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
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/197965
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CONICET Digital (CONICET) |
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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 Técnicas2025-09-03T10:08:23Zoai: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:34982025-09-03 10:08:23.411CONICET 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 |
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CONICET Digital (CONICET) |
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CONICET Digital (CONICET) |
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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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13.13397 |