A Two-Stage Differential Evolution Algorithm with Mutation Strategy Combination

For most of differential evolution (DE) algorithm variants, premature convergence is still challenging. The main reason is that the exploration and exploitation are highly coupled in the existing works. To address this problem, we present a novel DE variant that can symmetrically decouple exploratio...

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Autores principales:	Xingping Sun, Da Wang, Hongwei Kang, Yong Shen, Qingyi Chen
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	evolutionary computation differential evolution mutation combination Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/321664fbab174b6ea1bee917e28972ca
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spelling	oai:doaj.org-article:321664fbab174b6ea1bee917e28972ca2021-11-25T19:07:15ZA Two-Stage Differential Evolution Algorithm with Mutation Strategy Combination10.3390/sym131121632073-8994https://doaj.org/article/321664fbab174b6ea1bee917e28972ca2021-11-01T00:00:00Zhttps://www.mdpi.com/2073-8994/13/11/2163https://doaj.org/toc/2073-8994For most of differential evolution (DE) algorithm variants, premature convergence is still challenging. The main reason is that the exploration and exploitation are highly coupled in the existing works. To address this problem, we present a novel DE variant that can symmetrically decouple exploration and exploitation during the optimization process in this paper. In the algorithm, the whole population is divided into two symmetrical subpopulations by ascending order of fitness during each iteration; moreover, we divide the algorithm into two symmetrical stages according to the number of evaluations (FEs). On one hand, we introduce a mutation strategy, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>D</mi><mi>E</mi><mo>/</mo><mi>c</mi><mi>u</mi><mi>r</mi><mi>r</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo>/</mo><mn>1</mn></mrow></semantics></math></inline-formula>, which rarely appears in the literature. It can keep sufficient population diversity and fully explore the solution space, but its convergence speed gradually slows as iteration continues. To give full play to its advantages and avoid its disadvantages, we propose a heterogeneous two-stage double-subpopulation (HTSDS) mechanism. Four mutation strategies (including <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>D</mi><mi>E</mi><mo>/</mo><mi>c</mi><mi>u</mi><mi>r</mi><mi>r</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo>/</mo><mn>1</mn></mrow></semantics></math></inline-formula> and its modified version) with distinct search behaviors are assigned to superior and inferior subpopulations in two stages, which helps simultaneously and independently managing exploration and exploitation in different components. On the other hand, an adaptive two-stage partition (ATSP) strategy is proposed, which can adjust the stage partition parameter according to the complexity of the problem. Hence, a two-stage differential evolution algorithm with mutation strategy combination (TS-MSCDE) is proposed. Numerical experiments were conducted using CEC2017, CEC2020 and four real-world optimization problems from CEC2011. The results show that when computing resources are sufficient, the algorithm is competitive, especially for complex multimodal problems.Xingping SunDa WangHongwei KangYong ShenQingyi ChenMDPI AGarticleevolutionary computationdifferential evolutionmutation combinationMathematicsQA1-939ENSymmetry, Vol 13, Iss 2163, p 2163 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	evolutionary computation differential evolution mutation combination Mathematics QA1-939
spellingShingle	evolutionary computation differential evolution mutation combination Mathematics QA1-939 Xingping Sun Da Wang Hongwei Kang Yong Shen Qingyi Chen A Two-Stage Differential Evolution Algorithm with Mutation Strategy Combination
description	For most of differential evolution (DE) algorithm variants, premature convergence is still challenging. The main reason is that the exploration and exploitation are highly coupled in the existing works. To address this problem, we present a novel DE variant that can symmetrically decouple exploration and exploitation during the optimization process in this paper. In the algorithm, the whole population is divided into two symmetrical subpopulations by ascending order of fitness during each iteration; moreover, we divide the algorithm into two symmetrical stages according to the number of evaluations (FEs). On one hand, we introduce a mutation strategy, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>D</mi><mi>E</mi><mo>/</mo><mi>c</mi><mi>u</mi><mi>r</mi><mi>r</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo>/</mo><mn>1</mn></mrow></semantics></math></inline-formula>, which rarely appears in the literature. It can keep sufficient population diversity and fully explore the solution space, but its convergence speed gradually slows as iteration continues. To give full play to its advantages and avoid its disadvantages, we propose a heterogeneous two-stage double-subpopulation (HTSDS) mechanism. Four mutation strategies (including <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>D</mi><mi>E</mi><mo>/</mo><mi>c</mi><mi>u</mi><mi>r</mi><mi>r</mi><mi>e</mi><mi>n</mi><mi>t</mi><mo>/</mo><mn>1</mn></mrow></semantics></math></inline-formula> and its modified version) with distinct search behaviors are assigned to superior and inferior subpopulations in two stages, which helps simultaneously and independently managing exploration and exploitation in different components. On the other hand, an adaptive two-stage partition (ATSP) strategy is proposed, which can adjust the stage partition parameter according to the complexity of the problem. Hence, a two-stage differential evolution algorithm with mutation strategy combination (TS-MSCDE) is proposed. Numerical experiments were conducted using CEC2017, CEC2020 and four real-world optimization problems from CEC2011. The results show that when computing resources are sufficient, the algorithm is competitive, especially for complex multimodal problems.
format	article
author	Xingping Sun Da Wang Hongwei Kang Yong Shen Qingyi Chen
author_facet	Xingping Sun Da Wang Hongwei Kang Yong Shen Qingyi Chen
author_sort	Xingping Sun
title	A Two-Stage Differential Evolution Algorithm with Mutation Strategy Combination
title_short	A Two-Stage Differential Evolution Algorithm with Mutation Strategy Combination
title_full	A Two-Stage Differential Evolution Algorithm with Mutation Strategy Combination
title_fullStr	A Two-Stage Differential Evolution Algorithm with Mutation Strategy Combination
title_full_unstemmed	A Two-Stage Differential Evolution Algorithm with Mutation Strategy Combination
title_sort	two-stage differential evolution algorithm with mutation strategy combination
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/321664fbab174b6ea1bee917e28972ca
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A Two-Stage Differential Evolution Algorithm with Mutation Strategy Combination

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