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 paper, a cooperative coevolution with knowledge-based variable decomposition, called 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 cooperative coevolution 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.