fn, rho, wrk, nparms, MinMax, BoundaryEnforcement, Domains); phi = (fplus-u)/hf; wrk[i] = invals[i] - hf; fminus = func(fn, rho, wrk, nparms, MinMax, BoundaryEnforcement, Domains); wrk[i] = invals[i]; phic = (fplus-fminus)/(2.0*hf); ef = hf*fabs(phi2)*0.5 + 2.0*eps[i]/hf ; errval = 4; } outstruc->hf[i] = hf; outstruc->phi[i] = phi; outstruc->phic[i] = phic; outstruc->phi2[i] = phi2; outstruc->ef[i] = ef; outstruc->errors[i] = errval; // #endif } return outstruc; } void fdestimates(SEXP fn, SEXP rho, int parm, double fvalue, double *invals, double *wrk, double eps, double h, double *fplus, double *fminus, double *phif, double *phib, double *phic, double *phi2, double *cf, double *cb, double *c2, double (*func)(SEXP fn, SEXP rho, double *X, long nvars, short MinMax, short BoundaryEnforcement, double **Domains), int nparms, short MinMax, short BoundaryEnforcement, double **Domains) { double ih = 1.0/h; wrk[parm] = invals[parm] + h; *fplus = func(fn, rho, wrk, nparms, MinMax, BoundaryEnforcement, Domains); wrk[parm] = invals[parm] - h; *fminus = func(fn, rho, wrk, nparms, MinMax, BoundaryEnforcement, Domains); wrk[parm] = invals[parm]; *phif = (*fplus-fvalue) * ih; *phib = (fvalue-*fminus) * ih; *phic = (*fplus-*fminus) * 0.5 * ih; *phi2 = (*phif-*phib) * ih; *cf = 2.0*eps*ih/fabs(*phif); *cb = 2.0*eps*ih/fabs(*phib); *c2 = 4.0*eps*ih*ih/fabs(*phi2); } /* put strict lower triangle of numerical hessian into instruc->hessian */ /* instruc should have been set by algfd */ struct estints *numhessian(struct estints *instruc, double *invals, double *wrk, double (*func)(double *)) { int nparms; double *fplusi = NULL; int i,j; double hi, hj, ih, jh; double fvalue, fplus, phi2; nparms = instruc->nparms; fplusi = (double *) malloc(nparms*sizeof(double)); /* allocate storage for the hessian */ instruc->hessian = (double *) calloc((nparms*(nparms+1))/2,sizeof(double)); /* evaluate func at the input point */ fvalue = func(invals); /* copy the parameter values for point at which to evaluate the gradient */ for (i=0; ihf[i]; fplusi[i] = func(wrk); wrk[i] = invals[i]; } for (i=1; ihf[i]; ih = 1.0/hi; wrk[i] = invals[i] + hi; for (j=0; jhf[j]; jh = 1.0/hj; wrk[j] = invals[j] + hj; fplus = func(wrk); wrk[j] = invals[j]; phi2 = (fplus - fplusi[i] - fplusi[j] + fvalue) * ih * jh; instruc->hessian[(i*(i-1))/2 + j] = phi2; } wrk[i] = invals[i]; } free(fplusi); return instruc; } /* put strict lower triangle of numerical hessian into instruc->hessian */ /* uses central differences: */ /* phi2 = f(x+hj ej+hi ei) - f(x+hj ej-hi ei) - f(x-hj ej+hi ei) + f(x-hj ej-hi ei) */ /* instruc should have been set by algfd */ struct estints *numhessianc(SEXP fn, SEXP rho, struct estints *instruc, double *invals, double *wrk, double (*func)(SEXP fn, SEXP rho, double *X, long nvars, short MinMax, short BoundaryEnforcement, double **Domains), short MinMax, short BoundaryEnforcement, double **Domains) { int nparms; int nelems; double *fplusi; double *fminusi; double *fppi; double *fpmi; double *fmmi; int i,j, idx; double hi, hj, ih, jh; // double fvalue, fplus, fminus, phi2; double fvalue, phi2; nparms = instruc->nparms; nelems = (nparms*(nparms-1))/2; fplusi = (double *) malloc(nparms*sizeof(double)); fminusi = (double *) malloc(nparms*sizeof(double)); fppi = (double *) malloc(nelems*sizeof(double)); fpmi = (double *) malloc(nparms*nparms*sizeof(double)); fmmi = (double *) malloc(nelems*sizeof(double)); /* allocate storage for the hessian */ instruc->hessian = (double *) calloc(nelems,sizeof(double)); /* evaluate func at the input point */ fvalue = func(fn, rho, invals, nparms, MinMax, BoundaryEnforcement, Domains); /* copy the parameter values for point at which to evaluate the gradient */ for (i=0; ihf[i], 2.0/3.0); idx = (i*(i-1))/2; wrk[i] = invals[i] + 2.0*hi; fplusi[i] = func(fn, rho, wrk, nparms, MinMax, BoundaryEnforcement, Domains); wrk[i] = invals[i] - 2.0*hi; fminusi[i] = func(fn, rho, wrk, nparms, MinMax, BoundaryEnforcement, Domains); for (j=0; jhf[j], 2.0/3.0); wrk[i] = invals[i] + hi; wrk[j] = invals[j] + hj; fppi[idx + j] = func(fn, rho, wrk, nparms, MinMax, BoundaryEnforcement, Domains); wrk[i] = invals[i] + hi; wrk[j] = invals[j] - hj; fpmi[i*nparms + j] = func(fn, rho, wrk, nparms, MinMax, BoundaryEnforcement, Domains); wrk[i] = invals[i] - hi; wrk[j] = invals[j] + hj; fpmi[j*nparms + i] = func(fn, rho, wrk, nparms, MinMax, BoundaryEnforcement, Domains); wrk[i] = invals[i] - hi; wrk[j] = invals[j] - hj; fmmi[idx + j] = func(fn, rho, wrk, nparms, MinMax, BoundaryEnforcement, Domains); wrk[j] = invals[j]; } wrk[i] = invals[i]; } for (i=0; ihf[i], 2.0/3.0); ih = 1.0/hi; idx = (i*(i-1))/2; phi2 = (fplusi[i] - 2.0*fvalue + fminusi[i]) * ih * ih * 0.25; instruc->phi2[i] = phi2; for (j=0; jhf[j], 2.0/3.0); jh = 1.0/hj; phi2 = (fppi[idx+j] - fpmi[j*nparms+i] - fpmi[i*nparms+j] + fmmi[idx+j]) * ih * jh * 0.25; instruc->hessian[idx + j] = phi2; } } free(fmmi); free(fpmi); free(fppi); free(fplusi); return instruc; } void estoptint(SEXP fn, SEXP rho, double *epsacc, double *optint, int nparms, int ndiffs, int pflag, double *invals, double (*func)(SEXP fn, SEXP rho, double *X, long nvars, short MinMax, short BoundaryEnforcement, double **Domains), short MinMax, short BoundaryEnforcement, double **Domains) { double *wrk; int i,j,k; // int nsteps=1+2*ndiffs, nrows=nparms*nsteps, ncols=ndiffs+1; int nsteps=1+2*ndiffs; double h, beta, dwrk; double **table; struct estints *estructure; wrk = (double *) malloc(nparms*(ndiffs+1)*sizeof(double)); h = 0.0000002; table = eaccuracy(fn, rho, nparms, ndiffs, h, invals, wrk, func, MinMax, BoundaryEnforcement, Domains); for (i=0; i= EPS */ epsacc[i] = (dwrk > EPS ? dwrk : EPS) ; } #ifdef NEVERDEFINED Rprintf("accuracy estimates:\n"); for (i=0; ierrors[i]); Rprintf(" %17.10e", estructure->hf[i]); Rprintf(" %17.10e", estructure->phi[i]); Rprintf(" %17.10e", estructure->phic[i]); Rprintf(" %17.10e", estructure->phi2[i]); Rprintf(" %17.10e", estructure->ef[i]); Rprintf("\n"); } } /* put estimates for optimal interval into optint */ for (i=0; ihf[i]; } free(table); free(wrk); /* free the estructure */ free(estructure->errors); free(estructure->hf); free(estructure->phi); free(estructure->phic); free(estructure->phi2); free(estructure->ef); free(estructure); } void dohessians(SEXP fn, SEXP rho, double *epsacc, int nparms, int nobs, int ndiffs, double *invals, double (*func)(SEXP fn, SEXP rho, double *X, long nvars, short MinMax, short BoundaryEnforcment, double **Domains), double (*funco)(double *, double *), short MinMax, short BoundaryEnforcement, double **Domains) { double *wrk; int i,j; // int nsteps=1+2*ndiffs, nrows=nparms*nsteps, ncols=ndiffs+1; // int nsteps=1+2*ndiffs; struct estints *estructure; // double *opg; wrk = (double *) malloc(nparms*(ndiffs+1)*sizeof(double)); estructure = algfd(fn, rho, nparms, epsacc, invals, wrk, func, MinMax, BoundaryEnforcement, Domains); #ifdef NEVERDEFINED /* numerical hessian, using forward differences for off-diagonal elements */ numhessian(estructure, invals, wrk, func); Rprintf("numerical hessian, forward differences:\n"); for (i=0; iphi2[i] / 2.0); else if (i>j) Rprintf(" %19.12e", estructure->hessian[(i*(i-1))/2 + j] / 2.0); else if (j>i) Rprintf(" %19.12e", estructure->hessian[(j*(j-1))/2 + i] / 2.0); } Rprintf("\n"); } /* fflush(stdout); */ #endif /* numerical hessian, using central differences */ numhessianc(fn, rho, estructure, invals, wrk, func, MinMax, BoundaryEnforcement, Domains); Rprintf("numerical hessian, central differences:\n"); for (i=0; iphi2[i] / 2.0); else if (i>j) Rprintf(" %19.12e", estructure->hessian[(i*(i-1))/2 + j] / 2.0); else if (j>i) Rprintf(" %19.12e", estructure->hessian[(j*(j-1))/2 + i] / 2.0); } Rprintf("\n"); } /* fflush(stdout); */ #ifdef NEVERDEFINED /* numerical outer product of gradients, using central differences */ if (funco != NULL) { opg = numopgc(nparms, nobs, invals, opg, wrk, funco); Rprintf("numerical outer product of gradients, central differences:\n"); for (i=0; i Jasjeet Singh Sekhon UC Berkeley http://sekhon.polisci.berkeley.edu May 6, 2013 */ #include "genoud.h" extern "C" { double genoud_optim(SEXP fn_optim, SEXP rho, double *X, long parameters); } /********************************************************************************/ /* */ /* FUNCTION NAME : oper1() */ /* Uniform Mutation */ /* */ /* SYNOPSIS : void oper1(parent,domains,nvars) */ /* */ /* DESCRIPTION : This function returns a new vector generated */ /* from the parent vector, after applying */ /* the operator, uniform mutation. */ /* */ /********************************************************************************/ void oper1(VECTOR parent, double **domains, int nvars) /* VECTOR parent; The parent vector*/ { int comp; double llim,ulim;/*Lower and Upper limits of the value to be mutated*/ FLAG SAME; double tmp; long count; count=0; SAME=TRUE; while (SAME==TRUE) { count++; comp = irange_ran(1,nvars); /*Finding the lower and upper limits between which the values are to be mutated*/ find_range(&llim,&ulim,comp,domains,nvars,parent); /*Find a random value between the lower and the upper limits, to substitute*/ /*for the old value*/ tmp = frange_ran(llim,ulim); if ( parent[comp] != tmp) SAME=FALSE; else if (count >= MAX_OPER_UNIQUE_TRY) SAME=FALSE; } /* end of while */ parent[comp] = tmp; } /********************************************************************************/ /* */ /* FUNCTION NAME : oper2() */ /* Boundary Mutatation */ /* No Uniqueness checking here */ /* Don't use this oper often! */ /* */ /********************************************************************************/ void oper2(VECTOR parent, double **domains, int nvars) /* VECTOR parent; The parent vector*/ /* MATRIX fin_mat; The final matrix*/ { int comp; double llim,ulim;/*Lower and Upper limits of the value to be mutated*/ FLAG SAME; double tmp; long count; count=0; SAME=TRUE; while (SAME==TRUE) { count++; comp = irange_ran(1,nvars); /*Finding the lower and upper limits between which the values are to be mutated*/ find_range(&llim,&ulim,comp,domains,nvars,parent); /*Replace either the lower limit or the upper limit at random,*/ /*for the old value*/ tmp = (flip() == TAIL) ? llim : ulim; if ( tmp != parent[comp]) SAME=FALSE; else if (count >= MAX_OPER_UNIQUE_TRY) SAME=FALSE; } /* end of while */ parent[comp] = tmp; } /********************************************************************************/ /* */ /* FUNCTION NAME : oper3() */ /* */ /* SYNOPSIS : void oper3(parent,fin_mat,r,c,T,t,B) */ /* */ /********************************************************************************/ void oper3(VECTOR parent, double **domains, int nvars, int T, int t, int B) /* VECTOR parent; */ /* unsigned long T; Total number of generations*/ /* unsigned long t; Current generation number*/ /* int B; */ { int comp; double llim,ulim; FLAG SAME; double tmp; long count; count=0; SAME=TRUE; while (SAME==TRUE) { count++; comp = irange_ran(1,nvars); find_range(&llim,&ulim,comp,domains,nvars,parent); /*From the current value of the component to be mutated, chooose at random*/ /*whether to mutate with a lesser value or a greater value*/ /*Then find a value lesser or greater than the original value from the*/ /*function get_f()*/ tmp = (flip() == TAIL) ? parent[comp]-get_F(T,t,parent[comp]-llim,B) : parent[comp]+get_F(T,t,ulim-parent[comp],B); if ( parent[comp] != tmp) SAME=FALSE; else if (count >= MAX_OPER_UNIQUE_TRY) SAME=FALSE; } /* end of while */ parent[comp] = tmp; } /********************************************************************************/ /* */ /* FUNCTION NAME : oper4() */ /* Polytope Crossover */ /* */ /* */ /********************************************************************************/ void oper4(MATRIX p, int p2use, int nvars) /* int p The parents chosen for crossover */ /* p2use; number of parents (rows) in p */ /* int nvars Length of the parameter vector (cols in p) */ { double *A, sum; int i,k; A = (double *) malloc((p2use+1)*sizeof(double)); sum=0.0; for (k=1; k<=p2use; k++) { do A[k] = frange_ran(0.0,1.0); while (A[k]==0.0); /* insure A[k] is above 0.0 */ sum += A[k]; } sum = 1.0/sum; for (k=1; k<=p2use; k++) { /* rescale A[k] to sum to 1.0 */ A[k] *= sum; } for(i=1; i<=nvars; i++) { sum = p[1][i] * A[1]; for (k=2; k<=p2use; k++) sum += p[k][i] * A[k]; p[1][i] = sum; } free(A); } /* end of oper4 */ #ifdef NEVERDEFINED /* This is the arithmetic crossover operator */ void oper4(VECTOR p1, VECTOR p2, int nvars) /* VECTOR p1,p2; The two parents chosen for crossover*/ /* int nvars; Length of the vector*/ { double **child; long i; double A; FLAG SAME; long count, tcount; child = JaMatrixAllocate(3, nvars+1); count=0; SAME=TRUE; while (SAME==TRUE) { count++; do A = frange_ran(0.0,1.0); while (A==0); /* insure A is above 0 */ for(i=1; i<=nvars; i++) { child[1][i] = p1[i] * A + p2[i] * (1.0-A); child[2][i] = p2[i] * A + p1[i] * (1.0-A); } if (count >= MAX_OPER_UNIQUE_TRY) { SAME=FALSE; break; } /* Are the two new individuals unique? */ tcount=0; for (i=1; i<=nvars; i++) { if ( (int) child[1][i] != (int) p1[i] ) tcount++; if ( (int) child[2][i] != (int) p2[i] ) tcount++; } /* end of i loop */ if (tcount==(nvars*2)) SAME=FALSE; } /* end of while */ for(i=1; i<=nvars; i++) { p1[i] = child[1][i]; p2[i] = child[2][i]; } JaMatrixFree(child, 3); } /* end of oper4() */ #endif /********************************************************************************/ /* */ /* FUNCTION NAME : oper5() */ /* Simple Crossover */ /* */ /********************************************************************************/ void oper5(VECTOR p1, VECTOR p2, int STEP, double **domains, int nvars) /* VECTOR p1,p2; *The two parents for crossing over*/ /* int STEP; *Parameter for the crossover*/ { MATRIX child; FLAG BFLAG1 = FALSE,/*Check to see if the newly created vectors satisfies the*/ BFLAG2 = FALSE;/*set of constraints*/ int i,n=1,cut; /* unique check variables */ FLAG SAME; int count, tcount, ccount; child = matrix(1,2,1,nvars); count=0; SAME=TRUE; while (SAME==TRUE) { count++; /*Get a random spot on the vector for crossover*/ cut = irange_ran(1,nvars); /*Copy the parent vectors on to the child vectors*/ for(i=1; i<=cut; i++) { child[1][i] = p1[i]; child[2][i] = p2[i]; } do { /*Cross the two vectors*/ ccount = 0; for(i=cut + 1; i<=nvars; i++) { child[1][i] = p1[i] * (double)n/(double)STEP + p2[i] * (1.0-(double)n/(double)STEP); child[2][i] = p2[i] * (double)n/(double)STEP + p1[i] * (1.0-(double)n/(double)STEP); ccount++; } /*Check to see if they satisfy the constraints*/ BFLAG1 = InBounds(child[1],domains,nvars); BFLAG2 = InBounds(child[2],domains,nvars); n++; /*If the constraints not satisfied, then generate another*/ /*set of crossed over values*/ }while((n<=STEP) && ((BFLAG1 == FALSE) || (BFLAG2 == FALSE))); /* Are the two new individuals unique? */ if (count >= MAX_OPER_UNIQUE_TRY) { SAME=FALSE; break; } tcount=0; for (i=cut+1; i<=nvars; i++) { if ( child[1][i] != p1[i] ) tcount++; if ( child[2][i] != p2[i] ) tcount++; } /* end of i loop */ if (tcount>=(ccount*2)) SAME=FALSE; } /* end of while (SAME==TRUE) */ if (BFLAG1==TRUE && BFLAG2==TRUE) { for(i=1; i<=nvars; i++) { p1[i] = child[1][i]; p2[i] = child[2][i]; } } free_matrix(child,1,2,1); } /********************************************************************************/ /* */ /* FUNCTION NAME : oper6() */ /* Whole Non-Uniform Mutation */ /* */ /********************************************************************************/ void oper6(VECTOR parent, double **domains, int nvars, int T, int t, int B) /* VECTOR parent; MATRIX fin_mat; unsigned long T; Total number of generations unsigned long t; Current generation number int B; */ { int i; double llim,ulim; /* unique check variables */ FLAG SAME; long count; double tmp=0; count=0; SAME=TRUE; while (SAME==TRUE) { for (i=1; i<=nvars; i++) { count++; find_range(&llim,&ulim,i,domains,nvars,parent); /*From the current value of the component to be mutated, chooose at random*/ /*whether to mutate with a lesser value or a greater value*/ /*Then find a value lesser or greater than the original value from the*/ /*function get_f()*/ tmp = (flip() == TAIL) ? parent[i]-get_F(T,t,parent[i]-llim,B) : parent[i]+get_F(T,t,ulim-parent[i],B); if ( parent[i] != tmp) SAME=FALSE; else if (count >= MAX_OPER_UNIQUE_TRY) SAME=FALSE; parent[i] = tmp; }//end of for loop } // end of while loop }//oper6 /********************************************************************************/ /* */ /* FUNCTION NAME : oper7() */ /* Heuristic Crossover */ /* */ /********************************************************************************/ void oper7(VECTOR p1, VECTOR p2, double **domains, int nvars) { VECTOR child; FLAG BFLAG = FALSE;/*Check to see if the newly created vector satisfies the*/ /*set of constraints*/ int i,n=2,tries=MAX_OPER_UNIQUE_TRY; double A; /* unique check variables */ FLAG SAME; long count; child = Gvector(1,nvars); count=0; SAME=TRUE; while (SAME==TRUE) { count++; do { A = frange_ran(0.0,1.0); for(i=1; i<=nvars; i++) child[i] = ( A * (p2[i] - p1[i]) + p2[i] ); /*Check to see if it satisfies the constraints*/ BFLAG = InBounds(child,domains,nvars); n++; /*If the constraints not satisfied, then try again */ } while((n<=tries) && (BFLAG == FALSE)); /* Is the new individual unique? */ if (count >= MAX_OPER_UNIQUE_TRY) { SAME=FALSE; break; } for (i=1; i<=nvars; i++) { if ( child[i] != p1[i] ) { SAME=FALSE; break; } } } /* end of while SAME loop */ if (BFLAG==TRUE) { for(i=1; i<=nvars; i++) p1[i] = child[i]; } free_vector(child,1); } /* end of oper7() */ /********************************************************************************/ /* */ /* FUNCTION NAME : find_range() */ /* */ /* SYNOPSIS : void find_range(llim,ulim,domains,nvars, */ /* parent */ /* */ /* DESCRIPTION : This function finds the upper and lower */ /* limits, within which the mutation should */ /* occur. */ /* */ /********************************************************************************/ void find_range(double *llim, double *ulim, int comp, double **domains, int nvars, VECTOR parent) /* double *llim,*ulim; Upper and lower limits*/ /* int comp; Component of the vector to be mutated*/ /* VECTOR parent; The vector with the values of the variables*/ { double A, B; A = frange_ran(0.0,1.0); B = 1.0 - A; *llim = (A*domains[comp][1]) + B* parent[comp]; A = frange_ran(0.0,1.0); B = 1.0 - A; *ulim = B * parent[comp] + (A*domains[comp][3]); } /********************************************************************************/ /* */ /* FUNCTION NAME : find_rangeInt() */ /* */ /* SYNOPSIS : void find_range(llim,ulim,domains,nvars, */ /* parent */ /* */ /* DESCRIPTION : This function finds the upper and lower */ /* limits, within which the mutation should */ /* occur. */ /* */ /********************************************************************************/ void find_rangeInt(int *llim, int *ulim, int comp, double **domains, int nvars, VECTOR parent) /* int *llim,*ulim; Upper and lower limits*/ /* int comp; Component of the vector to be mutated*/ /* VECTOR parent; The vector with the values of the variables*/ { double A, B; A = frange_ran(0.0,1.0); B = 1.0 - A; *llim = (int) ( (A*domains[comp][1]) + B* parent[comp]); if( (int) domains[comp][1] > *llim) *llim = (int) domains[comp][1]; A = frange_ran(0.0,1.0); B = 1.0 - A; *ulim = (int) ( B * parent[comp] + (A*domains[comp][3]) ); if( (int) domains[comp][3] < *ulim) *ulim = (int) domains[comp][3]; } /********************************************************************************/ /* */ /* FUNCTION NAME : irange_ran() */ /* */ /* SYNOPSIS : int irange_ran(llim,ulim) */ /* */ /* DESCRIPTION : This function returns a random integer */ /* between the llim and ulim. */ /* */ /********************************************************************************/ int irange_ran(int llim, int ulim) { int num; do num = llim + ((int) ((newrand()*(long)(ulim-llim+1))/(long) 65535)); while ((num < llim) || (num > ulim)); return(num); } /********************************************************************************/ /* */ /* FUNCTION NAME : get_F() */ /* */ /* SYNOPSIS : double get_F(T,t,y,B) */ /* */ /* DESCRIPTION : This function returns the double value which */ /* is the evaluated value of the function, */ /* needed for the operators 3 and 6 */ /* */ /********************************************************************************/ double get_F(int T, int t, double y, int B) /* unsigned long t,T; int B; double y; */ { double factor; factor = (double) pow(1.0 - (double)t/(double)T,(double)B); factor = factor * frange_ran(0.0,1.0); if (factor < 0.00001) factor = 0.00001; return(y * factor); } /********************************************************************************/ /* */ /* FUNCTION NAME : oper8() */ /* Local-Minimum Crossover: bfgs */ /* */ /* SYNOPSIS : void oper8(parent,fin_mat,rc) */ /* */ /* DESCRIPTION : This function returns a new vector generated */ /* from the parent vector, after applying */ /* the operator, BFGS. */ /* */ /* */ /* CALLING FUNCITONS : optimization() */ /* */ /********************************************************************************/ void oper8(SEXP fn_optim, SEXP rho, VECTOR parent, MATRIX domains, double SolutionTolerance, long nvars, short BoundaryEnforcement, short PrintLevel, double mix) { double *parm, *work; long i, j, btest; double bfgsfit; double A, B; parm = (double *) malloc((nvars+1)*sizeof(double)); work = (double *) malloc((nvars+1)*sizeof(double)); if( mix < 0) { A = frange_ran(0.0,1.0); } else { A = mix; } B = 1.0 - A; for (i=0; i work[i]) || (work[i] > domains[i][3]) ; /* shrink point until all parameters are in bounds */ if (btest) { if(PrintLevel > 1) { Rprintf("NOTE: killing out-of-bounds individual created by bfgs oper(9). fit:%10.8lf\n",bfgsfit); Rprintf("NOTE: oper(9) Parameter: %d \t Value: %e\n\n", i, work[i]); } warning("killed out-of-bounds individual created by bfgs oper(9)"); } } if (btest==0) break; A *= 0.5 ; B = 1.0 - A; } if (j<20) { /* leave parent unchanged if not in boundary after 20 halvings */ for (i=1; i<=nvars; i++) { parent[i] = work[i]; } } } free(work); free(parm); return ; } /********************************************************************************/ /* Integer Operators! */ /* */ /********************************************************************************/ /********************************************************************************/ /* */ /* FUNCTION NAME : JaIntegerOper1() */ /* Uniform Mutation */ /* */ /* SYNOPSIS : void oper1(parent,fin_mat,rc) */ /* */ /* DESCRIPTION : This function returns a new vector generated */ /* from the parent vector, after applying */ /* the operator, uniform mutation. */ /* */ /********************************************************************************/ void JaIntegerOper1(VECTOR parent, double **domains, int nvars) /* VECTOR parent; The parent vector*/ /* MATRIX fin_mat; The final matrix*/ /* INDEX rc; Row and column of the final matrix*/ { long comp; int llim,ulim;/*Lower and Upper limits of the value to be mutated*/ FLAG SAME; int tmp; long count; count=0; SAME=TRUE; while (SAME==TRUE) { count++; comp = irange_ran(1,nvars); /*Finding the lower and upper limits between which the values are to be mutated*/ find_rangeInt(&llim,&ulim,comp,domains,nvars,parent); /*Find a random value between the lower and the upper limits, to substitute*/ /*for the old value*/ tmp = irange_ran(llim,ulim); if ( (int) parent[comp] != (int) tmp) SAME=FALSE; else if (count >= MAX_OPER_UNIQUE_TRY) SAME=FALSE; } /* end of while */ parent[comp] = (int) tmp; } /********************************************************************************/ /* */ /* FUNCTION NAME : JaIntegerOper2() */ /* Boundary Mutatation */ /* No Uniqueness checking here */ /* Don't use this oper often! */ /* */ /********************************************************************************/ void JaIntegerOper2(VECTOR parent, double **domains, int nvars) /* VECTOR parent; The parent vector*/ /* MATRIX fin_mat; The final matrix*/ /* INDEX rc; Row and column of the final matrix*/ { int comp; int llim,ulim;/*Lower and Upper limits of the value to be mutated*/ FLAG SAME; int tmp; long count; count=0; SAME=TRUE; while (SAME==TRUE) { count++; comp = irange_ran(1,nvars); /*Finding the lower and upper limits between which the values are to be mutated*/ find_rangeInt(&llim,&ulim,comp,domains,nvars,parent); /*Replace either the lower limit or the upper limit at random,*/ /*for the old value*/ tmp = (int) (flip() == TAIL) ? llim : ulim; if ( (int) tmp != (int) parent[comp]) SAME=FALSE; else if (count >= MAX_OPER_UNIQUE_TRY) SAME=FALSE; } /* end of while */ parent[comp] = (int) tmp; } /********************************************************************************/ /* */ /* FUNCTION NAME : JaIntegeroper3() */ /* Non-Uniform Mutation */ /* */ /* SYNOPSIS : VECTOR oper3(parent,fin_mat,r,c,T,t,B) */ /* */ /* DESCRIPTION : This function returns a new vector generated */ /* from the parent vector, after applying */ /* the operator, non-uniform mutation. */ /* */ /********************************************************************************/ void JaIntegerOper3(VECTOR parent, double **domains, int nvars, int T, int t, int B) /* VECTOR parent; MATRIX