Publicação
A trust-region approach for computing Pareto fronts in multiobjective optimization
| Resumo: | 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. |
|---|---|
| Autores principais: | Mohammadi, A. |
| Outros Autores: | Custódio, A. L. |
| Assunto: | Multiobjective optimization Pareto front Scalarization techniques Taylor models Trust-region methods Control and Optimization Computational Mathematics Applied Mathematics |
| Ano: | 2024 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso aberto |
| Instituição associada: | Universidade Nova de Lisboa |
| Idioma: | inglês |
| Origem: | Repositório Institucional da UNL |
| _version_ | 1868414815399051264 |
|---|---|
| author | Mohammadi, A. |
| author2 | Custódio, A. L. |
| author2_role | author |
| author_facet | Mohammadi, A. Custódio, A. L. |
| author_role | author |
| contributor_name_str_mv | CMA - Centro de Matemática e Aplicações DM - Departamento de Matemática Springer Science Business Media RUN |
| country_str | PT |
| creators_json_txt | [{\"Person.name\":\"Mohammadi, A.\"},{\"Person.name\":\"Custódio, A. L.\"}] |
| datacite.contributors.contributor.contributorName.fl_str_mv | CMA - Centro de Matemática e Aplicações DM - Departamento de Matemática Springer Science Business Media RUN |
| datacite.creators.creator.creatorName.fl_str_mv | Mohammadi, A. Custódio, A. L. |
| datacite.date.Accepted.fl_str_mv | 2024-01-01T00:00:00Z |
| datacite.date.available.fl_str_mv | 2024-09-17T22:21:27Z |
| datacite.date.embargoed.fl_str_mv | 2024-09-17T22:21:27Z |
| datacite.rights.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| datacite.subjects.subject.fl_str_mv | Multiobjective optimization Pareto front Scalarization techniques Taylor models Trust-region methods Control and Optimization Computational Mathematics Applied Mathematics |
| datacite.titles.title.fl_str_mv | A trust-region approach for computing Pareto fronts in multiobjective optimization |
| dc.contributor.none.fl_str_mv | CMA - Centro de Matemática e Aplicações DM - Departamento de Matemática Springer Science Business Media RUN |
| dc.creator.none.fl_str_mv | Mohammadi, A. Custódio, A. L. |
| dc.date.Accepted.fl_str_mv | 2024-01-01T00:00:00Z |
| dc.date.available.fl_str_mv | 2024-09-17T22:21:27Z |
| dc.date.embargoed.fl_str_mv | 2024-09-17T22:21:27Z |
| dc.format.none.fl_str_mv | application/pdf |
| dc.identifier.none.fl_str_mv | http://hdl.handle.net/10362/171956 |
| dc.language.none.fl_str_mv | eng |
| dc.rights.none.fl_str_mv | http://purl.org/coar/access_right/c_abf2 |
| dc.subject.none.fl_str_mv | Multiobjective optimization Pareto front Scalarization techniques Taylor models Trust-region methods Control and Optimization Computational Mathematics Applied Mathematics |
| dc.title.fl_str_mv | A trust-region approach for computing Pareto fronts in multiobjective optimization |
| dc.type.none.fl_str_mv | http://purl.org/coar/resource_type/c_6501 |
| description | 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. |
| dirty | 0 |
| eu_rights_str_mv | openAccess |
| format | article |
| fulltext.url.fl_str_mv | https://run.unl.pt/bitstreams/9014b765-992e-46d0-a70d-9af4942c5954/download |
| id | run_59aa8a9c4e63b89d6e301898cded4fdf |
| identifier.url.fl_str_mv | http://hdl.handle.net/10362/171956 |
| instacron_str | unl |
| institution | Universidade Nova de Lisboa |
| instname_str | Universidade Nova de Lisboa |
| language | eng |
| network_acronym_str | run |
| network_name_str | Repositório Institucional da UNL |
| oai_identifier_str | oai:run.unl.pt:10362/171956 |
| organization_str_mv | urn:organizationAcronym:unl |
| person_str_mv | Mohammadi, A. Custódio, A. L. |
| publishDate | 2024 |
| reponame_str | Repositório Institucional da UNL |
| repository_id_str | urn:repositoryAcronym:run |
| service_str_mv | urn:repositoryAcronym:run |
| spelling | engenMultiobjective 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.application/pdfenA trust-region approach for computing Pareto fronts in multiobjective optimizationMohammadi, A.Custódio, A. L.CMA - Centro de Matemática e AplicaçõesDM - Departamento de MatemáticaSpringer Science Business MediaHostingInstitutionOrganizationalRUNe-mailmailto:run@unl.ptrun@unl.ptISSNIsPartOf0926-6003URNIsPartOfPURE: 99126420URNIsPartOfPURE UUID: b66bc683-a6d8-47fd-82a9-85a33e3f10bbURNIsPartOfScopus: 85168362172URNIsPartOfWOS: 001051147000001DOIIsPartOf10.1007/s10589-023-00510-22024-09-17T22:21:27Z2024-012024-01-01T00:00:00ZHandlehttp://hdl.handle.net/10362/171956http://purl.org/coar/access_right/c_abf2open accessMultiobjective optimizationPareto frontScalarization techniquesTaylor modelsTrust-region methodsControl and OptimizationComputational MathematicsApplied Mathematics1511175 bytesliteraturehttp://purl.org/coar/resource_type/c_6501journal articlehttp://purl.org/coar/access_right/c_abf2application/pdffulltexthttps://run.unl.pt/bitstreams/9014b765-992e-46d0-a70d-9af4942c5954/download |
| 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 |
| status | SINGLETON |
| subject.fl_str_mv | Multiobjective optimization Pareto front Scalarization techniques Taylor models Trust-region methods Control and Optimization Computational Mathematics Applied Mathematics |
| title | 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_short | A trust-region approach for computing Pareto fronts in multiobjective optimization |
| title_sort | A trust-region approach for computing Pareto fronts in multiobjective optimization |
| topic | Multiobjective optimization Pareto front Scalarization techniques Taylor models Trust-region methods Control and Optimization Computational Mathematics Applied Mathematics |
| topic_facet | Multiobjective optimization Pareto front Scalarization techniques Taylor models Trust-region methods Control and Optimization Computational Mathematics Applied Mathematics |
| url | http://hdl.handle.net/10362/171956 |
| visible | 1 |