A decomposition approach for large-scale non-separable optimization problems

Abstract

Large-scale optimization is the key to many practical decision processes. To deal with the dimensional issue in such problems, many approaches incorporate a divide-and-conquer strategy. Among them, cooperative coevolution approaches have recently gained popularity. Depending on the problem’s structure, the decomposition of any large problem, into a number of smaller sub-problems, may leave some variables common in more than one sub-problem. Such a decomposition may have a negative effect on the quality of the final solution of an optimization problem. In this paper, we have proposed an algorithm that incorporates a novel decomposition method, where the objective of decomposition is to minimize the number of common variables between sub-problems, achieved by exploiting a variable interaction matrix developed from the problem. So the algorithm works as a two-stage approach, where the first stage is the problem decomposition, and the second stage is to find the solutions of the problem. The performance of our proposed algorithm is assessed by solving different sets of large-scale non-separable benchmark functions with up to 2,905 variables. The experimental results provide important insights into the efficiency of the proposed decomposition method, which in turn improves the performance of the optimization process.