Markov Models for Biogeography-Based Optimization and Genetic Algorithms with Global Uniform Recombination

Biogeography-based optimization (BBO) is a population-based evolutionary algorithm (EA) that is based on the mathematics of biogeography. Biogeography is the study of the geographical distribution of biological organisms. In BBO, problem solutions are represented as islands, and the sharing of features between solutions is represented as migration. BBO is similar to a genetic algorithm with global uniform recombination (GAGUR). This paper derives Markov models for BBO and GAGUR. Our models provide the limiting (stationary) probability of each population distribution for a given problem. We compare the Markov models for BBO, GAGUR, and GA with single-point crossover (GASP), which was derived by previous researchers. Comparisons on various types of simple problems (unimodal, multimodal, deceptive, and hierarchical) show that with high mutation rates the performance of BBO, GAGUR, and GASP is similar. With low mutation rates BBO outperforms GASP and GAGUR.