Effects of population size on the performance of genetic algorithms and the role of crossover

Abstract

One of the most important parameters in the application of genetic algorithms (GAs) is the population size N. In many cases, the choice of N determines the quality of the solutions obtained. The study of GAs with a finite population size requires a stochastic treatment of evolution. In this study, we examined the effects of genetic fluctuations on the performance of GA calculations. We considered the role of crossover by using the stochastic schema theory within the framework of the Wright-Fisher model of Markov chains. We also applied the diffusion approximation of the Wright-Fisher model. In numerical experiments, we studied effects of population size N and crossover rate pc on the success probability S. The success probability S is defined as the probability of obtaining the optimum solution within the limit of reaching the stationary state. We found that in a GA with pc, the diffusion equation can reproduce the success probability S. We also noted the role of crossover, which greatly increases S.