# Genetic algorithm for subset selection It uses a genetic algorithm to select $n_{Train}$ individuals so that optimality criterion is minimum. ```r GenAlgForSubsetSelection(P, Candidates, Test, ntoselect, npop = 100, nelite = 5, keepbest = TRUE, tabu = TRUE, tabumemsize = 1, mutprob = 0.8, 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 (and test) 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 (and test) individuals. - `Candidates`: vector of identifiers for the individuals in the candidate set. - `Test`: vector of identifiers for the individuals in the test set. - `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: #################################### library(EMMREML) library(STPGA) data(WheatData) svdWheat<-svd(Wheat.K, nu=5, nv=5) PC50WHeat<-Wheat.K%*%svdWheat$v plot(PC50WHeat[,1],PC50WHeat[,2]) rownames(PC50WHeat)<-rownames(Wheat.K) DistWheat<-dist(PC50WHeat) TreeWheat<-hclust(DistWheat) TreeWheat<-cutree(TreeWheat, k=4) Test<-rownames(PC50WHeat)[TreeWheat==4] length(Test) Candidates<-setdiff(rownames(PC50WHeat), Test) ###instead of using the algorithm directly using a wrapper to ###implement an for multiple starting points for genetic algorithm. repeatgenalg<-function(numrepsouter,numrepsinner){ StartingPopulation2=NULL for (i in 1:numrepsouter){ print("Rep:") print(i) StartingPopulation<-lapply(1:numrepsinner, function(x){ GenAlgForSubsetSelection(P=PC50WHeat,Candidates=Candidates, Test=Test, ntoselect=50, InitPop=StartingPopulation2, npop=50, nelite=5, mutprob=.5, mutintensity = rpois(1,4), niterations=10,minitbefstop=5, tabumemsize = 2,plotiters=TRUE, lambda=1e-9,errorstat="CDMEAN", mc.cores=1)}) StartingPopulation2<-vector(mode="list", length = numrepsouter*1) ij=1 for (i in 1:numrepsinner){ for (j in 1:1){ StartingPopulation2[[ij]]<-StartingPopulation[[i]][[j]] ij=ij+1 } } } ListTrain<-GenAlgForSubsetSelection(P=PC50WHeat,Candidates=Candidates, Test=Test,ntoselect=50, InitPop=StartingPopulation2,npop=100, nelite=10, mutprob=.5, mutintensity = 1,niterations=300, minitbefstop=100, tabumemsize = 1,plotiters=T, lambda=1e-9,errorstat="CDMEAN", mc.cores=1) return(ListTrain) } ListTrain<-repeatgenalg(20, 3) ###test sample deptestopt<-Wheat.Y[Wheat.Y$id%in%Test,] ##predictions by optimized sample deptrainopt<-Wheat.Y[(Wheat.Y$id%in%ListTrain[[1]]),] Ztrain<-model.matrix(~-1+deptrainopt$id) Ztest<-model.matrix(~-1+deptestopt$id) modelopt<-emmreml(y=deptrainopt$plant.height,X=matrix(1, nrow=nrow(deptrainopt), ncol=1), Z=Ztrain, K=Wheat.K) predictopt<-Ztest%*%modelopt$uhat corvecrs<-c() for (rep in 1:300){ ###predictions by a random sample of the same size rs<-sample(Candidates, 50) deptestrs<-Wheat.Y[Wheat.Y$id%in%Test,] deptrainrs<-Wheat.Y[(Wheat.Y$id%in%rs),] Ztrain<-model.matrix(~-1+deptrainrs$id) Ztest<-model.matrix(~-1+deptestrs$id) library(EMMREML) modelrs<-emmreml(y=deptrainrs$plant.height,X=matrix(1, nrow=nrow(deptrainrs), ncol=1), Z=Ztrain, K=Wheat.K) predictrs<-Ztest%*%modelrs$uhat corvecrs<-c(corvecrs,cor(predictrs, deptestrs$plant.height)) } mean(corvecrs) cor(predictopt, deptestopt$plant.height) plot(PC50WHeat[,1],PC50WHeat[,2], col=rownames(PC50WHeat)%in%ListTrain[[1]]+1, pch=2*rownames(PC50WHeat)%in%Test+1, xlab="pc1", ylab="pc2") ## End(Not run) ```

GenAlgForSubsetSelection function