fin_mat; INDEX rc; */ /* unsigned long T; Total number of generations*/ /* unsigned long t; Current generation number*/ /* int B; */ { int comp; int llim,ulim; FLAG SAME; int tmp; long count; count=0; SAME=TRUE; while (SAME==TRUE) { count++; comp = irange_ran(1,nvars); find_rangeInt(&llim,&ulim,comp,domains,nvars,parent); /*From the current value of the component to be mutated, chooose at random*/ /*whether to mutate with a lesser value or a greater value*/ /*Then find a value lesser or greater than the original value from the*/ /*function get_f()*/ tmp = (int) (flip() == TAIL) ? parent[comp]-get_F(T,t,parent[comp]-llim,B) : parent[comp]+get_F(T,t,ulim-parent[comp],B); if ( (int) parent[comp] != (int) tmp) SAME=FALSE; else if (count >= MAX_OPER_UNIQUE_TRY) SAME=FALSE; } /* end of while */ parent[comp] = (int) tmp; } /********************************************************************************/ /* */ /* FUNCTION NAME : JaIntegeroper4() */ /* Polytope Crossover */ /* */ /* */ /********************************************************************************/ void JaIntegeroper4(MATRIX p, int p2use, int nvars, double **domains) /* int p The parents chosen for crossover */ /* p2use; number of parents (rows) in p */ /* int nvars Length of the parameter vector (cols in p) */ { double *A, sum; int i,k; A = (double *) malloc((p2use+1)*sizeof(double)); sum=0.0; for (k=1; k<=p2use; k++) { do A[k] = frange_ran(0.0,1.0); while (A[k]==0.0); /* insure A[k] is above 0.0 */ sum += A[k]; } sum = 1.0/sum; for (k=1; k<=p2use; k++) { /* rescale A[k] to sum to 1.0 */ A[k] *= sum; } for(i=1; i<=nvars; i++) { sum = p[1][i] * A[1]; for (k=2; k<=p2use; k++) sum += p[k][i] * A[k]; p[1][i] = (int) sum; if( (int) domains[i][1] > (int) p[1][i]) p[1][i] = (int) domains[i][1]; if( (int) domains[i][3] < (int) p[1][i]) p[1][i] = (int) domains[i][3]; } free(A); } #ifdef NEVERDEFINED void JaIntegerOper4(VECTOR p1, VECTOR p2, int nvars) /* VECTOR p1,p2; The two parents chosen for crossover*/ /* int nvars; Length of the vector*/ { double **child; long i; double A; FLAG SAME; long count, tcount; child = JaMatrixAllocate(3, nvars+1); count=0; SAME=TRUE; while (SAME==TRUE) { count++; do A = frange_ran(0.0,1.0); while (A==0); /* insure A is above 0 */ for(i=1; i<=nvars; i++) { child[1][i] = ( p1[i] * A + p2[i] * (1.0-A) ); child[2][i] = ( p2[i] * A + p1[i] * (1.0-A) ); } if (count >= MAX_OPER_UNIQUE_TRY) { SAME=FALSE; break; } /* Are the two new individuals unique? */ tcount=0; for (i=1; i<=nvars; i++) { if ( (int) child[1][i] != (int) p1[i] ) tcount++; if ( (int) child[2][i] != (int) p2[i] ) tcount++; } /* end of i loop */ if (tcount==(nvars*2)) SAME=FALSE; } /* end of SAME while */ for(i=1; i<=nvars; i++) { p1[i] = (int) child[1][i]; p2[i] = (int) child[2][i]; } JaMatrixFree(child, 3); } /* end of JaIntegerOper4 */ #endif /********************************************************************************/ /* */ /* FUNCTION NAME : JaIntegerOper5() */ /* Simple Crossover */ /* */ /* SYNOPSIS : void oper5(p1,p2,STEP,rc,fin_mat,X,x2) */ /* */ /* DESCRIPTION : This function returns two new vectors */ /* generated after simple arithmetical */ /* crossover, from the two parent vectors. */ /* */ /********************************************************************************/ void JaIntegerOper5(VECTOR p1, VECTOR p2, int STEP, double **domains, int nvars) /* VECTOR p1,p2; *The two parents for crossing over*/ /* INDEX rc; *Row and column of the final matrix*/ /* MATRIX fin_mat; *The final matrix*/ /* int STEP; *Parameter for the crossover*/ { MATRIX child; FLAG BFLAG1 = FALSE,/*Check to see if the newly created vectors satisfies the*/ BFLAG2 = FALSE;/*set of constraints*/ int i,n=1,cut; /* unique check variables */ FLAG SAME; int count, tcount, ccount; child = matrix(1,2,1,nvars); count=0; SAME=TRUE; while (SAME==TRUE) { count++; /*Get a random spot on the vector for crossover*/ cut = irange_ran(1,nvars); /*Copy the parent vectors on to the child vectors*/ for(i=1; i<=cut; i++) { child[1][i] = p1[i]; child[2][i] = p2[i]; } do { /*Cross the two vectors*/ ccount = 0; for(i=cut + 1; i<=nvars; i++) { child[1][i] = p1[i] * (double)n/(double)STEP + p2[i] * (1.0-(double)n/(double)STEP); child[2][i] = p2[i] * (double)n/(double)STEP + p1[i] * (1.0-(double)n/(double)STEP); ccount++; } /*Check to see if they satisfy the constraints*/ BFLAG1 = InBounds(child[1],domains,nvars); BFLAG2 = InBounds(child[2],domains,nvars); n++; /*If the constraints not satisfied, then generate another*/ /*set of crossed over values*/ }while((n<=STEP) && ((BFLAG1 == FALSE) || (BFLAG2 == FALSE))); /* Are the two new individuals unique? */ if (count >= MAX_OPER_UNIQUE_TRY) { SAME=FALSE; break; } tcount=0; for (i=cut+1; i<=nvars; i++) { if ( (int) child[1][i] != (int) p1[i] ) tcount++; if ( (int) child[2][i] != (int) p2[i] ) tcount++; } /* end of i loop */ if (tcount>=(ccount*2)) SAME=FALSE; } /* end of while (SAME==TRUE); */ if (BFLAG1==TRUE && BFLAG2==TRUE) { for(i=1; i<=nvars; i++) { p1[i] = (int) child[1][i]; p2[i] = (int) child[2][i]; } } free_matrix(child,1,2,1); } /********************************************************************************/ /* */ /* FUNCTION NAME : JaIntegerOper6() */ /* Whole Non-Uniform Mutation */ /* */ /********************************************************************************/ void JaIntegerOper6(VECTOR parent, double **domains, int nvars, int T, int t, int B) /* VECTOR parent; unsigned long T; Total number of generations unsigned long t; Current generation number int B; */ { int i; int llim,ulim; /* unique check variables */ FLAG SAME; long count; int tmp; count=0; SAME=TRUE; while (SAME==TRUE) { for (i=1; i<=nvars; i++) { count++; find_rangeInt(&llim,&ulim,i,domains,nvars,parent); /*From the current value of the component to be mutated, chooose at random*/ /*whether to mutate with a lesser value or a greater value*/ /*Then find a value lesser or greater than the original value from the*/ /*function get_f()*/ tmp = (int) (flip() == TAIL) ? parent[i]-get_F(T,t,parent[i]-llim,B) : parent[i]+get_F(T,t,ulim-parent[i],B); if ( (int) parent[i] != (int) tmp) SAME=FALSE; else if (count >= MAX_OPER_UNIQUE_TRY) SAME=FALSE; parent[i] = (int) tmp; }//end of for loop } // end of while loop }//oper6 /********************************************************************************/ /* */ /* FUNCTION NAME : JaIntegerOper7() */ /* Heuristic Crossover */ /* */ /********************************************************************************/ void JaIntegerOper7(VECTOR p1, VECTOR p2, double **domains, int nvars) { VECTOR child; FLAG BFLAG = FALSE;/*Check to see if the newly created vector satisfies the*/ /*set of constraints*/ int i,n=2,tries=MAX_OPER_UNIQUE_TRY; double A; /* unique check variables */ FLAG SAME; long count; child = Gvector(1,nvars); count=0; SAME=TRUE; while (SAME==TRUE) { count++; do { A = frange_ran(0.0,1.0); for(i=1; i<=nvars; i++) child[i] = (int) ( A * (p2[i] - p1[i]) + p2[i] ); /*Check to see if it satisfies the constraints*/ BFLAG = InBounds(child,domains,nvars); n++; /*If the constraints not satisfied, then try again */ } while((n<=tries) && (BFLAG == FALSE)); /* Is the new individual unique? */ if (count >= MAX_OPER_UNIQUE_TRY) { SAME=FALSE; break; } for (i=1; i<=nvars; i++) { if ( (int) child[i] != (int) p1[i] ) { SAME=FALSE; break; } } } /* end of while SAME loop */ if (BFLAG==TRUE) { for(i=1; i<=nvars; i++) p1[i] = (int) child[i]; } free_vector(child,1); } /* end of JaIntegerOper7() */ /********************************************************************************/ /* */ /* FUNCTION NAME : InBounds(child, domains, nvars) */ /* */ /* DESCRIPTION : This function returns TRUE or FALSE depending*/ /* on whether the vector passed satisfies all */ /* the constraints or not. */ /* */ /********************************************************************************/ FLAG InBounds(VECTOR child, double **domains, int nvars) /* VECTOR child; The vector to be checked for violation of constriants*/ { int i; for(i=1; i<=nvars; i++) { if( (child[i] < domains[i][1]) || (child[i] > domains[i][3]) ) return(FALSE); } return(TRUE); } rgenoud/src/multiply.cpp0000644000176200001440000001115712553042713015076 0ustar liggesusers/* RGENOUD Walter R. Mebane, Jr. Cornell University http://macht.arts.cornell.edu/wrm1 Jasjeet Singh Sekhon UC Berkeley http://sekhon.polisci.berkeley.edu $Header: /home/jsekhon/xchg/genoud/rgenoud.distribution/sources/RCS/multiply.cpp,v 2.15 2005/10/29 06:14:44 jsekhon Exp jsekhon $ */ #include "genoud.h" /********************************************************************************/ /* */ /* FUNCTION NAME : mmprod() */ /* */ /* SYNOPSIS : void mmprod(m,nm,n,mul_cm,mul_am,mul_bm) */ /* */ /* DESCRIPTION : This function finds the product of two */ /* double matrices */ /* */ /* FUNCTIONS CALLED : None */ /* */ /* CALLING FUNCITONS : find_org_in_eq(), */ /* main(). */ /* */ /* */ /* REV DATE BY DESCRIPTION */ /* --- ---- -- ----------- */ /* */ /* */ /********************************************************************************/ void mmprod(int m, int nm, int n, MATRIX mul_cm, MATRIX mul_am, MATRIX mul_bm) /* int m, row of mul_am matrix nm, column of mul_am and row of mul_bm matrices n; row of mul_bm matrix MATRIX mul_cm, the final matrix mul_am, the first matrix to be multiplied mul_bm; the second matrix to be multiplied */ { int i,j,k; /*counter variables, where i=m, j=nm, k=n*/ for(i= 1; i<=m; i++) for(j = 1; j<=n; j++) { mul_cm[i][j] = 0.0; for (k= 1;k # # Jasjeet Singh Sekhon # UC Berkeley # http://sekhon.berkeley.edu # # genoud <- function(fn, nvars, max=FALSE, pop.size=1000, max.generations=100, wait.generations=10, hard.generation.limit=TRUE, starting.values=NULL, MemoryMatrix=TRUE, Domains=NULL, default.domains=10, solution.tolerance=0.001, gr=NULL, boundary.enforcement=0, lexical=FALSE, gradient.check=TRUE, BFGS=TRUE, data.type.int=FALSE, hessian=FALSE, unif.seed=812821, int.seed=53058, print.level=2, share.type=0, instance.number=0, output.path="stdout", output.append=FALSE, project.path=NULL, P1=50, P2=50, P3=50, P4=50, P5=50, P6=50, P7=50, P8=50, P9=0, P9mix=NULL, BFGSburnin=0, BFGSfn=NULL, BFGShelp = NULL, control = list(), optim.method=ifelse(boundary.enforcement < 2, "BFGS", "L-BFGS-B"), transform=FALSE, debug=FALSE, cluster=FALSE, balance=FALSE, ...) { if (transform!=FALSE & transform!=TRUE) { warning("'transform' must be TRUE or FALSE. Setting to FALSE") transform <- FALSE } if(transform) { return(do.call(what = genoud_transform, args = as.list(match.call())[-1], quote = FALSE, envir = parent.frame())) } if(!is.null(BFGShelp) && !is.function(BFGShelp)) stop("'BFGShelp' must be NULL or a function") #These used to be option. From >5.7-3, they are no longer available #because R CMD check complains about calls to 'stdout' if (output.path!="stdout") { output.path <- "stdout" warning("'output.path' can no longer be changed. Please use 'sink'. Option is only provided for backward compatibility of the API.") } if(output.append!=FALSE) { output.append <- FALSE warning("'output.append' can no longer be changed. Please use 'sink'. Option is only provided for backward compatibility of the API.") } if(!is.null(P9mix) && !is.double(P9mix)) { stop("'P9mix' must be NULL or a number between 0 and 1") } else { if(is.null(P9mix)) { P9mix <- -1 } else { if(! ( (1 >= P9mix) && (P9mix > 0) )) stop("'P9mix' must be NULL or a number between 0 and 1 (it may be equal to 1)") } } if( (BFGSburnin < 0) & !gradient.check ) { warning("If 'BFGSburnin' is negative, gradient.check must be TRUE for 'BFGSburnin' to have any effect.") } if(!is.list(control)) stop("'control' must be a list, see ?optim") g.scale <- control$fnscale if(!is.null(g.scale)) { if(g.scale > 0 & max) { stop("positive control$fnscale is inconsistent with maximization") } else if(g.scale < 0 & !max) { stop("negative control$fnscale is inconsistent with minimization") } else if(g.scale == 0) { stop("optim divides the function value by control$fnscale ", "setting control$fnscale to zero is therefore impossible") } FiniteBadFitValue <- ifelse(max, -.Machine$double.xmax, .Machine$double.xmax) } else { # NULL g.scale if (max == FALSE) { g.scale <- 1 FiniteBadFitValue <- .Machine$double.xmax } else { g.scale <- -1 FiniteBadFitValue <- -.Machine$double.xmax } } control$fnscale <- g.scale if(!lexical & !is.null(BFGSfn)) { stop("'BFGSfn' can only be provided with lexical optimization or when 'transform=TRUE'") } if (!is.null(BFGSfn) & BFGS==FALSE) { if (!is.function(BFGSfn)) stop("IF 'BFGSfn' is not a function, it must be NULL") warning("setting BFGS==TRUE because 'BFGSfn' is not null") BFGS <- TRUE } fn1 <- function(par) { fit <- fn(par, ...) if(is.null(fit)) fit <- FiniteBadFitValue if(length(fit)==1) if(!is.finite(fit)) fit <- FiniteBadFitValue return(fit) }#end of fn1 if(!is.null(BFGShelp)) { if (!is.null(gr)) { gr1 <- function(par, helper = do.call(BFGShelp, args = list(initial = par, done = TRUE))) { gr(par, helper, ...) } } else gr1 <- NULL } else { if (!is.null(gr)) { gr1 <- function(par) gr(par, ...) } else gr1 <- NULL } #setpath to tempdir if(is.null(project.path)) { project.path <- file.path(tempdir(), "genoud.pro") } #do we have stating values? if (is.null(starting.values)) { nStartingValues <- 0; } else if(is.matrix(starting.values)) { if(any(dim(starting.values) == nvars)) { if(nrow(starting.values) == nvars & ncol(starting.values) !=nvars) starting.values <- t(starting.values) nStartingValues <- nrow(starting.values) if(nStartingValues > pop.size) { warning("increasing 'pop.size' because too many starting.values were provided") pop.size <- nStartingValues } } else { warning("ignoring 'starting.values' because the wrong number of parameters was provided") nStartingValues <- 0 } } else if(is.numeric(starting.values) | is.logical(starting.values)) { nStartingValues <- 1; if(length(starting.values)!=nvars) { nStartingValues <- 0 warning("Ignoring 'starting.values' because length(staring.values)!=nvars") } else starting.values <- matrix(starting.values, nrow = 1) } else stop("starting.values must be NULL, a vector, or a matrix") #set output.type if (output.path=="stdout") { output.type <- 0; } else { if (output.append) { output.type <- 2; } else { output.type <- 1; } } # let's create the Domains if none have been passed. if (!(is.matrix(Domains))) { Domains <- matrix(nrow=nvars, ncol=2); for (i in 1:nvars) { Domains[i,1] <- -1*default.domains; Domains[i,2] <- default.domains; } # end of for loop } else if(nrow(Domains) != nvars) { stop("number of rows in Domains must match 'nvars'") } else if(ncol(Domains) != 2) { stop("number of cols in Domains must be 2") } if(!all(Domains[,1] <= Domains[,2])) { stop("Domains[,1] must be less than or equal to Domains[,2]") } if(any(Domains[,1] == Domains[,2])) { warning("some Domains[,1]==Domains[,2]") } # BG: now check all starting values are sane if(nStartingValues > 0 && any(is.na(starting.values))) { stop("Some starting values are NA") } if(nStartingValues > 0 && boundary.enforcement != 0 && !all(apply(starting.values, 1, FUN = function(x) Domains[,1] <= x & x <= Domains[,2])) ) warning("'starting.values' which are outside of the bounds have been provided. Continuing, but unexpected behavior can occur with 'boundary.enforcement!=0'") # has the user provided any seeds? if (unif.seed==812821 && int.seed==53058) provide.seeds <- FALSE else provide.seeds <- TRUE; #if lexical==TRUE we need to know how many items will be returned if (lexical < 0) { warning("lexical < 0. Resetting to FALSE\n") lexical <- 0 } if (lexical>=1) { #creating visible binding for variable "indx"; although it is #actually defined in fnLexicalSort() via an eval and paste if (!exists("indx")) { indx <- NULL; rm(indx) } if(share.type > 0) { warning("'share.type' being set to 0 because of lexical optimization") share.type <- 0 } if(nStartingValues) { foo <- fn1(starting.values[1,]) } else { rfoo <- stats::runif(nrow(Domains), Domains[,1], Domains[,2]) if(data.type.int) rfoo <- as.integer(round(rfoo)) foo <- fn1(rfoo) } foo.length <- length(as.vector(foo)) if(lexical > 1 && foo.length != lexical) { warning(paste("Function returns a vector of length", foo.length, "\nbut you specified lexical =", lexical)) } if(foo.length == 1) { lexical <- 0 warning("you specified lexical = TRUE but the function returns a scalar") } else lexical <- foo.length } else foo.length <- 1 if (lexical > 0) { if(is.null(BFGSfn)) { #All derivative stuff is turned off if we are going to do lexical if BFGSfn is not provided BFGS=FALSE gradient.check=FALSE if(hessian) { warning("'hessian' being set to false because of lexical optimization. See 'BFGSfn' for workaround") hessian=FALSE } P9 = 0 } else { if(!is.null(BFGShelp)) { fn1.bfgs <- function(par, helper = do.call(BFGShelp, args = list(initial = par, done = TRUE), envir = environment(fn))) { fit <- BFGSfn(par, helper, ...) if(is.null(fit)) fit <- FiniteBadFitValue if(length(fit)==1) if(!is.finite(fit)) fit <- FiniteBadFitValue return(fit) }#end of fn1.bfgs } else { fn1.bfgs <- function(par) { fit <- BFGSfn(par, ...) if(is.null(fit)) fit <- FiniteBadFitValue if(length(fit)==1) if(!is.finite(fit)) fit <- FiniteBadFitValue return(fit) }#end of fn1.bfgs } # end else if(is.null(gr)) { gr <- function(par, helper = NA, ...) { gr.fn1.bfgs <- function(par, helper, FBFV) { fit <- if(is.null(BFGShelp)) BFGSfn(par, ...) else BFGSfn(par, helper, ...) if(is.null(fit)) fit <- FBFV if(length(fit)==1) if(!is.finite(fit)) fit <- FBFV return(fit) } # end of gr.fn1.bfgs genoud.wrapper101.env <- new.env() assign("x", par, envir = genoud.wrapper101.env) assign("helper", helper, envir = genoud.wrapper101.env) assign("FiniteBadFitValue", FiniteBadFitValue, envir = genoud.wrapper101.env) foo <- as.double(attr(stats::numericDeriv(quote(gr.fn1.bfgs(x, helper, FiniteBadFitValue)), theta=c("x"), genoud.wrapper101.env), "gradient")) return(foo) } #end of gr gr1 <- if(is.null(BFGShelp)) function(par, ...) gr(par) else function(par, helper = do.call(BFGShelp, args = list(initial = par, done = TRUE), envir = environment(fn))) { gr(par, helper, ...) } # end of gr1 } # end of if(!is.null(gr)) gr1func <- gr1 }# end of else }#if lexical > 0 if (lexical==0) lexical <- 1 #optim st if(is.null(BFGSfn)) { if(optim.method != "L-BFGS-B") { genoud.optim.wrapper101 <- function(foo.vals) { ret <- stats::optim(foo.vals, fn=fn1, gr=gr1, method=optim.method, control=control); return(c(ret$value,ret$par)); } # end of genoud.optim.wrapper101 } else { genoud.optim.wrapper101 <- function(foo.vals) { ret <- stats::optim(foo.vals, fn=fn1, gr=gr1, method="L-BFGS-B", lower = Domains[,1], upper = Domains[,2], control=control); return(c(ret$value,ret$par)); } # end of genoud.optim.wrapper101 } } else { if(optim.method != "L-BFGS-B") { genoud.optim.wrapper101 <- function(foo.vals) { if(print.level > 2) { fit <- fn1(foo.vals) cat("\nPre-BFGS Complete Lexical Fit:\n") print(fit) } if(is.null(BFGShelp)) { ret <- stats::optim(foo.vals, fn=fn1.bfgs, gr=gr1, method=optim.method, control=control); } else { ret <- stats::optim(foo.vals, fn=fn1.bfgs, gr=gr1, method=optim.method, control=control, helper = do.call(BFGShelp, args = list(initial = foo.vals), envir = environment(fn)) ); } if(print.level > 2) { cat("BFGS Fit:",ret$value,"\n") fit <- fn1(ret$par) cat("Post-BFGS Complete Lexical Fit:\n") print(fit) } foo <- c(ret$value,ret$par) return(foo); } # end of genoud.optim.wrapper101 } else { # "L-BFGS-B" genoud.optim.wrapper101 <- function(foo.vals) { if(print.level > 2) { fit <- fn1(foo.vals) cat("\nPre-BFGS Complete Lexical Fit:\n") print(fit) } if(is.null(BFGShelp)) { ret <- stats::optim(foo.vals, fn=fn1.bfgs, gr=gr1, method="L-BFGS-B", lower = Domains[,1], upper = Domains[,2], control=control); } else { ret <- stats::optim(foo.vals, fn=fn1.bfgs, gr=gr1, method="L-BFGS-B", lower = Domains[,1], upper = Domains[,2], control=control, helper = do.call(BFGShelp, args = list(initial = foo.vals), envir = environment(fn)) ); } if(print.level > 2) { cat("BFGS Fit:",ret$value,"\n") fit <- fn1(ret$par) cat("Post-BFGS Complete Lexical Fit:\n") print(fit) } foo <- c(ret$value,ret$par) return(foo); } # end of genoud.optim.wrapper101 } } # create the P vector P <- vector(length=9, mode="numeric"); P[1] <- P1; P[2] <- P2; P[3] <- P3; P[4] <- P4; P[5] <- P5; P[6] <- P6; P[7] <- P7; P[8] <- P8; P[9] <- P9; clustertrigger=1 if (is.logical(cluster)) { if (cluster==FALSE) { clustertrigger=0 } else { stop("cluster option must be either FALSE, an object of the 'cluster' class (from the 'parallel' package) or a list of machines so 'genoud' can create such an object") } } if(clustertrigger) { parallel.exists = requireNamespace("parallel") if (!parallel.exists) { stop("The 'cluster' feature cannot be used unless the package 'parallel' can be loaded.") } } if(clustertrigger) { if(!MemoryMatrix) { MemoryMatrix = TRUE warning("MemoryMatrix has been set to 'TRUE' because the cluster option has been requested.") } GENclusterExport <- function (cl, list) { gets <- function(n, v) { assign(n, v) NULL } for (name in list) { parallel::clusterCall(cl, gets, name, get(name)) } } ExpandDots <- function(...) { return(match.call()) } dots <- ExpandDots(...) if ( (length(dots) > 1) & balance==TRUE) { balance <- FALSE warning("load balancing has been turned off because the function to be optimized requires extra arguments") } if (class(cluster)[1]=="SOCKcluster" | class(cluster)[1]=="PVMcluster" | class(cluster)[1]=="spawnedMPIcluster" | class(cluster)[1]=="MPIcluster") { clustertrigger=1 cl <- cluster GENclusterExport(cl, "fn") GENclusterExport(cl, "fn1") } else { clustertrigger=2 cluster <- as.vector(cluster) cat("Initializing Cluster\n") cl <- parallel::makePSOCKcluster(cluster) GENclusterExport(cl, "fn") GENclusterExport(cl, "fn1") } if (length(cl) < 2 ) { stop("You only have one node. You probably should not be using the cluster option") } } fnLexicalSort <- function(mat, parms) { # parms = (1) MinMax, (2) nvars, (3) lexical_end, (4) type (0, vars, 1, obj) decreasing=FALSE if(parms[1]==1) decreasing=TRUE if(parms[4]==0) { #on nvars not on obj function foo = "indx <- order(" for(i in (2:(parms[2]+1)) ) { foo = paste(foo,"mat[,",i,"], ",sep="") } foo = paste(foo,"mat[,",parms[2]+2,"], ",sep="") foo = paste(foo,"decreasing=FALSE)",sep="") eval(parse(text=foo)) mat = mat[indx,] } else { #lexical on obj function foo = "indx <- order(mat[,1], " for(i in (parms[2]+3):parms[3] ) { foo = paste(foo,"mat[,",i,"], ",sep="") } foo = paste(foo,"decreasing=",decreasing,")",sep="") eval(parse(text=foo)) mat = mat[indx,] } return(mat) } fnMemoryMatrixEvaluate <- function(Memory, population, parms) { EVALUATE = -93813381 MinMax = parms[1] nvars = parms[2] lexical = parms[3] lexical.end = ncol(population) pop.size = nrow(population) vars.indx <- 2:(nvars+1) lexical.indx <- c(1,(nvars+3):lexical.end) FIRSTTIME = TRUE if (nrow(Memory) > 1) FIRSTTIME = FALSE nevaluate = 0 mfunc <- function(pop,memory) { f <- function(...) paste(..., sep=":") a2 <- do.call("f", as.data.frame(pop)) b2 <- do.call("f", as.data.frame(memory)) return(match(a2,b2)) } population.mat = matrix(population[,vars.indx], ncol=nvars) if (!FIRSTTIME) { Memory.mat = matrix(Memory[,vars.indx], ncol=nvars) match.matrix.indx <- mfunc(population.mat,Memory.mat) for (i in 1:pop.size) { match.indx = match.matrix.indx[i] found.match <- FALSE if ( is.finite(match.indx) ) { #this is needed because mfunc truncates floats (by the call to paste) to 15 digits # if (all(population.mat[i,]==Memory.mat[match.indx,])) # { found.match <- TRUE population[i,] <- Memory[match.indx,] # } } if(!found.match) { if (population[i,nvars+2] != 0) { population[i,nvars+2] = EVALUATE nevaluate = nevaluate+1 } } } } else { for (i in 1:pop.size) { population[i,nvars+2] = EVALUATE nevaluate = nevaluate+1 } } #evaluation loop if (nevaluate > 0) { eval.indx <- population[,nvars+2]==EVALUATE ret=0 if (clustertrigger==0) { in.mat = matrix(population.mat[eval.indx,], ncol=nvars) ret <- matrix(t(apply(in.mat, 1, fn1)), ncol=lexical) } else { if (balance==TRUE) { in.mat = t(matrix(population.mat[eval.indx,], ncol=nvars)) cl.in <- as.list(as.data.frame(in.mat)) cl.out <- parallel::clusterApplyLB(cl, cl.in, fn1) try(ret <- matrix(t(data.frame(cl.out)), ncol=lexical), TRUE) if (!is.matrix(ret)) { if (!debug) { stop("Cluster returned an object which could not be turned into a data.frame. Cluster may be in bad state. Please consider restarting it. To see what the cluster returned please turn on the 'debug' option.") } else { cat("Cluster returned an object which could not be turned into a data.frame:\n") print(cl.out) stop("Cluster may be in bad state. Please consider restarting it.") } } } else { in.mat = matrix(population.mat[eval.indx,], ncol=nvars) if(length(cl) > 1 ) { cl.out = parallel::parRapply(cl, in.mat, fn1) } else { stop("You only have one node. Cluster option should not be used") } try(ret <- matrix(cl.out, byrow=TRUE, ncol=lexical), TRUE) if (!is.matrix(ret)) { if (!debug) { stop("Cluster returned an object which could not be turned into a data.frame. Cluster may be in bad state. Please consider restarting it. To see what the cluster returned please turn on the 'debug' option.") } else { cat("Cluster returned an object which could not be turned into a data.frame:\n") print(cl.out) stop("Cluster may be in bad state. Please consider restarting it.") } } } } # else clustertrigger==0 if (lexical < 2) { population[eval.indx,1] = ret[,1] } else { population[eval.indx,lexical.indx] = ret } population[eval.indx,nvars+2] = 0 if(!FIRSTTIME) { Memory = rbind(Memory,population[eval.indx,]) } else { Memory = matrix(population[eval.indx,], ncol=lexical.end) FIRSTTIME = FALSE } }#end of nevaluate if (lexical > 1) { population <- fnLexicalSort(population, c(MinMax,nvars,lexical.end,1)) } else { if (MinMax==0) { population <- population[order(population[,1]),] } else { population <- population[order(population[,1], decreasing=TRUE),] } } return(as.vector(c(nrow(Memory), Memory, population))) } #end of fnMemoryMatrixEvaluate if (!is.null(gr)) { UserGradient = TRUE gr1func <- gr1 } else { UserGradient = FALSE gr1func <- function() {} } if(data.type.int) { BFGS = FALSE gradient.check=FALSE } if(is.matrix(starting.values)) starting.values <- t(starting.values) #C++ code checks if at least Generation 0 has been run and if #print.level>0 and project.path!