A two-stage differential biogeography-based optimization algorithm and its performance analysis

Abstract

Abstract Biogeography-based optimization (BBO) has drawn a lot of attention as its outstanding performance. However, same with certain typical swarm optimization algorithm, BBO severely suffers from premature convergence problem and the rotational variance of migration operator. In this paper, a two-stage differential biogeography-based optimization (TDBBO) is proposed to address the premature convergence problem and alleviate the rotational variance. In the migration operator, the emigration model is selected according to the two-stage mechanism. The constant emigration model is employed to maintain the diversity of population in the early evolutionary process. The sinusoidal emigration model is selected to accelerate the convergence speed in the late evolutionary process. Meanwhile, the BBO/current-to-select/1, which is a rotationally invariant arithmetic crossover operator, is designed to alleviate the rotational variance. The standard mutation operator is replaced by the Gaussian mutation operator to jump out the local optimum effectively. The greedy selection strategy is introduced to accelerate the convergence speed after the migration and the mutation operators. Besides, the convergence performance of TDBBO is analyzed with the Markov model. Compared with the standard BBO and other outstanding BBO variants on CEC 2017 benchmarks, the TDBBO is superior to the state-of-art BBO variants in terms of solution quality, convergence speed and stability. The TDBBO lays a solid foundation for solving optimization problems of expert and intelligent systems.