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Broad learning approach to surrogate-assisted Multi-Objective evolutionary fuzzy clustering algorithm based on reference points for color image segmentation

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EXPERT SYSTEMS WITH APPLICATIONS 2022年 200卷 117015-117015页

作者： Zhao, Feng Liu, Yu Liu, Hanqiang Fan, Jiulun Xian Univ Posts & Telecommun Sch Commun & Informat Engn Xian 710121 Peoples R China Shaanxi Normal Univ Sch Comp Sci Xian 710119 Peoples R China

For some real-world problems, the objective function evaluation is time-consuming and computationally expensive in multi-objective evolutionary algorithms. surrogate-assistance approaches can be used to estimate the objective function and solve the computationally expensive problem. Taking advantages of the flatted structure and incremental learning, broad learning system (BLS) has shown a great improvement of time effi-ciency on the premise of ensuring the performance on the classification and regression problems. In this paper, BLS is adopted to design a BLS surrogate-assisted evolutionary framework to boost the time efficiency of clustering-based image segmentation. A BLS-assisted multi-objective evolutionary fuzzy clustering algorithm with reference points (BLS-MOEFC) is proposed. Firstly, two fuzzy clustering objective functions integrating image region information are constructed as the optimized fitness functions for obtaining satisfactory segmen-tation quality. Secondly, in order to improve the optimization efficiency and reduce the computational time cost, a BLS surrogate model-assisted multi-objective evolutionary framework with reference points is designed to optimize the constructed objective functions. Thirdly, an adaptively updating strategy of parameters and a model update mechanism based on the non-dominated sorting are adopted to improve the prediction accuracy of the BLS surrogate model. Finally, a novel fuzzy clustering validity index integrating region information is designed to select an optimal solution from the final set of non-dominated solutions. Experimental results on Berkeley and Weizmann images show that the proposed algorithm behaves well in the segmentation performance and time cost.

关键词： Image segmentation Fuzzy clustering Multi-objective optimization Broad learning system surrogate-assisted evolutionary algorithm Reference points

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Graph neural network-assisted evolutionary algorithm for rapid optimization design of shear-wall structures

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ADVANCED ENGINEERING INFORMATICS 2025年 65卷

作者： Fei, Yifan Qin, Sizhong Liao, Wenjie Guan, Hong Lu, Xinzheng Tsinghua Univ Dept Civil Engn Key Lab Civil Engn Safety & Durabil China Educ Minist Beijing 100084 Peoples R China Griffith Univ Sch Engn & Built Environm Gold Coast Campus Brisbane Qld 4222 Australia

When solving expensive optimization problems (EOPs), e.g., optimization design of shear-wall structures, conventional evolutionary algorithms (EAs) face a challenge of elevated costs related to fitness evaluation. On the other hand, surrogate-assisted evolutionary algorithms (SAEAs) can effectively reduce evaluation costs and are therefore widely used. However, when encountering new structure cases to be optimized, existing SAEAs require the effort of establishing datasets and training machine-learning surrogate models from scratch, which significantly lowers their efficiency. To address this issue, a novel graph neural network (GNN)-assisted evolutionary algorithm (GAEA) is proposed, which features a distinct framework and workflow from existing SAEAs. Then, a powerful GNN surrogate model is proposed, which is based on graph representations and exhibits good generalization abilities. After being trained on a large number of cases of the same type, the model can be applied to various new cases of that particular type. By integrating GNN with EA, GAEA can directly use the trained GNN surrogate model for fitness evaluation when dealing with new structure cases. Furthermore, a distance-based evaluation and updating strategy of surrogate models is innovatively proposed, which can efficiently correct the prediction error of GNN without retraining the model. The proposed GAEA is applied to the optimization design of reinforced concrete (RC) shear-wall structures, which is a typical EOP in the field of structural engineering. Numerical experiments show that: 1) for the same number of fitness evaluations, GAEA can achieve 64.4 % to 92.5 % of the optimization outcomes of typical EA or SAEA, respectively, with only 2.8 % to 33.2 % of their computational time;2) for the same optimization duration (10 min, 45 min, and 120 min), GAEA's optimization outcomes are superior to those of typical EA and SAEA, meeting the rapid optimization demands for shear-wall structures in the schem

关键词： surrogate-assisted evolutionary algorithm Graph neural network Optimization design Shear-wall structure Expensive optimization problem

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High-dimensional expensive optimization by Kriging-assisted multiobjective evolutionary algorithm with dimensionality reduction

