A Markov model of biogeography-based optimization for complex systems

Biogeography-based optimization (BBO) is an evolutionary algorithm that is inspired by nature. Because of its good performance relative to other evolutionary algorithms, it has become a popular algorithm for many different applications. Also, it has been modified in several ways to accommodate various types of problems. BBO for complex systems (BBO/Complex) is a recently-developed variation of BBO which provides a state-of-the-art algorithm for the optimization of complex systems (that is, systems with multiple related subsystems, each including multiple objectives and multiple constraints). Markov models have been used to theoretically model and analyze different versions of BBO, and to successfully predict steady-state BBO results. In this paper, we derive a Markov model for BBO/Complex. The Markov model derived here provides an exact mathematical model of BBO/Complex in the limit as the generation count becomes infinite. Simulation results are provided to confirm the new Markov model.