A hybrid biogeography-based optimization algorithm to solve high-dimensional optimization problems and real-world engineering problems

Abstract

According to our extensive investigation, Biogeography-based optimization (BBO) and its variants have not been applied to solve high-dimensional optimization problems. To make a breakthrough in this field, a new BBO variant with hybrid migration operator and feedback differential evolution mechanism, HFBBO, is proposed. Firstly, the example learning method is used to ensure the inferior solutions cannot destroy the superior solutions. Secondly, the hybrid migration operator is presented to balance the exploration and exploitation. It enables the algorithm to switch freely between local search and global search. Finally, the feedback differential evolution mechanism is designed to replace the random mutation operator. HFBBO can select the mutation mode intelligently by this mechanism to avoid getting stuck in local optima. Meanwhile, the Markov model is established to prove the convergence of HFBBO, and the complexity is also discussed. A series experiments are carried out on 24 benchmark functions, CEC2017 test suite and 12 real-world engineering problems. The results of the Wilcoxon’s rank-sum test and Friedman’s test show that HFBBO has better competitiveness and stability than the 27 compared algorithms. Furtherly, the performance of HFBBO is compared on 1000, 2000, 5000 and 10000 dimensions, respectively. Experimental results show that this method can effectively solve high-dimensional optimization problems.