An analysis of the migration rates for biogeography-based optimization

Biogeography-Based Optimization (BBO), inspired by the science of biogeography, is a novel population-based Evolutionary Algorithm (EA). For optimization problems, BBO builds the matching mathematical model of the organism distribution. In this evolutionary mechanism, species migrating among islands can be considered as the information transition among different solutions represented by habitats. Solutions are reassembled according to migration rates. However, so far, the migration models are generally designed by empirical studies. This leads to immature conclusions that are unreliable. To complete the previous works, this paper investigates transition probability matrices of BBO to clarify that the transition probability of median number of species is not the only determinant factor to influence performance. The impact of migration rates on BBO is mathematically discussed, which is helpful to design migration models. Using numerical simulations, the BBO and several other classical evolutionary algorithms are compared. The simulations also comprehensively explain the effect of the BBO's properties on its performance including dimension, population size, and migration models. The results validate the theoretical analysis in this paper.

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