[1]季新芳,贾璟伟,王晓峰,等.昂贵多模态优化问题的代理辅助进化算法综述[J].郑州大学学报(工学版),2027,48(XX):1-11.[doi:10.13705/j.issn.1671-6833.2026.04.014]
　JI Xinfang,JIA Jingwei,et al.A Review of Surrogate-assisted Evolutionary Algorithms for Expensive Multimodal Optimization Problems[J].Journal of Zhengzhou University (Engineering Science),2027,48(XX):1-11.[doi:10.13705/j.issn.1671-6833.2026.04.014]
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昂贵多模态优化问题的代理辅助进化算法综述()
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《郑州大学学报(工学版)》[ISSN:1671-6833/CN:41-1339/T]

卷:
48
期数:
2027年XX
页码:
1-11
栏目:
出版日期:
2027-12-10

文章信息/Info

Title:
A Review of Surrogate-assisted Evolutionary Algorithms for Expensive Multimodal Optimization Problems
作者:
季新芳1,2, 贾璟伟1,2, 王晓峰1,2, 成金鑫3, 姚佳兴1,2
1. 北方民族大学 计算机科学与工程学院,宁夏 银川 750021;2. 北方民族大学 图像图形智能处理国家民委重点实验室,宁夏 银川 750021;3. 北京科技大学 机械工程学院,北京 100083
Author(s):
JI Xinfang1, 2, JIA Jingwei1, 2, WANG Xiaofeng1, 2, CHENG Jinxin3, YAO Jiaxing1, 2
1. School of Computer Science and Engineering, North Minzu University, Yinchuan 750021, China; 2. The Key Laboratory of Images and Graphics Intelligent Processing of State Ethnic Affairs Commission, North Minzu University, Yinchuan 750021,China; 3. School of Mechanical Engineering, University of Science and Technology Beijing, Beijing 100083, China
关键词:
昂贵优化问题;  多模态优化问题;  进化算法;  代理模型
Keywords:
expensive optimization problems;  multimodal optimization problems;  evolutionary algorithms;  surrogate model
分类号:
TP18O224
DOI:
10.13705/j.issn.1671-6833.2026.04.014
文献标志码:
A
摘要:
针对工程设计中同时具有多模态特性与高评估代价的昂贵多模态优化问题(EMMOPs)，系统综述了代理辅助进化算法(SAEAs)的研究进展与关键技术。首先，介绍多项式回归模型及高斯过程等典型代理模型，分析其在样本拟合、非线性表达与不确定性量化方面的特点及适用场景。在此基础上，总结SAEAs的基本框架，并从单代理与多代理结构、全局-局部协同搜索及填充采样策略等方面归纳现有算法的主要设计思想。其次，依据昂贵多模态优化问题的不同特征，对单目标、多目标、约束型及高维等典型EMMOPs进行系统分类与梳理，分析代表性算法在模态识别、解多样性保持以及计算预算分配等方面的研究进展。再次，通过10个典型基准函数对多种主流SAEAs进行实验对比，从全局最优解和有效谷比例等指标分析各类算法的性能差异。同时结合船舶结构优化与超高压直流输电系统同步电机设计等工程实例，说明代理辅助进化算法在复杂工程优化中的应用潜力。最后，总结当前研究面临的关键挑战，并从自适应代理模型管理、并行化执行与调度以及模态间信息共享与迁移机制等方面展望未来发展方向。
Abstract:
Expensive multimodal optimization problems (EMMOPs) frequently arise in engineering design and are characterized by multimodal properties and extremely high evaluation costs. The research progress and key techniques of surrogate-assisted evolutionary algorithms (SAEAs) for solving such problems were systematically reviewed. Firstly, representative surrogate models, including polynomial regression model and Gaussian process, were introduced, with emphasis on their characteristics and applicability in sample fitting, nonlinear representation, and uncertainty quantification. On this basis, the general framework of SAEAs was summarized, and the main design ideas of existing algorithms were outlined in terms of single-surrogate and multi-surrogate structures, global-local collaborative search, and infill sampling strategies. Subsequently, according to the different characteristics of EMMOPs, typical EMMOPs, including single-objective, multi-objective, constrained, and high-dimensional problems, were systematically categorized and reviewed, with particular attention to advances in mode identification, solution diversity preservation, and computational budget allocation. Further experimental comparisons of multiple mainstream SAEAs were conducted on ten typical benchmark functions, and the performance differences among various algorithms were analyzed in terms of metrics such as global optimum solution and effective valley ratio. Meanwhile, engineering case studies, including ship structure optimization and synchronous machine design in ultra-high-voltage direct current transmission systems, were incorporated to illustrate the application potential of surrogate-assisted evolutionary algorithms in complex engineering optimization. Finally, the key challenges faced by current research were summarized, and future development directions were discussed from the perspectives of adaptive surrogate model management, parallel execution and scheduling, as well as inter-modal information sharing and transfer mechanisms.

