[1]于明渊,潘万里,梁　静,等.基于区域分解的代理辅助多种群差分进化算法[J].郑州大学学报(工学版),2026,47(02):16-26.[doi:10.13705/j.issn.1671-6833.2026.02.002]
　YU Mingyuan,PAN Wanli,LIANG Jing,et al.Surrogate-assisted Multi-population Differential Evolution AlgorithmBased on Region Decomposition[J].Journal of Zhengzhou University (Engineering Science),2026,47(02):16-26.[doi:10.13705/j.issn.1671-6833.2026.02.002]
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基于区域分解的代理辅助多种群差分进化算法()
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《郑州大学学报(工学版)》[ISSN:1671-6833/CN:41-1339/T]

卷:
47
期数:
2026年02期
页码:
16-26
栏目:
出版日期:
2026-02-13

文章信息/Info

Title:
Surrogate-assisted Multi-population Differential Evolution AlgorithmBased on Region Decomposition
文章编号:
1671-6833(2026)02-0016-11
作者:
于明渊;  潘万里;  梁　静;  岳彩通
郑州大学 电气与信息工程学院,河南 郑州 450001
Author(s):
YU Mingyuan;  PAN Wanli;  LIANG Jing;  YUE Caitong
School of Electrical and Information Engineering, Zhengzhou University, Zhengzhou 450001, China
关键词:
昂贵多模态优化;  差分进化;  局部搜索;  代理辅助进化算法
Keywords:
expensive multimodal optimization;  differential evolution;  local search;  surrogate-assisted evolution algorithm
分类号:
TP18 O224
DOI:
10.13705/j.issn.1671-6833.2026.02.002
文献标志码:
A
摘要:
在昂贵优化问题中,如果问题的最优解不唯一,那么此类问题被称为昂贵多模态优化问题。然而,在计算资源有限的情况下,求得多个最优解非常困难。并且,现有的代理模型辅助进化算法对多模态属性关注较少。鉴于此,提出了一种基于区域分解的代理辅助多种群差分进化算法以解决昂贵多模态优化问题。首先,在种群个体初始化阶段,利用个体间距离与目标值的相关性检测潜在子区域,并划分子种群以探索多个最优解。其次,进化前期,利用差分进化算法在每个子种群中进行全局搜索,以捕获多个最优解。在进化前期获取多个最优个体后,采用协方差矩阵自适应进化策略对最优个体开展局部搜索以提高最优解的质量。此外,提出了一种填充准则,可根据特定参数自适应选择合适的个体进行真实评价,以提升代理模型的精确性和泛化能力。最后,将所提算法与其他7种算法在20个测试函数上进行对比。结果表明:所提算法的PR指标在13个函数上取得了最优结果,且最多在5个函数上略差于对比算法,所提算法在求解昂贵多模态优化问题上性能良好。
Abstract:
In expensive optimization problems, if the optimal solution of the problem was not unique, such problems were referred to as expensive multimodal optimization problems. However, it was extremely difficult to obtain multiple optimal solutions with limited computational resources. Moreover, existing surrogate-assisted evolutionary algorithms paid less attention to multimodal attributes. In view of this, a surrogate-assisted multi-population differential evolution algorithm based on region decomposition was proposed to solve expensive multimodal optimization problems. Firstly, in the population individual initialization stage, the correlation between inter-individual distances and objective values was used to detect potential sub-regions, and sub-populations were divided to explore multiple optimal solutions. Secondly, in the early stage of evolution, the differential evolution algorithm was used to perform global search in each sub-population to capture multiple optimal solutions. After multiple optimal individuals were obtained in the early stage of evolution, the covariance matrix adaptive evolution strategy was adopted to carry out local search on them to improve the quality of optimal solutions. In addition, an infilling criterion was proposed, which could adaptively select appropriate individuals for real evaluation according to specific parameters to improve the accuracy and generalization ability of the surrogate model. Finally, the proposed algorithm was compared with seven other algorithms on 20 test functions. The results showed that the proposed algorithm achieved optimal performance on 13 functions with the PR metric, and was slightly inferior to the comparison algorithms on at most 5 functions. Overall, the proposed algorithm exhibited excellent performance in solving expensive multimodal optimization problems.

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更新日期/Last Update: 2026-03-04