Influence of Finite Population Size –Extinction of Favorable Schemata–

Abstract

Since genetic algorithms (GAs) treat a population of finite size, it is necessary to study stochastic fluctuations in evolution processes. In this study, we investigated the influence of genetic drift due to finite population size on the performance of a GA on the multiplicative landscape. There was large difference between numerical experiments with small population size and the prediction of deterministic model. It was observed in some experiments that favorable first order schemata were lost from the population. It was also noted that the population can be assumed to be in linkage equilibrium in the GA including crossover. Then we performed the theoretical investigation of frequencies of the first order schemata, and calculated their changes in time by using the Wright-Fisher model and diffusion equations. We showed that these mathematical theories reasonably predict various quantities including the ultimate extinction probability. We found that the extinction of favorable schemata is the most undesirable effect of genetic drift.