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INFORMATION SCIENCES 2025年 691卷

作者： Yan, Zeyuan Zhou, Yuren He, Xiaoyu Su, Chupeng Wu, Weigang Sun Yat Sen Univ Sch Comp Sci & Engn Guangzhou 510006 Peoples R China Sun Yat Sen Univ Sch Software Engn Zhuhai 519082 Peoples R China South China Univ Technol Shien Ming Wu Sch Intelligent Engn Guangzhou 511442 Peoples R China

surrogate-assisted multi-objective evolutionary algorithms (SA-MOEAs) have made significant progress in solving expensive multi- and many-objective optimization problems. However, most of them perform well in low-dimensional settings but often struggle with high-dimensional problems. The main reason is that some techniques used in SA-MOEAs, like the Kriging model, are ineffective in exploring high-dimensional search spaces. As a result, this research investigates frameworks incorporating dimensionality reduction techniques to conduct modeling and optimization tasks on dimensionality reduction decision spaces. This article uses a singular value decomposition method to map the high-dimensional decision space into a low-dimensional one, then employs a feature fusion strategy to combine low-dimensional features with high-dimensional ones for better representation. Subsequently, these low-dimensional features are used to train the Kriging-based surrogates to select promising solutions within a limited number of function evaluations. In addition, this article provides two types of evolutionary modes to balance exploration and exploitation. Experimental results demonstrate the effectiveness of the proposed SA-MOEA compared to several state-of-the-art algorithms.

关键词： surrogate-assisted evolutionary algorithm Feature extraction Feature fusion High-dimensional problems

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AIEA: An Asynchronous Influence-Based evolutionary algorithm for Expensive Many-Objective Optimization

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IEEE TRANSACTIONS ON CYBERNETICS 2025年第2期55卷 786-799页

作者： Wei, Feng-Feng Chen, Wei-Neng Zhang, Jun South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Peoples R China South China Univ Technol State Key Lab Subtrop Buildingand Urban Sci Guangzhou 510006 Peoples R China Nankai Univ Coll Artificial Intelligence Tianjin 30071 Peoples R China Zhejiang Normal Univ Sch Comp Sci & Technol Jinhua 321004 Peoples R China Hanyang Univ Dept Elect & Elect Engn Ansan 15588 South Korea

In expensive multi/many-objective optimization problems (EMOPs), the expensive objectives are generally accessed through different simulation tools, leading to different evaluation latencies and unbearable computational time for serial optimization. One promising approach to improve efficiency is to perform simulation and build surrogates separately for each objective in parallel. However, how to improve the model accuracy and select promising candidates without global information are big challenges. To alleviate these problems, this article proposes an asynchronous influence-based SAEA (AIEA) based on the client-server model. Each client approximates an objective and the server takes charge for evolution. To adaptively select promising candidates, the influence degree is introduced in candidate selection, which is calculated in the objective space to judge which candidate has more beneficial influence for evolution. With the selected candidate, the most-uncertain-first strategy is devised in objective selection for asynchronous evaluations and model improvement. To handle incomplete objective values, the nearest neighbor inheritance is adopted for unevaluated objectives. Comprehensive experiments compared with five surrogate-assisted EAs demonstrate the global optimization and scalability of AIEA.

关键词： Optimization Computational modeling Predictive models Training data Data models Vectors Servers Program processors evolutionary computation Distributed databases Expensive optimization many-objective optimization problems parallel and distributed evolutionary computation surrogate-assisted evolutionary algorithm

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A comparison-relationship-surrogate evolutionary algorithm for multi-objective optimization

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SWARM AND evolutionary COMPUTATION 2025年 95卷

作者： Pierce, Christopher M. Kim, Young-Kee Bazarov, Ivan Univ Chicago 5640 S Ellis Ave Chicago IL 60637 USA Cornell Univ 245 Feeney Way Ithaca NY 14853 USA

evolutionary algorithms often struggle to find well converged (e.g small inverted generational distance on test problems) solutions to multi-objective optimization problems on a limited budget of function evaluations (here, a few hundred). The family of surrogate-assisted evolutionary algorithms (SAEAs) offers a potential solution to this shortcoming through the use of data driven models which augment evaluations of the objective functions. A surrogate model which has shown promise in single-objective optimization is to predict the "comparison relationship" between pairs of solutions (i.e. who's objective function is smaller). In this paper, we investigate the performance of this model on multi-objective optimization problems. First, we propose a new algorithm "CRSEA" which uses the comparison-relationship model. Numerical experiments are then performed with the DTLZ and WFG test suites plus a real-world problem from the field of accelerator physics. We find that CRSEA finds better converged solutions than the tested SAEAs on many of the medium-scale, biobjective problems chosen from the WFG suite suggesting the "comparison-relationship surrogate" as a promising tool for improving the efficiency of multi-objective optimization algorithms.

