A trust-region approach for computing Pareto fronts in multiobjective optimization

Bibliographic Details
Main Author: Mohammadi, A.
Publication Date: 2024
Other Authors: Custódio, A. L.
Format: Article
Language: eng
Source: Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
Download full: http://hdl.handle.net/10362/171956
Summary: Funding Information: This work was funded by national funds through FCT - Fundação para a Ciência e a Tecnologia I.P., under the scope of projects PTDC/MAT-APL/28400/2017, UIDP/00297/2020, and UIDB/00297/2020 (Center for Mathematics and Applications). The work of the first author was additionally supported by the scholarship 2020.08249.BD, also granted by FCT - Fundação para a Ciência e a Tecnologia I.P.. Publisher Copyright: © 2023, The Author(s).
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spelling A trust-region approach for computing Pareto fronts in multiobjective optimizationMultiobjective optimizationPareto frontScalarization techniquesTaylor modelsTrust-region methodsControl and OptimizationComputational MathematicsApplied MathematicsFunding Information: This work was funded by national funds through FCT - Fundação para a Ciência e a Tecnologia I.P., under the scope of projects PTDC/MAT-APL/28400/2017, UIDP/00297/2020, and UIDB/00297/2020 (Center for Mathematics and Applications). The work of the first author was additionally supported by the scholarship 2020.08249.BD, also granted by FCT - Fundação para a Ciência e a Tecnologia I.P.. Publisher Copyright: © 2023, The Author(s).Multiobjective optimization is a challenging scientific area, where the conflicting nature of the different objectives to be optimized changes the concept of problem solution, which is no longer a single point but a set of points, namely the Pareto front. In a posteriori preferences approach, when the decision maker is unable to rank objectives before the optimization, it is important to develop algorithms that generate approximations to the complete Pareto front of a multiobjective optimization problem, making clear the trade-offs between the different objectives. In this work, an algorithm based on a trust-region approach is proposed to approximate the set of Pareto critical points of a multiobjective optimization problem. Derivatives are assumed to be known, allowing the computation of Taylor models for the different objective function components, which will be minimized in two main steps: the extreme point step and the scalarization step. The goal of the extreme point step is to expand the approximation to the Pareto front, by moving towards the extreme points of it, corresponding to the individual minimization of each objective function component. The scalarization step attempts to reduce the gaps on the Pareto front, by solving adequate scalarization problems. The convergence of the method is analyzed and numerical experiments are reported, indicating the relevance of each feature included in the algorithmic structure and its competitiveness, by comparison against a state-of-art multiobjective optimization algorithm.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaRUNMohammadi, A.Custódio, A. L.2024-09-17T22:21:27Z2024-012024-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article31application/pdfhttp://hdl.handle.net/10362/171956eng0926-6003PURE: 99126420https://doi.org/10.1007/s10589-023-00510-2info:eu-repo/semantics/openAccessreponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiainstacron:RCAAP2024-09-23T01:40:17Zoai:run.unl.pt:10362/171956Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireinfo@rcaap.ptopendoar:https://opendoar.ac.uk/repository/71602025-05-28T18:53:47.832075Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologiafalse
dc.title.none.fl_str_mv A trust-region approach for computing Pareto fronts in multiobjective optimization
title A trust-region approach for computing Pareto fronts in multiobjective optimization
spellingShingle A trust-region approach for computing Pareto fronts in multiobjective optimization
Mohammadi, A.
Multiobjective optimization
Pareto front
Scalarization techniques
Taylor models
Trust-region methods
Control and Optimization
Computational Mathematics
Applied Mathematics
title_short A trust-region approach for computing Pareto fronts in multiobjective optimization
title_full A trust-region approach for computing Pareto fronts in multiobjective optimization
title_fullStr A trust-region approach for computing Pareto fronts in multiobjective optimization
title_full_unstemmed A trust-region approach for computing Pareto fronts in multiobjective optimization
title_sort A trust-region approach for computing Pareto fronts in multiobjective optimization
author Mohammadi, A.
author_facet Mohammadi, A.
Custódio, A. L.
author_role author
author2 Custódio, A. L.
author2_role author
dc.contributor.none.fl_str_mv CMA - Centro de Matemática e Aplicações
DM - Departamento de Matemática
RUN
dc.contributor.author.fl_str_mv Mohammadi, A.
Custódio, A. L.
dc.subject.por.fl_str_mv Multiobjective optimization
Pareto front
Scalarization techniques
Taylor models
Trust-region methods
Control and Optimization
Computational Mathematics
Applied Mathematics
topic Multiobjective optimization
Pareto front
Scalarization techniques
Taylor models
Trust-region methods
Control and Optimization
Computational Mathematics
Applied Mathematics
description Funding Information: This work was funded by national funds through FCT - Fundação para a Ciência e a Tecnologia I.P., under the scope of projects PTDC/MAT-APL/28400/2017, UIDP/00297/2020, and UIDB/00297/2020 (Center for Mathematics and Applications). The work of the first author was additionally supported by the scholarship 2020.08249.BD, also granted by FCT - Fundação para a Ciência e a Tecnologia I.P.. Publisher Copyright: © 2023, The Author(s).
publishDate 2024
dc.date.none.fl_str_mv 2024-09-17T22:21:27Z
2024-01
2024-01-01T00:00:00Z
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
dc.type.driver.fl_str_mv info:eu-repo/semantics/article
format article
status_str publishedVersion
dc.identifier.uri.fl_str_mv http://hdl.handle.net/10362/171956
url http://hdl.handle.net/10362/171956
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 0926-6003
PURE: 99126420
https://doi.org/10.1007/s10589-023-00510-2
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv 31
application/pdf
dc.source.none.fl_str_mv reponame:Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
instname:FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron:RCAAP
instname_str FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
instacron_str RCAAP
institution RCAAP
reponame_str Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
collection Repositórios Científicos de Acesso Aberto de Portugal (RCAAP)
repository.name.fl_str_mv Repositórios Científicos de Acesso Aberto de Portugal (RCAAP) - FCCN, serviços digitais da FCT – Fundação para a Ciência e a Tecnologia
repository.mail.fl_str_mv info@rcaap.pt
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