Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problems

Autores
González, Begoña; Rossit, Daniel Alejandro; Méndez, Máximo; Frutos, Mariano
Año de publicación
2022
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
Overlapping solutions occur when more than one solution in the space of decisions maps to the same solution in the space of objectives. This situation threatens the exploration capacity of Multi- Objective Evolutionary Algorithms (MOEAs), preventing them from having a good diversity in their population. The influence of overlapping solutions is intensified on multi-objective combinatorial problems with a low number of objectives. This paper presents a hybrid MOEA for handling overlapping solutions that combines the classic NSGA-II with a strategy based on Objective Space Division (OSD). Basically, in each generation of the algorithm, the objective space is divided into several regions using the nadir solution calculated from the current generation solutions. Furthermore, the solutions in each region are classified into non-dominated fronts using different optimization strategies in each of them. This significantly enhances the achieved diversity of the approximate front of non-dominated solutions. The proposed algorithm (called NSGA-II/OSD) is tested on a classic Operations Research problem: The Multi-Objective Knapsack Problem (0-1 MOKP) with two objectives. Classic NSGA-II, MOEA/D and Global WASF-GA are used to compare the performance of NSGA-II/OSD. In the case of MOEA/D two different versions are implemented, each of them with a different strategy for specifying the reference point. These MOEA/D reference point strategies are thoroughly studied and new insights are provided. This paper analyses in depth the impact of overlapping solutions on MOEAs, studying the number of overlapping solutions, the number of solution repairs, the hypervolume metric, the attainment surfaces and the approximation to the real Pareto front, for different sizes of 0-1 MOKPs with two objectives. The proposed method offers very good performance when compared to the classic NSGA-II, MOEA/D and Global WASF-GA algorithms, all of them well-known in the literature.
Fil: González, Begoña. Universidad de Las Palmas de Gran Canaria; España
Fil: Rossit, Daniel Alejandro. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Méndez, Máximo. Universidad de Las Palmas de Gran Canaria; España
Fil: Frutos, Mariano. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentina
Materia
BI-OBJECTIVE KNAPSACK PROBLEM
MULTI-OBJECTIVE COMBINATORIAL OPTIMIZATION PROBLEMS
MULTI-OBJECTIVE EVOLUTIONARY ALGORITHMS
OBJECTIVE SPACE DIVISION
OVERLAPPING SOLUTIONS
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/197965
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/197965
network_acronym_str CONICETDig
repository_id_str 3498
network_name_str CONICET Digital (CONICET)
spelling Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problemsGonzález, BegoñaRossit, Daniel AlejandroMéndez, MáximoFrutos, MarianoBI-OBJECTIVE KNAPSACK PROBLEMMULTI-OBJECTIVE COMBINATORIAL OPTIMIZATION PROBLEMSMULTI-OBJECTIVE EVOLUTIONARY ALGORITHMSOBJECTIVE SPACE DIVISIONOVERLAPPING SOLUTIONShttps://purl.org/becyt/ford/2.11https://purl.org/becyt/ford/2Overlapping solutions occur when more than one solution in the space of decisions maps to the same solution in the space of objectives. This situation threatens the exploration capacity of Multi- Objective Evolutionary Algorithms (MOEAs), preventing them from having a good diversity in their population. The influence of overlapping solutions is intensified on multi-objective combinatorial problems with a low number of objectives. This paper presents a hybrid MOEA for handling overlapping solutions that combines the classic NSGA-II with a strategy based on Objective Space Division (OSD). Basically, in each generation of the algorithm, the objective space is divided into several regions using the nadir solution calculated from the current generation solutions. Furthermore, the solutions in each region are classified into non-dominated fronts using different optimization strategies in each of them. This significantly enhances the achieved diversity of the approximate front of non-dominated solutions. The proposed algorithm (called NSGA-II/OSD) is tested on a classic Operations Research problem: The Multi-Objective Knapsack Problem (0-1 MOKP) with two objectives. Classic NSGA-II, MOEA/D and Global WASF-GA are used to compare the performance of NSGA-II/OSD. In the case of MOEA/D two different versions are implemented, each of them with a different strategy for specifying the reference point. These MOEA/D reference point strategies are thoroughly studied and new insights are provided. This paper analyses in depth the impact of overlapping solutions on MOEAs, studying the number of overlapping solutions, the number of solution repairs, the hypervolume metric, the attainment surfaces and the approximation to the real Pareto front, for different sizes of 0-1 MOKPs with two objectives. The proposed method offers very good performance when compared to the classic NSGA-II, MOEA/D and Global WASF-GA algorithms, all of them well-known in the literature.Fil: González, Begoña. Universidad de Las Palmas de Gran Canaria; EspañaFil: Rossit, Daniel Alejandro. