Large-Scale Multiobjective Optimization via Reformulated Decision Variable Analysis

Abstract

With the rising number of large-scale multiobjective optimization problems (LSMOPs) from academia and industries, some multiobjective evolutionary algorithms (MOEAs) with different decision variable handling strategies have been proposed. Decision variable analysis (DVA) is widely used in large-scale optimization, aiming at identifying the connection between each decision variable and the objectives, and grouping those interacting decision variables to reduce the complexity of LSMOPs. Despite their effectiveness, existing DVA techniques require the unbearable cost of function evaluations for solving LSMOPs. We propose a reformulation based approach for efficient DVA to address this deficiency. Then a large-scale MOEA is proposed based on reformulated DVA, namely LERD. Specifically, the DVA process is reformulated into an optimization problem with binary decision variables, aiming to approximate different grouping results. Afterwards, each group of decision variables is used for convergence-related or diversity-related optimization. The effectiveness and efficiency of the reformulation based DVA are validated by replacing the corresponding DVA techniques in two large-scale MOEAs. Experiments in comparison with six state-of-the-art large-scale MOEAs on LSMOPs with up to 2000 decision variables have shown the promising performance of LERD.