A Markov Chain Analysis of Parallel Genetic Algorithms with Arbitrary Topologies and Migration Rates

Implementations of parallel genetic algorithms (GAs) with multiple populations are common , but they introduce several parameters whose eeect 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 shows how to predict the eeects of the parallel GA's parameters on its search quality. The analysis considers any number of populations of arbitrary size, and does not place limitations on the topology of communications or the migration rate. 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 arbitrary conngurations of parallel GAs. This investigation considers that migration occurs only after each population converges; then incoming individuals are incorporated into the populations and the algorithm restarts. The analysis nds the probability that each population converges to the correct solution after each restart, and also calculates the long-run chance of success.