="/dev/null". Otherwise, 'interrupted' #remains FALSE interrupted <- FALSE interrupt.message <- paste("genoud interrupted:\none may recover the best solution found so far by executing") interrupt.expression <- paste("pop <- read.table('",project.path, "', comment.char = 'G')", sep = "") interrupt.expression2 <- "best <- pop[pop$V1 == 1,, drop = FALSE]" interrupt.expression3 <- paste("very.best <- as.matrix(best[nrow(best), ", foo.length + 2, ":ncol(best)])", sep = "") on.exit(if(interrupted) cat(interrupt.message, "\n", interrupt.expression, "\n", interrupt.expression2, "\n", interrupt.expression3, "\n")) gout <- .Call("rgenoud", as.function(fn1), new.env(), as.integer(nvars), as.integer(pop.size), as.integer(max.generations), as.integer(wait.generations), as.integer(nStartingValues), as.double(starting.values), as.vector(P), as.matrix(Domains), as.integer(max), as.integer(gradient.check), as.integer(boundary.enforcement), as.double(solution.tolerance), as.integer(BFGS), as.integer(data.type.int), as.integer(provide.seeds), as.integer(unif.seed), as.integer(int.seed), as.integer(print.level), as.integer(share.type), as.integer(instance.number), as.integer(MemoryMatrix), as.integer(debug), as.character(output.path), as.integer(output.type), as.character(project.path), as.integer(hard.generation.limit), as.function(genoud.optim.wrapper101), as.integer(lexical), as.function(fnLexicalSort), as.function(fnMemoryMatrixEvaluate), as.integer(UserGradient), as.function(gr1func), as.double(P9mix), as.integer(BFGSburnin), as.integer(transform), PACKAGE="rgenoud"); indx1 <- 4; indx2 <- (indx1+lexical-1); value=gout[indx1:indx2]; indx1 <- indx2+1 indx2 <- indx1+nvars-1 par = gout[indx1:indx2] indx1 <- indx2+1 indx2 <- indx1+nvars-1 if(!gradient.check & !BFGS ) { gradients= gout[indx1:indx2] gradients = rep(NA, length(gradients)) } else { gradients = gout[indx1:indx2] } indx1 <- indx2+1 indx2 <- indx1+8 operators=gout[indx1:indx2] if (hessian==TRUE) { con <- list(trace = 0, fnscale = g.scale, parscale = rep.int(1, length(par)), ndeps = rep.int(0.001, length(par)), maxit = 100, abstol = -Inf, reltol = sqrt(.Machine$double.eps), alpha = 1, beta = 0.5, gamma = 2, REPORT = 10, type = 1, lmm = 5, factr = 1e+07, pgtol = 0, tmax = 10, temp = 10) nm <- names(gout[5:(nvars+4)]) if(lexical == 1) { hess.fn <- function(par) fn1(par, ...) hess <- stats::optimHess(par=gout[5:(nvars+4)], fn=fn1, gr=gr1, control=con) } else { help.stuff <- do.call(BFGShelp, args = list(initial = gout[5:(nvars+4)], done = TRUE), envir = environment(fn)) hess.fn <- function(par, helper = help.stuff) fn1.bfgs(par, helper, ...) hess <- stats::optimHess(par=gout[5:(nvars+4)], fn=hess.fn, gr=NULL, control=con) } hes <- 0.5 * (hess + t(hess)) if (!is.null(nm)) dimnames(hes) <- list(nm, nm) ret <- list(value=value, par=par, gradients=gradients, generations=gout[1], peakgeneration=gout[2], popsize=gout[3], operators=operators, hessian=hes) } else { ret <- list(value=value, par=par, gradients=gradients, generations=gout[1], peakgeneration=gout[2], popsize=gout[3], operators=operators) } if (clustertrigger==2) parallel::stopCluster(cl) interrupted <- FALSE return(ret) } #end of genoud() genoud_transform <- function(fn, nvars, max=FALSE, pop.size=1000, max.generations=100, wait.generations=10, hard.generation.limit=TRUE, starting.values=NULL, MemoryMatrix=TRUE, Domains=NULL, default.domains=10, solution.tolerance=0.001, gr=NULL, boundary.enforcement=0, lexical=FALSE, gradient.check=TRUE, BFGS=TRUE, data.type.int=FALSE, hessian=FALSE, unif.seed=812821, int.seed=53058, print.level=2, share.type=0, instance.number=0, output.path="stdout", output.append=FALSE, project.path=NULL, P1=50, P2=50, P3=50, P4=50, P5=50, P6=50, P7=50, P8=50, P9=0, P9mix=NULL, BFGSburnin=0, BFGSfn=NULL, BFGShelp = NULL, control = list(), optim.method=ifelse(boundary.enforcement < 2, "BFGS", "L-BFGS-B"), transform=FALSE, debug=FALSE, cluster=FALSE, balance=FALSE, ...) { #wrapper for the transform option. beta changes should go here as well if(data.type.int) stop("transform option cannot be used when 'data.type.int=TRUE'") if(MemoryMatrix) warning("setting MemoryMatrix to FALSE") MemoryMatrix <- FALSE if(!identical(cluster, FALSE)) warning("setting cluster to FALSE") cluster <- FALSE if(!is.null(BFGShelp) && !is.function(BFGShelp)) stop("'BFGShelp' must be NULL or a function") #creating visible binding for variable "indx"; although it is #actually defined in fnLexicalSort() via an eval and paste if (!exists("indx")) { indx <- NULL; rm(indx) } if(!is.null(P9mix) && !is.double(P9mix)) { stop("'P9mix' must be NULL or a number between 0 and 1") } else { if(is.null(P9mix)) { P9mix <- -1 } else { if(! ( (1 >= P9mix) && (P9mix > 0) )) stop("'P9mix' must be NULL or a number between 0 and 1 (it may be equal to 1)") } } if( (BFGSburnin < 0) & !gradient.check ) { warning("If 'BFGSburnin' is negative, gradient.check must be TRUE for 'BFGSburnin' to have any effect.") } if(!is.list(control)) stop("'control' must be a list, see ?optim") g.scale <- control$fnscale if(!is.null(g.scale)) { if(g.scale > 0 & max) { stop("positive control$fnscale is inconsistent with maximization") } else if(g.scale < 0 & !max) { stop("negative control$fnscale is inconsistent with minimization") } else if(g.scale == 0) { stop("optim divides the function value by control$fnscale ", "setting control$fnscale to zero is therefore impossible") } FiniteBadFitValue <- ifelse(max, -.Machine$double.xmax, .Machine$double.xmax) } else { # NULL g.scale if (max == FALSE) { g.scale <- 1 FiniteBadFitValue <- .Machine$double.xmax } else { g.scale <- -1 FiniteBadFitValue <- -.Machine$double.xmax } } control$fnscale <- g.scale ## BFGSfn can (and probably should) be provided if transform = TRUE # if(!lexical & !is.null(BFGSfn)) # { # stop("'BFGSfn' can only be provided with lexical optimization or when 'transform=TRUE'") # } if (!is.null(BFGSfn) & BFGS==FALSE) { if (!is.function(BFGSfn)) stop("IF 'BFGSfn' is not a function, it must be NULL") warning("setting BFGS==TRUE because 'BFGSfn' is not null") BFGS <- TRUE } fn1 <- function(par) { fit <- fn(par, ...) if(!is.finite(fit[1])) fit[1] <- FiniteBadFitValue ## only catch [1] return(fit) } if(!is.null(BFGShelp)) { if (!is.null(gr)) { gr1 <- function(par, helper = do.call(BFGShelp, args = list(initial = par, done = TRUE))) { gr(par, helper, ...) } } else gr1 <- NULL } else { if (!is.null(gr)) { gr1 <- function(par) gr(par, ...) } else gr1 <- NULL } #setpath to tempdir if(is.null(project.path)) { project.path <- file.path(tempdir(), "genoud.pro") } #do we have stating values? if (is.null(starting.values)) { nStartingValues <- 0; } else if(is.matrix(starting.values)) { if(any(dim(starting.values) == nvars)) { if(nrow(starting.values) == nvars & ncol(starting.values) !=nvars) starting.values <- t(starting.values) nStartingValues <- nrow(starting.values) if(nStartingValues > pop.size) { warning("increasing 'pop.size' because too many starting.values were provided") pop.size <- nStartingValues } } else { warning("ignoring 'starting.values' because the wrong number of parameters was provided") nStartingValues <- 0 } } else if(is.numeric(starting.values) | is.logical(starting.values)) { nStartingValues <- 1; if(length(starting.values)!=nvars) { nStartingValues <- 0 warning("Ignoring 'starting.values' because length(staring.values)!=nvars") } else starting.values <- matrix(starting.values, nrow = 1) } else stop("starting.values must be NULL, a vector, or a matrix") #set output.type if (output.path=="stdout") { output.type <- 0; } else { if (output.append) { output.type <- 2; } else { output.type <- 1; } } # let's create the Domains if none have been passed. if (!(is.matrix(Domains))) { Domains <- matrix(nrow=nvars, ncol=2); for (i in 1:nvars) { Domains[i,1] <- -1*default.domains; Domains[i,2] <- default.domains; } # end of for loop } else if(nrow(Domains) != nvars) { stop("number of rows in Domains must match 'nvars'") } else if(ncol(Domains) != 2) { stop("number of cols in Domains must be 2") } if(!all(Domains[,1] <= Domains[,2])) { stop("Domains[,1] must be less than or equal to Domains[,2]") } if(any(Domains[,1] == Domains[,2])) { warning("some Domains[,1]==Domains[,2]") } # BG: now check all starting values are sane if(nStartingValues > 0 && any(is.na(starting.values))) { stop("Some starting values are NA") } if(nStartingValues > 0 && boundary.enforcement != 0 && !all(apply(starting.values, 1, FUN = function(x) Domains[,1] <= x & x <= Domains[,2])) ) warning("'starting.values' which are outside of the bounds have been provided. Continuing, but unexpected behavior can occur with 'boundary.enforcement!=0'") # has the user provided any seeds? if (unif.seed==812821 && int.seed==53058) provide.seeds <- FALSE else provide.seeds <- TRUE; # we need to know how many items will be returned bf fn() if(nStartingValues) { foo <- fn1(starting.values[1,]) } else { rfoo <- stats::runif(nrow(Domains), Domains[,1], Domains[,2]) foo <- fn1(rfoo) } foo.length <- length(c(foo)) if(foo.length <= nvars) stop("'fn' must return criteria and all transformed parameters") lexical <- foo.length - nvars ## it is possible that lexical == 1 or lexical > 1 if (lexical >= 1) ## always TRUE { if(share.type > 0) { warning("'share.type' being set to 0 because of 'transform' option") share.type <- 0 } if(is.null(BFGSfn)) { #All derivative stuff is turned off if BFGSfn is not provided BFGS <- FALSE gradient.check <- FALSE if(hessian) { warning("'hessian' being set to false because of lexical optimization. See 'BFGSfn' for workaround") hessian <- FALSE } P9 = 0 } else { if(!is.null(BFGShelp)) { fn1.bfgs <- function(par, helper = do.call(BFGShelp, args = list(initial = par, done = TRUE), envir = environment(fn))) { fit <- BFGSfn(par, helper, ...) if(is.null(fit)) fit <- FiniteBadFitValue if(length(fit)==1) if(!is.finite(fit)) fit <- FiniteBadFitValue return(fit) }#end of fn1.bfgs } else { fn1.bfgs <- function(par) { fit <- BFGSfn(par, ...) if(is.null(fit)) fit <- FiniteBadFitValue if(length(fit)==1) if(!is.finite(fit)) fit <- FiniteBadFitValue return(fit) }#end of fn1.bfgs } # end else if(is.null(gr)) { ## should we do numerical gradients when transform = TRUE? gr <- function(par, helper = NA, ...) { gr.fn1.bfgs <- function(par, helper, FBFV) { fit <- if(is.null(BFGShelp)) BFGSfn(par, ...) else BFGSfn(par, helper, ...) if(is.null(fit)) fit <- FBFV if(length(fit)==1) if(!is.finite(fit)) fit <- FBFV return(fit) } # end of gr.fn1.bfgs genoud.wrapper101.env <- new.env() assign("x", par, envir = genoud.wrapper101.env) assign("helper", helper, envir = genoud.wrapper101.env) assign("FiniteBadFitValue", FiniteBadFitValue, envir = genoud.wrapper101.env) foo <- as.double(attr(stats::numericDeriv(quote(gr.fn1.bfgs(x, helper, FiniteBadFitValue)), theta=c("x"), genoud.wrapper101.env), "gradient")) return(foo) } #end of gr gr1 <- if(is.null(BFGShelp)) function(par, ...) gr(par) else function(par, helper = do.call(BFGShelp, args = list(initial = par, done = TRUE), envir = environment(fn))) { gr(par, helper, ...) } # end of gr1 } # end of if(!is.null(gr)) gr1func <- gr1 }# end of else }#if lexical > 1 #optim st if(is.null(BFGSfn)) { if(optim.method != "L-BFGS-B") { genoud.optim.wrapper101 <- function(foo.vals) { ret <- stats::optim(foo.vals, fn=fn1, gr=gr1, method=optim.method, control=control); return(c(ret$value,ret$par)); } # end of genoud.optim.wrapper101 } else { genoud.optim.wrapper101 <- function(foo.vals) { ret <- stats::optim(foo.vals, fn=fn1, gr=gr1, method="L-BFGS-B", lower = Domains[,1], upper = Domains[,2], control=control); return(c(ret$value,ret$par)); } # end of genoud.optim.wrapper101 } } else { if(optim.method != "L-BFGS-B") { genoud.optim.wrapper101 <- function(foo.vals) { if(print.level > 2) { fit <- fn1(foo.vals) cat("\nPre-BFGS Complete Lexical Fit:\n") print(fit) } if(is.null(BFGShelp)) { ret <- stats::optim(foo.vals, fn=fn1.bfgs, gr=gr1, method=optim.method, control=control); } else { ret <- stats::optim(foo.vals, fn=fn1.bfgs, gr=gr1, method=optim.method, control=control, helper = do.call(BFGShelp, args = list(initial = foo.vals), envir = environment(fn)) ); } if(print.level > 2) { cat("BFGS Fit:",ret$value,"\n") fit <- fn1(ret$par) cat("Post-BFGS Complete Lexical Fit:\n") print(fit) } foo <- c(ret$value,ret$par) return(foo); } # end of genoud.optim.wrapper101 } else { # "L-BFGS-B" genoud.optim.wrapper101 <- function(foo.vals) { if(print.level > 2) { fit <- fn1(foo.vals) cat("\nPre-BFGS Complete Lexical Fit:\n") print(fit) } if(is.null(BFGShelp)) { ret <- stats::optim(foo.vals, fn=fn1.bfgs, gr=gr1, method="L-BFGS-B", lower = Domains[,1], upper = Domains[,2], control=control); } else { ret <- stats::optim(foo.vals, fn=fn1.bfgs, gr=gr1, method="L-BFGS-B", lower = Domains[,1], upper = Domains[,2], control=control, helper = do.call(BFGShelp, args = list(initial = foo.vals), envir = environment(fn)) ); } if(print.level > 2) { cat("BFGS Fit:",ret$value,"\n") fit <- fn1(ret$par) cat("Post-BFGS Complete Lexical Fit:\n") print(fit) } foo <- c(ret$value,ret$par) return(foo); } # end of genoud.optim.wrapper101 } } # create the P vector P <- vector(length=9, mode="numeric"); P[1] <- P1; P[2] <- P2; P[3] <- P3; P[4] <- P4; P[5] <- P5; P[6] <- P6; P[7] <- P7; P[8] <- P8; P[9] <- P9; ## cluster is coerced to FALSE at the top so none of this matters clustertrigger=1 if (is.logical(cluster)) { if (cluster==FALSE) { clustertrigger=0 } else { stop("cluster option must be either FALSE, an object of the 'cluster' class (from the 'parallel' package) or a list of machines so 'genoud' can create such an object") } } if(clustertrigger) { parallel.exists = requireNamespace("parallel") if (!parallel.exists) { stop("The 'cluster' feature cannot be used unless the package 'parallel' can be loaded.") } } if(clustertrigger) { if(!MemoryMatrix) { MemoryMatrix = TRUE warning("MemoryMatrix has been set to 'TRUE' because the cluster option has been requested.") } GENclusterExport <- function (cl, list) { gets <- function(n, v) { assign(n, v) NULL } for (name in list) { parallel::clusterCall(cl, gets, name, get(name)) } } ExpandDots <- function(...) { return(match.call()) } dots <- ExpandDots(...) if ( (length(dots) > 1) & balance==TRUE) { balance <- FALSE warning("load balancing has been turned off because the function to be optimized requires extra arguments") } if (class(cluster)[1]=="SOCKcluster" | class(cluster)[1]=="PVMcluster" | class(cluster)[1]=="spawnedMPIcluster" | class(cluster)[1]=="MPIcluster") { clustertrigger=1 cl <- cluster GENclusterExport(cl, "fn") GENclusterExport(cl, "fn1") } else { clustertrigger=2 cluster <- as.vector(cluster) cat("Initializing Cluster\n") cl <- parallel::makePSOCKcluster(cluster) GENclusterExport(cl, "fn") GENclusterExport(cl, "fn1") } if (length(cl) < 2 ) { stop("You only have one node. You probably should not be using the cluster option") } } fnLexicalSort <- function(mat, parms) { # parms = (1) MinMax, (2) nvars, (3) lexical_end, (4) type (0, vars, 1, obj) decreasing=FALSE if(parms[1]==1) decreasing=TRUE if(parms[4]==0) { #on nvars not on obj function foo = "indx <- order(" for(i in (2:(parms[2]+1)) ) { foo = paste(foo,"mat[,",i,"], ",sep="") } foo = paste(foo,"mat[,",parms[2]+2,"], ",sep="") foo = paste(foo,"decreasing=FALSE)",sep="") eval(parse(text=foo)) mat = mat[indx,] } else { #lexical on obj function foo = "indx <- order(mat[,1], " for(i in (parms[2]+3):parms[3] ) { foo = paste(foo,"mat[,",i,"], ",sep="") } foo = paste(foo,"decreasing=",decreasing,")",sep="") eval(parse(text=foo)) mat = mat[indx,] } return(mat) } fnMemoryMatrixEvaluate <- function(Memory, population, parms) { stop("this function should not be called when transform = TRUE") EVALUATE = -93813381 MinMax = parms[1] nvars = parms[2] lexical = parms[3] lexical.end = ncol(population) pop.size = nrow(population) vars.indx <- 2:(nvars+1) lexical.indx <- c(1,(nvars+3):lexical.end) FIRSTTIME = TRUE if (nrow(Memory) > 1) FIRSTTIME = FALSE nevaluate = 0 mfunc <- function(pop,memory) { f <- function(...) paste(..., sep=":") a2 <- do.call("f", as.data.frame(pop)) b2 <- do.call("f", as.data.frame(memory)) return(match(a2,b2)) } population.mat = matrix(population[,vars.indx], ncol=nvars) if (!FIRSTTIME) { Memory.mat = matrix(Memory[,vars.indx], ncol=nvars) match.matrix.indx <- mfunc(population.mat,Memory.mat) for (i in 1:pop.size) { match.indx = match.matrix.indx[i] found.match <- FALSE if ( is.finite(match.indx) ) { #this is needed because mfunc truncates floats (by the call to paste) to 15 digits # if (all(population.mat[i,]==Memory.mat[match.indx,])) # { found.match <- TRUE population[i,] <- Memory[match.indx,] # } } if(!found.match) { if (population[i,nvars+2] != 0) { population[i,nvars+2] = EVALUATE nevaluate = nevaluate+1 } } } } else { for (i in 1:pop.size) { population[i,nvars+2] = EVALUATE nevaluate = nevaluate+1 } } #evaluation loop if (nevaluate > 0) { eval.indx <- population[,nvars+2]==EVALUATE ret=0 if (clustertrigger==0) { in.mat = matrix(population.mat[eval.indx,], ncol=nvars) ret <- matrix(t(apply(in.mat, 1, fn1)), ncol=lexical) } else { if (balance==TRUE) { in.mat = t(matrix(population.mat[eval.indx,], ncol=nvars)) cl.in <- as.list(as.data.frame(in.mat)) cl.out <- parallel::clusterApplyLB(cl, cl.in, fn1) try(ret <- matrix(t(data.frame(cl.out)), ncol=lexical), TRUE) if (!is.matrix(ret)) { if (!debug) { stop("Cluster returned an object which could not be turned into a data.frame. Cluster may be in bad state. Please consider restarting it. To see what the cluster returned please turn on the 'debug' option.") } else { cat("Cluster returned an object which could not be turned into a data.frame:\n") print(cl.out) stop("Cluster may be in bad state. Please consider restarting it.") } } } else { in.mat = matrix(population.mat[eval.indx,], ncol=nvars) if(length(cl) > 1 ) { cl.out = parallel::parRapply(cl, in.mat, fn1) } else { stop("You only have one node. Cluster option should not be used") } try(ret <- matrix(cl.out, byrow=TRUE, ncol=lexical), TRUE) if (!is.matrix(ret)) { if (!debug) { stop("Cluster returned an object which could not be turned into a data.frame. Cluster may be in bad state. Please consider restarting it. To see what the cluster returned please turn on the 'debug' option.") } else { cat("Cluster returned an object which could not be turned into a data.frame:\n") print(cl.out) stop("Cluster may be in bad state. Please consider restarting it.") } } } } # else clustertrigger==0 if (lexical < 2) { population[eval.indx,1] = ret[,1] } else { population[eval.indx,lexical.indx] = ret } population[eval.indx,nvars+2] = 0 if(!FIRSTTIME) { Memory = rbind(Memory,population[eval.indx,]) } else { Memory = matrix(population[eval.indx,], ncol=lexical.end) FIRSTTIME = FALSE } }#end of nevaluate if (lexical > 1) { population <- fnLexicalSort(population, c(MinMax,nvars,lexical.end,1)) } else { if (MinMax==0) { population <- population[order(population[,1]),] } else { population <- population[order(population[,1], decreasing=TRUE),] } } return(as.vector(c(nrow(Memory), Memory, population))) } #end of fnMemoryMatrixEvaluate if (!is.null(gr)) { UserGradient = TRUE gr1func <- gr1 } else { UserGradient = FALSE gr1func <- function() {} } ## impossible if(data.type.int) { BFGS = FALSE gradient.check=FALSE } if(is.matrix(starting.values)) starting.values <- t(starting.values) #C++ code checks if at least Generation 0 has been run and if #print.level>0 and project.path!="/dev/null". Otherwise, 'interrupted' #remains FALSE interrupted <- FALSE interrupt.message <- paste("genoud interrupted:\none may recover the best solution found so far by executing") interrupt.expression <- paste("pop <- read.table('",project.path, "', comment.char = 'G')", sep = "") interrupt.expression2 <- "best <- pop[pop$V1 == 1,, drop = FALSE]" interrupt.expression3 <- paste("very.best <- as.matrix(best[nrow(best), ", foo.length + 2, ":ncol(best)])", sep = "") on.exit(if(interrupted) cat(interrupt.message, "\n", interrupt.expression, "\n", interrupt.expression2, "\n", interrupt.expression3, "\n")) gout <- .Call("rgenoud", as.function(fn1), new.env(), as.integer(nvars), as.integer(pop.size), as.integer(max.generations), as.integer(wait.generations), as.integer(nStartingValues), as.double(starting.values), as.vector(P), as.matrix(Domains), as.integer(max), as.integer(gradient.check), as.integer(boundary.enforcement), as.double(solution.tolerance), as.integer(BFGS), as.integer(data.type.int), as.integer(provide.seeds), as.integer(unif.seed), as.integer(int.seed), as.integer(print.level), as.integer(share.type), as.integer(instance.number), as.integer(MemoryMatrix), as.integer(debug), as.character(output.path), as.integer(output.type), as.character(project.path), as.integer(hard.generation.limit), as.function(genoud.optim.wrapper101), as.integer(lexical), as.function(fnLexicalSort), as.function(fnMemoryMatrixEvaluate), as.integer(UserGradient), as.function(gr1func), as.double(P9mix), as.integer(BFGSburnin), as.integer(transform), PACKAGE="rgenoud"); indx1 <- 4; indx2 <- (indx1+lexical-1); value=gout[indx1:indx2]; indx1 <- indx2+1 indx2 <- indx1+nvars-1 par = gout[indx1:indx2] indx1 <- indx2+1 indx2 <- indx1+nvars-1 if(!gradient.check & !BFGS ) { gradients= gout[indx1:indx2] gradients = rep(NA, length(gradients)) } else { gradients = gout[indx1:indx2] } indx1 <- indx2+1 indx2 <- indx1+8 operators=gout[indx1:indx2] if (hessian==TRUE) ## only TRUE if BFGSfn is provided { con <- list(trace = 0, fnscale = g.scale, parscale = rep.int(1, length(par)), ndeps = rep.int(0.001, length(par)), maxit = 100, abstol = -Inf, reltol = sqrt(.Machine$double.eps), alpha = 1, beta = 0.5, gamma = 2, REPORT = 10, type = 1, lmm = 5, factr = 1e+07, pgtol = 0, tmax = 10, temp = 10) nm <- names(gout[5:(nvars+4)]) # if(lexical == 1) { # hess.fn <- function(par) fn1(par, ...) # hess <- stats::optimHess(par=gout[5:(nvars+4)], fn=fn1, gr=gr1, control=con) # } # else { help.stuff <- do.call(BFGShelp, args = list(initial = gout[5:(nvars+4)], done = TRUE), envir = environment(fn)) hess.fn <- function(par, helper = help.stuff) fn1.bfgs(par, helper, ...) hess <- stats::optimHess(par=gout[5:(nvars+4)], fn=hess.fn, gr=NULL, control=con) # } hes <- 0.5 * (hess + t(hess)) if (!is.null(nm)) dimnames(hes) <- list(nm, nm) ret <- list(value=value, par=par, gradients=gradients, generations=gout[1], peakgeneration=gout[2], popsize=gout[3], operators=operators, hessian=hes) } else { ret <- list(value=value, par=par, gradients=gradients, generations=gout[1], peakgeneration=gout[2], popsize=gout[3], operators=operators) } if (clustertrigger==2) parallel::stopCluster(cl) interrupted <- FALSE return(ret) } rgenoud/R/zzz.R0000644000176200001440000000253412552557302013110 0ustar liggesusers# RGENOUD # # Walter R. Mebane, Jr. # Cornell University # http://www-personal.umich.edu/~wmebane # # # Jasjeet Singh Sekhon # UC Berkeley # http://sekhon.berkeley.edu # # #.First.lib <- function(lib, pkg) library.dynam("rgenoud", pkg, lib) # use .onLoad instead of .First.lib for use with NAMESPACE and R(>= 1.7.0) .onLoad <- function(lib, pkg) { library.dynam("rgenoud", pkg, lib) }#end of .onLoad .onUnload <- function(libpath) { library.dynam.unload("rgenoud", libpath) } .onAttach <- function( ... ) { rgenoudLib <- dirname(system.file(package = "rgenoud")) version <- utils::packageDescription("rgenoud", lib.loc = rgenoudLib)$Version BuildDate <- utils::packageDescription("rgenoud", lib.loc = rgenoudLib)$Date foo <- paste("## rgenoud (Version ", version, ", Build Date: ", BuildDate, ")\n", "## See http://sekhon.berkeley.edu/rgenoud for additional documentation.\n", "## Please cite software as:\n", "## Walter Mebane, Jr. and Jasjeet S. Sekhon. 2011.\n", "## ``Genetic Optimization Using Derivatives: The rgenoud package for R.''