Markov chain models of parallel genetic algorithms

Implementations of parallel genetic algorithms (GA) with multiple populations are common, but they introduce several parameters whose effect on the quality of the search is not well understood. Parameters such as the number of populations, their size, the topology of communications, and the migration rate have to be set carefully to reach adequate solutions. This paper presents models that predict the effects of the parallel GA parameters on its search quality. The paper reviews some recent results on the case where each population is connected to all the others and the migration rate is set to the maximum value possible. This bounding case is the simplest to analyze, and it introduces the methodology that is used in the remainder of the paper to analyze parallel GA with arbitrary migration rates and communication topologies. This investigation considers that migration occurs only after each population converges; then, incoming individuals are incorporated into the populations and the algorithm restarts. The models find the probability that each population converges to the correct solution after each restart, and also calculate the long-run chance of success. The accuracy of the models is verified with experiments using one additively decomposable function.

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