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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Bibliographic Details
Published in:IEEE transactions on cybernetics Vol. 51; no. 6; pp. 3115 - 3128
Main Authors: Tian, Ye, Lu, Chang, Zhang, Xingyi, Tan, Kay Chen, Jin, Yaochu
Format: Journal Article
Language:English
Published: United States IEEE 01.06.2021
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
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
Online Access:Get full text
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Summary: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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ISSN:2168-2267
2168-2275
2168-2275
DOI:10.1109/TCYB.2020.2979930