\n", "## Journal of Statistical Software, 42(11): 1-26. \n##\n", sep = "") packageStartupMessage(foo) } rgenoud/vignettes/0000755000176200001440000000000012553042713013727 5ustar liggesusersrgenoud/vignettes/Figures/0000755000176200001440000000000012211655411015327 5ustar liggesusersrgenoud/vignettes/Figures/fig1.pdf0000644000176200001440000002366711762732324016677 0ustar liggesusers%PDF-1.5 % 1 0 obj << /Type /ObjStm /Length 425 /Filter /FlateDecode /N 11 /First 66 >> stream x]k0+޻>=J` l&BLJGwԉVA:}#!! $/"Jdyq@ $ RAH|sy ^5+1Rsiko nRyBGqgg]5TkZ8W1:խy︼8z!nMj F\s uőCе9ֺԝۚHq+ sZW'$jŵOj Z:n^٧Fp!7,[MxŪ>Ptp~ݺ$LPf hd: S2q qZYM"Y5:4qdlߝ^gxƾvt7OLѐV|endstream endobj 13 0 obj << /Subtype /XML /Type /Metadata /Length 1319 >> stream 2012-06-03T12:02:44-07:00 2012-06-03T12:02:44-07:00 UnknownApplication Untitled endstream endobj 14 0 obj << /Filter /FlateDecode /Length 7608 >> stream x|Ku9n;[F]@AcThAõu*6IHjI___y~;՟~ï_֏?Vd}>eԯAُX|LǗ9˳~qUUbH {VҒmrjqHs/k\PvR)9רmQЎYZ) {c3˞YcQy*%FN4F=55vʵfP4 ZdoCe!{(<8O[ikOh^yJT:H 4Ϟ4~V)_%"7c:j9VZTmU5{BBC,5"pm)-z~/rsQoZ>5gh^:=,eLi3JjNh %'}}ԙ3K2/\KPJ~,IYVWKVYU\o9[7r:)5۫'jeΑ֎\A q>e($c`+}o3!st(+ј)nUjhk?:hUe!/dRI!qL) %ʆ;MI;? jeHɻأ^%ZV!.Bb!G"!*-l zQYvzkAg*V=46QtghDÉj1, T1|`LS$ߺJCQaDo9kMc@-lm_m, N_hȲBDЯ!RN) mwQ AbANtgΛ>/{*ztzt#(I| IUˢKZ>/TS룅-ޒ;$ }fO&tkPtYA!蚯 <ƮsSl|}GvCH=)-n¶WiRap,(}o۬kAZK;Eњut{ˆ>5d'g0žxVa 65[ il<jkfG8e.7L68]Vy[kI9Gˠ;mZa_[Eev(ʠP/'tjlyS"RFj2(:֑y48L@PSIPXՒܛ|دd :-ԘS0UN{8|)0/DBa5'i=IRiЇσ߹$8,U8ФY}yȽS2?C`6xVѰ6 kT%iyR!wú&Z6R/Jny?liI/tN?`M]av'~`J|R; j Ծ J7 rOi+gQ5Zv+5M tZIt]-X:wL<}Y۶?tӡ看$∦N]nn(Q7IdZ&8G}J#n{'d iZY(O'ܠ$R֪TZٹ*z:kls,L|Qԩ M+;g+ڥwM 4jy[gfNujivW:+\nPQ76˳84 Jy:MrbS^O-=C?iZWN3Yٲ@i[ҳ&N[^X͝&[vYUuYBkNGjik ݴ608W*kv坲Z:ee=W<h6VH(8z?I~I<$ͱ^;s4t+mTŶ}3`rgh4le=Չt⧕&|+yKml1Ԟ%h̃ɲĦK6vӫ.hyجhvXX˶wYYFjŖM+b>[v33JV-ZYZ';v<'ɿig]N֦dؖ-PZP@[wS-#)tYcN,<(ZV5m^Ҁo&k`[DO^x~glֆzwIҶDc_jvRWnVbsMro=s}Ė&R_g=(TI+*:udWY̞ҴRFmzh95JPVmBԚCɠm͸M".$挢ii2bbt z9a44Zg'MVhgc<] ze=N;185]U*'xޤ  k J%Oק4 :A,lZMcC2qiaE/,&mBj7-,N'5ɽ_(-Z'+*.ZF]`<13an>ͻ;gypgqJɒ`_I)NxJOjWZ]9>V/IDckZ:}w|vr }WsCr®.giUhZD%:5ihTN8(iPNsnKgn>\VtEwOt8gw2uXSI=YCVu?.(SV=iU.{ߋ6?i/oAtZU7Iz7PAe%H7G?‡ѵNC>`yU!9@z,)jQhS<*wNe Z;'}Ѵw9ƃ L+hSWI4(ZԭQmN{zJsQ4Ԫɻ*AAP=//h_lݰwpk4!syL?s nޠF'+w,}*?~lHЙ-m#Hn-T{{fG{t:mb랼㘫nG,|J/k%l/J)4"yyR.-:M5Ӏ/M8sg86]8`5@NX Qtz&1)ُs 0O܄ [ZX& |ţ"C0F\}_ pODRԤuO[\=RϯIۺT\՗Ez =]0MC1><}y_G޴D8ɟgiăƸmLCbDQγaۄFn6*N֊4-7pǶZmIV2u,ent:<礱5Vi#C&b ^4w*0cjs}ΛbvxT>&#['ֳ(]WK@yeEA[z::YTڴdSMto:SS 7 ZK3UIv8HvnV8(ٶI;FLGS*}R g*#ns5k)xd^orILu竬CiH0p,ѩ({vx-[^裳;Ewt/].JwX&:IPիAJ'*c7{W6t.=c nmM4m=KZt M:Os}ZO&p+EdIԤ]r& >-?vj3P:K9RsCTn^|o86wSM ]X2wxxq^.C#~z+@AWێ(F5ʒU J;[Ȕ=mtI<iUFc1˗4 Q !1jotki"oҞ+8@FSu4[֥w8ElmUO.Tm!e}y׮ȌG/lgHahGDKzsksK$A󺌵&z-/jv\M'ϓz18c6=cdxPNut7,iau?:tcDv'K 8WۭvȺuDOZC}%7/@Ѻ;77d[y~ek8^P: ޜt޳_3xA1hq!./{vћ={׍W`s  7:sM>#/>I33tw}O@oA1B7ݸ{܎;A;O; !wxsAwQww Sw܃Txw <|Py>0owf;{w'4w Ko\;wڍK+n|@ݸy߾"wqoTEPq_1+"ÝJN8#0*ā~Ċ8o$<<~cMET w❓ƸnLP%ӌnύ +;]7.q}ܸG߸m7 Υ q{nLQДBs1IAD,.L޹xWB9n8)ToUмg_qVA+z-㰼/EGחv__[5KkKoE2nYЊ^4Gk溼ƶy?_#frn\\Њ^˸9jGkw}qy>2n/hů=V6z1k {c Cq-}U #V8Gsuxi{y}$yz1®= !&a|>]Qv&nO[ը"G OXk}ñ][퓷inPw#;Hb#nq;@F! 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@string{je = "Journal of Econometrics"} @string{jel = "Journal of Economic Literature"} @string{jep = "Journal of Economic Perspectives"} @string{jet = "Journal of Economic Theory"} @string{jmcb= "Journal of Money, Credit, and Banking"} @string{jme = "Journal of Monetary Economics"} @string{jpe = "Journal of Political Economy"} @string{jop = "Journal of Politics"} @string{jrsa= "Journal of the Royal Statistical Society, Series A"} @string{jrssb= "Journal of the Royal Statistical Society, Series B"} @string{lsq = "Legislative Studies Quarterly"} @string{pa = "Political Analysis"} @string{pm = "Political Methodology"} @string{pop = "Perspectives on Politics"} @string{ps = "PS: Political Science and Politics"} @string{qje = "Quarterly Journal of Economics"} @string{c-h = "Chapman \& Hall"} @string{cup = "Cambridge University Press"} @string{cornell.up = "Cornell University Press"} @string{hup = "Harvard University Press"} @string{mit = "MIT Press"} @string(pup = {Princeton University Press}) @string{s-v = "Springer-Verlag"} @string(sup = "Stanford University Press") @string{ucp = "University of California Press"} @string{uchp = "University of Chicago Press"} @string{ump = "University of Michigan Press"} @string{yup = "Yale University Press"} @string{cq = "Congressional Quarterly"} @string{aa = "Ann Arbor"} @string{berk= "Berkeley"} @string{bos = "Boston"} @string{cam = "Cambridge, MA"} @string{camUK = "Cambridge, UK"} @string{chic= "Chicago"} @string{dc = "Washington, D.C."} @string{nh = "New Haven"} @string{nj = "New Jersey"} @string{ny = "New York"} @string{sf = "San Francisco"} @string{st = "Stanford"} @article( abadie2002, author= {Abadie, Alberto}, title= {Bootstrap Tests for Distributional Treatment Effect in Instrumental Variable Models}, journal= jasa, volume=97, number=457, pages= {284--292}, year= 2002 ) @article( AbadieGardeazabal2003, author= {Abadie, Alberto and Javier Gardeazabal}, title= {The Economic Costs of Conflict: a Case-Control Study for the 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Sekhon}, title = {Multivariate and Propensity Score Matching Software with Automated Balance Optimization: The \pkg{Matching} Package for \proglang{R}}, journal = {Journal of Statistical Software}, year = {2011}, note = {Forthcoming}, url = {http://www.jstatsoft.org/} } @Manual{Rcore, title = {R: A Language and Environment for Statistical Computing}, author = {{R Development Core Team}}, organization = {R Foundation for Statistical Computing}, address = {Vienna, Austria}, year = {2009}, note = {{ISBN} 3-900051-07-0}, url = {http://www.R-project.org}, } @Comment LocalWords: apsr booktitle Finifter Zaller NES Iyengar Shanto Brehm @Comment LocalWords: AlvarezBrehm ajps HorvitzThompson Horvitz jasa ny kunsch @Comment LocalWords: MannWhitney Psychometrika Biometrika rubinMI Stefanski @Comment LocalWords: Cantoni Elvezio Ronchetti CarrollPederson Pederson jssrb @Comment LocalWords: copas jrssb sekhon glmRob Probit Fearon Laitin's althaus @Comment LocalWords: Bartels's MebaneSekhon Keisuke Geert ec Allyson Berent @Comment LocalWords: Krosnick Visser Boninger Hausman Kosuke Rosenbaum Bon Ai @Comment LocalWords: Kornhauser Jamieson hersh url huntington Zakaria Fareed @Comment LocalWords: zakaria rustow Dankwart Lipset geddes MacKuen Brunell @Comment LocalWords: BrunellNiNardo DiNardo Reweighting AldrichMcKelvey rubin @Comment LocalWords: McKelvey imbens abadie incollection dominguez nguez jop @Comment LocalWords: Chappell Ordeshook Lupia fishkin Subclassification Jong @Comment LocalWords: CochranRubin BertsimasTsitsiklis Bertsimas Dimitris Yung @Comment LocalWords: Tsitsiklis Kaufmann Quantile Ellipsoidally Galiani Segal @Comment LocalWords: Gertler Schargrodsky GalianiGertlerSchargrodsky Diprete @Comment LocalWords: DipreteEngelhardt Engelhardt herbert Winship Jin PKfit @Comment LocalWords: WinshipMorgan BowersHansen Pharmacokinetics Vinod aer @Comment LocalWords: McCulloughVinod SchacharNalebuff Shachar Nalebuff Hsin @Comment LocalWords: AltmanGillMcDonald Braumoeller Jasjeet ivivc vitro vivo @Comment LocalWords: IVIVC Hainmueller Synth Mebane GENetic @Comment LocalWords: GENOUD DiceOptim Ginsbourger Roustant @Comment LocalWords: Kriging rgenoud/vignettes/rgenoud.Rnw0000644000176200001440000021542711762766337016115 0ustar liggesusers\documentclass[nojss]{jss} \usepackage{amsmath} \usepackage{dcolumn} %%My declarations \newcommand{\hlink}{\htmladdnormallink} \newcommand{\MyPerp}{\perp \! \! \! \perp} \newcommand{\e}{\text{e-}} \newcolumntype{C}{>{$}c<{$}} \newcolumntype{L}{>{$}l<{$}} \newcolumntype{R}{>{$}r<{$}} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% declarations for jss.cls %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %%%%%%%%%%%%%%%%%%%%%%%%%%%%%% %% almost as usual \author{Walter R. Mebane, Jr. \\ University of Michigan \And Jasjeet S. Sekhon \\ UC Berkeley} %% for pretty printing and a nice hypersummary also set: \title{Genetic Optimization Using Derivatives: The \pkg{rgenoud} Package for \proglang{R}} \Plaintitle{Genetic Optimization Using Derivatives: The rgenoud Package for R} \Plainauthor{Walter R. Mebane, Jr., Jasjeet S. Sekhon} %% comma-separated \Shorttitle{\pkg{rgenoud}: Genetic Optimization Using Derivatives in \proglang{R}} %% an abstract and keywords \Abstract{ This introduction to the \proglang{R} package \pkg{rgenoud} is a modified version of \cite{MebaneJr.+Sekhon:2011}, published in the \textit{Journal of Statistical Software}. That version of the introduction contains higher resolution figures. \code{genoud} is an \proglang{R} function that combines evolutionary algorithm methods with a derivative-based (quasi-Newton) method to solve difficult optimization problems. \code{genoud} may also be used for optimization problems for which derivatives do not exist. \code{genoud} solves problems that are nonlinear or perhaps even discontinuous in the parameters of the function to be optimized. When the function to be optimized (for example, a log-likelihood) is nonlinear in the model's parameters, the function will generally not be globally concave and may have irregularities such as saddlepoints or discontinuities. Optimization methods that rely on derivatives of the objective function may be unable to find any optimum at all. Multiple local optima may exist, so that there is no guarantee that a derivative-based method will converge to the global optimum. On the other hand, algorithms that do not use derivative information (such as pure genetic algorithms) are for many problems needlessly poor at local hill climbing. Most statistical problems are regular in a neighborhood of the solution. Therefore, for some portion of the search space, derivative information is useful. The function supports parallel processing on multiple CPUs on a single machine or a cluster of computers.} \Keywords{genetic algorithm, evolutionary program, optimization, parallel computing, \proglang{R}} \Plainkeywords{genetic algorithm, evolutionary program, optimization, parallel computing, R} %% without formatting %% at least one keyword must be supplied %% publication information %% NOTE: This needs to filled out ONLY IF THE PAPER WAS ACCEPTED. %% If it was not (yet) accepted, leave them commented. \Volume{42} \Issue{11} %\Month{September} \Year{2011} \Submitdate{2007-02-11} \Acceptdate{2007-11-21} %% The address of (at least) one author should be given %% in the following format: \Address{ Walter R. Mebane, Jr.\\ % Professor\\ Department of Political Science\\ Department of Statistics\\ University of Michigan\\ Ann Arbor, MI 48109-1045\\ E-mail: \email{wmebane@umich.edu}\\ URL: \url{http://www.umich.edu/~wmebane} \\ [2ex] Jasjeet S. Sekhon\\ Department of Political Science\\ Department of Statistics\\ 210 Barrows Hall \#1950\\ UC Berkeley\\ Berkeley, CA 94720-1950\\ E-mail: \email{sekhon@berkeley.edu}\\ URL: \url{http://sekhon.berkeley.edu} } %% It is also possible to add a telephone and fax number %% before the e-mail in the following format: %% Telephone: +43/1/31336-5053 %% Fax: +43/1/31336-734 %% for those who use Sweave please include the following line (with % symbols): %% need no \usepackage{Sweave.sty} %% end of declarations %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% \graphicspath{{Figures/}} \begin{document} \SweaveOpts{engine=R} %\VignetteIndexEntry{Using genoud} %\VignetteDepends{rgenoud} %\VignetteKeywords{rgenoud} %\VignettePackage{rgenoud} \section{Introduction} We developed the \proglang{R} package \pkg{rgenoud} to solve difficult optimization problems such as often arise when estimating nonlinear statistical models or solving complicated nonlinear, nonsmooth and even discontinuous functions.\footnote{The \pkg{rgenoud} software package is available from the Comprehensive \proglang{R} \citep{Rcore} Archive Network at \url{http://CRAN.R-project.org/package=rgenoud}.} Optimization difficulties often arise when the objective function (for instance, the log-likelihood) is a nonlinear function of the parameters. In such cases the function to be optimized is usually not globally concave. An objective function that is not globally concave may have multiple local optima, saddle points, boundary solutions or discontinuities. While the objective function for a statistical model is often concave in a neighborhood of the optimal solution, that neighborhood is often a small proportion of the parameter space of potential interest, and outside that neighborhood the function may be irregular. In such cases, methods of optimization that depend entirely on derivatives can be unreliable and often are virtually unusable. Newton-Raphson and quasi-Newton methods are among the commonly used optimization methods that rely completely on derivatives. Such methods work well when the function to be optimized is regular and smooth over the domain of parameter values that is of interest, but otherwise the methods often fail \citep{GillMurrayWright1981}. Even in models where such methods can be expected to work most of the time, resampling techniques such as the bootstrap \citep{EfronTibshirani1994} can generate resamples in which derivative-based optimization algorithms encounter severe difficulties. This is unfortunate because the methods most frequently used for optimization in problems of statistical estimation are entirely based on derivatives. The \pkg{rgenoud} package has been used by wide variety of users and developers. More than twelve \proglang{R} packages currently rely upon \pkg{rgenoud} including: \pkg{anchors} \citep[analyzing survey data with anchoring vignettes,][]{Wand+King:2011,WandKingLau2007,KingWand2007}; \pkg{BARD} \citep[automated redistricting,][]{Altman+McDonald:2011}; \pkg{boolean} \citep[boolean binary response models,][]{braumoeller2003,BraumoellerGoodrichKline2006}; \pkg{DiceOptim} \citep[kriging-based optimization for computer experiments,][]{DiceOptim}; \pkg{FAiR} \citep[factor analysis,][]{goodrich.fair}; \pkg{JOP} \citep[simultaneous optimization of multiple responses,][]{JOP}; \pkg{KrigInv} \citep[kriging-based inversion,][]{KrigInv}; \pkg{PKfit} \citep[data analysis in pharmacokinetics,][]{LeeLee2006}; \pkg{Matching} \citep[propensity score and multivariate matching,][]{SekhonMatching,Sekhon:2011}; \pkg{ivivc} \citep[in vitro-in vivo correlation modeling,][]{ivivc}; \pkg{multinomRob} \citep[robust multinomial models,][]{MebaneSekhon.multinomRob,MebaneSekhon2004}; and \pkg{Synth} \citep[synthetic control group method for comparative case studies,][]{AbadieGardeazabal2003,synth2008,Abadie+Diamond+Hainmueller:2011}. We present in Section \ref{sec:examples} an example using benchmark functions taken from \citet{yao.liu.lin1999}, followed by an example motivated by the \code{multinomRob} package. The benchmark suite includes functions that are high-dimensional, discontinuous or that have many local optima. The \code{multinomRob} package robustly estimates overdispersed multinomial regression models and uses \pkg{rgenoud} to solve a least quartile difference (LQD) generalized S-estimator \citep{MebaneSekhon2004}. The LQD is not a smooth function of the regression model parameters. The function is continuous, but the parameter space is finely partitioned by nondifferentiable boundaries. In another paper in this volume, the \pkg{Matching} package and its use of \pkg{rgenoud} are described in detail \citep{Sekhon:2011}. \pkg{Matching} provides functions for multivariate and propensity score matching and for finding optimal covariate balance based on a genetic search algorithm implemented in \pkg{rgenoud}. The search over optimal matches is discontinuous so no derivatives are used.\footnote{The \code{BFGS} option of \code{genoud} is set to \code{FALSE}, and the ninth operator which depends on derivatives is not used.} The search also involves lexical optimization which is a unique feature implemented in \pkg{rgenoud}.\footnote{Lexical optimization is useful when there are multiple fitness criteria; the parameters are chosen so as to maximize fitness values in lexical order---i.e., the second fit criterion is only considered if the parameters have the same fit for the first. See the \code{lexical} option and \citet{Sekhon:2011} for details. All of \code{genoud}'s options are described in the \proglang{R} help file for the function.} % If one wishes to use such a model, %significant optimization difficulties may need to be overcome. For %example, the estimating functions of all of the following models are %not in general globally concave: models with multivariate qualitative %variables, censoring or endogenous switching %\citep{maddala1983,amemiya1985}; linear covariance structures %\citep{bollen1989}; models for durations or transitions with %unobserved heterogeneity \citep{HeckmanSinger1985,lancaster1990}; %quasi-likelihood and extended quasi-likelihood models %\citep{McCullaghNelder1989} and systems based on such models %\citep{FahrmeirTutz1994}; and nonlinear simultaneous equation models %\citep{gallant1987}. For such models, optimization methods driven %entirely by derivatives are often unreliable. For some versions of %some of these models, algorithms such as EM that involve data %augmentation have been successfully applied to produce optimization %problems that derivative-based methods can solve %\citep[e.g.,][197]{lancaster1990}. The \pkg{rgenoud} package implements an updated and extended version of the \proglang{C} program \code{GENOUD} \citep{MebaneSekhon1997} described in \citep{SekhonMebane1998}. The many improvements include among other things the interface with \proglang{R}, which includes the ability to optimize functions written in \proglang{R}, options to optimize both floating point and integer-valued parameters, the ability to optimize loss functions which return multiple fitness values (lexical optimization), the ability to call \code{genoud} recursively, the ability to have the optimizer evaluate fits only for new parameter values, and the ability to use multiple computers, CPUs or cores to perform parallel computations. The \pkg{rgenoud} program combines an evolutionary algorithm with a quasi-Newton method. The quasi-Newton method is the Broyden-Fletcher-Goldfarb-Shanno (BFGS) method \citep[][119]{GillMurrayWright1981} implemented in \proglang{R}'s \code{optim} function. When the BFGS is being used, our program offers the option of using either \pkg{rgenoud}'s built-in numerical derivatives (which are based on code taken from \citealt[][337--344]{GillMurrayWright1981}) or user-supplied analytical derivatives.\footnote{User supplied derivatives may be provides via the \code{gr} option.} Our program can also work without the BFGS, in which case no derivatives are needed and the optimizer will work even when the function is discontinuous. The primary benefit from using derivatives is that the algorithm will then quickly find a local optimum when a current set of trial solution parameter values is in a smooth neighborhood of the local optimum point. Appropriate use of the BFGS can make the algorithm converge to the global optimum much more quickly. But premature or excessive use of the BFGS can prevent convergence to the global optimum.\footnote{The user can control whether \code{genoud} uses the BFGS at all (via the \code{BFGS} option), and if operators that use the BFGS are used (via the \code{P9} option), how often they are used.} As always, it is hazardous to rely on an optimizer's default settings. Our program does not eliminate the need for judgment, testing and patience. As Gill, Murray and Wright observe, ``there is no guaranteed strategy that will resolve every difficulty'' \citep[285]{GillMurrayWright1981}. In this article, we very briefly review the theory of random search algorithms that supports the assertion that \pkg{rgenoud} has a high probability of finding the global optimum when such exists. And we present three examples of how to use the \code{genoud} function: to optimize a simple but fiendish scalar Normal mixture model; to minimize a suite of benchmark functions that have previously been used to test evolutionary programming optimization algorithms; and to optimize a version of the only intermittently differentiable LQD estimator. Additional details on both the theory and performance of \code{genoud} can be found in our article that describes \code{GENOUD} \citep{SekhonMebane1998}. \section{Background on Genetic Optimization} An evolutionary algorithm (EA) uses a collection of heuristic rules to modify a population of trial solutions in such a way that each generation of trial values tends to be, on average, better than its predecessor. The measure for whether one trial solution is better than another is the trial solution's fitness value. In statistical applications, the fitness is a function of the summary statistic being optimized (e.g., the log-likelihood). \pkg{rgenoud} works for cases in which a solution is a vector of floating-point or integer numbers that serve as the parameters of a function to be optimized. The search for a solution proceeds via a set of heuristic rules, or \textit{operators}, each of which acts on one or more trial solutions from the current population to produce one or more trial solutions to be included in the new population. EAs do not require derivatives to exist or the function to be continuous in order find the global optimum. The EA in \pkg{rgenoud} is fundamentally a genetic algorithm (GA) in which the code-strings are vectors of numbers rather than bit strings, and the GA operators take special forms tuned for the floating-point or integer vector representation. A GA uses a set of randomized genetic operators to evolve a finite population of finite code-strings over a series of generations \citep{holland1975,goldberg1989,GrefenstetteBaker1989}. The operators used in GA implementations vary \citep{davis1991,FilhoTreleavenAlippi1994}, but in an analytical sense the basic set of operators can be defined as reproduction, mutation, crossover and inversion. The variation in these operators across different GA implementations reflects the variety of codes best suited for different applications. Reproduction entails selecting a code-string with a probability that increases with the code-string's fitness value. Crossover and inversion use pairs or larger sets of the selected code-strings to create new code-strings. Mutation randomly changes the values of elements of a single selected code-string. Used in suitable combinations, the genetic operators tend to improve average fitness of each successive generation, though there is no guarantee that average fitness will improve between every pair of successive generations. Average fitness may well decline. But theorems exist to prove that parts of the trial solutions that have above average fitness values in the current population are sampled at an exponential rate for inclusion in the subsequent population \citep[][139--140]{holland1975}. Each generation's population contains a biased sample of code-strings, so that a substring's performance in that population is a biased estimate of its average performance over all possible populations \citep{dejong1993,grefenstette1993}. The long-run properties of a GA may be understood by thinking of the GA as a Markov chain. A state of the chain is a code-string population of the size used in the GA. For code-strings of finite length and GA populations of finite size, the state space is finite. If such a GA uses random reproduction and random mutation, all states always have a positive probability of occurring. A finite GA with random reproduction and mutation is therefore approximately a finite and irreducible Markov chain.\footnote{\citet[][372--419]{feller1970} and \citet[][107--142]{billingsley1986} review the relevant properties of Markov chains. The randomness in an actual GA depends on the performance of pseudorandom number generators. This and the limitations of floating point arithmetic mean it is not literally true that an actual GA has a positive probability of reaching any state from any other state, and some states may in fact not be reachable from a given set of initial conditions.