One of the most fundamental problems in the practice of Genetic Algorithms (GAs) is the choice of population size N. Theoretical investigation of this problem with a finite population size requires stochastic theory. In this study, We examined effects of stochastic fluctuation in a GA on the multiplicative landscape. We used Markov chain model and its diffusion approximation to calculate the distribution of the first order schemata. In numerical experiments, we found that the effect of stochastic fluctuation becomes larger when we use smaller population size N. If selection strength is small, the effect of stochastic fluctuation is very strong, and this causes significant N-dependence. We applied diffusion approximation in the analysis of GA calculations, and found that this theory can explain various aspects of the GA on the multiplicative landscape.
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