Surrogate-Assisted Evolutionary Multi-Objective Optimization Grouped by Significant Influence for High-Dimensional Problems

Surrogate-assisted evolutionary algorithms (SAEAs) have demonstrated strong performance in solving low- and medium-dimensional expensive multi-objective optimization problems (EMOPs). However, their scalability to high-dimensional problems remains a critical challenge. To address this issue, several SAEAs based on variable grouping have been proposed. Yet they often fail to deliver satisfactory results under limited real function evaluations. In this paper, we propose a SAEA grouped by significant influence (SAEA-SI), in which variable grouping is adaptively adjusted according to the optimization state. The method is motivated by the observation that different decision variables often contribute unequally to different objectives. SAEA-SI adopts a two-phase optimization framework, where the first phase focuses on convergence, while the second phase enhances diversity through adaptive variable grouping. Specifically, before each optimization process, correlation analysis in the objective space is performed to identify solution combinations for each objective. These combinations are used to estimate the influence of each decision variable, and decision variables exhibiting consistent and significant influence are grouped accordingly. Each group is then optimized independently using surrogate-assisted Differential Evolution. We conduct comparative experiments with the five state-of-the-art SAEAs on multiple test suites with up to 1000 decision variables. The results demonstrate that SAEA-SI is able to strike a good balance between convergence and diversity under limited real function evaluations. Furthermore, experiments on real-world test problems confirm the effectiveness of SAEA-SI in high-dimensional EMOPs.