参考文献/References:

[1] Gao Weifeng, Wei Zhifang, Gong Maoguo, et al. Solving expensive multimodal optimization problem by a decomposition differential evolution algorithm[J]. IEEE Transactions on Cybernetics, 2023, 53(4): 2236-2246.
[2] Chica M, Barranquero J, Kajdanowicz T, et al. Multimodal optimization: an effective framework for model calibration[J]. Information Sciences, 2017, 375: 79-97.
[3] Thawkar S, Sharma S, Khanna M, et al. Breast cancer prediction using a hybrid method based on butterfly optimization algorithm and ant lion optimizer[J]. Computers in Biology and Medicine, 2021, 139: 104968.
[4] Brereton R G, Lloyd G R. Support vector machines for classification and regression[J]. The Analyst, 2010, 135(2): 230-267.
[5] Aguirre-Urreta M I, Rönkkä M, Hu Jiang. Polynomial regression and measurement error: implications for information systems research[J]. ACM SIGMIS Database: the DATABASE for Advances in Information Systems, 2020, 51(3): 55-80.
[6] Wang Zilong, Ierapetritou M. A novel feasibility analysis method for black-box processes using a radial basis function adaptive sampling approach[J]. AIChE Journal, 2017, 63(2): 532-550.
[7] Liu Haitao, Ong Y S, Shen Xiaobo, et al. When Gaussian process meets big data: a review of scalable GPs[J]. IEEE Transactions on Neural Networks and Learning Systems, 2020, 31(11): 4405-4423.
[8] Liu Xinwang, Zhao Weiwen, Wan Decheng. Multi-fidelity Co-Kriging surrogate model for ship hull form optimization[J]. Ocean Engineering, 2022, 243: 110239.
[9] Manning C D, Clark K, Hewitt J, et al. Emergent linguistic structure in artificial neural networks trained by self-supervision[J]. PNAS, 2020, 117(48): 30046-30054.
[10] Pham B T, Van Phong T, Nguyen-Thoi T, et al. Ensemble modeling of landslide susceptibility using random subspace learner and different decision tree classifiers[J]. Geocarto International, 2022, 37(3): 735-757.
[11] Speiser J L, Miller M E, Tooze J, et al. A comparison of random forest variable selection methods for classification prediction modeling[J]. Expert Systems with Applications, 2019, 134: 93-101.
[12] Jones D R, Schonlau M, Welch W J. Efficient global optimization of expensive black-box functions[J]. Journal of Global Optimization, 1998, 13(4): 455-492.
[13] Cai Xiwen, Gao Liang, Li Xinyu, et al. Surrogate-guided differential evolution algorithm for high dimensional expensive problems[J]. Swarm and Evolutionary Computation, 2019, 48: 288-311.
[14] Zhan Zhihui, Liu Xiaofang, Zhang Huaxiang, et al. Cloudde: a heterogeneous differential evolution algorithm and its distributed cloud version[J]. IEEE Transactions on Parallel and Distributed Systems, 2017, 28(3): 704-716.
[15] Jin Yaochu. Surrogate-assisted evolutionary computation: recent advances and future challenges[J]. Swarm and Evolutionary Computation, 2011, 1(2): 61-70.
[16] Li Genghui, Zhang Qingfu, Lin Qiuzhen, et al. A three-level radial basis function method for expensive optimization[J]. IEEE Transactions on Cybernetics, 2022, 52(7): 5720-5731.
[17] Li Zhongguo, Dong Zhen, Liang Zhongchao, et al. Surrogate-based distributed optimisation for expensive black-box functions[J]. Automatica, 2021, 125: 109407.
[18] Goel T, Haftka R T, Shyy W, et al. Ensemble of surrogates[J]. Structural and Multidisciplinary Optimization, 2007, 33(3): 199-216.