} An irreducible, finite Markov chain converges at an exponential rate to a unique stationary distribution \citep[][128]{billingsley1986}. This means that the probability that each population occurs rapidly converges to a constant, positive value. \citet{NixVose1992} and \citet{vose1993} use a Markov chain model to show that in a GA where the probability that each code-string is selected to reproduce is proportional to its observed fitness, the stationary distribution strongly emphasizes populations that contain code-strings that have high fitness values. They show that asymptotic in the population size---i.e., in the limit for a series of GAs with successively larger populations---populations that have suboptimal average fitness have probabilities approaching zero in the stationary distribution, while the probability for the population that has optimal average fitness approaches one. If $k>1$ populations have optimal average fitness, then in the limiting stationary distribution the probability for each approaches $1/k$. The theoretical results of Nix and Vose imply that a GA's success as an optimizer depends on having a sufficiently large population of code-strings. If the GA population is not sufficiently large, then the Markov chain that the GA approximately implements is converging to a stationary distribution in which the probabilities of optimal and suboptimal states are not sharply distinguished. Suboptimal populations can be as likely to occur as optimal ones. If the stationary distribution is not favorable, the run time in terms of generations needed to produce an optimal code-string will be excessive. For all but trivially small state spaces, an unfavorable stationary distribution can easily imply an expected running time in the millions of generations. But if the stationary distribution strongly emphasizes optimal populations, relatively few generations may be needed to find an optimal code-string. In general, the probability of producing an optimum in a fixed number of generations tends to increase with the GA population size. \begin{table} \begin{center} \line(1,0){450} \end{center} \begin{enumerate} \item[\code{P1}] Cloning. Copy $\mathbf{X}_{t}$ into the next generation, $\mathbf{X}_{t+1}$. \item[\code{P2}] Uniform Mutation. At random choose $i\in\mathbf{N}$. Select a value $\tilde{x}_i \sim U(\underline{x}_i, \overline{x}_i)$. Set $X_i=\tilde{x}_i$. \item[\code{P3}] Boundary Mutation. At random choose $i\in\mathbf{N}$. Set either $X_i=\underline{x}_i$ or $X_i=\overline{x}_i$, with probability $1/2$ of using each value. \item[\code{P4}] Non-uniform Mutation. At random choose $i\in\mathbf{N}$. Compute $p = (1-t/T)^B u$, where $t$ is the current generation number, $T$ is the maximum number of generations, $B>0$ is a tuning parameter and $u \sim U(0,1)$. Set either $X_i=(1-p)x_i + p\underline{x}_i$ or $X_i=(1-p)x_i + p\overline{x}_i$, with probability $1/2$ of using each value. \item[\code{P5}] Polytope Crossover. Using $m=\max(2,n)$ vectors $\mathbf{x}$ from the current population and $m$ random numbers $p_j\in(0,1)$ such that $\sum_{j=1}^m p_j = 1$, set $\mathbf{X} = \sum_{j=1}^m p_j \mathbf{x}_j$. \item[\code{P6}] Simple Crossover. Choose a single integer $i$ from $\mathbf{N}$. Using two parameter vectors, $\mathbf{x}$ and $\mathbf{y}$, set $X_i = p x_i + (1-p) y_i$ and $Y_i = p y_i + (1-p) x_i$, where $p\in(0,1)$ is a fixed number. \item[\code{P7}] Whole Non-uniform Mutation. Do non-uniform mutation for all the elements of $\mathbf{X}$. \item[\code{P8}] Heuristic Crossover. Choose $p \sim U(0,1)$. Using two parameter vectors, $\mathbf{x}$ and $\mathbf{y}$, compute $\mathbf{z} = p(\mathbf{x} - \mathbf{y}) + \mathbf{x}$. If $\mathbf{z}$ satisfies all constraints, use it. Otherwise choose another $p$ value and repeat. Set $\mathbf{z}$ equal to the better of $\mathbf{x}$ and $\mathbf{y}$ if a satisfactory mixed $\mathbf{z}$ is not found by a preset number of attempts. In this fashion produce two $\mathbf{z}$ vectors. \item[\code{P9}] Local-minimum Crossover. Choose $p \sim U(0,1)$. Starting with $\mathbf{x}$, run BFGS optimization up to a preset number of iterations to produce $\mathbf{\tilde{x}}$. Compute $\mathbf{z} = p\mathbf{\tilde{x}} + (1-p)\mathbf{x}$. If $\mathbf{z}$ satisfies boundary constraints, use it. Otherwise shrink $p$ by setting $p = p/2$ and recompute $\mathbf{z}$. If a satisfactory $\mathbf{z}$ is not found by a preset number of attempts, return $\mathbf{x}$. This operators is extremely computationally intensive, use sparingly. \end{enumerate} \begin{flushleft} Notation: \\ [2ex] $\mathbf{X} =\begin{bmatrix}X_1,\dots,X_n\end{bmatrix}$ is the vector of $n$ parameters $X_i$. $\underline{x}_i$ is the lower bound and $\overline{x}_i$ is the upper bound on values for $X_i$. $x_i$ is the current value of $X_i$, and $\mathbf{x}$ is the current value of $\mathbf{X}$. $\mathbf{N} = \{1,\dots,n\}$. $p \sim U(0,1)$ means that $p$ is drawn from the uniform distribution on the $[0,1]$ interval. \end{flushleft} \caption{`genoud' Operators. Adapted from \citet{SekhonMebane1998}.} \label{tab:operators} \begin{center} \line(1,0){450} \end{center} \end{table} The evolutionary algorithm in \pkg{rgenoud} uses nine operators that are listed in Table~\ref{tab:operators}. The operators extend and modify a set of operators used in \code{GENOCOP} \citep{MichalewiczSwaminathanLogan1993, Michalewicz1992}. The operators are numbered using syntax matching that used to refer to them by \pkg{rgenoud}. The \textit{cloning} operator simply makes copies of the best trial solution in the current generation (independent of this operator, \pkg{rgenoud} always retains one instance of the best trial solution). The \textit{uniform mutation}, \textit{boundary mutation} and \textit{non-uniform mutation} operators act on a single trial solution. Uniform mutation changes one parameter in the trial solution to a random value uniformly distributed on the domain specified for the parameter. Boundary mutation replaces one parameter with one of the bounds of its domain. Non-uniform mutation shrinks one parameter toward one of the bounds, with the amount of shrinkage decreasing as the generation count approaches the specified maximum number of generations. \textit{Whole non-uniform mutation} does non-uniform mutation for all the parameters in the trial solution. \textit{Heuristic crossover} uses two trial solutions to produce a new trial solution located along a vector that starts at one trial solution and points away from the other one. \textit{Polytope crossover} (inspired by simplex search, \citealt[][94--95]{GillMurrayWright1981}) computes a trial solution that is a convex combination of as many trial solutions as there are parameters. \textit{Simple crossover} computes two trial solutions from two input trial solutions by swapping parameter values between the solutions after splitting the solutions at a randomly selected point. This operator can be especially effective if the ordering of the parameters in each trial solution is consequential. \textit{Local-minimum crossover} computes a new trial solution in two steps: first it does a preset number of BFGS iterations starting from the input trial solution; then it computes a convex combination of the input solutions and the BFGS iterate. \section{Examples} \label{sec:examples} The only function in the \pkg{rgenoud} package is \code{genoud}. The interface of this function is similar to that of the \code{optim} function in \proglang{R}. But the function has many additional arguments that control the behavior of the evolutionary algorithm. \subsection{Asymmetric Double Claw:} Our first example, which we also studied in \citet{SekhonMebane1998}, is a normal mixture called the Asymmetric Double Claw (ADC). We plot the function in Figure~\ref{fig:mixture1}. \begin{figure} \caption{Normal Mixture: Asymmetric Double Claw} \vspace{-.5in} \label{fig:mixture1} \begin{center} \includegraphics{fig1.pdf} \end{center} \vspace{-.7in} \end{figure} Mathematically, this mixture is defined as \begin{eqnarray} \label{eq:adclaw} f_{\mathrm{ADC}} & = \sum_{m=0}^{1} \frac{46}{100} \mathrm{N}\left(2m-1,\frac{2}{3}\right) + \sum_{m=1}^{3} \frac{1}{300} \mathrm{N}\left(\frac{-m}{2},\frac{1}{100}\right) + \sum_{m=1}^{3} \frac{7}{300} \mathrm{N}\left(\frac{m}{2},\frac{7}{100}\right), \end{eqnarray} where N is the normal density. The asymmetric double claw is difficult to maximize because there are many local solutions. There are five local maxima in Figure \ref{fig:mixture1}. Standard derivative-based optimizers would simply climb up the hill closest to the starting value. To optimize this normal mixture we must first create a function for it <>= claw <- function(xx) { x <- xx[1] y <- (0.46*(dnorm(x,-1.0,2.0/3.0) + dnorm(x,1.0,2.0/3.0)) + (1.0/300.0)*(dnorm(x,-0.5,.01) + dnorm(x,-1.0,.01) + dnorm(x,-1.5,.01)) + (7.0/300.0)*(dnorm(x,0.5,.07) + dnorm(x,1.0,.07) + dnorm(x,1.5,.07))) return(y) } @ And we now make a call to \pkg{rgenoud} using this function: <>= library("rgenoud") claw1 <- genoud(claw, nvars=1, max=TRUE, pop.size=3000) @ The first argument of \code{genoud} is the function to be optimized. The first argument of that function must be the vector of parameters over which optimizing is to occur. Generally, the function should return a scalar result.\footnote{The function to be optimized may return a vector if one wishes to do lexical optimization. Please see the \code{lexical} option to \code{genoud}.} The second argument of \code{genoud} in this example (\code{nvars}) is the number of variables the function to be optimized takes. The third argument, \code{max=TRUE}, tells \code{genoud} to maximize the function instead of its default behavior which is to minimize. The fourth option \code{pop.size} controls the most important part of the evolutionary algorithm, the population size. This is the number of individuals \code{genoud} uses to solve the optimization problem. As noted in the theoretical discussion, the theorems related to evolutionary algorithms are asymptotic in the population size so larger is generally better but obviously takes longer. The maximum solution of the double claw density is reliably found by \code{genoud} even using the default value of \code{pop.size=1000}. Reliability does increase as the \code{pop.size} is made larger. Unfortunately, because of the stochastic nature of the algorithm, it is impossible to generally answer the question of what is the best population size to use. Other options determine the maximum number of generations the evolutionary algorithm computes. These options are \code{max.generations}, \code{wait.generations} and \code{hard.generation.limit}. The specified termination point also affects how some of the operators perform: the two non-uniform mutation operators introduce smaller ranges of variation in the trial solutions as the generation count approaches the specified \code{max.generations} value. There are many more options that can be used to fine-tune the behavior of the algorithm. The output printed by \code{genoud} is controlled by a \code{print.level} argument. The default value, \code{print.level=2}, produces relatively verbose output that gives extensive information about the set of operators being used and the progress of the optimization. Normally \proglang{R} conventions would suggest setting the default to be \code{print.level=0}, which would suppress output to the screen, but because \code{genoud} runs may take a long time, it can be important for the user to receive some feedback to see the program has not died and to be able to see where the program got stuck if it eventually fails to make adequate progress. The output printed by the preceding invocation of \code{genoud}, which uses the default value for a \code{print.level} argument, is as follows. \begin{CodeChunk} \begin{CodeOutput} Fri Feb 9 19:33:42 2007 Domains: -1.000000e+01 <= X1 <= 1.000000e+01 Data Type: Floating Point Operators (code number, name, population) (1) Cloning........................... 372 (2) Uniform Mutation.................. 375 (3) Boundary Mutation................. 375 (4) Non-Uniform Mutation.............. 375 (5) Polytope Crossover................ 375 (6) Simple Crossover.................. 376 (7) Whole Non-Uniform Mutation........ 375 (8) Heuristic Crossover............... 376 (9) Local-Minimum Crossover........... 0 HARD Maximum Number of Generations: 100 Maximum Nonchanging Generations: 10 Population size : 3000 Convergence Tolerance: 1.000000e-03 Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation. Checking Gradients before Stopping. Using Out of Bounds Individuals. Maximization Problem. GENERATION: 0 (initializing the population) Fitness value... 4.112017e-01 mean............ 4.990165e-02 variance........ 9.708147e-03 #unique......... 3000, #Total UniqueCount: 3000 var 1: best............ 9.966758e-01 mean............ 3.453097e-02 variance........ 3.373681e+01 GENERATION: 1 Fitness value... 4.113123e-01 mean............ 2.237095e-01 variance........ 2.566140e-02 #unique......... 1858, #Total UniqueCount: 4858 var 1: best............ 9.995043e-01 mean............ 4.615946e-01 variance........ 7.447887e+00 [...] GENERATION: 10 Fitness value... 4.113123e-01 mean............ 2.953888e-01 variance........ 2.590842e-02 #unique......... 1831, #Total UniqueCount: 21708 var 1: best............ 9.995033e-01 mean............ 8.403935e-01 variance........ 5.363241e+00 GENERATION: 11 Fitness value... 4.113123e-01 mean............ 2.908561e-01 variance........ 2.733896e-02 #unique......... 1835, #Total UniqueCount: 23543 var 1: best............ 9.995033e-01 mean............ 8.084638e-01 variance........ 6.007372e+00 'wait.generations' limit reached. No significant improvement in 10 generations. Solution Fitness Value: 4.113123e-01 Parameters at the Solution (parameter, gradient): X[ 1] : 9.995033e-01 G[ 1] : -6.343841e-09 Solution Found Generation 1 Number of Generations Run 11 Fri Feb 9 19:33:45 2007 Total run time : 0 hours 0 minutes and 3 seconds \end{CodeOutput} \end{CodeChunk} %DESCRIBE OUTPUT After printing the date and time of the run, the program prints the domain of values it is allowing for each parameter of the function being optimized. In this case the default domain values are being used. Naturally it is important to specify domains wide enough to include the solution. In practice with highly nonlinear functions it is often better to specify domains that are relatively wide than to have domains that narrowly and perhaps even correctly bound the solution. This surprising behavior reflects the fact with a highly nonlinear function, a point that is close to the solution in the sense of simple numerical proximity may not be all that close in the sense of there being a short feasible path to get to the solution. Next the program prints the Data Type. This indicates whether the parameters of the function to be optimized are being treated as floating point numbers or integers. For more information about this, see the \code{data.type.int} argument. The program then displays the number of operators being used, followed by the values that describe the other characteristics set for this particular run: the maximum number of generations, the population size and the tolerance value to be used to determine when the parameter values will be deemed to have converged. The output then reports whether BFGS optimization will be applied to the best trial solution produced by the operators in each generation. For problems that are smooth and concave in a neighborhood of the global optimum, using the BFGS in this way can help \code{genoud} quickly converge once the best trial solution is in the correct neighborhood. This run of \code{genoud} will also compute the gradient at the best trial solution before stopping. In fact this gradient checking is used as a convergence check. The algorithm will not start counting its final set of generations (the \code{wait.generations}) until each element of the gradient is smaller in magnitude than the convergence tolerance. Gradients are never used and BFGS optimization is not used when the parameters of the function to be optimized are integers. The next message describes how strictly \code{genoud} is enforcing the boundary constraints specified by the domain values. By default (\code{boundary.enforcement=0}), the trial solutions are allowed to wander freely outside the boundaries. The boundaries are used only to define domains for those operators that use the boundary information. Other settings of the \code{boundary.enforcement} argument induce either more stringent or completely strict enforcement of the boundary constraints. Notice that the boundary constraints apply to the parameters one at a time. To enforce constraints that are defined by more complicated functional or data-dependent relationships, one can include an appropriate penalty function as part of the definition of the function to be optimized, letting that function define an extremely high (if minimizing) or low (if maximizing) value to be returned if the desired conditions are violated. After reporting whether it is solving a minimization or a maximization problem, \code{genoud} reports summary statistics that describe the distribution of the fitness value and the parameter values across the trial solutions at the end of each generation. In the default case where \code{genoud} is keeping track of all the distinct solutions considered over the whole course of the optimizing run, these generational reports also include a report of the number of unique trial solutions in the current population and the number of unique solutions ever considered. The benefit of keeping track of the solutions is to avoid repeatedly evaluating the function being optimized for the identical set of parameter values. This can be an important efficiency when function evaluations are expensive, as they can be in statistical applications where the data are extensive. This tracking behavior is controlled by the \code{MemoryMatrix} argument. Upon convergence, or when the hard maximum generation limit is reached, the program prints the fitness value at the best trial solution and that solution's parameter values. In this case the solution was found after one generation. While the Asymmetric Double Claw might present a difficult challenge for a gradient-based optimizer that uses only local hill climbing, it is an almost trivially simple problem for \code{genoud}. \subsection{Benchmark Functions:} The second example is a suite of 23 benchmark nonlinear functions used in \citet{yao.liu.lin1999} to study a pair of evolutionary programming optimization algorithms. Function definitions are in Table~\ref{tab:23funcs}. Because it includes a random component and so lacks a reproducible minimum value, we ignore the function numbered function 7 in their sequence.\footnote{The omitted function is $\sum_{i=1}^n ix_i^4 +U(0,1)$, where $U(0,1)$ is a uniformly distributed random variable on the unit interval that takes a new value whenever the function is evaluated. This stochastic aspect means that even given the set of parameters that minimize the nonstochastic component $\sum_{i=1}^n ix_i^4$, i.e., $x_i=0$, the value of the function virtually never attains the minimum possible value of zero. An optimizer that evaluated the function at $x_i=0$ would not in general obtain a function value smaller than the function value obtained for a wide range of different parameter values. Hence we do not consider this function to be a good test for function optimization algorithms.} Implementations of these functions are available in the supplemental \proglang{R} file provided with this article.\footnote{This supplemental file is available at \url{http://sekhon.berkeley.edu/rgenoud/func23.R}.} These \proglang{R} definitions include the values of the constants used in functions 14, 15 and 19 through 23. The function argument domains are restricted to the specific domains used by \citet{yao.liu.lin1999} via bounds that are stated in the list named \code{testbounds} in the supplemental file. \begin{table} \begin{center} \line(1,0){450} \end{center} \begin{tabular}{LLLL} \text{func.} & \text{definition} & n & \text{minimum}^a \\ 1 & \sum_{i=1}^n x_i^2 & 30 & 0 \\ 2 & \sum_{i=1}^n |x_i| + \prod_{i=1}^n |x_i| & 30 & 0 \\ 3 & \sum_{i=1}^n (\sum_{j=1}^i x_j)^2 & 30 & 0 \\ 4 & \max_i \{|x_i|, 1\leq i\leq n\} & 30 & 0 \\ 5 & \sum_{i=1}^{n-1} [100(x_{i+1}-x_i^2)^2 +(x_i-1)^2], & 30 & 0 \\ 6 & \sum_{i=1}^n (\lfloor x_i + 0.5\rfloor)^2 & 30 & 0 \\ 7 & \sum_{i=1}^n ix_i^4 +U(0,1) & 30 & 0 \\ 8 & \sum_{i=1}^n -x_i\sin(\sqrt{|x_i|}) & 30 & -12569.5 \\ 9 & \sum_{i=1}^n [x_i^2-10\cos(2\pi x_i)+10] & 30 & 0 \\ 10 & -20\exp\left(-0.2\sqrt{n^{-1}\sum_{i=1}^n x_i^2}\,\right) \\ & \qquad -\exp(n^{-1}\sum_{i=1}^n\cos 2\pi x_i)+20+e & 30 & 0 \\ 11 & (1/1000) \sum_{i=1}^n x_i^2 - \prod_{i=1}^n\cos\left(x_i/\sqrt{i}\right) + 1 & 30 & 0 \\ 12 & n^{-1}\pi \left\{10 \sin^2(\pi y_1)+\sum_{i=1}^{n-1}(y_i-1)^2 [1+10\sin^2(\pi y_{i+1})]+(y_n-1)^2\right\} \\ & \quad +\sum_{i=1}^n u(x_i,10,100,4), & 30 & 0 \\ & y_i=1+(x_i+1)/4, \quad u(x_i,a,k,m)=\begin{cases} k(x_i-a)^m, & x_i>a, \\ 0, & -a\leq x_i\leq a,\\ k(-x_i-a)^m, & x_i<-a, \end{cases} & \\ 13 & \left\{ \sin^2(3\pi x_1)+\sum_{i=1}^{n-1}(x_i-1)^2[1+\sin^2(3\pi x_{i+1})]\right\}/10 \\ & \quad +(x_n-1)[1+\sin^2(2\pi x_n)]/10 +\sum_{i=1}^n u(x_i,5,100,4) & 30 & 0 \\ 14 & \left\{1/500+ \sum_{j=1}^{25} 1/\left[j+\sum_{i=1}^2(x_i-a_{ij})^6\right]\right\}^{-1} & 2 & 1 \\ 15 & \sum_{i=1}^{11} [a_i-x_1(b_i^2+b_ix_2)/(b_i^2+b_ix_3+x_4)]^2 & 4 & 0.0003075 \\ 16 & 4x_1^2-2.1x_1^4+x_1^6/3+x_1x_2-4x_2^2+4x_2^4 & 2 & -1.0316285 \\ 17 & [x_2-5.1x_1^2/(4\pi^2) + 5x_1/\pi - 6]^2 + 10[1-1/(8\pi)]\cos(x_1) + 10 & 2 & 0.398 \\ 18 & [1+(x_1+x_2+1)^2(19-14 x_1+3 x_1^2-14 x_2+6 x_1 x_2+3 x_2^2)] \\ & \quad \times [30+(2 x_1-3 x_2)^2 (18-32 x_1+12 x_1^2+48 x_2-36 x_1 x_2+27 x_2^2)] & 2 & 3 \\ 19 & -\sum_{i=1}^4 c_i\exp\left[-\sum_{j=1}^4 a_{ij}(x_i-p_{ij})^2\right] & 4 & -3.86 \\ 20 & -\sum_{i=1}^4 c_i\exp\left[-\sum_{j=1}^6 a_{ij}(x_i-p_{ij})^2\right] & 6 & -3.32 \\ 21 & \sum_{i=1}^5 [(x-a_i)^{\prime}(x-a_i)+c_i]^{-1} & 4 & -10 \\ 22 & \sum_{i=1}^7 [(x-a_i)^{\prime}(x-a_i)+c_i]^{-1} & 4 & -10 \\ 23 & \sum_{i=1}^{10} [(x-a_i)^{\prime}(x-a_i)+c_i]^{-1} & 4 & -10 \end{tabular} \begin{flushleft} Notes: $^a$Minimum function value within specified bounds as given by \citet[85]{yao.liu.lin1999}. \end{flushleft} \vspace*{.1in} \caption{23 Benchmark Functions} \label{tab:23funcs} \begin{center} \line(1,0){450} \end{center} \end{table} As \citet{yao.liu.lin1999} describe, optimizing each of functions 1--13 presents a high-dimensional problem. These functions each have $n=30$ free parameters. Functions 1--5 are unimodal, with function 5 being a 30-dimensional version of the banana-shaped Rosenbrock function. Function 6 is a step function. Function 6 has one minimum value that occurs when all arguments are in the interval $x_i\in[0,.5)$, and the function is discontinuous. Functions 8--13 are multimodal, defined such that the number of local minima increases exponentially with the number of arguments. \citet[84]{yao.liu.lin1999} describe these functions as among ``the most difficult class of problems for many optimization algorithms (including [evolutionary programming]).'' Functions 14--23, which have between two and six free parameters each, each have only a few local minima. Nonetheless the evolutionary programming algorithms considered by \citet{yao.liu.lin1999} have trouble optimizing functions 21--23. Although \citet[85]{yao.liu.lin1999} state that each of these functions has a minimum value of $-10$, over 50 replications the two algorithms they consider achieve solutions averaging between $-5.52$ and $-9.10$ \citep[88, Table~IV]{yao.liu.lin1999}. We use these benchmark functions to illustrate not only how effective \code{genoud} can be with a range of difficult problems, but also to emphasize an important aspect of how one should think about trying to tune the optimizer's performance. Theory regarding genetic algorithms suggests that optimal solutions are more likely to appear as both the population size of candidate solutions and the number of generations increase. In \code{genoud} two arguments determine the number of generations. One is \code{max.generations}: if \code{hard.generation.limit=TRUE}, then the value specified for \code{max.generations} is a binding upper limit. The other is \code{wait.generations}, which determines when the algorithm terminates if \code{hard.generation.limit=FALSE}. But even if \code{hard.generation.limit=TRUE}, then \code{wait.generations} determines for how many generations the algorithm continues once the best parameter vector and the value of the function being optimized appear to have settled down. The fact that the current best solution is not changing should not be treated as decisive, because this solution may be merely a local optimum or a saddlepoint. If the population size is sufficient, the algorithm tends to build a population of trial solutions that contain parameters in neighborhoods of all the competitive local optima in the domain defined by the parameter boundaries. Even while the current best solution is stable, the algorithm is improving the solutions near other local optima. So having a higher \code{wait.generations} value never worsens the algorithm's efficacy. Increasing \code{max.generations} may or may not in itself improve optimization. The value of \code{max.generations} sets the value of $T$ used in the mutation operators---operators 4 and 7 in Table~\ref{tab:operators}. These mutation operators perform random search near a trial solution that has been selected for mutation only when the current generation count is an appreciable fraction of $T$. So increasing \code{max.generations} without changing \code{wait.generations} increases the period during which random search is occurring over a wider domain. For multimodal functions such a wider search may be helpful, but sometimes failing to search more densely near the current trial solutions is not good. We use \code{genoud} to minimize the 23 functions using two values for \code{pop.size} (5000 and 10000) and two values for \code{max.generations} (30 and 100). Following \citet{yao.liu.lin1999}, we replicate each optimization 50 times. The following code describes the computations. The list \code{testfuncs}, vector \code{testNparms} and list \code{testbounds} are defined in the supplemental \proglang{R} file, and it is assume that this file is loaded with the \code{source("supplemental.R")} command. The vector \code{gradcheck} is true for all elements except the ones corresponding to functions 6 and 7. <>= source("supplemental.R") gradcheck <- rep(TRUE,23) gradcheck[6:7] <- FALSE sizeset <- c(5000,10000) genset <- c(30,100) nreps <- 50 gsarray <- array(NA, dim=c(length(sizeset), length(genset), 23, nreps)) asc <- function(x) { as.character(x) } dimnames(gsarray) <- list(asc(sizeset), asc(genset), NULL, NULL); for (gsize in sizeset) { for (ngens in genset) { for (i in 1:23) { for (j in 1:nreps) { gsarray[as.character(gsize), as.character(ngens),i,j] <- genoud(testfuncs[[i]], nvars=testNparms[i], pop.size=gsize, max.gen=ngens, hard.gen=TRUE, Domains=testbounds[[i]], solution.tol=1e-6, boundary=1, gradient.check=gradcheck[i], print=0)$value } } } } @ Using \code{genoud} to minimize the benchmark functions produces excellent results, at least when the \code{pop.size} and \code{max.generations} arguments are sufficiently large. Table~\ref{tab:23mean} reports the mean function values for each configuration of the arguments. These values may be compared both to the true function minima given by \citet{yao.liu.lin1999} (see the rightmost column in Table~\ref{tab:23funcs}) and to the average minimum function values \citet{yao.liu.lin1999} report for their ``fast'' evolutionary programming (FEP) algorithm, which appear in the last column of Table~\ref{tab:23mean}. The \code{genoud} averages for the \code{max.gen=100} configurations equal or are close to the true minima for all the functions except function 13. One can reasonably argue that the average solutions for function 5 are not as close to zero as might be desired: these averages are close to $10^{-7}$, while the averages for other functions that have a true minimum of zero are $10^{-15}$ or smaller. And the averages for functions 6, 12 and 15 in the \code{pop.size=5000} case are off. The effect of increasing \code{pop.size} is apparent with respect to both those three functions and also functions 13 and 20--23: the average minima are smaller with \code{pop.size=10000} than with \code{pop.size=5000}. Except for functions 6 and 12 in the \code{pop.size=5000} case and function 13, all the \code{genoud} solution averages for \code{max.gen=100} are either slightly or substantially better than the corresponding FEP solution averages. The results in Table~\ref{tab:23mean} clearly illustrate the potential consequences of not allowing \code{genoud} to run for a sufficient number of generations. While some of the \code{genoud} solutions for \code{max.gen=30} have competitive means, several of the means are not good at all. \begin{table} \begin{center} \line(1,0){450} \end{center} \begin{tabular}{llllll} & \multicolumn{4}{c}{\code{genoud}} & \\ \cline{2-5} & \multicolumn{2}{c}{\code{pop.size=5000}$^a$} & \multicolumn{2}{c}{\code{pop.size=10000}$^a$} & \\ \text{func.