A supercomputing method for large-scale optimization: a feedback biogeography-based optimization with steepest descent method

To apply biogeography-based optimization (BBO) to large scale optimization problems, this paper proposes a novel BBO variant based on feedback differential evolution mechanism and steepest descent method, referred to as FBBOSD. Firstly, the immigration refusal mechanism is proposed to eliminate the damage of inferior solutions to superior solutions. Secondly, the dynamic hybrid migration operator is designed to balance the exploration and exploitation, which makes BBO suitable for high-dimensional environment. Thirdly, the feedback differential evolution mechanism is designed to make FBBOSD can select mutation modes intelligently. Finally, the steepest descent method is creatively combined with BBO, which further improves the convergence accuracy. Meanwhile, a sequence convergence model is established to prove the convergence of FBBOSD. Quantitative evaluations: FBBOSD is compared with BBO, seven BBO variants and seven state-of-the-art evolutionary algorithms, respectively. The experimental results on 24 benchmark functions and CEC2017 show that FBBOSD outperforms all compared algorithms, and the dimension of solving optimization problems can reach 10,000. Then, FBBPOSD is applied to engineering design problems. The simulation results demonstrate that it is also effective on constrained optimization problems. In short, FBBOSD has excellent performance and outstanding stability, which is a new algorithm worthy of adoption and promotion.