An expensive multi-objective evolutionary algorithm based on grid and relation learning
In many real-world applications, there is often a need to optimize multiple objectives, which are frequently and simultaneously conflicting. The evaluation process consumes computational resources or funds, making it difficult to provide adequate function evaluations for converging evolutionary algo...
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| Vydáno v: | Applied soft computing Ročník 186; s. 114135 |
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| Hlavní autoři: | , , , , , |
| Médium: | Journal Article |
| Jazyk: | angličtina |
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Elsevier B.V
01.01.2026
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| Témata: | |
| ISSN: | 1568-4946 |
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| Abstract | In many real-world applications, there is often a need to optimize multiple objectives, which are frequently and simultaneously conflicting. The evaluation process consumes computational resources or funds, making it difficult to provide adequate function evaluations for converging evolutionary algorithms. Surrogate models have become an effective solution for obtaining more virtual evaluations, particularly when computational resources are limited. Most existing surrogate models are either regression-based or classification-based, and their performance heavily depends on the quality of training data. Imbalanced datasets may significantly impact the quality of surrogate models. To address this, a relationship-based surrogate-assisted evolutionary algorithm is proposed in this paper. This algorithm utilizes the surrogate model to compare candidate solutions rather than directly predicting the fitness values of solutions. This can better balance positive and negative samples. Considering the characteristics of data generated during optimization, a grid-based data partitioning method is used to discretize the objective space into grids. A balanced training dataset is created based on the grid positions, and a classifier is built to learn relationships from the training dataset. A reference point selection mechanism is introduced to choose reference points using reference vectors, thereby filtering out promising solutions. The proposed method was validated using the Wilcoxon rank-sum test (α=0.05) on 88 benchmark test instances and one real-world engineering optimization problem. Experimental results demonstrate that the proposed method achieves statistically significant optimal results (p<0.05) in 62 instances compared to state-of-the-art surrogate-assisted evolutionary algorithms.
•Propose a relationship-based surrogate model trained on pairwise solution comparisons.•Employ grid-based ranking to select superior solutions for constructing training pairs.•Propose GRE-MOEA to solve multi-objective problems with limited function evaluations.•Validate the algorithm on problems with up to 50 variables and 10 objectives.•Demonstrate superior performance on both benchmark and real-world problems. |
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| AbstractList | In many real-world applications, there is often a need to optimize multiple objectives, which are frequently and simultaneously conflicting. The evaluation process consumes computational resources or funds, making it difficult to provide adequate function evaluations for converging evolutionary algorithms. Surrogate models have become an effective solution for obtaining more virtual evaluations, particularly when computational resources are limited. Most existing surrogate models are either regression-based or classification-based, and their performance heavily depends on the quality of training data. Imbalanced datasets may significantly impact the quality of surrogate models. To address this, a relationship-based surrogate-assisted evolutionary algorithm is proposed in this paper. This algorithm utilizes the surrogate model to compare candidate solutions rather than directly predicting the fitness values of solutions. This can better balance positive and negative samples. Considering the characteristics of data generated during optimization, a grid-based data partitioning method is used to discretize the objective space into grids. A balanced training dataset is created based on the grid positions, and a classifier is built to learn relationships from the training dataset. A reference point selection mechanism is introduced to choose reference points using reference vectors, thereby filtering out promising solutions. The proposed method was validated using the Wilcoxon rank-sum test (α=0.05) on 88 benchmark test instances and one real-world engineering optimization problem. Experimental results demonstrate that the proposed method achieves statistically significant optimal results (p<0.05) in 62 instances compared to state-of-the-art surrogate-assisted evolutionary algorithms.
•Propose a relationship-based surrogate model trained on pairwise solution comparisons.•Employ grid-based ranking to select superior solutions for constructing training pairs.•Propose GRE-MOEA to solve multi-objective problems with limited function evaluations.•Validate the algorithm on problems with up to 50 variables and 10 objectives.•Demonstrate superior performance on both benchmark and real-world problems. |
| ArticleNumber | 114135 |
| Author | Cheng, Yan Yao, Yuxiao Yu, Gongcheng Li, Guowei Wang, Jiaqi Chen, Yanyin |
| Author_xml | – sequence: 1 givenname: Yan surname: Cheng fullname: Cheng, Yan email: Chyan88888@jxnu.edu.cn organization: School of Artificial Intelligence, Jiangxi Normal University, 330022, Nanchang Jiangxi, China – sequence: 2 givenname: Jiaqi surname: Wang fullname: Wang, Jiaqi organization: Key Laboratory of Intelligent Information Processing and Emotional Computing of Jiangxi, 330022, Nanchang Jiangxi, China – sequence: 3 givenname: Gongcheng surname: Yu fullname: Yu, Gongcheng organization: Key Laboratory of Intelligent Information Processing and Emotional Computing of Jiangxi, 330022, Nanchang Jiangxi, China – sequence: 4 givenname: Yuxiao surname: Yao fullname: Yao, Yuxiao organization: Key Laboratory of Intelligent Information Processing and Emotional Computing of Jiangxi, 330022, Nanchang Jiangxi, China – sequence: 5 givenname: Yanyin surname: Chen fullname: Chen, Yanyin organization: Key Laboratory of Intelligent Information Processing and Emotional Computing of Jiangxi, 330022, Nanchang Jiangxi, China – sequence: 6 givenname: Guowei surname: Li fullname: Li, Guowei organization: Key Laboratory of Intelligent Information Processing and Emotional Computing of Jiangxi, 330022, Nanchang Jiangxi, China |
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| Keywords | Evolutionary algorithms Surrogate-assisted optimization Relation learning Expensive multi-objective optimization Grid |
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