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On the computation of all supported efficient solutions in multi-objective integer network flow problems
| datacite.subject.fos | Ciências Naturais::Matemáticas | |
| datacite.subject.fos | Ciências Sociais::Economia e Gestão | |
| datacite.subject.fos | Ciências Naturais::Ciências da Computação e da Informação | |
| dc.contributor.author | Eusébio, Augusto | |
| dc.contributor.author | Figueira, José Rui | |
| dc.date.accessioned | 2025-05-20T11:46:13Z | |
| dc.date.available | 2025-05-20T11:46:13Z | |
| dc.date.issued | 2009-11 | |
| dc.description.abstract | This paper presents a new algorithm for identifying all supported non-dominated vectors (or outcomes) in the objective space, as well as the corresponding efficient solutions in the decision space, for multi-objective integer network flow problems. Identifying the set of supported non-dominated vectors is of the utmost importance for obtaining a first approximation of the whole set of non-dominated vectors. This approximation is crucial, for example, in two-phase methods that first compute the supported non-dominated vectors and then the unsupported non-dominated ones. Our approach is based on a negative-cycle algorithm used in single objective minimum cost flow problems, applied to a sequence of parametric problems. The proposed approach uses the connectedness property of the set of supported non-dominated vectors/efficient solutions to find all integer solutions in maximal non-dominated/efficient facets. | eng |
| dc.identifier.citation | Augusto Eusébio, José Rui Figueira, On the computation of all supported efficient solutions in multi-objective integer network flow problems, European Journal of Operational Research, Volume 199, Issue 1, 2009, Pages 68-76, ISSN 0377-2217, https://doi.org/10.1016/j.ejor.2008.10.031. | |
| dc.identifier.doi | 10.1016/j.ejor.2008.10.031 | |
| dc.identifier.issn | 0377-2217 | |
| dc.identifier.uri | http://hdl.handle.net/10400.8/12937 | |
| dc.language.iso | eng | |
| dc.peerreviewed | yes | |
| dc.publisher | Elsevier | |
| dc.relation.hasversion | https://www.sciencedirect.com/science/article/pii/S0377221708009697 | |
| dc.relation.ispartof | European Journal of Operational Research | |
| dc.rights.uri | http://creativecommons.org/licenses/by/4.0/ | |
| dc.subject | Multi-objective linear and integer programming | |
| dc.subject | Multi-objective network flows | |
| dc.subject | Negative-cycle algorithms | |
| dc.subject | Parametric programming | |
| dc.title | On the computation of all supported efficient solutions in multi-objective integer network flow problems | eng |
| dc.type | journal article | |
| dspace.entity.type | Publication | |
| oaire.citation.endPage | 76 | |
| oaire.citation.issue | 1 | |
| oaire.citation.startPage | 68 | |
| oaire.citation.title | European Journal of Operational Research | |
| oaire.citation.volume | 199 | |
| oaire.version | http://purl.org/coar/version/c_970fb48d4fbd8a85 | |
| person.familyName | Eusébio | |
| person.givenName | Augusto | |
| person.identifier.orcid | 0000-0002-6800-2016 | |
| person.identifier.scopus-author-id | 24779439000 | |
| relation.isAuthorOfPublication | e1266cbb-dcd0-47d5-92e8-1c345ea5e675 | |
| relation.isAuthorOfPublication.latestForDiscovery | e1266cbb-dcd0-47d5-92e8-1c345ea5e675 |
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- This paper presents a new algorithm for identifying all supported non-dominated vectors (or outcomes) in the objective space, as well as the corresponding efficient solutions in the decision space, for multi-objective integer network flow problems. Identifying the set of supported non-dominated vectors is of the utmost importance for obtaining a first approximation of the whole set of non-dominated vectors. This approximation is crucial, for example, in two-phase methods that first compute the supported non-dominated vectors and then the unsupported non-dominated ones. Our approach is based on a negative-cycle algorithm used in single objective minimum cost flow problems, applied to a sequence of parametric problems. The proposed approach uses the connectedness property of the set of supported non-dominated vectors/efficient solutions to find all integer solutions in maximal non-dominated/efficient facets.
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