Cooperative Coevolution With Knowledge-Based Dynamic Variable Decomposition for Bilevel Multiobjective Optimization

Many practical multiobjective optimization problems have a nested bilevel structure in variables, which can be modeled as bilevel multiobjective optimization problems (BLMOPs). In this article, a cooperative coevolution (CC) with knowledge-based variable decomposition, called bilevel multiobjective CC (BLMOCC), is proposed for BLMOPs. In BLMOCC, the variable interactions are represented by an interaction matrix. The perturbation-based variable decomposition combined with the matrix completion approach has been designed for dynamically discovering the correlation among the bilevel variables, based on which the variables are divided into different groups. To further handle possible weak correlations among various groups of variables, a CC has been adopted for optimizing them in a collaborative way. In experimental studies, BLMOCC is compared with a nested method (NS) and a state-of-the-art algorithm (H-BLEMO) on a set of benchmark problems. The effects of each component in BLMOCC have also been verified by comparing it with its three variants. The experimental results demonstrate that BLMOCC has the best performance among all the compared algorithms. In addition, BLMOCC has also been applied to a real-world management decision-making problem, which further validates its efficiency and effectiveness.

Automated summary

This article proposes a cooperative coevolution method called bilevel multiobjective CC (BLMOCC) for solving bilevel multiobjective optimization problems. BLMOCC handles the interactions among variables through variable decomposition and matrix completion, and optimizes them collaboratively using a cooperative coevolution approach. Experimental studies show that BLMOCC achieves the best performance among compared algorithms on benchmark problems, and it is also effective in a real-world management decision-making problem.