Cooperative coevolution for large-scale global optimization based on fuzzy decomposition

Cooperative coevolution (CC) is an effective evolutionary divide-and-conquer strategy that solves large-scale global optimization (LSGO) by decomposing the problem into a set of lower-dimensional subproblems. The main challenge of CC is to find an optimal decomposition. Differential Grouping (DG) is a competitive decomposition method to identify the variable interaction with several improved versions like GDG and DG2. Although DG-based decomposition methods have shown superior performance compared to the other decomposition methods, they still have difficulty to deal with the overlapping problems since their optimal decomposition is unknown. To address this issue, instead of pursuing the high accuracy of decomposition, we propose a novel fuzzy decomposition algorithm that groups the variables according to their interaction degree. In the proposed fuzzy decomposition algorithm, the interaction structure matrix and the interactive degree for a LSGO problem are calculated at first according to the interaction among all the decision variables. Then the number of subgroups is determined based on the interactive degree. Based on the interaction structure matrix, a spectral clustering algorithm is proposed to decompose the decision variables with regard to the number of subgroups in order to achieve a better balance between high grouping accuracy and suitable group size. The proposed decomposition algorithm with DECC has been proven to outperform several state-of-the-art algorithms on the latest LSGO benchmark functions.

Automated summary

Cooperative coevolution is an effective strategy for solving large-scale global optimization by decomposing the problem into lower-dimensional subproblems. Differential Grouping is a competitive decomposition method, but faces challenges with overlapping problems. A novel fuzzy decomposition algorithm based on interaction degree has been proposed to address this issue.