[19] Li Bingdong, Yang Yanting, Liu Dacheng, et al. Accelerating surrogate assisted evolutionary algorithms for expensive multi-objective optimization via explainable machine learning[J]. Swarm and Evolutionary Computation, 2024, 88: 101610.
[20] Duan Libin, Xue Kaiwen, Jiang Tao, et al. A parallel constrained Bayesian optimization algorithm for high-dimensional expensive problems and its application in optimization of VRB structures[J]. Structural and Multidisciplinary Optimization, 2024, 67(4): 50.
[21] Pang Yong, Zhang Shuai, Jin Yaochu, et al. Surrogate information transfer and fusion in high-dimensional expensive optimization problems[J]. Swarm and Evolutionary Computation, 2024, 88: 101586.
[22] Shang Jin, Li Guiying, Hao Hao, et al. Efficient surrogate model assisted estimation of distribution algorithm for expensive optimization[J]. IEEE Access, 2024, 12: 78248-78260.
[23] Deng Chuanyi, Sun Chaoli, Liu Xiaotong, et al. An inertial grouping and overlapping feature selection assisted algorithm for expensive large-scale optimization problems[J]. Journal of Zhengzhou University (Engineering Science), 2023, 44(5): 32-39.
[24] Pan Linqiang, Lin Jianqing, Wang Handing, et al. Computationally expensive high-dimensional multiobjective optimization via surrogate-assisted reformulation and decomposition[J]. IEEE Transactions on Evolutionary Computation, 2025, 29(4): 921-935.
[25] Wu Haofeng, Chen Qingda, Jin Yaochu, et al. A surrogate-assisted expensive constrained multi-objective optimization algorithm based on adaptive switching of acquisition functions[J]. IEEE Transactions on Emerging Topics in Computational Intelligence, 2024, 8(2): 2050-2064.
[26] Zhang Zhiyao, Wang Yong, Liu Jiao, et al. A two-phase Kriging-assisted evolutionary algorithm for expensive constrained multiobjective optimization problems[J]. IEEE Transactions on Systems, Man, and Cybernetics: Systems, 2024, 54(8): 4579-4591.
[27] Long Teng, Ye Nianhui, Chen Rong, et al. Surrogate-assisted differential evolution using manifold learning-based sampling for high-dimensional expensive constrained optimization problems[J]. Chinese Journal of Aeronautics, 2024, 37(7): 252-270.
[28] Li Bingdong, Lu Yongfan, Qian Hong, et al. Regularity model based offspring generation in surrogate-assisted evolutionary algorithms for expensive multi-objective optimization[J]. Swarm and Evolutionary Computation, 2024, 86: 101506.
[29] Li Yingwei, Feng Xiang, Yu Huiqun. Solving high-dimensional expensive multiobjective optimization problems by adaptive decision variable grouping[J]. IEEE Transactions on Evolutionary Computation, 2025, 29(4): 1041-1054.
[30] Tan Shenglian, Wang Yong, Sun Guangyong, et al. A surrogate-assisted evolutionary framework for expensive multitask optimization problems[J]. IEEE Transactions on Evolutionary Computation, 2025, 29(3): 779-793.
[31] Du Wenhao, Ren Zhigang, Wang Jihong, et al. A surrogate-assisted evolutionary algorithm for solving large-scale multimodal multiobjective optimization problems[J]. IEEE Transactions on Evolutionary Computation, 2021, 25(3): 405-418.
[32] Lyu Zhiming, Niu Dangdang, Li Shuqin, et al. Multi-surrogate assisted PSO with adaptive speciation for expensive multimodal multi-objective optimization[J]. Applied Soft Computing, 2023, 147: 110724.
[33] Ji Jingyu, Tan Zusheng, Zeng Sanyou, et al. A surrogate-assisted evolutionary algorithm for seeking multiple solutions of expensive multimodal optimization problems[J]. IEEE Transactions on Emerging Topics in Computational Intelligence, 2024, 8(1): 377-388.
