A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III

In multi/many-objective evolutionary algorithms (MOEAs), to alleviate the degraded convergence pressure of Pareto dominance with the increase in the number of objectives, numerous modified dominance relationships were proposed. Recently, the strengthened dominance relation (SDR) has been proposed, w...

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Autores principales:	Saykat Dutta, Sri Srinivasa Raju M, Rammohan Mallipeddi, Kedar Nath Das, Dong-Gyu Lee
Formato:	article
Lenguaje:	EN
Publicado:	MDPI AG 2021
Materias:	convergence decomposition diversity dominance ensemble Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/b8050951ba5c4f06a3bf86b31cbf1c41
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spelling	oai:doaj.org-article:b8050951ba5c4f06a3bf86b31cbf1c412021-11-25T18:16:27ZA Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III10.3390/math92228372227-7390https://doaj.org/article/b8050951ba5c4f06a3bf86b31cbf1c412021-11-01T00:00:00Zhttps://www.mdpi.com/2227-7390/9/22/2837https://doaj.org/toc/2227-7390In multi/many-objective evolutionary algorithms (MOEAs), to alleviate the degraded convergence pressure of Pareto dominance with the increase in the number of objectives, numerous modified dominance relationships were proposed. Recently, the strengthened dominance relation (SDR) has been proposed, where the dominance area of a solution is determined by convergence degree and niche size (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>θ</mi><mo>¯</mo></mover></semantics></math></inline-formula>). Later, in controlled SDR (CSDR), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>θ</mi><mo>¯</mo></mover></semantics></math></inline-formula> and an additional parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> associated with the convergence degree are dynamically adjusted depending on the iteration count. Depending on the problem characteristics and the distribution of the current population, different situations require different values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>k</mi></semantics></math></inline-formula>, rendering the linear reduction of <i>k</i> based on the generation count ineffective. This is because a particular value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>k</mi></semantics></math></inline-formula> is expected to bias the dominance relationship towards a particular region on the Pareto front (PF). In addition, due to the same reason, using SDR or CSDR in the environmental selection cannot preserve the diversity of solutions required to cover the entire PF. Therefore, we propose an MOEA, referred to as NSGA-III, where (1) a modified SDR (MSDR)-based mating selection with an adaptive ensemble of parameter <i>k</i> would prioritize parents from specific sections of the PF depending on <i>k</i>, and (2) the traditional weight vector and non-dominated sorting-based environmental selection of NSGA-III would protect the solutions corresponding to the entire PF. The performance of NSGA-III is favourably compared with state-of-the-art MOEAs on DTLZ and WFG test suites with up to 10 objectives.Saykat DuttaSri Srinivasa Raju MRammohan MallipeddiKedar Nath DasDong-Gyu LeeMDPI AGarticleconvergencedecompositiondiversitydominanceensembleMathematicsQA1-939ENMathematics, Vol 9, Iss 2837, p 2837 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	convergence decomposition diversity dominance ensemble Mathematics QA1-939
spellingShingle	convergence decomposition diversity dominance ensemble Mathematics QA1-939 Saykat Dutta Sri Srinivasa Raju M Rammohan Mallipeddi Kedar Nath Das Dong-Gyu Lee A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III
description	In multi/many-objective evolutionary algorithms (MOEAs), to alleviate the degraded convergence pressure of Pareto dominance with the increase in the number of objectives, numerous modified dominance relationships were proposed. Recently, the strengthened dominance relation (SDR) has been proposed, where the dominance area of a solution is determined by convergence degree and niche size (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>θ</mi><mo>¯</mo></mover></semantics></math></inline-formula>). Later, in controlled SDR (CSDR), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mover accent="true"><mi>θ</mi><mo>¯</mo></mover></semantics></math></inline-formula> and an additional parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mrow><mo>(</mo><mi>k</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> associated with the convergence degree are dynamically adjusted depending on the iteration count. Depending on the problem characteristics and the distribution of the current population, different situations require different values of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>k</mi></semantics></math></inline-formula>, rendering the linear reduction of <i>k</i> based on the generation count ineffective. This is because a particular value of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>k</mi></semantics></math></inline-formula> is expected to bias the dominance relationship towards a particular region on the Pareto front (PF). In addition, due to the same reason, using SDR or CSDR in the environmental selection cannot preserve the diversity of solutions required to cover the entire PF. Therefore, we propose an MOEA, referred to as NSGA-III, where (1) a modified SDR (MSDR)-based mating selection with an adaptive ensemble of parameter <i>k</i> would prioritize parents from specific sections of the PF depending on <i>k</i>, and (2) the traditional weight vector and non-dominated sorting-based environmental selection of NSGA-III would protect the solutions corresponding to the entire PF. The performance of NSGA-III is favourably compared with state-of-the-art MOEAs on DTLZ and WFG test suites with up to 10 objectives.
format	article
author	Saykat Dutta Sri Srinivasa Raju M Rammohan Mallipeddi Kedar Nath Das Dong-Gyu Lee
author_facet	Saykat Dutta Sri Srinivasa Raju M Rammohan Mallipeddi Kedar Nath Das Dong-Gyu Lee
author_sort	Saykat Dutta
title	A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III
title_short	A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III
title_full	A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III
title_fullStr	A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III
title_full_unstemmed	A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III
title_sort	mating selection based on modified strengthened dominance relation for nsga-iii
publisher	MDPI AG
publishDate	2021
url	https://doaj.org/article/b8050951ba5c4f06a3bf86b31cbf1c41
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A Mating Selection Based on Modified Strengthened Dominance Relation for NSGA-III

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