Gaussian diffusion in a simple genetic algorithm

Abstract

We present a central limit theorem for the population process of a simple genetic algorithm. This theory approximates the discrete population process with s population size by a continuous Gaussian - process. As a special application we consider a search space with only two elements. For this case we present a complete solution of the differential equation arising in the calculation of the Gaussian - process. This analysis gives first insight into the theory of the general case. Some applications of the theory and extensions to the general case are mentioned, too.