The problem of ﬁnding the binomial population with the highest success probability is considered when the number of binomial populations is large. A new rigorous indifference zone subset selection procedure for binomial populations is proposed with the proof of the corresponding least favorable conﬁguration. For cases involving large numbers of binomial populations, a simulation optimization method combining the proposed subset selection procedure with an elitist Genetic Algorithm (GA) is proposed to ﬁnd the highest-mean solution. Convergence of the proposed GA frame work are established under general assumptions. The problem of deriving supersaturated screening designs is described and used to illustrate the application of all methods. Computational comparisons are also presented for the problem of generating supersaturated experimental designs.