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A Novel Approach to Designing Surrogate-assisted Genetic Algorithms by Combining Efficient Learning of Walsh Coefficients and Dependencies

A Novel Approach to Designing Surrogate-assisted Genetic Algorithms by Combining Efficient... Surrogate-assisted evolutionary algorithms have the potential to be of high value for real-world optimization problems when fitness evaluations are expensive, limiting the number of evaluations that can be performed. In this article, we consider the domain of pseudo-Boolean functions in a black-box setting. Moreover, instead of using a surrogate model as an approximation of a fitness function, we propose to precisely learn the coefficients of the Walsh decomposition of a fitness function and use the Walsh decomposition as a surrogate. If the coefficients are learned correctly, then the Walsh decomposition values perfectly match with the fitness function, and, thus, the optimal solution to the problem can be found by optimizing the surrogate without any additional evaluations of the original fitness function. It is known that the Walsh coefficients can be efficiently learned for pseudo-Boolean functions with k-bounded epistasis and known problem structure. We propose to learn dependencies between variables first and, therefore, substantially reduce the number of Walsh coefficients to be calculated. After the accurate Walsh decomposition is obtained, the surrogate model is optimized using GOMEA, which is considered to be a state-of-the-art binary optimization algorithm. We compare the proposed approach with standard GOMEA and two other Walsh decomposition-based algorithms. The benchmark functions in the experiments are well-known trap functions, NK-landscapes, MaxCut, and MAX3SAT problems. The experimental results demonstrate that the proposed approach is scalable at the supposed complexity of O(ℓlogℓ) function evaluations when the number of subfunctions is O(ℓ) and all subfunctions are k-bounded, outperforming all considered algorithms. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Evolutionary Learning and Optimization Association for Computing Machinery

A Novel Approach to Designing Surrogate-assisted Genetic Algorithms by Combining Efficient Learning of Walsh Coefficients and Dependencies

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2021 Association for Computing Machinery.
ISSN
2688-299X
eISSN
2688-3007
DOI
10.1145/3453141
Publisher site
See Article on Publisher Site

Abstract

Surrogate-assisted evolutionary algorithms have the potential to be of high value for real-world optimization problems when fitness evaluations are expensive, limiting the number of evaluations that can be performed. In this article, we consider the domain of pseudo-Boolean functions in a black-box setting. Moreover, instead of using a surrogate model as an approximation of a fitness function, we propose to precisely learn the coefficients of the Walsh decomposition of a fitness function and use the Walsh decomposition as a surrogate. If the coefficients are learned correctly, then the Walsh decomposition values perfectly match with the fitness function, and, thus, the optimal solution to the problem can be found by optimizing the surrogate without any additional evaluations of the original fitness function. It is known that the Walsh coefficients can be efficiently learned for pseudo-Boolean functions with k-bounded epistasis and known problem structure. We propose to learn dependencies between variables first and, therefore, substantially reduce the number of Walsh coefficients to be calculated. After the accurate Walsh decomposition is obtained, the surrogate model is optimized using GOMEA, which is considered to be a state-of-the-art binary optimization algorithm. We compare the proposed approach with standard GOMEA and two other Walsh decomposition-based algorithms. The benchmark functions in the experiments are well-known trap functions, NK-landscapes, MaxCut, and MAX3SAT problems. The experimental results demonstrate that the proposed approach is scalable at the supposed complexity of O(ℓlogℓ) function evaluations when the number of subfunctions is O(ℓ) and all subfunctions are k-bounded, outperforming all considered algorithms.

Journal

ACM Transactions on Evolutionary Learning and OptimizationAssociation for Computing Machinery

Published: Jul 29, 2021

Keywords: Linkage-learning

References