An analysis of the equilibrium of migration models for biogeography-based optimization

Motivated by the migration mechanisms of ecosystems, various extensions to biogeography-based optimization (BBO) are proposed here. As a global optimization method, BBO is an original algorithm based on the mathematical model of organism distribution in biological systems. BBO is an evolutionary process that achieves information sharing by biogeography-based migration operators. In BBO, habitats represent candidate problem solutions, and species migration represents the sharing of features between candidate solutions according to the fitness of the habitats. This paper generalizes equilibrium species count results in biogeography theory, explores the behavior of six different migration models in BBO, and investigates performance through 23 benchmark functions with a wide range of dimensions and diverse complexities. The performance study shows that sinusoidal migration curves provide the best performance among the six different models that we explored. In addition, comparison with other biology-based optimization algorithms is investigated, and the influence of the population size, problem dimension, mutation rate, and maximum migration rate of BBO are also studied.