A dynamic system model of biogeography-based optimization

Abstract

Abstract We derive a dynamic system model for biogeography-based optimization (BBO) that is asymptotically exact as the population size approaches infinity. The states of the dynamic system are equal to the proportion of each individual in the population; therefore, the dimension of the dynamic system is equal to the search space cardinality of the optimization problem. The dynamic system model allows us to derive the proportion of each individual in the population for a given optimization problem using theory rather than simulation. The results of the dynamic system model are more precise than simulation, especially for individuals that are very unlikely to occur in the population. Since BBO is a generalization of a certain type of genetic algorithm with global uniform recombination (GAGUR), an additional contribution of our work is a dynamic system model for GAGUR. We verify our dynamic system models with simulation results. We also use the models to compare BBO, GAGUR, and a GA with single-point crossover (GASP) for some simple problems. We see that with small mutation rates, as are typically used in real-world problems, BBO generally results in better optimization results than GAs for the problems that we investigate.