} & \code{max=30} & \code{max=100} & \code{max=30} & \code{max=100} & \text{FEP}$^b$ \\ 1 & 1.453\e 32 & 1.658\e 32 & 2.416\e 32 & 6.134\e 32 & 5.7\e 4 \\ 2 & 6.55\e 16 & 7.212\e 16 & 9.652\e 16 & 1.043\e 15 & 8.1\e 3 \\ 3 & 4.633\e 18 & 3.918\e 18 & 3.787\e 18 & 4.032\e 18 & 1.6\e 2 \\ 4 & 6.203\e 17 & 6.542\e 17 & 9.453\e 17 & 7.85\e 17 & 0.3 \\ 5 & 0.07973 & 5.887\e 08 & 8.133\e 08 & 8.917\e 08 & 5.06 \\ 6 & 18.58 & 0.08 & 9.38 & 0 & 0 \\ % 7 & 0.1114 & 0.07473 & 0.1114 & 0.06466 & 7.6\e 3 \\ 8 & -12569.49 & -12569.49 & -12569.49 & -12569.49 & -12554.5 \\ 9 & 2.786 & 0 & 0.9353 & 0 & 4.6\e 2 \\ 10 & 2.849 & 3.997\e 15 & 2.199 & 3.997\e 15 & 1.8\e 2 \\ 11 & 7.994\e 17 & 7.105\e 17 & 9.548\e 17 & 6.439\e 17 & 1.6\e 2 \\ 12 & 5.371\e 19 & 0.004147 & 0.002073 & 1.178\e 19 & 9.2\e 6 \\ 13 & 0.02095 & 0.006543 & 0.006629 & 0.003011 & 1.6\e 4 \\ 14 & 0.998 & 0.998 & 0.998 & 0.998 & 1.22 \\ 15 & 0.0003441 & 0.0004746 & 0.0003807 & 0.0003807 & 5.0\e 4 \\ 16 & -1.0316285 & -1.0316285 & -1.0316285 & -1.0316285 & -1.03 \\ 17 & 0.3979 & 0.3979 & 0.3979 & 0.3979 & 0.398 \\ 18 & 3 & 3 & 3 & 3 & 3.02 \\ 19 & -3.863 & -3.863 & -3.863 & -3.863 & -3.86 \\ 20 & -3.274 & -3.277 & -3.279 & -3.286 & -3.27 \\ 21 & -9.85 & -9.444 & -9.95 & -10.05 & -5.52 \\ 22 & -9.771 & -10.09 & -10.19 & -10.3 & -5.52 \\ 23 & -10.1 & -9.997 & -10.32 & -10.21 & -6.57 \end{tabular} \begin{flushleft} Note: $^b$Average minimum function values (over 50 replications) obtained using \code{genoud}. $^a$Mean best function values (over 50 replications) reported for the ''fast'' evolutionary programming algorithm, from \citet[85 and 88, Tables II--IV]{yao.liu.lin1999}. \end{flushleft} \vspace*{.1in} \caption{Mean Values of 22 Optimized Functions} \label{tab:23mean} \begin{center} \line(1,0){450} \end{center} \end{table} The effect of increasing \code{pop.size} are even more clearly apparent in Table~\ref{tab:23sdev}, which reports the standard deviations of the respective minima across the 50 replications. With the exceptions of functions 6, 12, 13, 15 and 21 with \code{pop.size=5000}, the \code{genoud} solutions for \code{max.gen=100} vary much less than the corresponding FEP solutions. For those functions and also for functions 20, 22 and 23, the \code{max.gen=100} solutions with \code{pop.size=10000} vary noticeably less than the solutions with \code{pop.size=5000}. \begin{table} \begin{center} \line(1,0){450} \end{center} \begin{tabular}{llllll} & \multicolumn{4}{c}{\code{genoud}} & \\ \cline{2-5} & \multicolumn{2}{c}{\code{pop.size=5000}$^a$} & \multicolumn{2}{c}{\code{pop.size=10000}$^a$} & \\ \text{func.} & \code{max=30} & \code{max=100} & \code{max=30} & \code{max=100} & \text{FEP}$^b$ \\ 1 & 9.997\e 32 & 7.059\e 32 & 9.562\e 32 & 2.1\e 31 & 1.3\e 4 \\ 2 & 1.668\e 15 & 1.621\e 15 & 2.116\e 15 & 2.102\e 15 & 7.7\e 4 \\ 3 & 4.568\e 18 & 3.342\e 18 & 4.38\e 18 & 5.136\e 18 & 1.4\e 2 \\ 4 & 1.793\e 16 & 1.758\e 16 & 2.055\e 16 & 2.002\e 16 & 0.5 \\ 5 & 0.5638 & 4.921\e 08 & 5.573\e 08 & 4.955\e 08 & 5.87 \\ 6 & 5.65 & 0.274 & 3.528 & 0 & 0 \\ % 7 & 0.0837 & 0.05153 & 0.08042 & 0.04883 & 2.6\e 3 \\ 8 & 3.749\e 10 & 1.071\e 12 & 8.948\e 09 & 6.365\e 13 & 52.6 \\ 9 & 1.864 & 0 & 1.179 & 0 & 1.2\e 2 \\ 10 & 0.7146 & 0 & 0.702 & 0 & 2.1\e 3 \\ 11 & 1.209\e 16 & 1.582\e 16 & 1.289\e 16 & 8.713\e 17 & 2.2\e 2 \\ 12 & 2.336\e 18 & 0.02052 & 0.01466 & 7.423\e 19 & 3.6\e 6 \\ 13 & 0.03427 & 0.006867 & 0.006903 & 0.001508 & 7.3\e 5 \\ 14 & 5.638\e 12 & 8.894\e 11 & 1.029\e 12 & 4.35\e 12 & 0.56 \\ 15 & 0.0001813 & 0.0003546 & 0.000251 & 0.0002509 & 3.2\e 4 \\ 16 & 1.315\e 14 & 9.751\e 15 & 1.233\e 14 & 1.054\e 14 & 4.9\e 7 \\ 17 & 5.422\e 15 & 5.51\e 15 & 4.925\e 15 & 1.392\e 14 & 1.5\e 7 \\ 18 & 1.509\e 13 & 3.477\e 14 & 6.18\e 14 & 2.907\e 14 & 0.11 \\ 19 & 7.349\e 15 & 1.521\e 15 & 1.344\e 14 & 7.255\e 15 & 1.4\e 5 \\ 20 & 0.05884 & 0.0583 & 0.05765 & 0.05504 & 5.9\e 2 \\ 21 & 1.212 & 1.776 & 1.005 & 0.7145 & 1.59 \\ 22 & 1.937 & 1.269 & 1.052 & 0.7459 & 2.12 \\ 23 & 1.479 & 1.636 & 1.066 & 1.29 & 3.14 \end{tabular} \begin{flushleft} Note: $^a$Standard deviation of the minimum function values (over 50 replications) obtained using \code{genoud}. $^b$Standard deviation of the best function values (over 50 replications) reported for the ''fast'' evolutionary programming algorithm, from \citet[85 and 88, Tables II--IV]{yao.liu.lin1999}. \end{flushleft} \vspace*{.1in} \caption{Standard Deviations of Values of 22 Optimized Functions} \label{tab:23sdev} \begin{center} \line(1,0){450} \end{center} \end{table} \subsection{A Logistic Least Quartile Difference Estimator:} Our third example is a version of the LQD estimator used in \code{multinomRob}. Using the \proglang{R} function \code{IQR} to compute the interquartile range, the function to be minimized may be defined as follows.\footnote{The LQD problem solved in \code{multinomRob} is somewhat different. There the problem is to minimize the $\binom{h_{K}}{2}$ order statistic of the set of absolute differences among the standardized residuals, where $h_K$ is a function of the sample size and the number of unknown regression model coefficients \citep{MebaneSekhon2004}. The problem considered in the current example is simpler but exhibits similar estimation difficulties.} <>= LQDxmpl <- function(b) { logistic <- function(x) { 1/(1+exp(-x)) } sIQR <- function(y, yhat, n) { IQR((y-yhat)/sqrt(yhat*(n-yhat)), na.rm=TRUE) } sIQR(y, m*logistic(x %*% b), m) } @ For this example we define \code{LQDxmpl} after we compute the simulated data, so the data vector \code{y}, matrix \code{x} and scalar \code{m} are in scope to evaluate to have the values we simulate: <>= m <- 100 x <- cbind(1,rnorm(1000),rnorm(1000)) b1 <- c(.5, 1, -1) b2 <- c(0, -1, 1) logistic <- function(x) { 1/(1+exp(-x)) } y <- rbinom(1000, m, logistic(c(x[1:900,] %*% b1, x[901:1000,] %*% b2))) @ The data simulate substantial contamination. The first 900 observations are generated by one binomial regression model while the last 100 observations come from a very different model. Presuming we are interested in the model that generated the bulk of the data, ignoring the contamination in a generalized linear model with the binomial family produces very poor results: <>= summary(glm1 <- glm(cbind(y,m-y) ~ x[,2] + x[,3], family="binomial")) @ \begin{CodeChunk} \begin{CodeOutput} Call: glm(formula = cbind(y, m - y) ~ x[, 2] + x[, 3], family = "binomial") Deviance Residuals: Min 1Q Median 3Q Max -22.9168 -1.1693 0.3975 1.5895 24.6439 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 0.439492 0.007097 61.93 <2e-16 *** x[, 2] 0.679847 0.007985 85.14 <2e-16 *** x[, 3] -0.716963 0.007852 -91.31 <2e-16 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 \end{CodeOutput} \end{CodeChunk} Of course, if we knew which observations to omit the results would be much better: <>= suby <- y[1:900] subx <- x[1:900,] summary(glm2 <- glm(cbind(suby,m-suby) ~ subx[,2] + subx[,3], family="binomial")) @ \begin{CodeChunk} \begin{CodeOutput} Call: glm(formula = cbind(suby, m - suby) ~ subx[, 2] + subx[, 3], family = "binomial") Deviance Residuals: Min 1Q Median 3Q Max -3.21478 -0.71699 0.03528 0.67867 2.88314 Coefficients: Estimate Std. Error z value Pr(>|z|) (Intercept) 0.501880 0.008036 62.46 <2e-16 *** subx[, 2] 1.003592 0.009779 102.63 <2e-16 *** subx[, 3] -0.984295 0.009437 -104.30 <2e-16 *** --- Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1 \end{CodeOutput} \end{CodeChunk} But in practical applications it is unknown apriori which observations should be treated as outliers. As the definition of \code{LQDxmpl} indicates, the LQD is based on minimizing the interquartile range (IQR) of the standardized residuals. Because the quartiles correspond to different data points for different values of the regression coefficients, the fitness function is not smooth, which is to say it is not everywhere differentiable. In general, at every point in the parameter space where the identity of the first or third quartile point changes, the function is not differentiable. Figure~\ref{fig:lqd1} illustrates this. A higher resolution version of this figure is available in \cite{MebaneJr.+Sekhon:2011}---also see \url{http://sekhon.berkeley.edu/papers/rgenoudJSS.pdf}. The IQR clearly has a minimum in the vicinity of the coefficient values used to generate most of the data. But contour plots for the numerically evaluated partial derivative with respect to the second coefficient parameter testify to the function's local irregularity. The function we use to evaluate this numerical derivative is defined as follows. <>= dLQDxmpl <- function(b) { eps <- 1e-10 logistic <- function(x) { 1/(1+exp(-x)) } sIQR <- function(y, yhat, n) { IQR((y-yhat)/sqrt(yhat*(n-yhat)), na.rm=TRUE) } dsIQR <- vector() for (i in 1:length(b)) { beps <- b beps[i] <- b[i]+eps dsIQR <- c(dsIQR, (sIQR(y, m*logistic(x %*% beps), m)- sIQR(y, m*logistic(x %*% b), m))/eps) } return(dsIQR) } @ Setting the intercept equal to 0.5, the code to generate the plotted values is % -rw-rw---- 1 wrm1 research 1878 Feb 10 2007 lqdxmpl2plotB.R <>= blen <- 3 lenbseq <- length(bseq <- seq(-2,2,length=200)) bseq3 <- seq(-1.2,-.9,length=200) bseq2 <- seq(.89,1.1,length=200) IQRarr <- IQRarrA <- array(NA, dim=c((1+blen), lenbseq, lenbseq)) dimnames(IQRarrA) <- list(NULL, as.character(bseq), as.character(bseq)) dimnames(IQRarr) <- list(NULL, as.character(bseq2), as.character(bseq3)) for (i in 1:lenbseq) { for (j in 1:lenbseq) { IQRarrA[1,i,j] <- LQDxmpl(c(.5, bseq[i], bseq[j])) IQRarrA[-1,i,j] <- dLQDxmpl(c(.5, bseq[i], bseq[j])) IQRarr[1,i,j] <- LQDxmpl(c(.5, bseq2[i], bseq3[j])) IQRarr[-1,i,j] <- dLQDxmpl(c(.5, bseq2[i], bseq3[j])) } } @ The following code produces the plots: <>= par(mfrow=c(2,2), lwd=.1) contour(bseq,bseq, IQRarrA[1,,], main="IQR", xlab="b[2]", ylab="b[3]") contour(bseq,bseq, IQRarrA[3,,], main="partial derivative w/r/t b[2]", xlab="b[2]", ylab="b[3]") loc2 <- (150:160)-5 loc3 <- (40:50)+5 contour(bseq[loc2],bseq[loc3], IQRarrA[3,loc2,loc3], main="partial derivative w/r/t b[2]", xlab="b[2]", ylab="b[3]") contour(bseq2,bseq3, IQRarr[3,,], main="partial derivative w/r/t b[2]", xlab="b[2]", ylab="b[3]") @ If the IQR function were smooth, we would see clearly separated, slightly curved contour lines, reflecting the nonlinearity of the \code{logistic} function, but there is nothing like that. Instead, looking over the domain $[-2,2]^2$ for the second and third regression coefficient parameters, with 200 points evaluated along each axis (the upper right plot), there is a splotchy cloud. This reflects the fact that the derivative changes sign very frequently over the domain: of the 40,000 points at which the derivative is evaluated, it is positive at 12,460 points and negative at 27,540 points. \begin{figure}[t] \caption{Contour Plots of the LQD Fitness Function and of its Partial Derivatives} \label{fig:lqd1} \begin{center} \includegraphics{lqdxmpl2B.pdf} % -rw-rw---- 1 wrm1 research 2745 Feb 10 23:15 lqdxmpl2plotB.Rout \end{center} \vspace{-.3in} \end{figure} The LQD fitness function is not appreciably smoother close to the true values. The bottom two plots show the partial derivatives with respect to the second coefficient parameter evaluated over the domain $[.89,1.1]\times[-1.2,-.9]$. The bottom left plot evaluates the derivatives at 11 points along each axis while the bottom right plot uses 200 points along each axis. In the left plot it is easier to see the intricacy of the partitioning of the parameter space as the identity of the first or third quartile point changes. The bottom right plot shows the intricacy in fact replicates at the finer grain of the more detailed evaluations (to see this it is probably necessary to magnify the plot while viewing online the \textit{Journal of Statistical Software} version of this documentation).\footnote{Please see \cite{MebaneJr.+Sekhon:2011} or \url{http://sekhon.berkeley.edu/papers/rgenoudJSS.pdf}.} Within this smaller domain the sign of the derivative changes even more frequently than it does over the domain $[-2,2]^2$: the derivative is positive at 18,098 points and negative at 21,902 points. While the LQD fitness function may be differentiable in a neighborhood of the global solution, that neighborhood, if it exists, is clearly not very big. As likely is that the global solution is located at a point where the function is not differentiable. Hence a numerically evaluated gradient is not meaningful for evaluating whether the solution has been found. At the true solution, numerical gradient values may differ substantially from zero. To use the LQD to estimate the binomial regression model parameters we use the following call to \code{genoud}. Because gradient information is of questionable relevance for this problem, we turn off the termination condition that the gradient at the solution be smaller than the value specified for the \code{solution.tolerance} argument. We retain the default setting \code{BFGS=TRUE} because, in principle, gradient-driven optimization may help in each of the many differentiable neighborhoods, even if it is useless across the nondifferentiable boundaries. Our experience optimizing the LQD \citep{MebaneSekhon2004} shows that using the BFGS in this way improves performance, even though the gradient is not useful for evaluating whether the solution has been found. <>= LQD1 <- genoud(LQDxmpl, nvars=3, max=FALSE, pop.size=2000, max.generations=300, wait.generations=100, gradient.check=FALSE, print=1) @ This invocation of the \code{LQDxmpl} function matches the behavior of \code{multinomRob} in that it produces an estimate for the intercept parameter along with the other coefficients. In a linear regression context, the interquartile range statistic contains no information about the intercept, so the LQD is not an estimator for that parameter. With a binomial regression model there is some information about the intercept due to the nonlinearity of the \code{logistic} function. The LQD estimate for the intercept should nonetheless be expected not to be very good. Results from the preceding estimation are as follows. % macht:/home/xchg/jss07/rgenoud: % -rw-rw---- 1 wrm1 research 5080 Aug 7 02:31 lqdxmpl1b.Rout \begin{CodeChunk} \begin{CodeOutput} Tue Aug 7 02:27:08 2007 Domains: -1.000000e+01 <= X1 <= 1.000000e+01 -1.000000e+01 <= X2 <= 1.000000e+01 -1.000000e+01 <= X3 <= 1.000000e+01 [...] HARD Maximum Number of Generations: 300 Maximum Nonchanging Generations: 100 Population size : 2000 Convergence Tolerance: 1.000000e-06 Using the BFGS Derivative Based Optimizer on the Best Individual Each Generation. Not Checking Gradients before Stopping. Using Out of Bounds Individuals. Minimization Problem. Generation# Solution Value 0 4.951849e-01 56 1.298922e-01 57 1.298891e-01 59 1.298848e-01 60 1.298820e-01 61 1.298793e-01 62 1.298768e-01 63 1.298744e-01 'wait.generations' limit reached. No significant improvement in 100 generations. Solution Fitness Value: 1.298743e-01 Parameters at the Solution (parameter, gradient): X[ 1] : 8.130357e-02 G[ 1] : 9.616492e-03 X[ 2] : 8.889485e-01 G[ 2] : -1.167897e-01 X[ 3] : -9.327966e-01 G[ 3] : -3.090130e-02 Solution Found Generation 63 Number of Generations Run 164 Tue Aug 7 02:31:09 2007 Total run time : 0 hours 4 minutes and 1 seconds \end{CodeOutput} \end{CodeChunk} Recall that the gradient is not reliably informative at the solution. To check whether this solution is believable, we might try reestimating the model using a larger population and larger specified number of generations: <>= LQD1 <- genoud(LQDxmpl, nvars=3, max=FALSE, pop.size=10000, max.generations=1000, wait.generations=300, gradient.check=FALSE, print=1) @ At the price of a greatly increased running time (from four minutes up to one hour 53 minutes), the results are better than the first run (even though the summary measure of fit is slightly worse): % macht:/home/xchg/jss07/rgenoud: % -rw-rw---- 1 wrm1 research 5236 Aug 7 05:16 lqdxmpl1d.Rout \begin{CodeChunk} \begin{CodeOutput} Minimization Problem. Generation# Solution Value 0 2.238865e-01 2 1.301149e-01 3 1.300544e-01 4 1.300482e-01 6 1.300375e-01 7 1.300343e-01 8 1.300323e-01 134 1.299662e-01 135 1.299099e-01 136 1.298867e-01 137 1.298843e-01 138 1.298822e-01 139 1.298791e-01 141 1.298774e-01 'wait.generations' limit reached. No significant improvement in 300 generations. Solution Fitness Value: 1.298770e-01 Parameters at the Solution (parameter, gradient): X[ 1] : 2.013748e-01 G[ 1] : -7.394125e-02 X[ 2] : 9.526390e-01 G[ 2] : 7.807607e-02 X[ 3] : -9.642458e-01 G[ 3] : 3.834052e-02 Solution Found Generation 141 Number of Generations Run 442 Tue Aug 7 05:16:37 2007 Total run time : 1 hours 53 minutes and 45 seconds \end{CodeOutput} \end{CodeChunk} %$ This example demonstrates a key difficulty that arises when optimizing irregular functions in the absence of gradients. It is difficult to assess when or whether an optimum has been found. The estimated coefficient values are close to the ones used to generate most of the data, except as expected the estimate for the intercept is not good. The estimates are better than if we had ignored the possibility of contamination. But whether these are the best possible estimates is not clear. If we were to use an even larger population and specify that an even greater number of generations be run, perhaps a better solution would be found. %http://sekhon.berkeley.edu/rgenoud/R/genoud_cluster_manual.R %http://sekhon.berkeley.edu/rgenoud/R/genoud_cluster_manual_tunnel.R %\code{genoud} can be tricked into doing constrained optimization by %passing in a function which contains a penalty function. Even for less irregular problems convergence is difficult to determine. Nonlinear optimizers often report false convergence, and users should not simply trust whatever convergence criteria an optimizer uses. \citet{McCulloughVinod2003} offer four criteria for verifying the solution of a nonlinear solver. These criteria are meaningful only for problems that meet regularity conditions at the solution, notably differentiability, and as such are not useful for the LQD example offered above. The four criteria are: (1) making sure the gradients are zero; (2) inspecting the solution path (i.e., the trace) to make sure it follows the expected rate of convergence; (3) evaluating the Hessian to make sure it is well-conditioned;\footnote{Following an exchange with \citet{DrukkerWiggins2004}, \citet{McCulloughVinod2004b} modify their third suggestion to note that determining if the Hessian is well-conditioned in part depends on how the data are scaled. That is, a Hessian that appears to be ill-conditioned may be made well-conditioned by rescaling. So if an Hessian appears to be ill-conditioned, \citet{McCulloughVinod2004b} recommend that the analyst attempt to determine if rescaling the data can result in a well-conditioned Hessian.