Influence of binomial crossover on approximation error of evolutionary algorithms

Wang, C., He, J. ORCID: 0000-0002-5616-4691, Chen, Y. and Zou, X., 2022. Influence of binomial crossover on approximation error of evolutionary algorithms. Mathematics, 10 (16): 2850. ISSN 2227-7390

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Although differential evolution (DE) algorithms perform well on a large variety of complicated optimization problems, only a few theoretical studies are focused on the working principle of DE algorithms. To make the first attempt to reveal the function of binomial crossover, this paper aims to answer whether it can reduce the approximation error of evolutionary algorithms. By investigating the expected approximation error and the probability of not finding the optimum, we conduct a case study comparing two evolutionary algorithms with and without binomial crossover on two classical benchmark problems: OneMax and Deceptive. It is proven that using binomial crossover leads to the dominance of transition matrices. As a result, the algorithm with binomial crossover asymptotically outperforms that without crossover on both OneMax and Deceptive, and outperforms on OneMax, however, not on Deceptive. Furthermore, an adaptive parameter strategy is proposed which can strengthen the superiority of binomial crossover on Deceptive.

Item Type: Journal article
Publication Title: Mathematics
Creators: Wang, C., He, J., Chen, Y. and Zou, X.
Publisher: MDPI
Date: 10 August 2022
Volume: 10
Number: 16
ISSN: 2227-7390
Rights: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// 4.0/).
Divisions: Schools > School of Science and Technology
Record created by: Jonathan Gallacher
Date Added: 20 Sep 2022 09:04
Last Modified: 20 Sep 2022 09:04

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