A Reduced Markov Model of GAs Without the Exact Transition Matrix

Abstract

Modelling a finite population genetic algorithm (GA) as a Markov chain can quickly become unmanageable since the number of population states increases rapidly with the population size and search space size. One approach to resolving this issue is to “lump” similar states together, so that a tractable Markov chain can be produced. A paper by Spears and De Jong in [1] presents an algorithm that can be used to lump states together, thus compressing the probability transition matrix. However, to obtain a lumped model, one needs to calculate the exact transition matrix before the algorithm can be applied to it. In this paper, we explore the possibility of producing a reduced Markov model without the need to first produce the exact model. We illustrate this approach using the Vose model and Spears lumping algorithm on the Onemax problem with a selection-mutation GA.