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; ArgentinaFil: Méndez, Máximo. Universidad de Las Palmas de Gran Canaria; EspañaFil: Frutos, Mariano. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; ArgentinaAmerican Institute of Mathematical Sciences2022-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/197965González, Begoña; Rossit, Daniel Alejandro; Méndez, Máximo; Frutos, Mariano; Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problems; American Institute of Mathematical Sciences; Mathematical Biosciences And Engineering; 19; 4; 1-2022; 3369-34011547-10631551-0018CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/http://www.aimspress.com/article/doi/10.3934/mbe.2022156info:eu-repo/semantics/altIdentifier/doi/10.3934/mbe.2022156info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:36:44Zoai:ri.conicet.gov.ar:11336/197965instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:36:44.735CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problems
title Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problems
spellingShingle Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problems
González, Begoña
BI-OBJECTIVE KNAPSACK PROBLEM
MULTI-OBJECTIVE COMBINATORIAL OPTIMIZATION PROBLEMS
MULTI-OBJECTIVE EVOLUTIONARY ALGORITHMS
OBJECTIVE SPACE DIVISION
OVERLAPPING SOLUTIONS
title_short Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problems
title_full Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problems
title_fullStr Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problems
title_full_unstemmed Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problems
title_sort Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problems
dc.creator.none.fl_str_mv González, Begoña
Rossit, Daniel Alejandro
Méndez, Máximo
Frutos, Mariano
author González, Begoña
author_facet González, Begoña
Rossit, Daniel Alejandro
Méndez, Máximo
Frutos, Mariano
author_role author
author2 Rossit, Daniel Alejandro
Méndez, Máximo
Frutos, Mariano
author2_role author
author
author
dc.subject.none.fl_str_mv BI-OBJECTIVE KNAPSACK PROBLEM
MULTI-OBJECTIVE COMBINATORIAL OPTIMIZATION PROBLEMS
MULTI-OBJECTIVE EVOLUTIONARY ALGORITHMS
OBJECTIVE SPACE DIVISION
OVERLAPPING SOLUTIONS
topic BI-OBJECTIVE KNAPSACK PROBLEM
MULTI-OBJECTIVE COMBINATORIAL OPTIMIZATION PROBLEMS
MULTI-OBJECTIVE EVOLUTIONARY ALGORITHMS
OBJECTIVE SPACE DIVISION
OVERLAPPING SOLUTIONS
purl_subject.fl_str_mv https://purl.org/becyt/ford/2.11
https://purl.org/becyt/ford/2
dc.description.none.fl_txt_mv Overlapping solutions occur when more than one solution in the space of decisions maps to the same solution in the space of objectives. This situation threatens the exploration capacity of Multi- Objective Evolutionary Algorithms (MOEAs), preventing them from having a good diversity in their population. The influence of overlapping solutions is intensified on multi-objective combinatorial problems with a low number of objectives. This paper presents a hybrid MOEA for handling overlapping solutions that combines the classic NSGA-II with a strategy based on Objective Space Division (OSD). Basically, in each generation of the algorithm, the objective space is divided into several regions using the nadir solution calculated from the current generation solutions. Furthermore, the solutions in each region are classified into non-dominated fronts using different optimization strategies in each of them. This significantly enhances the achieved diversity of the approximate front of non-dominated solutions. The proposed algorithm (called NSGA-II/OSD) is tested on a classic Operations Research problem: The Multi-Objective Knapsack Problem (0-1 MOKP) with two objectives. Classic NSGA-II, MOEA/D and Global WASF-GA are used to compare the performance of NSGA-II/OSD. In the case of MOEA/D two different versions are implemented, each of them with a different strategy for specifying the reference point. These MOEA/D reference point strategies are thoroughly studied and new insights are provided. This paper analyses in depth the impact of overlapping solutions on MOEAs, studying the number of overlapping solutions, the number of solution repairs, the hypervolume metric, the attainment surfaces and the approximation to the real Pareto front, for different sizes of 0-1 MOKPs with two objectives. The proposed method offers very good performance when compared to the classic NSGA-II, MOEA/D and Global WASF-GA algorithms, all of them well-known in the literature.