} and (4) profiling the likelihood to ascertain if a quadratic approximation is adequate. One may need to take the results from \code{genoud} and pass them to \code{optim} to conduct some of these diagnostic tests such as to profile the likelihood. It is also good practice to use more than one optimizer to verify the solution \citep{stokes2004}. Note that \code{genoud} uses its own random number seeds and internal pseudorandom number generators to insure backward compatibility with the original C version of the software and to make cluster behavior more predictable. These seeds are set by the \code{unif.seed} and \code{int.seed} options. The \proglang{R} \code{set.seed} command is ignored by \code{genoud}. %user supplied gradients and lexical search? \section{Conclusion} \label{sec:conclusion} The \code{genoud} function provides many more options than can be reviewed in this brief paper. These options are described in the \proglang{R} help file. The most important option influencing how well the evolutionary algorithm works is the \code{pop.size} argument. This argument controls the population size---i.e., it is the number of individuals \code{genoud} uses to solve the optimization problem. As noted above, the theorems proving that genetic algorithms find good solutions are asymptotic in both population size and the number of generations. It is therefore important that the \code{pop.size} value not be small. On the other hand, computational time is finite so obvious trade-offs must be made. As the LQD example illustrates, a larger population size is not necessarily demonstrably better. The most important options to ensure that a good solution is found, aside from \code{pop.size}, are \code{wait.generations}, \code{max.generations} and \code{hard.generation.limit}. Many statistical models have objective functions that are nonlinear functions of the parameters, and optimizing such functions is tricky business \citep{AltmanGillMcDonald2003}. Optimization difficulties often arise even for problems that are generally considered to be simple. For a cautionary tale on how optimization can be a difficult task even for such problems see Stokes' (\citeyear{stokes2004}) effort to replicate a probit model estimated by \citet[pp. 335]{maddala1992}. A recent controversy over estimating a nonlinear model estimated by maximum likelihood offers another cautionary tale \citep{DrukkerWiggins2004,McCulloughVinod2003,McCulloughVinod2004a,McCulloughVinod2004b,SchacharNalebuff2004}. End users are generally surprised to learn that such optimization issues can arise, and that results can substantially vary across optimizers and software implementations. The \pkg{rgenoud} package provides a powerful and flexible global optimizer. When compared with traditional derivative-based optimization methods, \pkg{rgenoud} performs well \citep{SekhonMebane1998}. Optimization of irregular functions is, however, as much of an art as science. And an optimizer cannot be used without thought even for simple surfaces, let alone spaces that require a genetic algorithm. We hope that the availability of a scalable global optimizer will allow users to work with difficult functions more effectively. \bibliography{rgenoud} \end{document} % LocalWords: optima GillMurrayWright EfronTibshirani GENOUD MebaneSekhon LQD % LocalWords: SekhonMebane multinomRob overdispersed nondifferentiable Broyden % LocalWords: Goldfarb Shanno BFGS optim genoud EA EAs GA holland goldberg GAs % LocalWords: GrefenstetteBaker davis FilhoTreleavenAlippi generation's dejong % LocalWords: substring's grefenstette billingsley Vose NixVose vose GA's ADC % LocalWords: GENOCOP MichalewiczSwaminathanLogan Michalewicz Polytope dnorm % LocalWords: nvars Nonchanging UniqueCount var MemoryMatrix IQR LQDxmpl exp % LocalWords: sIQR yhat na rm cbind rnorm rbinom Min Std Pr Signif suby subx % LocalWords: apriori Raphson saddlepoints fn Genoud's gr hessian unif int ssh % LocalWords: Tausworthe stdout tempdir polytope musil deckard makeSOCKcluster % LocalWords: usernames username PVM MPI peakgeneration parm UC Outlier seq mu % LocalWords: lapply xlab ylab col biclaw mNd ALTMAN rgenoud WandKingLau PKfit % LocalWords: KingWand braumoeller BraumoellerGoodrichKline pharmacokinetics % LocalWords: LeeLee pseudorandom pdf glm rw wrm lqdxmpl cl makeCluster probit % LocalWords: localhost clusterExport stopCluster AltmanGillMcDonald GENetic % LocalWords: McCulloughVinod SchacharNalebuff GenMatch GUI URL boolean Sekhon % LocalWords: CPUs nonlinearity FAiR goodrich SekhonMatching ivivc vitro vivo % LocalWords: multinomial Synth AbadieGardeazabal synth nonsmooth Rcore maxima % LocalWords: resampling resamples optimizer's eval nonstochastic testbounds % LocalWords: LLLL func ij unimodal Rosenbrock multimodal minima saddlepoint % LocalWords: testfuncs testNparms gradcheck sizeset genset nreps gsarray tol % LocalWords: gsize ngens FEP LLLLLL sqrt dLQDxmpl eps dsIQR beps blen lenbseq % LocalWords: bseq IQRarr IQRarrA dimnames mfrow lwd loc online DrukkerWiggins % LocalWords: maddala funcs sapply runif ifelse rbind crossprod byrow vXXi % LocalWords: interquartile rgenoud/MD50000644000176200001440000000370012553121055012224 0ustar liggesusers03031d7393b444fb126b60b64e11fb87 *ChangeLog 011cd745379495c2173b8c558a21430e *DESCRIPTION 7041fdf1d47575612a5530f22815c74b *INDEX d0e648e7a542fefef8ded0093a377d0c *NAMESPACE e876d80633dfbe62bc02b1bfac2182cc *R/rgenoud.R 1a33ab1680d185e8ac27ccbfee0a69c5 *R/zzz.R 5b89fbb8f5ded1292c887abd380d9ed3 *THANKS b4e36fbfec752be4e34ac7be2a1df462 *build/vignette.rds c1555556931726b8c05fb5eca07023ed *inst/CITATION fc974e2bc8d4159f9ef7c20f2e4d2d40 *inst/doc/Figures/fig1.pdf c1c87156136ee41de970e4fce41fe4ed *inst/doc/Figures/lqdxmpl2B.pdf 301934099bc3c999ad3b509374fccd7f *inst/doc/rgenoud.R 688f42dd89519765ad82e2ec6eb8b9ce *inst/doc/rgenoud.Rnw 6da32365e697f8c1d280b3bf1c346ef2 *inst/doc/rgenoud.bib 5ff472c622145eb456da868ca0c1d987 *inst/doc/rgenoud.pdf e9bf210be99470cc4bc1dc2f33d7c6fb *man/genoud.Rd 9e5f395a8f7532118c723dab203d314d *src/change_order.cpp 0e2173333529000bcd8a2b2cdceec2c6 *src/eval.cpp 41e73b115fe52a57d90f9771202ab5e7 *src/evaluate.cpp c064f9e6cdb0634bc0062a044f5d1eb6 *src/frange_ran.cpp 1a9a34c6ab01598c176ef45ec10e5e70 *src/genoud.cpp dfa87419e843d8e6fb959e156004c550 *src/genoud.h 3213f79851150f99629a7e2a1719a7d6 *src/gradient.cpp 682a4a00ac9b06f5063f248f59989f0d *src/gradient.h 824d9f5d338ecaa274098127fbfe987b *src/math.cpp 1ac6ed98c2cb0267453dcdfe1c8029ce *src/multiply.cpp 62b05e4d2b6ccf20af199dc8db6f4436 *src/numerics.cpp 1dfcf27b62c83849ee8bd8b361d06e11 *src/operators.cpp 33b6a2cd3d214a86355fb03ae840034d *src/print_format.cpp 6232a071dae711bba098c886b76bbdee *src/rgenoud.cpp 5a028c6ece078d870ee528ca300a9776 *src/unif.cpp fa19da33dee62a703d43ed766e8d2985 *src/unif.h 4ef64fab110b8894a0a4871f34f5692f *src/urans.h 1bd5ce070de3e38986c27c888120005e *tests/tests.R de48b17cafdb9e88eb76e1a6cd7b6074 *tests/tests.Rout.save fc974e2bc8d4159f9ef7c20f2e4d2d40 *vignettes/Figures/fig1.pdf c1c87156136ee41de970e4fce41fe4ed *vignettes/Figures/lqdxmpl2B.pdf 688f42dd89519765ad82e2ec6eb8b9ce *vignettes/rgenoud.Rnw 6da32365e697f8c1d280b3bf1c346ef2 *vignettes/rgenoud.bib rgenoud/build/0000755000176200001440000000000012553042713013016 5ustar liggesusersrgenoud/build/vignette.rds0000644000176200001440000000031012553042713015347 0ustar liggesusersb```b`fbd`b2 1# '.JO/M +G -KWV& 7h0XU{H&$aּbt.y) DM;<f6̜T3B2K7(1Ix(\%^PL4@bts$$ Eټrgenoud/DESCRIPTION0000644000176200001440000000103512553121055013421 0ustar liggesusersPackage: rgenoud Version: 5.7-12.4 Date: 2015-07-19 Title: R Version of GENetic Optimization Using Derivatives Author: Walter R. Mebane, Jr. , Jasjeet Singh Sekhon Maintainer: Jasjeet Singh Sekhon Description: A genetic algorithm plus derivative optimizer. Depends: R (>= 2.15), utils Suggests: parallel License: GPL-3 URL: http://sekhon.berkeley.edu/rgenoud/ NeedsCompilation: yes Packaged: 2015-07-20 00:50:19 UTC; jas Repository: CRAN Date/Publication: 2015-07-20 09:24:29 rgenoud/THANKS0000644000176200001440000000035611236750565012646 0ustar liggesusersThe authors would like to thank the following people for their help and assistance: Ben Goodrich Erin Hartman Todd Rice Jonathan Wand rgenoud/ChangeLog0000644000176200001440000002362212553042657013505 0ustar liggesusers2015-07-19 Version: 5.7-12.4 * genoud.R: creating visible binding for variable "indx" 2015-07-18 Version: 5.7-12.3 * genoud.R: import non-base functions explicitly 2015-07-17 Version: 5.7-12.2 * DESCRIPTION: improves description 2013-06-28 Version: 5.7-12.1 * test.R: suppress message on load 2013-06-28 Version: 5.7-12 * genoud.Rd: Updated the documentation to reflect the usage of the 'parallel' package instead of the deprecated package 'snow' * vignettes: moved vignettes from /inst/doc to /vignettes. 2013-06-28 Version: 5.7-10 * genoud.R: now uses the 'parallel' package instead of the deprecated package 'snow' 2013-06-27 Version: 5.7-9.2 * evaluate.cpp: JaIntegerOptimization(), Correct memory issue. When reading in an old population file a segmentation fault could result when an old population file was read that had a larger population than the new population. Issue only arose for integer optimization. 2013-05-06 Version: 5.7-9.1 * operators.cpp: oper5(), Simple Crossover, always hit the maximum unique individual limit. Corrected the logic to only check for unique children in the crossover portion. Note that this makes results different from previous versions even if the random number seeds are set. 2012-06-03 Version: 5.7-8 * rgenoud.R: Added the following options back in for backward compatibility, but a warning is printed if they are used: output.path and output.append. Please use 'sink' instead. 2012-06-03 Version: 5.7-7 * rgenoud.R: Call to optimHess() now explicitly names the arguments to be matched. 2012-06-03 Version: 5.7-6 * evaluate.cpp: output streams are no longer flushed because of R's rules about calling stdout. * rgenoud.pdf: has been compacted to save space. * .Rinstignore: new file has been added to sure that inst/doc/Figures are not installed to save space. 2012-06-03 Version: 5.7-5 * rgenoud.R: Because of the switch to Rprintf (see below), the 'output.path' and 'output.append' options have been removed. * evaluate.cpp: Routed printing calls through Rprintf rather than fprintf. Made sure all error handling is done by R's error() function. Many cpp files affected: genoud.cpp, genoud.h, gradient.cpp, operators.cpp, math.cpp, numerics.cpp, print_format.cpp. 2012-06-02 Version: 5.7-4 * rgenoud.R: Removes calls to .Internal(optimhess). Now calls optimHess(). * zzz.R: Now uses packageStartupMessage() to display .onAttach message. 2011-05-04 Version: 5.7-3 * rgenoud.Rd: Update for Journal of Statistical Software * inst/CITATION: Final update for Journal of Statistical Software 2011-04-16 Version: 5.7-2 * inst/CITATION: Updated for Journal of Statistical Software 2010-08-26 Version: 5.7-1 * operators.cpp: Fixed boundary issue for integer optimization (when 'data.type.int=TRUE') created by changes in the GNU CC compiler, operators P3,P4,P5,P7 were affected. * evaluate.cpp: See above and corrected printing of population means and variances when doing integer optimization. * genound.h: See above * print_format.cpp: Changed longs to ints to prevent warnings produced by the call to fscanf() in the ReadPopulation() file. 2010-06-01 Version: 5.6-7 * rgenoud.R: Improved handling of the parent environment when the 'transform' option is used * operators.ccp: Fixed boundary issue for the integer version of the Polytope Crossover operator (P5 and function JaIntegeroper4). 2009-08-14 Version: 5.6-6 * rgenoud.Rd: Improved the documentation of the 'transform' option. 2009-08-07 Version: 5.6-5 * rgenoud.Rnw: created vignette file to generate rgenoud.pdf, rgenoud.tex and rgenoud.R. Support files also added---i.e., rgenoud.bib and figures in the inst/doc/Figures directory added. * COPYRIGHTS: file added * COPYING: file added * THANKS: file added 2009-08-06 Version: 5.6-4 * evaluate.cpp: Adds boundary checking for the parameters returned by the 'transform' option. For the transform option, only checks bounds in generation 0 because of computational efficiency concerns. The standard bounds checking remains unchanged. * genoud.Rd: Documentation updated to reflect above. 2009-08-04 Version: 5.6-3 * print_format.cpp: Corrects issue when 'share.type=1' and 'starting.values' are provided. * evaluate.cpp and multiple other files: Some warning messages are now simply notes. 2009-08-03 Version: 5.6-2 * multiple files: optim() can now be called by any valid method using the 'optim.method' option: namely one of "BFGS", "L-BFGS-B", "Nelder-Mead", "CG", or "SANN". * rgenoud.R: The error checking of user provided starting values has been improved. 2009-08-03 Version: 5.6-1 * multiple files: Major revision. Adds the transform option which is required by the FAiR package by Ben Goodrich . * pint_format.cpp: share.type=1 works correctly again. * multiple files: Printing is cleaning up when share.type=1, and relevant warning messages are improved. 2009-03-13 Version: 5.5-1 * genoud.Rd: Corrected formatting issues in the help page. * evaluate.cpp: Corrected overloading ambiguity between "std::fmod(double, double)" and "std::fmod(long double, long double)" which prevented building on Solaris. 2008-01-04 Version: 5.4-7 * evaluate.cpp, rgenoud.cpp: The 'BFGSburnin' option may now be set to a negative value. If \code{BFGSburnin < 0}, the BFGS will be used if and when \code{wait.generations} is doubled because at least one gradient is too large, which can only occur when \code{gradient.check = TRUE}. Note that 'BFGSburnin' was an option added in version 5.3-3. Premature use of the BFGS can lead to convergence to a local minimum instead of the global one. This option allows the user to control how many generations are run before the BFGS is started. This option delays the use of both the BFGS on the best individual and of the P9 operator. * multiple files: Better interrupt handling. When genoud is interrupted, it now prints a message on how to recover the best individual found so far. * multiple files: Helper function of analytical gradients is enabled. Better checking to make sure that input parameters are legal. * rgenoud.R and other files: User may now pass in "control" (a list of control parameters) for optim including control$fnscale. * rgenoud.Rd: Updated rgenoud.Rd project.path description. It is now noted in genoud.Rd that with boundary.enforcement=2, no out-of-bounds evaluations will ever be requested. In this case, boundary enforcement is also applied to the BFGS algorithm, which prevents candidates from straying beyond the bounds defined by \code{Domains}. Note that this forces the use of the "L-BFGS-B" algorithm for \code{\link[stats]{optim}}. This algorithm requires that all fit values and gradients be defined and finite for all function evaluations. If this causes an error, it is suggested that the "BFGS" algorithm be used instead by setting \code{boundary.enforcement=1}. 2007-11-19 Version: 5.3-4 * multiple files: Made some changes for the Portland Group Compiler (pgCC). Converted some longs to ints. 2007-10-18 Version: 5.3-3 * multiple files: A number of starting values can now be provided by passing a matrix to the 'starting.values' option. * multiple files: A new option has been added named 'BFGSburnin' which control the number of generations which are run before the BFGS is first used. Premature use of the BFGS can lead to convergence to a local minimum instead of the global one. This option allows the user to control how many generations are run before the BFGS is started. This option delays the use of both the BFGS on the best individual and of the P9 operator. * rgenoud.R: The dimensions of the 'Domains' object are now checked both if they have the correct number of dimensions and if the values are sane. * evaluate.cpp and other files: Fixed warnings in gcc >4.2: evaluate.cpp:304: warning: deprecated conversion from string constant to 'char*' * evaluate.cpp: Fixed a MemoryMatrix issue with data.type.int=TRUE. MemoryMatrix now gives the same results as !MemoryMatrix. The issues was that the number of UniquePairs that were hunted down for P6 and P8 were different between the two setups. 2007-08-04 Version: 5.1-14 * multiple files: Minor changes. Changed #includes so that the package now compiles with Sun Studio compilers: extern "C" is not needed for R header files. Added a regression suite to the "tests" directory. 2007-03-23 Version: 5.1-9 Major changes: * multiple files: Lexical searching now allows for one of the fit functions to be optimized by the derivative based optimizer. This functionality is made available via the "BFGSfn" option. Also see the "BFGShelp" option. * multiple files: The 9th operator which takes the convex combination of the parent and its BFGS fit can now by tuned via the "P9mix" option. If this is set to equal 1, then the BFGS fit is simply used. Minor changes: * multiple files: If BFGS results in out-of-bounds individuals, warning is only printed if print.level > 1 2007-02-20 Version: 5.0-5 * zzz.R: Prints version and build date on load. * rgenoud.R: If starting values are provided and the lexical option is TRUE, then the starting values instead of domains[,1] are used to figure out how many return fits the function provides. 2007-02-11 Version: 5.0-2 * genoud.Rd: Improved documentation file. 2007-01-30 Version: 5.0-1 * evaluate.cpp: remove needless if statement in evaluate.cpp 2007-01-30 Version: 5.0-0 * genoud.Rd: Multiple point crossover now accurately called simple crossover in docs * operators.cpp: corrected whole mutation to actually do whole mutation * evaluate.cpp: fixed minor no improvement bug which involved going from gen0 to gen1 * multiple files: simplified printing Copyright 1997-2012 Walter R. Mebane, Jr. and Jasjeet S. Sekhon. Copying and distribution of this file, without modification, are permitted provided the copyright notice and this notice are preserved. rgenoud/man/0000755000176200001440000000000012211533373012470 5ustar liggesusersrgenoud/man/genoud.Rd0000644000176200001440000011212512163247246014251 0ustar liggesusers\name{genoud} \alias{genoud} \title{ GENetic Optimization Using Derivatives } \description{ \code{Genoud} is a function that combines evolutionary search algorithms with derivative-based (Newton or quasi-Newton) methods to solve difficult optimization problems. \code{Genoud} may also be used for optimization problems for which derivatives do not exist. \code{Genoud}, via the \code{cluster} option, supports the use of multiple computers, CPUs or cores to perform parallel computations. } \usage{genoud(fn, nvars, max=FALSE, pop.size=1000, max.generations=100, wait.generations=10, hard.generation.limit=TRUE, starting.values=NULL, MemoryMatrix=TRUE, Domains=NULL, default.domains=10, solution.tolerance=0.001, gr=NULL, boundary.enforcement=0, lexical=FALSE, gradient.check=TRUE, BFGS=TRUE, data.type.int=FALSE, hessian=FALSE, unif.seed=812821, int.seed=53058, print.level=2, share.type=0, instance.number=0, output.path="stdout", output.append=FALSE, project.path=NULL, P1=50, P2=50, P3=50, P4=50, P5=50, P6=50, P7=50, P8=50, P9=0, P9mix=NULL, BFGSburnin=0, BFGSfn=NULL, BFGShelp=NULL, control=list(), optim.method=ifelse(boundary.enforcement < 2, "BFGS", "L-BFGS-B"), transform=FALSE, debug=FALSE, cluster=FALSE, balance=FALSE, ...) } \arguments{ \item{fn}{ The function to be minimized (or maximized if max=\code{TRUE}). The first argument of the function must be the vector of parameters over which minimizing is to occur. The function must return a scalar result (unless \code{lexical=TRUE}). For example, if we wish to \emph{maximize} the \code{sin()} function. We can simply call genoud by \code{genoud(sin, nvars=1,max=TRUE)}.} \item{nvars}{The number of parameters to be selected for the function to be minimized (or maximized).} \item{max}{ Maximization (\code{TRUE}) or Minimizing (\code{FALSE}). Determines if \code{genoud} minimizes or maximizes the objective function.} \item{pop.size}{ Population Size. This is the number of individuals \code{genoud} uses to solve the optimization problem. There are several restrictions on what the value of this number can be. No matter what population size the user requests, the number is automatically adjusted to make certain that the relevant restrictions are satisfied. These restrictions originate in what is required by several of the operators. In particular, operators 6 (Simple Crossover) and 8 (Heuristic Crossover) require an even number of individuals to work on---i.e., they require two parents. Therefore, the \code{pop.size} variable and the operators sets must be such that these three operators have an even number of individuals to work with. If this does not occur, the population size is automatically increased until this constraint is satisfied.} \item{max.generations}{ Maximum Generations. This is the maximum number of generations that \code{genoud} will run when attempting to optimize a function. This is a \emph{soft} limit. The maximum generation limit will be binding for \code{genoud} only if \code{hard.generation.limit} has been set equal to \code{TRUE}. If it has not been set equal to \code{TRUE}, two soft triggers control when \code{genoud} stops: \code{wait.generations} and \code{gradient.check}. \cr Although the \code{max.generations} variable is not, by default, binding, it is nevertheless important because many operators use it to adjust their behavior. In essence, many of the operators become less random as the generation count gets closer to the \code{max.generations} limit. If the limit is hit and \code{genoud} decides to continue working, \code{genoud} automatically increases the \code{max.generation} limit.\cr Please see \code{MemoryMatrix} for some important interactions with memory management.} \item{wait.generations}{ If there is no improvement in the objective function in this number of generations, \code{genoud} will think that it has found the optimum. If the \code{gradient.check} trigger has been turned on, \code{genoud} will only start counting \code{wait.generations} if the gradients are within \code{solution.tolerance} of zero. The other variables controlling termination are \code{max.generations} and \code{hard.generation.limit}.} \item{hard.generation.limit}{ This logical variable determines if the \code{max.generations} variable is a binding constraint for \code{genoud}. If \code{hard.generation.limit} is \code{FALSE}, then \code{genoud} may exceed the \code{max.generations} count if either the objective function has improved within a given number of generations (determined by \code{wait.generations}) or if the gradients are not zero (determined by \code{gradient.check}). \cr Please see \code{MemoryMatrix} for some important interactions with memory management.} \item{starting.values}{A vector or matrix containing parameter values which \code{genoud} will use at startup. Using this option, the user may insert one or more individuals into the starting population. If a matrix is provided, the columns should be the variables and the rows the individuals. \code{genoud} will randomly create the other individuals.} \item{MemoryMatrix}{ This variable controls if \code{genoud} sets up a memory matrix. Such a matrix ensures that \code{genoud} will request the fitness evaluation of a given set of parameters only once. The variable may be \code{TRUE} or \code{FALSE}. If it is \code{FALSE}, \code{genoud} will be aggressive in conserving memory. The most significant negative implication of this variable being set to \code{FALSE} is that \code{genoud} will no longer maintain a memory matrix of all evaluated individuals. Therefore, \code{genoud} may request evaluations which it has already previously requested. \cr Note that when \code{nvars} or \code{pop.size} are large, the memory matrix consumes a large amount of RAM. \code{Genoud}'s memory matrix will require somewhat less memory if the user sets \code{hard.generation.limit} equal to \code{TRUE}.} \item{Domains}{ This is a \code{nvars} \eqn{\times 2}{*2} matrix. For each variable, in the first column is the lower bound and in the second column the upper bound. None of \code{genoud}'s starting population will be generated outside of the bounds. But some of the operators may generate children which will be outside of the bounds unless the \code{boundary.enforcement} flag is turned on. \cr If the user does not provide any values for Domains, \code{genoud} will setup default domains using \code{default.domains}. \cr For linear and nonlinear constraints please see the discussion in the \code{Note} section.} \item{default.domains}{ If the user does not want to provide a \code{Domains} matrix, domains may nevertheless be set by the user with this easy to use scalar option. \code{Genoud} will create a Domains matrix by setting the lower bound for all of the parameters equal to -1 \eqn{\times}{*} \code{default.domains} and the upper bound equal to \code{default.domains}.} \item{solution.tolerance}{ This is the tolerance level used by \code{genoud}. Numbers within \code{solution.tolerance} are considered to be equal. This is particularly important when it comes to evaluating \code{wait.generations} and conducting the \code{gradient.check}.} \item{gr}{A function to provide the gradient for the \code{BFGS} optimizer. If it is \code{NULL}, numerical gradients will be used instead.} \item{boundary.enforcement}{ This variable determines the degree to which \code{genoud} obeys the boundary constraints. Notwithstanding the value of the variable, none of \code{genoud}'s starting population values will be outside of the bounds. \cr \code{boundary.enforcement} has three possible values: 0 (anything goes), 1 (partial), and 2 (no trespassing): \itemize{ \item{\emph{0: Anything Goes}}{ This option allows any of the operators to create out-of-bounds individuals and these individuals will be included in the population if their fit values are good enough. The boundaries are only important when generating random individuals.} \item{\emph{1: partial enforcement}}{ This allows operators (particularly those operators which use the derivative based optimizer, BFGS) to go out-of-bounds during the creation of an individual (i.e., out-of-bounds values will often be evaluated). But when the operator has decided on an individual, it \emph{must} be in bounds to be acceptable.} \item{\emph{2: No Trespassing}}{ No out-of-bounds evaluations will ever be requested. In this case, boundary enforcement is also applied to the BFGS algorithm, which prevents candidates from straying beyond the bounds defined by \code{Domains}. Note that this forces the use of the L-BFGS-B algorithm for \code{\link[stats]{optim}}. This algorithm requires that all fit values and gradients be defined and finite for all function evaluations. If this causes an error, it is suggested that the BFGS algorithm be used instead by setting \code{boundary.enforcement=1}.}}} \item{lexical}{This option enables lexical optimization. This is where there are multiple fit criteria and the parameters are chosen so as to maximize fitness values in lexical order---i.e., the second fit criterion is only relevant if the parameters have the same fit for the first etc. The fit function used with this option should return a numeric vector of fitness values in lexical order. This option can take on the values of \code{FALSE}, \code{TRUE} or an integer equal to the number of fit criteria which are returned by \code{fn}. The \code{value} object which is returned by \code{genoud} will include all of the fit criteria at the solution. The \code{\link[Matching]{GenMatch}} function makes extensive use of this option.} \item{gradient.check}{ If this variable is \code{TRUE}, \code{genoud} will not start counting \code{wait.generations} unless each gradient is \code{solution.tolerance} close to zero. This variable has no effect if the \code{max.generations} limit has been hit and the \code{hard.generation.limit} option has been set to \code{TRUE}. If \code{BFGSburnin < 0}, then it will be ignored unless \code{gradient.check = TRUE}. } \item{BFGS}{ This variable denotes whether or not \code{genoud} applies a quasi-Newton derivative optimizer (BFGS) to the best individual at the end of each generation after the initial one. See the \code{optim.method} option to change the optimizer. Setting BFGS to \code{FALSE} does not mean that the BFGS will never be used. In particular, if you want BFGS never to be used, \code{P9} (the Local-Minimum Crossover operator) must also be set to zero.