[34] Ji Xinfang, Zhang Yong, Gong Dunwei, et al. Dual-surrogate-assisted cooperative particle swarm optimization for expensive multimodal problems[J]. IEEE Transactions on Evolutionary Computation, 2021, 25(4): 794-808.
[35] Chen Renzhi, Li Ke. Multioutput surrogate assisted evolutionary algorithm for expensive multi-modal optimization problems[C]//Proceedings of the 2023 IEEE International Conference on Systems, Man, and Cybernetics (SMC). Piscataway: IEEE, 2024: 5176-5181.
[36] Ji Xinfang, Zhang Yong, Gong Dunwei, et al. Interval multimodal particle swarm optimization algorithm assisted by heterogeneous ensemble surrogate[J]. Acta Automatica Sinica, 2024, 50(9): 1831-1853.
[37] Ji Xinfang, Zhang Yong, Gong Dunwei, et al. Multisurrogate-assisted multitasking particle swarm optimization for expensive multimodal problems[J]. IEEE Transactions on Cybernetics, 2023, 53(4): 2516-2530.
[38] Deb K. Multi-objective optimisation using evolutionary algorithms: an introduction[M]//Multi-objective evolutionary optimisation for product design and manufacturing. London: Springer London, 2011: 3-34.
[39] Tian Ye, Liu Ruchen, Zhang Xingyi, et al. A multipopulation evolutionary algorithm for solving large-scale multimodal multiobjective optimization problems[J]. IEEE Transactions on Evolutionary Computation, 2021, 25(3): 405-418.
[40] Mehta P, Panagant N, Wansasueb K, et al. Optimization of vehicle conceptual design problems using an enhanced hunger games search algorithm[J]. Materials Testing, 2024, 66(11): 1864-1889.
[41] Zhang Yong, Ji Xinfang, Gao Xiaozhi, et al. Objective-constraint mutual-guided surrogate-based particle swarm optimization for expensive constrained multimodal problems[J]. IEEE Transactions on Evolutionary Computation, 2023, 27(4): 908-922.
[42] Blank J, Deb K. Handling constrained multi-objective optimization problems with heterogeneous evaluation times: proof-of-principle results[J]. Memetic Computing, 2022, 14(2): 135-150.
[43] Blank J, Deb K. Constrained bi-objective surrogate-assisted optimization of problems with heterogeneous evaluation times: expensive objectives and inexpensive constraints[C]//Evolutionary Multi-Criterion Optimization. Cham: Springer, 2021: 257-269.
[44] Wang Xilu. Bayesian evolutionary optimization for heterogeneously expensive multi-objective problems[D]. Guildford, South East England, UK: University of Surrey, 2022.
[45] Ji Xinfang, Zhang Yong, He Chunlin, et al. Surrogate and autoencoder-assisted multitask particle swarm optimization for high-dimensional expensive multimodal problems[J]. IEEE Transactions on Evolutionary Computation, 2024, 28(4): 1009-1023.
[46] Wang Junze, Wang Yuan, Yi Jiaxiang, et al. Genetic optimization method of ship strong frame based on sequential surrogate model[J]. Chinese Journal of Ship Research, 2021, 16(4): 44-52.[47] Ma Y, Wang J, Xiao Y, et al. Two-level surrogate-assisted transient parameters design optimization of a wound-field synchronous machine[J]. IEEE Transactions on Energy Conversion, 2022, 37(1): 737-747.

备注/Memo

备注/Memo:
收稿日期:2026-01-06;修订日期:2026-01-23
基金项目:宁夏自然科学基金资助项目(2024AAC03169) ;国家自然科学基金资助项目( 62563001) ;广东省基础与应用基础研究基金(2022A1515110055)
作者简介:季新芳(1987— ) ,女,江苏泰州人,北方民族大学讲师,博士,主要从事机器学习、进化计算的研究,E-mail:mimosa_615615@126.com。
更新日期/Last Update: 2026-04-08