Comparing Decomposition-Based Evolutionary Algorithms for Multi and Many-Objective Optimization Problems

Detalhes bibliográficos
Autor(a) principal: Peito, Marcela C. C.
Data de Publicação: 2023
Outros Autores: da Costa Vargas, Denis Emanuel, Wanner, Elizabeth Fialho
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Vetor (Online)
Texto Completo: https://periodicos.furg.br/vetor/article/view/16444
Resumo: Many real-world problems can be mathematically modeled as Multiobjective Optimization Problems (MOPs), as they involve multiple conflicting objective functions that must be minimized simultaneously. MOPs with more than 3 objective functions are called Many-objective Optimization Problems (MaOPs). MOPs are typically solved through Multiobjective Evolutionary Algorithms (MOEAs), which can obtain a set of non-dominated optimal solutions, known as a Pareto front, in a single run. The MOEA Based on Decomposition (MOEA/D) is one of the most efficient, dividing a MOP into several single-objective subproblems and optimizing them simultaneously. This study evaluated the performance of MOEA/D and four variants representing the state of the art in the literature (MOEA/DD, MOEA/D-DE, MOEA/D-DU, and MOEA/D-AWA) in MOPs and MaOPs. Computational experiments were conducted using benchmark MOPs and MaOPs from the DTLZ suite considering 3 and 5 objective functions. Additionally, a statistical analysis, including the Wilcoxon test, was performed to evaluate the results obtained in the IGD+ performance indicator. The Hypervolume performance indicator was also considered in the combined Pareto front, formed by all solutions obtained by each MOEA. The experiments revealed that MOEA/DD performed best in IGD+, and MOEA/D-AWA achieved the highest Hypervolume in the combined Pareto front, while MOEA/D-DE registered the worst result in this set of problems.
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spelling Comparing Decomposition-Based Evolutionary Algorithms for Multi and Many-Objective Optimization ProblemsComparando Algoritmos Evolutivos Baseados em Decomposição para Problemas de Otimização Multiobjetivo e com Muitos ObjetivosAlgoritmo EvolutivoDecomposiçãoOtimização MultiobjetivoEvolutionary AlgorithmDecompositionMultiobjective OptimizationEvolutionary AlgorithmDecompositionMultiobjective OptimizationMany real-world problems can be mathematically modeled as Multiobjective Optimization Problems (MOPs), as they involve multiple conflicting objective functions that must be minimized simultaneously. MOPs with more than 3 objective functions are called Many-objective Optimization Problems (MaOPs). MOPs are typically solved through Multiobjective Evolutionary Algorithms (MOEAs), which can obtain a set of non-dominated optimal solutions, known as a Pareto front, in a single run. The MOEA Based on Decomposition (MOEA/D) is one of the most efficient, dividing a MOP into several single-objective subproblems and optimizing them simultaneously. This study evaluated the performance of MOEA/D and four variants representing the state of the art in the literature (MOEA/DD, MOEA/D-DE, MOEA/D-DU, and MOEA/D-AWA) in MOPs and MaOPs. Computational experiments were conducted using benchmark MOPs and MaOPs from the DTLZ suite considering 3 and 5 objective functions. Additionally, a statistical analysis, including the Wilcoxon test, was performed to evaluate the results obtained in the IGD+ performance indicator. The Hypervolume performance indicator was also considered in the combined Pareto front, formed by all solutions obtained by each MOEA. The experiments revealed that MOEA/DD performed best in IGD+, and MOEA/D-AWA achieved the highest Hypervolume in the combined Pareto front, while MOEA/D-DE registered the worst result in this set of problems.Muitos problemas oriundos do mundo real podem ser modelados matematicamente como