Solving Large-Scale Multiobjective Optimization Problems With Sparse Optimal Solutions via Unsupervised Neural Networks

Due to the curse of dimensionality of search space, it is extremely difficult for evolutionary algorithms to approximate the optimal solutions of large-scale multiobjective optimization problems (LMOPs) by using a limited budget of evaluations. If the Pareto-optimal subspace is approximated during t...

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Vydané v:	IEEE transactions on cybernetics Ročník 51; číslo 6; s. 3115 - 3128
Hlavní autori:	Tian, Ye, Lu, Chang, Zhang, Xingyi, Tan, Kay Chen, Jin, Yaochu
Médium:	Journal Article
Jazyk:	English
Vydavateľské údaje:	United States IEEE 01.06.2021 The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:	Approximation Computer science Denoising autoencoder (DAE) Evolutionary algorithms Evolutionary computation Genetic algorithms large-scale multiobjective optimization Machine learning Multiple objective analysis Neural networks Noise reduction Optimization Pareto optimization Pareto optimum Pareto-optimal subspace Representations restricted Boltzmann machine (RBM) Search problems Searching Sociology sparse Pareto-optimal solutions Statistics Subspaces
ISSN:	2168-2267, 2168-2275, 2168-2275
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Abstract	Due to the curse of dimensionality of search space, it is extremely difficult for evolutionary algorithms to approximate the optimal solutions of large-scale multiobjective optimization problems (LMOPs) by using a limited budget of evaluations. If the Pareto-optimal subspace is approximated during the evolutionary process, the search space can be reduced and the difficulty encountered by evolutionary algorithms can be highly alleviated. Following the above idea, this article proposes an evolutionary algorithm to solve sparse LMOPs by learning the Pareto-optimal subspace. The proposed algorithm uses two unsupervised neural networks, a restricted Boltzmann machine, and a denoising autoencoder to learn a sparse distribution and a compact representation of the decision variables, where the combination of the learnt sparse distribution and compact representation is regarded as an approximation of the Pareto-optimal subspace. The genetic operators are conducted in the learnt subspace, and the resultant offspring solutions then can be mapped back to the original search space by the two neural networks. According to the experimental results on eight benchmark problems and eight real-world problems, the proposed algorithm can effectively solve sparse LMOPs with 10000 decision variables by only 100000 evaluations.
AbstractList	Due to the curse of dimensionality of search space, it is extremely difficult for evolutionary algorithms to approximate the optimal solutions of large-scale multiobjective optimization problems (LMOPs) by using a limited budget of evaluations. If the Pareto-optimal subspace is approximated during the evolutionary process, the search space can be reduced and the difficulty encountered by evolutionary algorithms can be highly alleviated. Following the above idea, this article proposes an evolutionary algorithm to solve sparse LMOPs by learning the Pareto-optimal subspace. The proposed algorithm uses two unsupervised neural networks, a restricted Boltzmann machine, and a denoising autoencoder to learn a sparse distribution and a compact representation of the decision variables, where the combination of the learnt sparse distribution and compact representation is regarded as an approximation of the Pareto-optimal subspace. The genetic operators are conducted in the learnt subspace, and the resultant offspring solutions then can be mapped back to the original search space by the two neural networks. According to the experimental results on eight benchmark problems and eight real-world problems, the proposed algorithm can effectively solve sparse LMOPs with 10000 decision variables by only 100000 evaluations. Due to the curse of dimensionality of search space, it is extremely difficult for evolutionary algorithms to approximate the optimal solutions of large-scale multiobjective optimization problems (LMOPs) by using a limited budget of evaluations. If the Pareto-optimal subspace is approximated during the evolutionary process, the search space can be reduced and the difficulty encountered by evolutionary algorithms can be highly alleviated. Following the above idea, this article proposes an evolutionary