In order to study genetic algorithms in co-evolutionary environments, we construct a Markov model of co-evolution of populations with fixed, finite population sizes. In this combined Markov model, the behavior toward the limit can be utilized to study the relative performance of the algorithms. As an application of the model, we perform an analysis of the relative performance of haploid versus diploid genetic algorithms in the co-evolutionary setup, under several parameter settings. Because of the use of Markov chains, this paper provides exact stochastic results on the expected performance of haploid and diploid algorithms in the proposed co-evolutionary model.
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