Markov chain model of schema evolution and its application to stationary distribution

Abstract

Markov chain is a powerful tool for analyzing the evolutionary process of a stochastic system. To select GA parameters such as mutation rate and population size are important in practical application. The value of this parameter has a big effect on the viewpoint of Markov chain. In this paper, we consider properties of stationary distribution with mutation in GAs. We used Markov chain to calculate distribution. If the population is in linkage equilibrium, we used Wright-Fisher model to get the distribution of first order schema. We define the mixing time is the time to arrive stationary distribution. We adopt Hunter's mixing time to estimate the mixing time Tm of the first order schema.