algorithm to solve sparse LMOPs by learning the Pareto-optimal subspace. The proposed algorithm uses two unsupervised neural networks, a restricted Boltzmann machine, and a denoising autoencoder to learn a sparse distribution and a compact representation of the decision variables, where the combination of the learnt sparse distribution and compact representation is regarded as an approximation of the Pareto-optimal subspace. The genetic operators are conducted in the learnt subspace, and the resultant offspring solutions then can be mapped back to the original search space by the two neural networks. According to the experimental results on eight benchmark problems and eight real-world problems, the proposed algorithm can effectively solve sparse LMOPs with 10000 decision variables by only 100000 evaluations.Due to the curse of dimensionality of search space, it is extremely difficult for evolutionary algorithms to approximate the optimal solutions of large-scale multiobjective optimization problems (LMOPs) by using a limited budget of evaluations. If the Pareto-optimal subspace is approximated during the evolutionary process, the search space can be reduced and the difficulty encountered by evolutionary algorithms can be highly alleviated. Following the above idea, this article proposes an evolutionary algorithm to solve sparse LMOPs by learning the Pareto-optimal subspace. The proposed algorithm uses two unsupervised neural networks, a restricted Boltzmann machine, and a denoising autoencoder to learn a sparse distribution and a compact representation of the decision variables, where the combination of the learnt sparse distribution and compact representation is regarded as an approximation of the Pareto-optimal subspace. The genetic operators are conducted in the learnt subspace, and the resultant offspring solutions then can be mapped back to the original search space by the two neural networks. According to the experimental results on eight benchmark problems and eight real-world problems, the proposed algorithm can effectively solve sparse LMOPs with 10000 decision variables by only 100000 evaluations.
Author	Lu, Chang Zhang, Xingyi Tan, Kay Chen Tian, Ye Jin, Yaochu
Author_xml	– sequence: 1 givenname: Ye orcidid: 0000-0002-3487-5126 surname: Tian fullname: Tian, Ye email: field910921@gmail.com organization: Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, Institutes of Physical Science and Information Technology, Anhui University, Hefei, China – sequence: 2 givenname: Chang surname: Lu fullname: Lu, Chang email: lucy_lc@outlook.com organization: Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, Institutes of Physical Science and Information Technology, Anhui University, Hefei, China – sequence: 3 givenname: Xingyi orcidid: 0000-0002-5052-000X surname: Zhang fullname: Zhang, Xingyi email: xyzhanghust@gmail.com organization: Key Laboratory of Intelligent Computing and Signal Processing of Ministry of Education, Institutes of Physical Science and Information Technology, Anhui University, Hefei, China – sequence: 4 givenname: Kay Chen orcidid: 0000-0002-6802-2463 surname: Tan fullname: Tan, Kay Chen email: kaytan@cityu.edu.hk organization: Department of Computer Science, City University of Hong Kong, Hong Kong – sequence: 5 givenname: Yaochu orcidid: 0000-0003-1100-0631 surname: Jin fullname: Jin, Yaochu email: yaochu.jin@surrey.ac.uk organization: Department of Computer Science, University of Surrey, Guildford, U.K
BackLink	https://www.ncbi.nlm.nih.gov/pubmed/32217494$$D View this record in MEDLINE/PubMed
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Snippet	Due to the curse of dimensionality of search space, it is extremely difficult for evolutionary algorithms to approximate the optimal solutions of large-scale...
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SubjectTerms	Approximation Computer science Denoising autoencoder (DAE) Evolutionary algorithms Evolutionary computation Genetic algorithms large-scale multiobjective optimization Machine learning Multiple objective analysis Neural networks Noise reduction Optimization Pareto optimization Pareto optimum Pareto-optimal subspace Representations restricted Boltzmann machine (RBM) Search problems Searching Sociology sparse Pareto-optimal solutions Statistics Subspaces
Title	Solving Large-Scale Multiobjective Optimization Problems With Sparse Optimal Solutions via Unsupervised Neural Networks
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