An analysis on genetic algorithms using Markov process with rewards

We propose a new method to analyze the behavior of genetic algorithms (GAs) using Markov processes with rewards, which are extensions of Markov processes by introducing a concept of rewards. We analyze some simple models of GAs by our method and derive expected maximum and mean fitness values of these models. These values are explicitly expressed as functions of generations and can be calculated without simulations, even for the generations at infinity. We discuss the optimum value of mutation rate and compare the maximum and mean fitness based on these results