期刊
IEEE TRANSACTIONS ON CYBERNETICS
卷 51, 期 6, 页码 3115-3128出版社
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TCYB.2020.2979930
关键词
Optimization; Neural networks; Evolutionary computation; Search problems; Computer science; Sociology; Statistics; Denoising autoencoder (DAE); large-scale multiobjective optimization; Pareto-optimal subspace; restricted Boltzmann machine (RBM); sparse Pareto-optimal solutions
类别
资金
- Key Project of Science and Technology Innovation 2030 - Ministry of Science and Technology of China [2018AAA0100105]
- National Natural Science Foundation of China [61672033, 61876123, 61906001, U1804262]
- Hong Kong Scholars Program [XJ2019035]
- Anhui Provincial Natural Science Foundation [1808085J06, 1908085QF271]
- State Key Laboratory of Synthetical Automation for Process Industries [PAL-N201805]
- Research Grants Council of the Hong Kong Special Administrative Region, China [CityU11202418, CityU11209219]
- Royal Society International Exchanges [IEC\NSFC\170279]
This article proposes an evolutionary algorithm to solve sparse large-scale multiobjective optimization problems by learning the Pareto-optimal subspace. The algorithm uses neural networks to learn a sparse distribution and a compact representation of decision variables, conducts genetic operators in the learned subspace, and maps the resultant offspring solutions back to the original search space. Experimental results show that the proposed algorithm can effectively solve sparse large-scale multiobjective optimization problems with a limited budget of 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.
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