A Hierarchical Surrogate-Assisted Differential Evolution With Core Space Localization

Surrogate-assisted evolutionary algorithms (SAEAs) are extensively used to tackle expensive optimization problems (EOPs). The integration of surrogate-based global and local search is a prevalent hierarchical SAEA framework, which can effectively balance exploration and exploitation capabilities. However, it still faces challenges when tackling high-dimensional EOPs (HEOPs) owing to the curse of dimensionality. In this article, we propose a hierarchical surrogate-assisted differential evolution with core space localization (HSADE-CS) to solve HEOPs. Its contributions are listed as follows: 1) a top-promising sampling strategy is introduced in the global search to mitigate the challenges posed by the uncertainty in the performance of the surrogate model; 2) a core space localization (CSL) method is proposed to identify a high-potential space within the local promising region, enhancing the effectiveness of local search; and 3) a fitness-independent adaptive parameter control method based on the Minkowski distance is developed within the differential evolution (DE) optimizer to improve the performance of surrogate model-driven local search. The performance of HSADE-CS has been validated on numerous benchmark problems from the commonly used expensive optimization benchmark suite, as well as the CEC2014 and CEC2017 benchmark suites, with problem dimensions up to 500. It has also been tested on a real-world problem, i.e., circular antenna array design optimization. Experimental results demonstrate that HSADE-CS is highly competitive compared to the state-of-the-art SAEAs.