Evolutionary Surrogate-Assisted Multiobjective Optimization Over High-Dimensional Search Spaces: A Comparative Study

Many existing surrogate-assisted multiobjective evolutionary algorithms (SAMOEAs) struggle in high-dimensional search spaces. Recently, efforts to address this important challenge have intensified, leading to intense performance competition. However, most performance comparisons have been conducted solely among SAMOEAs, with limited benchmarking against standard optimizers such as MOEAs. This lack of a comprehensive comparison has obscured substantive progress in the field and raised concerns regarding the effectiveness of SAMOEAs over MOEAs. To fill this gap, this article presents a comparative study of SAMOEAs designed for expensive high-dimensional problems. We evaluate eight SAMOEAs against seven MOEAs across six test suites with a limited number of function evaluations, where all algorithms are configured with their default parameter settings. Surprisingly, our results indicate that popular baseline SAMOEAs perform comparably to, or even worse than, most MOEAs. Although state-of-the-art SAMOEAs, particularly decomposition-based algorithms, generally outperform MOEAs, their advantages diminish in certain test suites. Further analysis suggests that these decomposition-based algorithms may be overfitted to the specific shape of the feasible region commonly observed in popular test suites, and this observation was also confirmed in two real-world applications. Based on these findings, we propose an improved experimental design to better assess the effectiveness of SAMOEAs. Moreover, we suggest the importance of developing SAMOEAs that adapt to various shapes of feasible regions, contributing to the further advancement of SAMOEAs.