Multi-region hierarchical surrogate-assisted quantum-behaved particle swarm optimization for expensive optimization problems

Abstract

Surrogate-assisted evolutionary algorithms (SAEAs) have been successfully applied to solve computationally expensive optimization problems. However, most SAEAs struggle to achieve good results in solving complex multimodal problems, especially high-dimensional ones. Moreover, for problems with complex landscapes, SAEAs typically require constructing complex global surrogates to model the landscape and performing many iterations to identify the surrogate’s optimum, thereby reducing the efficiency of SAEAs. To deal with these issues, this paper proposes a multi-region hierarchical surrogate-assisted quantum-behaved particle swarm optimization (MHS-QPSO) algorithm for expensive optimization problems. To better balance exploration and exploitation, a search behavior selection strategy is proposed, enabling MHS-QPSO to appropriately switch between global and local searches. For the global search, the search space is divided into multiple regions that can adaptively adjust the size of the areas. A surrogate is constructed in each region, requiring only a small number of QPSO iterations to find the optimum of each surrogate. Furthermore, a novel reliability-based criterion is proposed to screen candidate solutions in different regions for exact evaluations, which can save the number of exact function evaluations and can rapidly improve the fitting accuracy of the surrogates in regions with superior fitness. During local searches, a dynamic boundary adjustment strategy is introduced to guide the QPSO to faster approach the potential optimal region. Experimental results on seven benchmark functions with dimensions from 10 to 100, and on a complex real application, demonstrate that MHS-QPSO significantly outperforms several state-of-the-art algorithms within a limited computational budget. Code for MHS-QPSO is available at https://github.com/quanshuzhang/MHS-QPSO.git.