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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Bibliographic Details
Published in:IEEE transactions on evolutionary computation Vol. 26; no. 5; pp. 1157 - 1170
Main Authors: Hao, Hao, Zhou, Aimin, Qian, Hong, Zhang, Hu
Format: Journal Article
Language:English
Published: New York IEEE 01.10.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
ISSN:1089-778X, 1941-0026
Online Access:Get full text
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Summary: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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ISSN:1089-778X
1941-0026
DOI:10.1109/TEVC.2022.3152582