A Surrogate-Assisted Gray Prediction Evolution Algorithm for High-Dimensional Expensive Optimization Problems

Xiaoliang Huang, Hongbing Liu (), Quan Zhou () and Qinghua Su
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Xiaoliang Huang: School of Information and Mathematics, Yangtze University, Jingzhou 434023, China
Hongbing Liu: School of Information Engineering, Jiaxing Nanhu University, Jiaxing 314001, China
Quan Zhou: School of Information and Mathematics, Yangtze University, Jingzhou 434023, China
Qinghua Su: School of Information and Mathematics, Yangtze University, Jingzhou 434023, China

Mathematics, 2025, vol. 13, issue 6, 1-19

Abstract: Surrogate-assisted evolutionary algorithms (SAEAs), which combine the search capabilities of evolutionary algorithms (EAs) with the predictive capabilities of surrogate models, are effective methods for solving expensive optimization problems (EOPs). However, the over-reliance on the accuracy of the surrogate model causes the optimization performance of most SAEAs to decrease drastically with the increase in dimensionality. To tackle this challenge, this paper proposes a surrogate-assisted gray prediction evolution (SAGPE) algorithm based on gray prediction evolution (GPE). In SAGPE, both the global and local surrogate model are constructed to assist the GPE search alternately. The proposed algorithm improves optimization efficiency by combining the macro-predictive ability of the even gray model in GPE for population update trends and the predictive ability of surrogate models to synergistically guide population searches in promising directions. In addition, an inferior offspring learning strategy is proposed to improve the utilization of population information. The performance of SAGPE is tested on eight common benchmark functions and a speed reducer design problem. The optimization results are compared with existing algorithms and show that SAGPE has significant performance advantages in terms of convergence speed and solution accuracy.

Keywords: expensive optimization problems; gray prediction evolution; surrogate-assisted evolutionary algorithms (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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