} \item{data.type.int}{ This option sets the data type of the parameters of the function to be optimized. If the variable is \code{TRUE}, \code{genoud} will search over integers when it optimizes the parameters. \cr With integer parameters, \code{genoud} never uses derivative information. This implies that the BFGS quasi-Newton optimizer is never used---i.e., the \code{BFGS} flag is set to \code{FALSE}. It also implies that Operator 9 (Local-Minimum Crossover) is set to zero and that gradient checking (as a convergence criterion) is turned off. No matter what other options have been set to, \code{data.type.int} takes precedence---i.e., if \code{genoud} is told that it is searching over an integer parameter space, gradient information is never considered. \cr There is no option to mix integer and floating point parameters. If one wants to mix the two, it is suggested that the user pick integer type and in the objective function map a particular integer range into a floating point number range. For example, tell \code{genoud} to search from 0 to 100 and divide by 100 to obtain a search grid of 0 to 1.0 (by .1). \cr Alternatively, the user could use floating point numbers and round the appropriate parameters to the nearest integer inside \code{fn} before the criterion (or criteria if \code{lexical = TRUE}) is evaluated. In that case, the \code{transform} option can be used to create the next generation from the current generation when the appropriate parameters are in the rounded state. } \item{hessian}{ When this flag is set to \code{TRUE}, \code{genoud} will return the hessian matrix at the solution as part of its return list. A user can use this matrix to calculate standard errors.} \item{unif.seed}{This sets the seed for the floating-point pseudorandom number generator \code{genoud} uses. The default value of this seed is 81282. \code{genoud} uses its own internal pseudorandom number generator (a Tausworthe-Lewis-Payne generator) to allow for recursive and parallel calls to \code{genoud}. Repeated invocations without specifying this argument cause the program to continue drawing from its internal pseudorandom number stream, which is preserved in a static structure between invocations during the same R session, so the second invocation does not use the same pseudorandom numbers as the first. To produce exactly the same results in a subsequent invocation, one must explicitly provide the same, nondefault value for this argument. \code{genoud} does not use the seed set by R's \code{\link{set.seed}} function. This will change in a subsequent version.} \item{int.seed}{This sets the seed for the integer pseudorandom number generator \code{genoud} uses. The default value of this seed is 53058. \code{genoud} uses its own internal pseudorandom number generator (a Tausworthe-Lewis-Payne generator) to allow for recursive and parallel calls to \code{genoud}. Repeated invocations without specifying this argument cause the program to continue drawing from its internal pseudorandom number stream, which is preserved in a static structure between invocations during the same R session, so the second invocation does not use the same pseudorandom numbers as the first. To produce exactly the same results in a subsequent invocation, one must explicitly provide the same, nondefault value for this argument. \code{genoud} does not use the seed set by R's \code{\link{set.seed}} function. This will change in a subsequent version.} \item{print.level}{ This variable controls the level of printing that \code{genoud} does. There are four possible levels: 0 (minimal printing), 1 (normal), 2 (detailed), and 3 (debug). If level 2 is selected, \code{genoud} will print details about the population at each generation. The \code{print.level} variable also significantly affects how much detail is placed in the project file---see \code{project.path}. Note that R convention would have us at print level 0 (minimal printing). However, because \code{genoud} runs may take a long time, it is important for the user to receive feedback. Hence, print level 2 has been set as the default.} \item{share.type}{ If \code{share.type} is equal to 1, then \code{genoud}, at startup, checks to see if there is an existing project file (see \code{project.path}). If such a file exists, it initializes its original population using it. This option can be used neither with the \code{lexical} nor the \code{transform} options.\cr If the project file contains a smaller population than the current \code{genoud} run, \code{genoud} will randomly create the necessary individuals. If the project file contains a larger population than the current \code{genoud} run, \code{genoud} will kill the necessary individuals using exponential selection. \cr If the number of variables (see \code{nvars}) reported in the project file is different from the current \code{genoud} run, \code{genoud} does not use the project file (regardless of the value of \code{share.type}) and \code{genoud} generates the necessary starting population at random.} \item{instance.number}{ This number (starting from 0) denotes the number of recursive instances of \code{genoud}. \code{genoud} then sets up its random number generators and other such structures so that the multiple instances do not interfere with each other. It is up to the user to make certain that the different instances of \code{genoud} are not writing to the same output file(s): see \code{project.path}. \cr For the R version of \code{genoud} this variable is of limited use. It is basically there in case a \code{genoud} run is being used to optimize the result of another \code{genoud} run (i.e., a recursive implementation).} \item{output.path}{This option is no longer supported. It used to allow one to redirect the output. Now please use \code{\link{sink}}. The option remains in order to provide backward compatibility for the API.} \item{output.append}{This option is no longer supported. Please see \code{\link{sink}}. The option remains in order to provide backward compatibility for the API.} \item{project.path}{ This is the path of the \code{genoud} project file. The project file prints one individual per line with the fit value(s) printed first and then the parameter values. By default \code{genoud} places its output in a file called "genoud.pro" located in the temporary directory provided by \code{\link{tempdir}}. The behavior of the project file depends on the \code{print.level} chosen. If the \code{print.level} variable is set to 1, then the project file is rewritten after each generation. Therefore, only the currently fully completed generation is included in the file. If the \code{print.level} variable is set to 2, then each new generation is simply appended to the project file. For \code{print.level=0}, the project file is not created. } \item{P1}{ This is the cloning operator. \code{genoud} always clones the best individual each generation. But this operator clones others as well. Please see the Operators Section for details about operators and how they are weighted.} \item{P2}{ This is the uniform mutation operator. One parameter of the parent is mutated. Please see the Operators Section for details about operators and how they are weighted.} \item{P3}{ This is the boundary mutation operator. This operator finds a parent and mutates one of its parameters towards the boundary. Please see the Operators Section for details about operators and how they are weighted.} \item{P4}{ Non-Uniform Mutation. Please see the Operators Section for details about operators and how they are weighted.} \item{P5}{ This is the polytope crossover. Please see the Operators Section for details about operators and how they are weighted.} \item{P6}{ Simple Crossover. Please see the Operators Section for details about operators and how they are weighted.} \item{P7}{ Whole Non-Uniform Mutation. Please see the Operators Section for details about operators and how they are weighted.} \item{P8}{ Heuristic Crossover. Please see the Operators Section for details about operators and how they are weighted.} \item{P9}{ Local-Minimum Crossover: BFGS. This is rather CPU intensive, and should be generally used less than the other operators. Please see the Operators Section for details about operators and how they are weighted.} \item{P9mix}{This is a tuning parameter for the \code{P9} operator. The local-minimum crossover operator by default takes the convex combination of the result of a BFGS optimization and the parent individual. By default the mixing (weight) parameter for the convex combination is chosen by a uniform random draw between 0 and 1. The \code{P9mix} option allows the user to select this mixing parameter. It may be any number greater than 0 and less than or equal to 1. If 1, then the BFGS result is simply used.} \item{BFGSburnin}{The number of generations which are run before the BFGS is first used. Premature use of the BFGS can lead to convergence to a local optimum instead of the global one. This option allows the user to control how many generations are run before the BFGS is started and would logically be a non-negative integer. However, if \code{BFGSburnin < 0}, the BFGS will be used if and when \code{wait.generations} is doubled because at least one gradient is too large, which can only occur when \code{gradient.check = TRUE}. This option delays the use of both the BFGS on the best individual and the \code{P9} operator. } \item{BFGSfn}{This is a function for the BFGS optimizer to optimize, if one wants to make it distinct from the \code{fn} function. This is useful when doing \code{lexical} optimization because otherwise a derivative based optimizer cannot be used (since it requires a single fit value). It is suggested that if this functionality is being used, both the \code{fn} and \code{BFGSfn} functions obtain all of the arguments they need (except for the parameters being optimized) by lexical scope instead of being passed in as arguments to the functions. Alternatively, one may use the \code{BFGShelp} option to pass arguments to \code{BFGSfn}. If \code{print.level > 2}, the results from the BFGS optimizer are printed every time it is called.} \item{BFGShelp}{An optional function to pass arguments to \code{BFGSfn}. This function should take an argument named `initial', an argument named `done' that defaults to \code{FALSE}, or at least allow \code{...} to be an argument. \code{BFGSfn} must have an argument named `helper' if \code{BFGShelp} is used because the call to \code{\link[stats]{optim}} includes the hard-coded expression \code{helper = do.call(BFGShelp, args = list(initial = foo.vals), envir = environment(fn)))}, which evaluates the \code{BFGShelp} function in the environment of \code{BFGSfn} (\code{fn} is just a wrapper for \code{BFGSfn}) at \code{par = foo.vals} where \code{foo.vals} contains the starting values for the BFGS algorithm. The `done' argument to \code{BFGSfn} is used if the user requests that the Hessian be calculated at the \code{genoud} solution.} \item{control}{A list of control parameters that is passed to \code{\link[stats]{optim}} if \code{BFGS = TRUE} or \code{P9 > 0}. Please see the \code{\link[stats]{optim}} documentation for details. } \item{optim.method}{A character string among those that are admissible for the \code{method} argument to the \code{\link{optim}} function, namely one of \code{"BFGS"}, \code{"L-BFGS-B"}, \code{"Nelder-Mead"}, \code{"CG"}, or \code{"SANN"}. By default, \code{optim.method} is \code{"BFGS"} if \code{boundary.enforcement < 2} and is \code{"L-BFGS-B"} if \code{boundary.enforcement = 2}. For discontinuous objective functions, it may be advisable to select \code{"Nelder-Mead"} or \code{"SANN"}. If selecting \code{"L-BFGS-B"} causes an error message, it may be advisable to select another method or to adjust the \code{control} argument. Note that the various arguments of \code{genoud} that involve the four letters \dQuote{BFGS} continue to be passed to \code{\link[stats]{optim}} even if \code{optim.method != "BFGS"}.} \item{transform}{A logical that defaults to \code{FALSE}. If \code{TRUE}, it signifies that \code{fn} will return a numeric vector that contains the fit criterion (or fit criteria if \code{lexical = TRUE}), followed by the parameters. If this option is used, \code{fn} should have the following general form in its body:\cr \code{par <- myTransformation(par)}\cr \code{criter <- myObjective(par)}\cr \code{return( c(criter, par) )}\cr This option is useful when parameter transformations are necessary because the next generation of the population will be created from the current generation in the transformed state, rather than the original state. This option can be used by users to implement their own operators. \cr There are some issues that should be kept in mind. This option cannot be used when \code{data.type.int = TRUE}. Also, this option coerces \code{MemoryMatrix} to be \code{FALSE}, implying that the \code{cluster} option cannot be used. And, unless \code{BFGSfn} is specified, this option coerces \code{gradient.check} to \code{FALSE}, \code{BFGS} to \code{FALSE}, and \code{P9} to \code{0}. If \code{BFGSfn} is specified, that function should perform the transformation but should only return a scalar fit criterion, for example:\cr \code{par <- myTransformation(par)}\cr \code{criter <- myCriterion(par)}\cr \code{return(criter)}\cr Finally, if \code{boundary.enforcement > 0}, care must be taken to assure that the transformed parameters are within the \code{Domains}, otherwise unpredictable results could occur. In this case, the transformations are checked for consistency with \code{Domains} but only in the initial generation (to avoid an unacceptable loss in computational speed). } \item{debug}{ This variable turns on some debugging information. This variable may be \code{TRUE} or \code{FALSE}.} \item{cluster}{This can either be an object of the 'cluster' class returned by one of the \code{\link[parallel]{makeCluster}} commands in the \code{parallel} package or a vector of machine names so \code{genoud} can setup the cluster automatically. If it is the latter, the vector should look like: \cr \code{c("localhost","musil","musil","deckard")}.\cr This vector would create a cluster with four nodes: one on the localhost another on "deckard" and two on the machine named "musil". Two nodes on a given machine make sense if the machine has two or more chips/cores. \code{genoud} will setup a SOCK cluster by a call to \code{\link[parallel]{makePSOCKcluster}}. This will require the user to type in her password for each node as the cluster is by default created via \code{ssh}. One can add on usernames to the machine name if it differs from the current shell: "username@musil". Other cluster types, such as PVM and MPI, which do not require passwords can be created by directly calling \code{\link[parallel]{makeCluster}}, and then passing the returned cluster object to \code{genoud}. For an example of how to manually setup up a cluster with a direct call to \code{\link[parallel]{makeCluster}} see \url{http://sekhon.berkeley.edu/rgenoud/R/genoud_cluster_manual.R}. For an example of how to get around a firewall by ssh tunneling see: \url{http://sekhon.berkeley.edu/rgenoud/R/genoud_cluster_manual_tunnel.R}.} \item{balance}{This logical flag controls if load balancing is done across the cluster. Load balancing can result in better cluster utilization; however, increased communication can reduce performance. This option is best used if the function being optimized takes at least several minutes to calculate or if the nodes in the cluster vary significantly in their performance. If cluster==FALSE, this option has no effect.} \item{...}{Further arguments to be passed to \code{fn} and \code{gr}.} } \details{\code{Genoud} solves problems that are nonlinear or perhaps even discontinuous in the parameters of the function to be optimized. When a statistical model's estimating function (for example, a log-likelihood) is nonlinear in the model's parameters, the function to be optimized will generally not be globally concave and may have irregularities such as saddlepoints or discontinuities. Optimization methods that rely on derivatives of the objective function may be unable to find any optimum at all. Multiple local optima may exist, so that there is no guarantee that a derivative-based method will converge to the global optimum. On the other hand, algorithms that do not use derivative information (such as pure genetic algorithms) are for many problems needlessly poor at local hill climbing. Most statistical problems are regular in a neighborhood of the solution. Therefore, for some portion of the search space, derivative information is useful for such problems. \code{Genoud} also works well for problems that no derivative information exists. For additional documentation and examples please see \url{http://sekhon.berkeley.edu/rgenoud}.} \value{\code{genoud} returns a list with 7 objects. 8 objects are returned if the user has requested the hessian to be calculated at the solution. Please see the \code{hessian} option. The returned objects are: \item{value}{ This variable contains the fitness value at the solution. If \code{lexical} optimization was requested, it is a vector.} \item{par}{ This vector contains the parameter values found at the solution.} \item{gradients}{ This vector contains the gradients found at the solution. If no gradients were calculated, they are reported to be \code{NA}.} \item{generations}{ This variable contains the number of generations \code{genoud} ran for.} \item{peakgeneration}{ This variable contains the generation number at which \code{genoud} found the solution.} \item{pop.size}{ This variable contains the population size that \code{genoud} actually used. See \code{pop.size} for why this value may differ from the population size the user requested.} \item{operators}{ This vector reports the actual number of operators (of each type) \code{genoud} used. Please see the Operators Section for details.} \item{hessian}{ If the user has requested the hessian matrix to be returned (via the \code{hessian} flag), the hessian at the solution will be returned. The user may use this matrix to calculate standard errors.} } \section{Operators}{ \code{Genoud} has nine operators that it uses. The integer values which are assigned to each of these operators (P1\eqn{\cdots}{...}P9) are weights. \code{Genoud} calculates the sum of \eqn{s = P1+P2+\cdots+P9}{s = P1+P2+...+P9}. Each operator is assigned a weight equal to \eqn{W_{n} = \frac{s}{P_{n}}}{W_n = s/(P_n)}. The number of times an operator is called usually equals \eqn{c_{n} = W_{n} \times pop.size}{c_n = W_n * pop.size}. \cr Operators 6 (Simple Crossover) and 8 (Heuristic Crossover) require an even number of individuals to work on---i.e., they require two parents. Therefore, the \code{pop.size} variable and the operators sets must be such that these three operators have an even number of individuals to work with. If this does not occur, \code{genoud} automatically upwardly adjusts the population size to make this constraint hold. \cr Strong uniqueness checks have been built into the operators to help ensure that the operators produce offspring different from their parents, but this does not always happen. \cr Note that \code{genoud} always keeps the best individual each generation. \cr \code{genoud}'s 9 operators are: \cr \enumerate{ \item Cloning \item Uniform Mutation \item Boundary Mutation \item Non-Uniform Crossover \item Polytope Crossover \item Simple Crossover \item Whole Non-Uniform Mutation \item Heuristic Crossover \item Local-Minimum Crossover: BFGS} For more information please see Table 1 of the reference article: \url{http://sekhon.berkeley.edu/papers/rgenoudJSS.pdf}.} \note{ The most important options affecting performance are those determining population size (\code{pop.size}) and the number of generations the algorithm runs (\code{max.generations}, \code{wait.generations}, \code{hard.generation.limit} and \code{gradient.check}). Search performance is expected to improve as the population size and the number of generations the program runs for increase. These and the other options should be adjusted for the problem at hand. Please pay particular attention to the search domains (\code{Domains} and \code{default.domains}). For more information please see the reference article. \cr Linear and nonlinear constraints among the parameters can be introduced by users in their fit function. For example, if the sum of parameters 1 and 2 must be less than 725, the following can be placed in the fit function the user is going to have \code{genoud} maximize: \code{if ( (parm1 + parm2) >= 725) \{ return(-99999999) \}}. In this example, a very bad fit value is returned to \code{genoud} if the linear constrain is violated. \code{genoud} will then attempt to find parameter values that satisfy the constraint. \cr Alternatively, one can use lexical optimization where the first criterion is a binary variable that equals 1.0 iff \code{ (parm1 + parm2) < 725} and the second criterion is the fit function, which should also be passed to \code{BFGSfn}. All candidates where \code{ (parm1 + parm2) >= 725} will be ranked below all candidates where \code{ (parm1 + parm2) < 725} and within these two groups, candidates will be ranked by their fit on the second criterion. The optimal candidate is thus the one with the best fit on the second criterion among candidates that satisfy this restriction.} \references{ Mebane, Walter R., Jr. and Jasjeet S. Sekhon. 2011. "Genetic Optimization Using Derivatives: The rgenoud Package for R." \emph{Journal of Statistical Software}, 42(11): 1-26. \url{http://www.jstatsoft.org/v42/i11/} \cr Sekhon, Jasjeet Singh and Walter R. Mebane, Jr. 1998. ``Genetic Optimization Using Derivatives: Theory and Application to Nonlinear Models.'' \emph{Political Analysis}, 7: 187-210. \url{http://sekhon.berkeley.edu/genoud/genoud.pdf} \cr Mebane, Walter R., Jr. and Jasjeet S. Sekhon. 2004. ``Robust Estimation and Outlier Detection for Overdispersed Multinomial Models of Count Data.'' \emph{American Journal of Political Science}, 48 (April): 391-410. \url{http://sekhon.berkeley.edu/multinom.pdf} \cr Bright, H. and R. Enison. 1979. Quasi-Random Number Sequences from a Long-Period TLP Generator with Remarks on Application to Cryptography. \emph{Computing Surveys}, 11(4): 357-370. } \author{Walter R. Mebane, Jr., University of Michigan, \email{wmebane@umich.edu}, \url{http://www-personal.umich.edu/~wmebane/} \cr Jasjeet S. Sekhon, UC Berkeley, \email{sekhon@berkeley.edu}, \url{http://sekhon.berkeley.edu/}} \seealso{ \code{\link[stats]{optim}}. } \examples{ #maximize the sin function sin1 <- genoud(sin, nvars=1, max=TRUE) #minimize the sin function sin2 <- genoud(sin, nvars=1, max=FALSE) \dontrun{ #maximize a univariate normal mixture which looks like a claw claw <- function(xx) { x <- xx[1] y <- (0.46*(dnorm(x,-1.0,2.0/3.0) + dnorm(x,1.0,2.0/3.0)) + (1.0/300.0)*(dnorm(x,-0.5,.01) + dnorm(x,-1.0,.01) + dnorm(x,-1.5,.01)) + (7.0/300.0)*(dnorm(x,0.5,.07) + dnorm(x,1.0,.07) + dnorm(x,1.5,.07))) return(y) } claw1 <- genoud(claw, nvars=1,pop.size=3000,max=TRUE) } \dontrun{ #Plot the previous run xx <- seq(-3,3,.05) plot(xx,lapply(xx,claw),type="l",xlab="Parameter",ylab="Fit", main="GENOUD: Maximize the Claw Density") points(claw1$par,claw1$value,col="red") # Maximize a bivariate normal mixture which looks like a claw. biclaw <- function(xx) { mNd2 <- function(x1, x2, mu1, mu2, sigma1, sigma2, rho) { z1 <- (x1-mu1)/sigma1 z2 <- (x2-mu2)/sigma2 w <- (1.0/(2.0*pi*sigma1*sigma2*sqrt(1-rho*rho))) w <- w*exp(-0.5*(z1*z1 - 2*rho*z1*z2 + z2*z2)/(1-rho*rho)) return(w) } x1 <- xx[1]+1 x2 <- xx[2]+1 y <- (0.5*mNd2(x1,x2,0.0,0.0,1.0,1.0,0.0) + 0.1*(mNd2(x1,x2,-1.0,-1.0,0.1,0.1,0.0) + mNd2(x1,x2,-0.5,-0.5,0.1,0.1,0.0) + mNd2(x1,x2,0.0,0.0,0.1,0.1,0.0) + mNd2(x1,x2,0.5,0.5,0.1,0.1,0.0) + mNd2(x1,x2,1.0,1.0,0.1,0.1,0.0))) return(y) } biclaw1 <- genoud(biclaw, default.domains=20, nvars=2,pop.size=5000,max=TRUE) } # For more examples see: http://sekhon.berkeley.edu/rgenoud/R. } \keyword{optimize} \keyword{nonlinear} % LocalWords: genoud GENetic GAs fn nvars max MemoryMatrix BFGS hessian unif % LocalWords: stdout Polytope cr emph eqn GENOUD's peakgeneration dfrac optim % LocalWords: seealso saddlepoints lapply xlab ylab biclaw mNd polytope cdots % LocalWords: frac url jasjeet RGENOUD PVM MPI parm Overdispersed UC dontrun % LocalWords: bivariate CPUs startup Genoud's GenMatch tempdir makeCluster % LocalWords: localhost musil deckard makePSOCKcluster usernames univariate % LocalWords: SANN dQuote BFGSburnin BFGSfn BFGShelp myCriterion iff Mebane TLP % LocalWords: Singh rgenoud Multinomial Enison dnorm pseudorandom Tausworthe % LocalWords: nondefault args vals envir Nelder myTransformation criter % LocalWords: myObjective rgenoud/.Rinstignore0000644000176200001440000000004611762640255014231 0ustar liggesusersinst/doc/Figures/* inst/doc/Figures rgenoud/INDEX0000644000176200001440000000007710330611541012505 0ustar liggesusersgenoud GENetic Optimization Using Derivatives