# Genetic algorithm for subset selection no given test It uses a genetic algorithm to select $n_{Train}$ individuals so that optimality criterion is minimum. The test set is taken as the complement of the training individuals. ```r GenAlgForSubsetSelectionNoTest(P, ntoselect, npop = 100, nelite = 5, keepbest = TRUE, tabu = TRUE, tabumemsize = 1, mutprob=.8, mutintensity = 1, niterations = 500, minitbefstop = 200, niterreg = 5, lambda = 1e-06, plotiters = FALSE, plottype=1, errorstat = "PEVMEAN2", C = NULL, mc.cores = 1, InitPop = NULL, tolconv = 1e-07, Vg = NULL, Ve = NULL, Fedorov=FALSE) ``` ## Arguments - `P`: depending on the criterion this is either a numeric data matrix or a symmetric similarity matrix. When it is a data matrix, the union of the identifiers of the candidate individuals should be put as rownames (and column names in case of a similarity matrix). For methods using the relationships, this is the inverse of the relationship matrix with row and column names as the the identifiers of the candidate individuals. - `ntoselect`: $n_{Train}:$ number of individuals to select in the training set. - `npop`: genetic algorithm parameter, number of solutions at each iteration - `nelite`: genetic algorithm parameter, number of solutions selected as elite parents which will generate the next set of solutions. - `keepbest`: genetic algorithm parameter, TRUE or FALSE. If TRUE then the best solution is always kept in the next generation of solutions (elitism). - `tabu`: genetic algorithm parameter, TRUE or FALSE. If TRUE then the solutions that are saved in tabu memory will not be retried. - `tabumemsize`: genetic algorithm parameter, integer>0. Number of generations to hold in tabu memory. - `mutprob`: genetic algorithm parameter, probability of mutation for each generated solution. - `mutintensity`: mean of the poisson variable that is used to decide the number of mutations for each cross. - `niterations`: genetic algorithm parameter, number of iterations. - `minitbefstop`: genetic algorithm parameter, number of iterations before stopping if no change is observed in criterion value. - `niterreg`: genetic algorithm parameter, number of iterations to use regressions, an integer with minimum value of 1 - `lambda`: scalar shrinkage parameter ($\lambda>0$). - `plotiters`: plot the convergence: TRUE or FALSE. Default is TRUE. - `plottype`: type of plot, default is 1. possible values 1,2,3. - `errorstat`: optimality criterion: One of the optimality criterion. Default is "PEVMEAN". It is possible to use user defined functions as shown in the examples. - `mc.cores`: number of cores to use. - `InitPop`: a list of initial solutions - `tolconv`: if the algorithm cannot improve the errorstat more than tolconv for the last minitbefstop iterations it will stop. - `C`: Contrast Matrix. - `Vg`: covariance matrix between traits generated by the relationship K (only for multi-trait version of PEVMEANMM). - `Ve`: residual covariance matrix for the traits (only for multi-trait version of PEVMEANMM). - `Fedorov`: Whether the Fedorovs exchange algorithm from `AlgDesign` Package should be used for initial solutions. ## Returns A list of length nelite+1. The first nelite elements of the list are optimized training samples of size $n_{train}$ and they are listed in increasing order of the optimization criterion. The last item on the list is a vector that stores the minimum values of the objective function at each iteration. ## Author(s) Deniz Akdemir ## Note The GA does not guarantee convergence to globally optimal solutions and it is highly recommended that the algorithm is replicated to obtain ''good'' training samples. ## Examples ```r ## Not run: ###################### Example for three level designs for the #second order model in two factors with a square design region X<-matrix(0,nrow=3^2,ncol=5) ij=0 for (i in -1:1){ for (j in -1:1){ ij=ij+1 X[ij,]<-c(i,j, i^2,j^2, i*j) } } X<-cbind(1,X) D<-as.matrix(dist(X)) K<-tcrossprod(X) rownames(K)<-colnames(K)<-rownames(D)<-colnames(D)<-rownames(X)<-paste("x",1:3^2, sep="") X library(STPGA) ListTrain1<-GenAlgForSubsetSelectionNoTest(P=X,ntoselect=4, InitPop=NULL, npop=100, nelite=5, mutprob=.5, mutintensity = 1, niterations=200,minitbefstop=20, tabu=F,tabumemsize = 0,plotiters=F, lambda=1e-9,errorstat="DOPT", mc.cores=1) ListTrain2<-GenAlgForSubsetSelectionNoTest(P=solve(K+1e-6*diag(ncol(K))),ntoselect=4, InitPop=NULL, npop=100, nelite=5, mutprob=.5, mutintensity = 1, niterations=200,minitbefstop=20, tabu=F,tabumemsize = 0,plotiters=F, lambda=1,errorstat="CDMEANMM", mc.cores=1) par(mfrow=c(1,2),mar=c(1,1,1,1)) labelling1<-rownames(X)%in%ListTrain1[[1]]+1 plot(X[,2], X[,3], col=labelling1, pch=2*labelling1,cex=2*(labelling1-1), xlab="", ylab="", main="DOPT", cex.main=.7,xaxt='n',yaxt='n') for (i in -1:1){ abline(v=i, lty=2) abline(h=i,lty=2) } labelling2<-rownames(X)%in%ListTrain2[[1]]+1 plot(X[,2], X[,3], col=labelling2, pch=2*labelling2,cex=2*(labelling2-1), xlab="", ylab="", main="CDMEANMM", cex.main=.7,xaxt='n',yaxt='n') for (i in -1:1){ abline(v=i, lty=2) abline(h=i,lty=2) } ########################Dopt design three level designs for the second order #model in two factors with a square design region par(mfrow=c(2,2),mar=c(1,1,1,1)) for (ntoselect in c(5,6,7,8)){ ListTrain<-GenAlgForSubsetSelectionNoTest(P=X,ntoselect=ntoselect, InitPop=NULL, npop=10, nelite=3, mutprob=.5, mutintensity = 1, niterations=200,minitbefstop=200, tabu=F,tabumemsize = 0,plotiters=F, lambda=1e-9,errorstat="DOPT", mc.cores=1) labelling<-rownames(X)%in%ListTrain[[1]]+1 plot(as.numeric(X[,2]), as.numeric(X[,3]), col=labelling, pch=2*labelling,cex=2*(labelling-1), xlab="", ylab="", main="DOPT", cex.main=.7,xaxt='n',yaxt='n') for (i in -1:1){ abline(v=i, lty=2) abline(h=i,lty=2) } } par(mfrow=c(1,1)) ## End(Not run) ```

GenAlgForSubsetSelectionNoTest function