Biogeography-Based Multi-Objective Discrete Optimization with Constraints

Biogeography-based optimization (BBO) is an intelligent evolutionary algorithm based on biological populations, increasing the optimization search ability by adaptive migration operation. However, the original BBO is only feasible for continuous optimization with single-objective optimization, instead of more complex optimization problems, such as discrete and multi-objective optimization problems. Therefore, in this article, we propose the improved BBO algorithm to solve multi-objective discrete optimization problem with multiple constraints. We define the decision matrix, objective vector to fit variables and objective functions of the multi-objective discrete optimization problem, and define the ideal point and utility function so that different candidate solutions can be judged according to a metric. We propose similarity threshold, repeatability threshold, cost threshold, and stagnation threshold to make the proposed algorithm improve the diversity of search solutions and give consideration to convergence. Moreover, we conduct a case study on the NP-hard problem of composite functions, and the experimental results verify the effectiveness and efficiency of our approach.