Solving High-Dimensional Expensive Multiobjective Optimization Problems by Adaptive Decision Variable Grouping

Plenty of decision variable grouping based algorithms have shown satisfactory performance in solving high-dimensional optimization problems. However, most of them are tailored for inexpensive optimization problems. Extending variable grouping method to expensive optimization problems poses many challenges. One of the greatest challenges is that most grouping approaches require additional function evaluations (FEs) to discover interactions among decision variables, which is intolerable for expensive optimization problems as it incurs prohibitive computational costs. To address this issue, an adaptive variable grouping method is proposed in this paper, which can achieve relatively accurate grouping results without additional FE consumption. Specifically, variables are grouped based on the contrasts between well-converged solutions and poorly-converged solutions. Furthermore, the grouping scheme is adjusted dynamically during the optimization process to improve the grouping accuracy. Besides, an adaptive environmental selection based sampling strategy is suggested, which attempts to provide the currently required solutions for reevaluation according to the demands of different optimization stages. The proposed algorithm is compared with the other five state-of-the-art multiobjective optimization evolutionary algorithms on both benchmark problems and real-world problems. The experimental results demonstrate the promising performance and the superior computational efficiency of the proposed algorithm in tackling high-dimensional expensive multiobjective optimization problems.