关键词： surrogate-assisted evolutionary algorithm (SAEA) Expensive optimization Medium-scale multi-objective optimization Comparison-relationship surrogate Pairwise comparison

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A surrogate-assisted Many-Objective evolutionary algorithm Using Multi- Classification and Coevolution for Expensive Optimization Problems

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IEEE ACCESS 2021年 9卷 159160-159174页

作者： Wang, Ruoyu Zhou, Yuee Chen, Hanning Ma, Lianbo Zheng, Meng Northeastern Univ Software Coll Shenyang 110016 Peoples R China Tiangong Univ Sch Comp Sci & Technol Tianjin 300387 Peoples R China Chinese Acad Sci Shenyang Inst Automat Key Lab Robot Shenyang 110169 Peoples R China Chinese Acad Sci Shenyang Inst Automat Key Lab Networked Control Syst Shenyang 110169 Peoples R China

surrogate-assisted evolutionary algorithms have received a surge of attentions for their promising ability of solving expensive optimization problems. Existing surrogate-assisted evolutionary algorithms usually adopt the regression models and the binary classification models to guide the evolution of the population for solving the multiobjective optimization problems. However, the regression models will make the algorithm to be increasingly computation-expensive as the number of objectives increases, while the use of the binary classification models might suffer from the poor diversity since the diversified information of solutions cannot be reflected in these classification models. For this issue, this paper proposes a surrogate-assisted many-objective evolutionary algorithm using the cooperation of the multi-classification and regression models to improve the search quality while reducing the computational cost. Our approach includes two parts: At the model training stage, a multi-classification model is constructed to divide the whole population into several classes for ensuring diversity, a distance regression model and an angle regression model are used to select solutions with better convergence and diversity in each class;At the evolution stage, a coevolutionary framework is used to guide the evolution according to a new selection criterion. Experimental results verify the effectiveness of the proposed algorithm on a set of expensive test problems with up to 10 objectives.

关键词： Statistics Sociology Optimization Computational modeling evolutionary computation Training Linear programming Coevolution expensive optimization multi-classification surrogate-assisted evolutionary algorithm

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Neighborhood samples and surrogate assisted multi-objective evolutionary algorithm for expensive many-objective optimization problems

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APPLIED SOFT COMPUTING 2021年 105卷 107268-107268页

作者： Zhao, Yi Zeng, Jianchao Tan, Ying Taiyuan Univ Sci & Technol Coll Mech Engn Taiyuan 030024 Peoples R China North Univ China Dept Comp Sci & Control Engn Taiyuan 030051 Peoples R China Taiyuan Univ Sci & Technol Dept Comp Sci & Technol Taiyuan 030024 Peoples R China

Many surrogate-assisted meta-heuristic algorithms have been proposed for single-objective expensive optimization problems, however, not so much attention has been paid to multi-objective expensive problems, especially for those with more than four objectives. In this paper, we use reference vector guided evolutionary algorithm (RVEA) to select suitable individuals, and radial basis function (RBF) networks are used to estimate the fitness of the original objective function to reduce the computational cost. These suitable individuals are optimized by the RBF network for several iterations. Then in surrogate model management, an infill strategy is proposed to select promising individuals for exact evaluations. Euclidean distance to origin or uncertainty is adaptively considered, according to the convergence degree of the current population in the infill strategy. The approximation uncertainty of each solution is calculated according to its distance to the modeling samples in the decision space. The experimental results on a number of many-objective optimization problems showed that the proposed method is competitive to three state-of-the-art algorithms for solving computationally expensive many-objective optimization problems. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Expensive many-objective optimization Radial basis function surrogate-assisted evolutionary algorithm surrogate model

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A classifier-assisted evolutionary algorithm with knowledge transfer for expensive multitasking problems

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COMPLEX & INTELLIGENT SYSTEMS 2025年第7期11卷 1-22页

