Influence of Binomial Crossover on Approximation Error of Evolutionary Algorithms

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 answe...
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Autor*in:	Cong Wang [verfasserIn] Jun He [verfasserIn] Yu Chen [verfasserIn] Xiufen Zou [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2022

Schlagwörter:	binomial crossover differential evolution fixed-budget analysis evolutionary computation approximation error

Übergeordnetes Werk:	In: Mathematics - MDPI AG, 2013, 10(2022), 16, p 2850
Übergeordnetes Werk:	volume:10 ; year:2022 ; number:16, p 2850

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DOI / URN:	10.3390/math10162850

Katalog-ID:	DOAJ024209910

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520			\|a 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.
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allfieldsGer	10.3390/math10162850 doi (DE-627)DOAJ024209910 (DE-599)DOAJ5206985fa501494da38b205ff2089456 DE-627 ger DE-627 rakwb eng QA1-939 Cong Wang verfasserin aut Influence of Binomial Crossover on Approximation Error of Evolutionary Algorithms 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. binomial crossover differential evolution fixed-budget analysis evolutionary computation approximation error Mathematics Jun He verfasserin aut Yu Chen verfasserin aut Xiufen Zou verfasserin aut In Mathematics MDPI AG, 2013 10(2022), 16, p 2850 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:10 year:2022 number:16, p 2850 https://doi.org/10.3390/math10162850 kostenfrei https://doaj.org/article/5206985fa501494da38b205ff2089456 kostenfrei https://www.mdpi.com/2227-7390/10/16/2850 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 16, p 2850
allfieldsSound	10.3390/math10162850 doi (DE-627)DOAJ024209910 (DE-599)DOAJ5206985fa501494da38b205ff2089456 DE-627 ger DE-627 rakwb eng QA1-939 Cong Wang verfasserin aut Influence of Binomial Crossover on Approximation Error of Evolutionary Algorithms 2022 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier 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. binomial crossover differential evolution fixed-budget analysis evolutionary computation approximation error Mathematics Jun He verfasserin aut Yu Chen verfasserin aut Xiufen Zou verfasserin aut In Mathematics MDPI AG, 2013 10(2022), 16, p 2850 (DE-627)737287764 (DE-600)2704244-3 22277390 nnns volume:10 year:2022 number:16, p 2850 https://doi.org/10.3390/math10162850 kostenfrei https://doaj.org/article/5206985fa501494da38b205ff2089456 kostenfrei https://www.mdpi.com/2227-7390/10/16/2850 kostenfrei https://doaj.org/toc/2227-7390 Journal toc kostenfrei GBV_USEFLAG_A SYSFLAG_A GBV_DOAJ GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_65 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_95 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_2005 GBV_ILN_2009 GBV_ILN_2014 GBV_ILN_2055 GBV_ILN_2111 GBV_ILN_4012 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4249 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4700 AR 10 2022 16, p 2850
language	English
source	In Mathematics 10(2022), 16, p 2850 volume:10 year:2022 number:16, p 2850
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callnumber-first	Q - Science
author	Cong Wang
spellingShingle	Cong Wang misc QA1-939 misc binomial crossover misc differential evolution misc fixed-budget analysis misc evolutionary computation misc approximation error misc Mathematics Influence of Binomial Crossover on Approximation Error of Evolutionary Algorithms
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topic_title	QA1-939 Influence of Binomial Crossover on Approximation Error of Evolutionary Algorithms binomial crossover differential evolution fixed-budget analysis evolutionary computation approximation error
topic	misc QA1-939 misc binomial crossover misc differential evolution misc fixed-budget analysis misc evolutionary computation misc approximation error misc Mathematics
topic_unstemmed	misc QA1-939 misc binomial crossover misc differential evolution misc fixed-budget analysis misc evolutionary computation misc approximation error misc Mathematics
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title	Influence of Binomial Crossover on Approximation Error of Evolutionary Algorithms
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title_sort	influence of binomial crossover on approximation error of evolutionary algorithms
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title_auth	Influence of Binomial Crossover on Approximation Error of Evolutionary Algorithms
abstract	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.
abstractGer	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.
abstract_unstemmed	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.
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title_short	Influence of Binomial Crossover on Approximation Error of Evolutionary Algorithms
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Influence of Binomial Crossover on Approximation Error of Evolutionary Algorithms

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