Fil: González, Begoña. Universidad de Las Palmas de Gran Canaria; España
Fil: Rossit, Daniel Alejandro. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Matemática Bahía Blanca. Universidad Nacional del Sur. Departamento de Matemática. Instituto de Matemática Bahía Blanca; Argentina
Fil: Méndez, Máximo. Universidad de Las Palmas de Gran Canaria; España
Fil: Frutos, Mariano. Universidad Nacional del Sur. Departamento de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Bahía Blanca. Instituto de Investigaciones Económicas y Sociales del Sur. Universidad Nacional del Sur. Departamento de Economía. Instituto de Investigaciones Económicas y Sociales del Sur; Argentina
description Overlapping solutions occur when more than one solution in the space of decisions maps to the same solution in the space of objectives. This situation threatens the exploration capacity of Multi- Objective Evolutionary Algorithms (MOEAs), preventing them from having a good diversity in their population. The influence of overlapping solutions is intensified on multi-objective combinatorial problems with a low number of objectives. This paper presents a hybrid MOEA for handling overlapping solutions that combines the classic NSGA-II with a strategy based on Objective Space Division (OSD). Basically, in each generation of the algorithm, the objective space is divided into several regions using the nadir solution calculated from the current generation solutions. Furthermore, the solutions in each region are classified into non-dominated fronts using different optimization strategies in each of them. This significantly enhances the achieved diversity of the approximate front of non-dominated solutions. The proposed algorithm (called NSGA-II/OSD) is tested on a classic Operations Research problem: The Multi-Objective Knapsack Problem (0-1 MOKP) with two objectives. Classic NSGA-II, MOEA/D and Global WASF-GA are used to compare the performance of NSGA-II/OSD. In the case of MOEA/D two different versions are implemented, each of them with a different strategy for specifying the reference point. These MOEA/D reference point strategies are thoroughly studied and new insights are provided. This paper analyses in depth the impact of overlapping solutions on MOEAs, studying the number of overlapping solutions, the number of solution repairs, the hypervolume metric, the attainment surfaces and the approximation to the real Pareto front, for different sizes of 0-1 MOKPs with two objectives. The proposed method offers very good performance when compared to the classic NSGA-II, MOEA/D and Global WASF-GA algorithms, all of them well-known in the literature.
publishDate 2022
dc.date.none.fl_str_mv 2022-01
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/197965
González, Begoña; Rossit, Daniel Alejandro; Méndez, Máximo; Frutos, Mariano; Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problems; American Institute of Mathematical Sciences; Mathematical Biosciences And Engineering; 19; 4; 1-2022; 3369-3401
1547-1063
1551-0018
CONICET Digital
CONICET
url http://hdl.handle.net/11336/197965
identifier_str_mv González, Begoña; Rossit, Daniel Alejandro; Méndez, Máximo; Frutos, Mariano; Objective space division-based hybrid evolutionary algorithm for handing overlapping solutions in combinatorial problems; American Institute of Mathematical Sciences; Mathematical Biosciences And Engineering; 19; 4; 1-2022; 3369-3401
1547-1063
1551-0018
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/http://www.aimspress.com/article/doi/10.3934/mbe.2022156
info:eu-repo/semantics/altIdentifier/doi/10.3934/mbe.2022156
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Institute of Mathematical Sciences
publisher.none.fl_str_mv American Institute of Mathematical Sciences
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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