Variations of biogeography-based optimization and Markov analysis

Biogeography-based optimization (BBO) is a new evolutionary algorithm that is inspired by biogeography. Previous work has shown that BBO is a competitive optimization algorithm, and it demonstrates good performance on various benchmark functions and real-world optimization problems. Motivated by biogeography theory and previous results, three variations of BBO migration are introduced in this paper. We refer to the original BBO algorithm as partial immigration-based BBO. The new BBO variations that we propose are called total immigration-based BBO, partial emigration-based BBO, and total emigration-based BBO. Their corresponding Markov chain models are also derived based on a previously-derived BBO Markov model. The optimization performance of these BBO variations is analyzed, and new theoretical results that are confirmed with simulation results are obtained. Theoretical results show that total emigration-based BBO and partial emigration-based BBO perform the best for three-bit unimodal problems, partial immigration-based BBO performs the best for three-bit deceptive problems, and all these BBO variations have similar results for three-bit multimodal problems. Performance comparison is further investigated on benchmark functions with a wide range of dimensions and complexities. Benchmark results show that emigration-based BBO performs the best for unimodal problems, and immigration-based BBO performs the best for multimodal problems. In addition, BBO is compared with a stud genetic algorithm (SGA), standard particle swarm optimization (SPSO 07), and adaptive differential evolution (ADE) on real-world optimization problems. The numerical results demonstrate that BBO outperforms SGA and SPSO 07, and performs similarly to ADE for the real-world problems.