Problemas de Otimização Multiobjetivo (POMs), já que possuem diversas funções objetivo conflitantes entre si que devem ser minimizadas simultaneamente. POMs com mais de 3 funções objetivo recebem o nome de Problemas de Otimização com Muitos Objetivos (MaOPs, do inglês Many-objective Optimization Problems). Os POMs geralmente são resolvidos através de Algoritmos Evolutivos Multiobjetivos (MOEAs, do inglês Multiobjective Evolutionary Algorithms), os quais conseguem obter um conjunto de soluções ótimas não dominadas entre si, conhecidos como frente de Pareto, em uma única execução. O MOEA baseado em decomposição (MOEA/D) é um dos mais eficientes, o qual divide um POM em vários subproblemas monobjetivos otimizando-os ao mesmo tempo. Neste estudo foi realizada uma avaliação dos desempenhos do MOEA/D e quatro de suas variantes que representam o estado da arte da literatura (MOEA/DD, MOEA/D-DE, MOEA/D-DU e MOEA/D-AWA) em POMs e MaOPs. Foram conduzidos experimentos computacionais utilizando POMs e MaOPs benchmark do suite DTLZ considerando 3 e 5 funções objetivo. Além disso, foi realizada uma análise estatística que incluiu o teste de Wilcoxon para avaliar os resultados obtidos no indicador de desempenho IGD+. Também foi considerado o indicador de desempenho Hypervolume na frente de Pareto combinada, que é formada por todas as soluções obtidas por cada MOEA. Os experimentos revelaram que o MOEA/DD apresentou a melhor performance no IGD+ e o MOEA/D-AWA obteve o maior Hypervolume na frente de Pareto combinada, enquanto o MOEA/D-DE registrou o pior resultado nesse conjunto de problemas.Universidade Federal do Rio Grande2023-12-23info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionapplication/pdfhttps://periodicos.furg.br/vetor/article/view/1644410.14295/vetor.v33i2.16444VETOR - Journal of Exact Sciences and Engineering; Vol. 33 No. 2 (2023); 41-51VETOR - Revista de Ciências Exatas e Engenharias; v. 33 n. 2 (2023); 41-512358-34520102-7352reponame:Vetor (Online)instname:Universidade Federal do Rio Grande (FURG)instacron:FURGenghttps://periodicos.furg.br/vetor/article/view/16444/10463Copyright (c) 2023 VETOR - Revista de Ciências Exatas e Engenhariasinfo:eu-repo/semantics/openAccessPeito, Marcela C. C.da Costa Vargas, Denis EmanuelWanner, Elizabeth Fialho2023-12-23T15:36:23Zoai:ojs.periodicos.furg.br:article/16444Revistahttps://periodicos.furg.br/vetorPUBhttps://periodicos.furg.br/vetor/oaigmplatt@furg.br2358-34520102-7352opendoar:2023-12-23T15:36:23Vetor (Online) - Universidade Federal do Rio Grande (FURG)false
dc.title.none.fl_str_mv Comparing Decomposition-Based Evolutionary Algorithms for Multi and Many-Objective Optimization Problems
Comparando Algoritmos Evolutivos Baseados em Decomposição para Problemas de Otimização Multiobjetivo e com Muitos Objetivos
title Comparing Decomposition-Based Evolutionary Algorithms for Multi and Many-Objective Optimization Problems
spellingShingle Comparing Decomposition-Based Evolutionary Algorithms for Multi and Many-Objective Optimization Problems
Peito, Marcela C. C.
Algoritmo Evolutivo
Decomposição
Otimização Multiobjetivo
Evolutionary Algorithm
Decomposition
Multiobjective Optimization
Evolutionary Algorithm
Decomposition
Multiobjective Optimization
title_short Comparing Decomposition-Based Evolutionary Algorithms for Multi and Many-Objective Optimization Problems
title_full Comparing Decomposition-Based Evolutionary Algorithms for Multi and Many-Objective Optimization Problems
title_fullStr Comparing Decomposition-Based Evolutionary Algorithms for Multi and Many-Objective Optimization Problems
title_full_unstemmed Comparing Decomposition-Based Evolutionary Algorithms for Multi and Many-Objective Optimization Problems
title_sort Comparing Decomposition-Based Evolutionary Algorithms for Multi and Many-Objective Optimization Problems
author Peito, Marcela C. C.
