Gene pool recombination, genetic algorithm, and the onemax function

Abstract

In this paper we present an analysis of gene pool recombination in genetic algorithms in the context of the onemax function. We have developed a Markov chain framework for computing the probability of convergence, and have shown how the analysis can be used to estimate the critical population size. The Markov model is used to investigate drift in the multiple-loci case. Additionally, we have estimated the minimum population size needed for optimality, and recurrence relations describing the growth of the advantageous allele in the infinite-population case have been derived. Simulation results are presented.