A semi-supervised learning technique assisted multi-objective evolutionary algorithm for computationally expensive problems

Abstract Existing multi-objective evolutionary algorithms (MOEAs) have demonstrated excellent efficiency when tackling multi-objective tasks. However, its use in computationally expensive multi-objective issues is hindered by the large number of reliable evaluations needed to find Pareto-optimal sol...

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Main Authors: Zijian Jiang, Chaoli Sun, Xiaotong Liu, Hui Shi, Sisi Wang
Format: Article
Language:English
Published: Springer 2025-01-01
Series:Complex & Intelligent Systems
Subjects:
Online Access:https://doi.org/10.1007/s40747-024-01715-6
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author Zijian Jiang
Chaoli Sun
Xiaotong Liu
Hui Shi
Sisi Wang
author_facet Zijian Jiang
Chaoli Sun
Xiaotong Liu
Hui Shi
Sisi Wang
author_sort Zijian Jiang
collection DOAJ
description Abstract Existing multi-objective evolutionary algorithms (MOEAs) have demonstrated excellent efficiency when tackling multi-objective tasks. However, its use in computationally expensive multi-objective issues is hindered by the large number of reliable evaluations needed to find Pareto-optimal solutions. This paper employs the semi-supervised learning technique in model training to aid in evolutionary algorithms for addressing expensive multi-objective issues, resulting in the semi-supervised learning technique assisted multi-objective evolutionary algorithm (SLTA-MOEA). In SLTA-MOEA, the value of every objective function is determined as a weighted mean of values approximated by all surrogate models for that objective function, with the weights optimized through a convex combination problem. Furthermore, the number of unlabelled solutions participating in model training is adaptively determined based on the objective evaluations conducted. A group of tests on DTLZ test problems with 3, 5, and 10 objective functions, combined with a practical application, are conducted to assess the effectiveness of our proposed method. Comparative experimental results versus six state-of-the-art evolutionary algorithms for expensive problems show high efficiency of SLTA-MOEA, particularly for problems with irregular Pareto fronts.
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spelling doaj-art-c618c4a505f145129b36fbdd641f7cfe2025-02-09T13:01:19ZengSpringerComplex & Intelligent Systems2199-45362198-60532025-01-0111211110.1007/s40747-024-01715-6A semi-supervised learning technique assisted multi-objective evolutionary algorithm for computationally expensive problemsZijian Jiang0Chaoli Sun1Xiaotong Liu2Hui Shi3Sisi Wang4School of Computer Science and Technology, Taiyuan University of Science and TechnologySchool of Computer Science and Technology, Taiyuan University of Science and TechnologySchool of Electronic Information Engineering, Taiyuan University of Science and TechnologySchool of Electronic Information Engineering, Taiyuan University of Science and TechnologyShanxi Gangke Carbon Material Co., Ltd.Abstract Existing multi-objective evolutionary algorithms (MOEAs) have demonstrated excellent efficiency when tackling multi-objective tasks. However, its use in computationally expensive multi-objective issues is hindered by the large number of reliable evaluations needed to find Pareto-optimal solutions. This paper employs the semi-supervised learning technique in model training to aid in evolutionary algorithms for addressing expensive multi-objective issues, resulting in the semi-supervised learning technique assisted multi-objective evolutionary algorithm (SLTA-MOEA). In SLTA-MOEA, the value of every objective function is determined as a weighted mean of values approximated by all surrogate models for that objective function, with the weights optimized through a convex combination problem. Furthermore, the number of unlabelled solutions participating in model training is adaptively determined based on the objective evaluations conducted. A group of tests on DTLZ test problems with 3, 5, and 10 objective functions, combined with a practical application, are conducted to assess the effectiveness of our proposed method. Comparative experimental results versus six state-of-the-art evolutionary algorithms for expensive problems show high efficiency of SLTA-MOEA, particularly for problems with irregular Pareto fronts.https://doi.org/10.1007/s40747-024-01715-6Expensive multi-objective evolutionary algorithmSemi-supervised learningGaussian process model
spellingShingle Zijian Jiang
Chaoli Sun
Xiaotong Liu
Hui Shi
Sisi Wang
A semi-supervised learning technique assisted multi-objective evolutionary algorithm for computationally expensive problems
Complex & Intelligent Systems
Expensive multi-objective evolutionary algorithm
Semi-supervised learning
Gaussian process model
title A semi-supervised learning technique assisted multi-objective evolutionary algorithm for computationally expensive problems
title_full A semi-supervised learning technique assisted multi-objective evolutionary algorithm for computationally expensive problems
title_fullStr A semi-supervised learning technique assisted multi-objective evolutionary algorithm for computationally expensive problems
title_full_unstemmed A semi-supervised learning technique assisted multi-objective evolutionary algorithm for computationally expensive problems
title_short A semi-supervised learning technique assisted multi-objective evolutionary algorithm for computationally expensive problems
title_sort semi supervised learning technique assisted multi objective evolutionary algorithm for computationally expensive problems
topic Expensive multi-objective evolutionary algorithm
Semi-supervised learning
Gaussian process model
url https://doi.org/10.1007/s40747-024-01715-6
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