author_facet Peito, Marcela C. C.
da Costa Vargas, Denis Emanuel
Wanner, Elizabeth Fialho
author_role author
author2 da Costa Vargas, Denis Emanuel
Wanner, Elizabeth Fialho
author2_role author
author
dc.contributor.author.fl_str_mv Peito, Marcela C. C.
da Costa Vargas, Denis Emanuel
Wanner, Elizabeth Fialho
dc.subject.por.fl_str_mv Algoritmo Evolutivo
Decomposição
Otimização Multiobjetivo
Evolutionary Algorithm
Decomposition
Multiobjective Optimization
Evolutionary Algorithm
Decomposition
Multiobjective Optimization
topic Algoritmo Evolutivo
Decomposição
Otimização Multiobjetivo
Evolutionary Algorithm
Decomposition
Multiobjective Optimization
Evolutionary Algorithm
Decomposition
Multiobjective Optimization
description Many real-world problems can be mathematically modeled as Multiobjective Optimization Problems (MOPs), as they involve multiple conflicting objective functions that must be minimized simultaneously. MOPs with more than 3 objective functions are called Many-objective Optimization Problems (MaOPs). MOPs are typically solved through Multiobjective Evolutionary Algorithms (MOEAs), which can obtain a set of non-dominated optimal solutions, known as a Pareto front, in a single run. The MOEA Based on Decomposition (MOEA/D) is one of the most efficient, dividing a MOP into several single-objective subproblems and optimizing them simultaneously. This study evaluated the performance of MOEA/D and four variants representing the state of the art in the literature (MOEA/DD, MOEA/D-DE, MOEA/D-DU, and MOEA/D-AWA) in MOPs and MaOPs. Computational experiments were conducted using benchmark MOPs and MaOPs from the DTLZ suite considering 3 and 5 objective functions. Additionally, a statistical analysis, including the Wilcoxon test, was performed to evaluate the results obtained in the IGD+ performance indicator. The Hypervolume performance indicator was also considered in the combined Pareto front, formed by all solutions obtained by each MOEA. The experiments revealed that MOEA/DD performed best in IGD+, and MOEA/D-AWA achieved the highest Hypervolume in the combined Pareto front, while MOEA/D-DE registered the worst result in this set of problems.
publishDate 2023
dc.date.none.fl_str_mv 2023-12-23
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv https://periodicos.furg.br/vetor/article/view/16444
10.14295/vetor.v33i2.16444
url https://periodicos.furg.br/vetor/article/view/16444
identifier_str_mv 10.14295/vetor.v33i2.16444
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv https://periodicos.furg.br/vetor/article/view/16444/10463
dc.rights.driver.fl_str_mv Copyright (c) 2023 VETOR - Revista de Ciências Exatas e Engenharias
info:eu-repo/semantics/openAccess
rights_invalid_str_mv Copyright (c) 2023 VETOR - Revista de Ciências Exatas e Engenharias
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Universidade Federal do Rio Grande
publisher.none.fl_str_mv Universidade Federal do Rio Grande
dc.source.none.fl_str_mv VETOR - Journal of Exact Sciences and Engineering; Vol. 33 No. 2 (2023); 41-51
VETOR - Revista de Ciências Exatas e Engenharias; v. 33 n. 2 (2023); 41-51
2358-3452
0102-7352
reponame:Vetor (Online)
instname:Universidade Federal do Rio Grande (FURG)
instacron:FURG
instname_str Universidade Federal do Rio Grande (FURG)
instacron_str FURG
institution FURG
reponame_str Vetor (Online)
collection Vetor (Online)
repository.name.fl_str_mv Vetor (Online) - Universidade Federal do Rio Grande (FURG)
repository.mail.fl_str_mv gmplatt@furg.br
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