Surrogate-assisted Evolutionary Algorithm with Adaptive Local Region Search for High-Dimensional Expensive Multi-Objective Optimization Problems

High-dimensional expensive multi-objective optimization problems (HEMOPs) are ubiquitous in scientific and engineering domains. They pose significant challenges for surrogate-assisted evolutionary algorithms (SAEAs), primarily due to the curse of dimensionality and prohibitive computational costs. A common approach involves partitioning the high-dimensional search space into local regions potentially containing Pareto optimal solutions, followed by in-depth exploration using SAEAs. However, existing partition-based evolutionary methods are limited by the lack of adaptability of local regions to environmental changes. To overcome this limitation, we propose AS-SMEA, a Surrogate-assisted Multi-objective Evolutionary Algorithm with Adaptive local region Search. The algorithm dynamically identifies and partitions promising regions in the high-dimensional space, conducting parallel surrogate-assisted evolutionary searches for efficient cooperative optimization. It is enhanced by two key strategies: a Covariance Matrix Adaptation-based method for initializing and updating local regions, and a Multi-Armed Bandit-guided adaptive selection mechanism for balancing exploration and exploitation. Moreover, theoretical analysis based on cumulative hypervolume regret establishes the global convergence of AS-SMEA. Comprehensive experiments on 69 benchmark problems and one real-world very large-scale integration design flow problem demonstrate that AS-SMEA consistently outperforms six state-of-the-art SAEAs.