Entropy-Informed Variable Grouping for Expensive Large-Scale Multiobjective Optimization

The decision variable grouping approach has proven effective in solving large-scale multiobjective optimization problems (LSMOPs). However, expensive large-scale multiobjective optimization poses additional challenges because the number of allowable function evaluations (FEs) is highly limited, making it difficult to perform decision variable grouping without relying on additional real FEs. To overcome this limitation, a novel entropy-informed variable grouping method that quantifies the distribution characteristics of each decision variable based on previously evaluated solutions is proposed in this study. In particular, the entropy of each decision variable is calculated to rank the variables. Those with similar entropy values are grouped to ensure that the grouping process accurately reflects the inherent distributional characteristics of the decision variables. The entropy-informed grouping results are then leveraged to guide the search process by prioritizing convergence for decision variables with higher entropy while focusing on diversity for those with lower entropy. Experimental evaluations demonstrate that the proposed method outperforms six state-of-the-art surrogate-assisted evolutionary algorithms (SAEAs) in both computational efficiency and solution quality, offering a robust solution for expensive LSMOPs.