Expensive Multiobjective Optimization by Relation Learning and Prediction
Expensive multiobjective optimization problems pose great challenges to evolutionary algorithms due to their costly evaluation. Building cheap surrogate models to replace the expensive real models has been proved to be a practical way to reduce the number of costly evaluations. Supervised learning t...
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| Veröffentlicht in: | IEEE transactions on evolutionary computation Jg. 26; H. 5; S. 1157 - 1170 |
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01.10.2022
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| Abstract | Expensive multiobjective optimization problems pose great challenges to evolutionary algorithms due to their costly evaluation. Building cheap surrogate models to replace the expensive real models has been proved to be a practical way to reduce the number of costly evaluations. Supervised learning techniques from the community of machine learning have been widely applied to build either regressors, which approximate the fitness values of candidate solutions, or classifiers, which estimate the categories of candidate solutions. Considering the characteristics of the data produced in optimization, this article proposes a new surrogate model, called a relation model, for evolutionary multiobjective optimization. Instead of estimating the qualities of candidate solutions directly, the relation model tries to estimate the relationship between a pair of solutions <inline-formula> <tex-math notation="LaTeX">\langle \mathbf {x}, \mathbf {y}\rangle </tex-math></inline-formula>, i.e., <inline-formula> <tex-math notation="LaTeX">\mathbf {x} </tex-math></inline-formula> dominates <inline-formula> <tex-math notation="LaTeX">\mathbf {y} </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">\mathbf {x} </tex-math></inline-formula> is dominated by <inline-formula> <tex-math notation="LaTeX">\mathbf {y} </tex-math></inline-formula>, or <inline-formula> <tex-math notation="LaTeX">\mathbf {x} </tex-math></inline-formula> is nondominated with <inline-formula> <tex-math notation="LaTeX">\mathbf {y} </tex-math></inline-formula> in the case of multiobjective optimization. To implement this idea, first a balanced training set is prepared, then a classifier is built based on the training data set to learn the relationship, and finally, the classifier with a voting-scoring strategy is applied to estimate the relationship between the candidate solutions and parent solutions. By this way, the promising candidate solutions are recognized and evaluated by the real models. The new approach is applied to three well-known benchmark suites and two real-world applications, and the experimental results suggest that the proposed method outperforms some state-of-the-art methods based on regression and classification models on the given instances. |
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| AbstractList | Expensive multiobjective optimization problems pose great challenges to evolutionary algorithms due to their costly evaluation. Building cheap surrogate models to replace the expensive real models has been proved to be a practical way to reduce the number of costly evaluations. Supervised learning techniques from the community of machine learning have been widely applied to build either regressors, which approximate the fitness values of candidate solutions, or classifiers, which estimate the categories of candidate solutions. Considering the characteristics of the data produced in optimization, this article proposes a new surrogate model, called a relation model, for evolutionary multiobjective optimization. Instead of estimating the qualities of candidate solutions directly, the relation model tries to estimate the relationship between a pair of solutions <inline-formula> <tex-math notation="LaTeX">\langle \mathbf {x}, \mathbf {y}\rangle </tex-math></inline-formula>, i.e., <inline-formula> <tex-math notation="LaTeX">\mathbf {x} </tex-math></inline-formula> dominates <inline-formula> <tex-math notation="LaTeX">\mathbf {y} </tex-math></inline-formula>, <inline-formula> <tex-math notation="LaTeX">\mathbf {x} </tex-math></inline-formula> is dominated by <inline-formula> <tex-math notation="LaTeX">\mathbf {y} </tex-math></inline-formula>, or <inline-formula> <tex-math notation="LaTeX">\mathbf {x} </tex-math></inline-formula> is nondominated with <inline-formula> <tex-math notation="LaTeX">\mathbf {y} </tex-math></inline-formula> in the case of multiobjective optimization. To implement this idea, first a balanced training set is prepared, then a classifier is built based on the training data set to learn the relationship, and finally, the classifier with a voting-scoring strategy is applied to estimate the relationship between the candidate solutions and parent solutions. By this way, the promising candidate solutions are recognized and evaluated by the real models. The new approach is applied to three well-known benchmark suites and two real-world applications, and the experimental results suggest that the proposed method outperforms some state-of-the-art methods based on regression and classification models on the given instances. Expensive multiobjective optimization problems pose great challenges to evolutionary algorithms due to their costly evaluation. Building cheap surrogate models to replace the expensive real models has been proved to be a practical way to reduce the number of costly evaluations. Supervised learning techniques from the community of machine learning have been widely applied to build either regressors, which approximate the fitness values of candidate solutions, or classifiers, which estimate the categories of candidate solutions. Considering the characteristics of the data produced in optimization, this article proposes a new surrogate model, called a relation model, for evolutionary multiobjective optimization. Instead of estimating the qualities of candidate solutions directly, the relation model tries to estimate the relationship between a pair of solutions [Formula Omitted], i.e., [Formula Omitted] dominates [Formula Omitted], [Formula Omitted] is dominated by [Formula Omitted], or [Formula Omitted] is nondominated with [Formula Omitted] in the case of multiobjective optimization. To implement this idea, first a balanced training set is prepared, then a classifier is built based on the training data set to learn the relationship, and finally, the classifier with a voting-scoring strategy is applied to estimate the relationship between the candidate solutions and parent solutions. By this way, the promising candidate solutions are recognized and evaluated by the real models. The new approach is applied to three well-known benchmark suites and two real-world applications, and the experimental results suggest that the proposed method outperforms some state-of-the-art methods based on regression and classification models on the given instances. |
| Author | Qian, Hong Hao, Hao Zhou, Aimin Zhang, Hu |
| Author_xml | – sequence: 1 givenname: Hao orcidid: 0000-0003-3171-6194 surname: Hao fullname: Hao, Hao email: 52194506007@stu.ecnu.edu.cn organization: Shanghai Frontiers Science Center of Molecule Intelligent Syntheses, Shanghai Institute of AI for Education, and the School of Computer Science and Technology, East China Normal University, Shanghai, China – sequence: 2 givenname: Aimin orcidid: 0000-0002-4768-5946 surname: Zhou fullname: Zhou, Aimin email: amzhou@cs.ecnu.edu.cn organization: Shanghai Frontiers Science Center of Molecule Intelligent Syntheses, Shanghai Institute of AI for Education, and the School of Computer Science and Technology, East China Normal University, Shanghai, China – sequence: 3 givenname: Hong surname: Qian fullname: Qian, Hong email: hqian@cs.ecnu.edu.cn organization: Shanghai Frontiers Science Center of Molecule Intelligent Syntheses, Shanghai Institute of AI for Education, and the School of Computer Science and Technology, East China Normal University, Shanghai, China – sequence: 4 givenname: Hu surname: Zhang fullname: Zhang, Hu email: jxzhanghu@126.com organization: Science and Technology on Complex System Control and Intelligent Agent Cooperation Laboratory, Beijing Electro-Mechanical Engineering Institute, Beijing, China |
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| SubjectTerms | Classifiers Computational modeling Data models Evaluation Evolutionary algorithms Expensive optimization Machine learning multiobjective optimization Multiple objective analysis Optimization Pareto optimization Predictive models relation model surrogate-assisted evolutionary algorithm (SAEA) Training Training data |
| Title | Expensive Multiobjective Optimization by Relation Learning and Prediction |
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