作者： Hu, Min Ren, Zhigang Cao, Zhirui Guo, Yifeng Sun, Haitao Zhou, Hongyao Guo, Yu Xi An Jiao Tong Univ Sch Automat Sci & Engn Xian 710049 Peoples R China China Mobile Syst Integrat Co Ltd Shijiazhuang 050011 Peoples R China

surrogate-assisted evolutionary algorithms provide an effective means for complex and computationally expensive optimization problems. However, due to the scarcity of training samples, the prediction accuracy of frequently-used regression surrogate models can hardly be guaranteed as the difficulty of the problem increases, resulting in performance degradation of the whole algorithm. Since real-world problems rarely exist in isolation, it is expected to alleviate the above issue by properly exploiting the knowledge shared across different problems. In this context, this study proposes a novel evolutionary multitasking optimization algorithm assisted by a classifier rather than a regression model for expensive multitasking problems, where the accuracy of the classifier is boosted by knowledge transfer. To be specific, a support vector classifier (SVC) is first developed and integrated into a classic evolutionary algorithm, i.e., covariance matrix adaptation evolution strategy (CMA-ES). With a low computational cost, it helps CMA-ES to prescreen parent solutions from the current population. Following that, a knowledge transfer strategy is designed to enrich the training samples for each task-oriented classifier by sharing high-quality solutions among different tasks, where a PCA-based subspace alignment technique is employed. Extensive experiments indicate that the SVC-assisted CMA-ES gains significant superiority over general CMA-ES in terms of both robustness and scalability, and the knowledge transfer strategy further helps it earn a competitive edge over some state-of-the-art algorithms on expensive multitasking optimization problems.

关键词： surrogate-assisted evolutionary algorithm Classifier Expensive multitasking optimization Knowledge transfer

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A surrogate-assisted radial space division evolutionary algorithm for expensive many-objective optimization problems

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APPLIED SOFT COMPUTING 2021年 111卷 107703-107703页

作者： Gu, Qinghua Zhou, Yufeng Li, Xuexian Ruan, Shunling Xian Univ Architecture & Technol Sch Management Xian 710055 Shaanxi Peoples R China Xian Univ Architecture & Technol Sch Resources Engn Xian 710055 Shaanxi Peoples R China

Model management is the key for surrogate-assisted evolutionary algorithms to provide high-quality solutions for computationally expensive optimization problems. In this paper, a surrogate-assisted evolutionary algorithm based on radial space division is proposed for expensive many-objective optimization problems. The algorithm projects the individuals in the high-dimensional space to the radial space. Then, the location distribution of the individuals in the radial space and the uncertain information provided by the Kriging model are used for managing the surrogate model. In addition, two archives are used to manage the model, a fixed archive is used to hold the data that builds the Kriging model, and a variable archive is used to save the non-dominant solution. Finally, the performance of the proposed algorithm is tested on three sets of benchmark problems and two automobile structure design problem. The simulation results show that the algorithm is more competitive than the commonly used surrogate-assisted evolutionary algorithms. (C) 2021 Elsevier B.V. All rights reserved.

关键词： Expensive many-objective optimization surrogate-assisted evolutionary algorithm Kriging model Radial space division

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Multi-Objective Multi-Variable Large-Size Fan Aerodynamic Optimization by Using Multi-Model Ensemble Optimization algorithm

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Journal of Thermal Science 2024年第3期33卷 914-930页

作者： XIONG Jin GUO Penghua LI Jingyin School of Energy and Power Engineering Xi’an Jiaotong UniversityXi’an710049China

The constrained multi-objective multi-variable optimization of fans usually needs a great deal of computational fluid dynamics(CFD)calculations and is *** this study,a new multi-model ensemble optimization algorithm is proposed to tackle such an expensive optimization *** multi-variable and multi-objective optimization are conducted with a new flexible multi-objective infill *** addition,the search direction is determined by the multi-model ensemble assisted evolutionary algorithm and the feature extraction by the principal component analysis is used to reduce the dimension of optimization ***,the proposed algorithm and other two optimization algorithms which prevail in fan optimizations were compared by using test *** the same number of objective function evaluations,the proposed algorithm shows a fast convergency rate on finding the optimal objective function ***,this algorithm was used to optimize the rotor and stator blades of a large axial fan,with the efficiencies as the objectives at three flow rates,the high,the design and the low flow ***-two variables were included in the optimization *** results show that compared with the prototype fan,the total pressure efficiencies of the optimized fan at the high,the design and the low flow rate were increased by 3.35%,3.07%and 2.89%,respectively,after CFD simulations for 500 fan candidates with the constraint for the design *** optimization results validate the effectiveness and feasibility of the proposed algorithm.

关键词： multi-objective optimization surrogate-assisted evolutionary algorithm axial fan computational fluid dynamics aerodynamic optimization

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