Academic Journal
On location-routing formulations for the Hamiltonian [formula omitted]-median problem.
| Τίτλος: | On location-routing formulations for the Hamiltonian [formula omitted]-median problem. |
|---|---|
| Συγγραφείς: | Canas, Francisco1 (AUTHOR) fmcanas@fc.ul.pt, Gouveia, Luís1 (AUTHOR) |
| Πηγή: | European Journal of Operational Research. May2026, Vol. 331 Issue 1, p62-76. 15p. |
| Θεματικοί όροι: | *Capital costs, *Mathematical optimization, Location problems (Programming), Assignment problems (Programming), Combinatorial optimization, Optimization algorithms |
| Περίληψη: | • New formulations for the Hamiltonian p-Median Problem are proposed. • Strong formulations with fewer variables are obtained through projection results. • Branch-and-cut algorithms based on the new formulations are implemented and tested. • The most effective of these is very competitive with the current state-of-the-art. • Algorithms are tested for a variant with setup costs and new "Difficult" instances. Given a positive integer p and a weighted undirected graph G = (V , E) , the Hamiltonian p -Median Problem (H p MP) on G is to find a minimum weight set of p elementary cycles partitioning V. We study extended formulations for this problem including node-depot assignment (NDA) variables, in addition to edge variables. These formulations are based on the selection of certain nodes as depots and thus can be viewed as formulations for location-routing problems. Known NDA formulations and valid inequalities are reviewed, and new extended formulations, including edge-depot assignment (EDA) variables, are presented. We relate EDA formulations with known NDA formulations and, from the former, derive new exponentially sized sets of constraints defined with the edge and NDA variables. Computational results show that the EDA formulations produce very strong lower bounds and are effective for instances with up to 100 nodes and large values of p , and that the branch-and-cut algorithms based on NDA formulations including (some of) the generalized constraints are competitive with (and often outperform) the current state of the art (which involves solving instances with up to 400 nodes). We also address and present computational results for a variant of the H p MP in which setup costs for depots are considered. [ABSTRACT FROM AUTHOR] |
| Copyright of European Journal of Operational Research is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Βάση Δεδομένων: | Business Source Index |
| FullText | Links: – Type: other Text: Availability: 0 CustomLinks: – Url: https://www.doi.org/10.1016/j.ejor.2025.10.023? Name: ScienceDirect (all content) (s7799221) Category: fullText Text: View record from ScienceDirect MouseOverText: View record from ScienceDirect |
|---|---|
| Header | DbId: bsx DbLabel: Business Source Index An: 191495906 RelevancyScore: 1412 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 1411.61413574219 |
| IllustrationInfo | |
| Items | – Name: Title Label: Title Group: Ti Data: On location-routing formulations for the Hamiltonian [formula omitted]-median problem. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Canas%2C+Francisco%22">Canas, Francisco</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> fmcanas@fc.ul.pt</i><br /><searchLink fieldCode="AR" term="%22Gouveia%2C+Luís%22">Gouveia, Luís</searchLink><relatesTo>1</relatesTo> (AUTHOR) – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22European+Journal+of+Operational+Research%22">European Journal of Operational Research</searchLink>. May2026, Vol. 331 Issue 1, p62-76. 15p. – Name: Subject Label: Subject Terms Group: Su Data: *<searchLink fieldCode="DE" term="%22Capital+costs%22">Capital costs</searchLink><br />*<searchLink fieldCode="DE" term="%22Mathematical+optimization%22">Mathematical optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Location+problems+%28Programming%29%22">Location problems (Programming)</searchLink><br /><searchLink fieldCode="DE" term="%22Assignment+problems+%28Programming%29%22">Assignment problems (Programming)</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatorial+optimization%22">Combinatorial optimization</searchLink><br /><searchLink fieldCode="DE" term="%22Optimization+algorithms%22">Optimization algorithms</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: • New formulations for the Hamiltonian p-Median Problem are proposed. • Strong formulations with fewer variables are obtained through projection results. • Branch-and-cut algorithms based on the new formulations are implemented and tested. • The most effective of these is very competitive with the current state-of-the-art. • Algorithms are tested for a variant with setup costs and new "Difficult" instances. Given a positive integer p and a weighted undirected graph G = (V , E) , the Hamiltonian p -Median Problem (H p MP) on G is to find a minimum weight set of p elementary cycles partitioning V. We study extended formulations for this problem including node-depot assignment (NDA) variables, in addition to edge variables. These formulations are based on the selection of certain nodes as depots and thus can be viewed as formulations for location-routing problems. Known NDA formulations and valid inequalities are reviewed, and new extended formulations, including edge-depot assignment (EDA) variables, are presented. We relate EDA formulations with known NDA formulations and, from the former, derive new exponentially sized sets of constraints defined with the edge and NDA variables. Computational results show that the EDA formulations produce very strong lower bounds and are effective for instances with up to 100 nodes and large values of p , and that the branch-and-cut algorithms based on NDA formulations including (some of) the generalized constraints are competitive with (and often outperform) the current state of the art (which involves solving instances with up to 400 nodes). We also address and present computational results for a variant of the H p MP in which setup costs for depots are considered. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of European Journal of Operational Research is the property of Elsevier B.V. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
| PLink | https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=bsx&AN=191495906 |
| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1016/j.ejor.2025.10.023 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 15 StartPage: 62 Subjects: – SubjectFull: Capital costs Type: general – SubjectFull: Mathematical optimization Type: general – SubjectFull: Location problems (Programming) Type: general – SubjectFull: Assignment problems (Programming) Type: general – SubjectFull: Combinatorial optimization Type: general – SubjectFull: Optimization algorithms Type: general Titles: – TitleFull: On location-routing formulations for the Hamiltonian [formula omitted]-median problem. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Canas, Francisco – PersonEntity: Name: NameFull: Gouveia, Luís IsPartOfRelationships: – BibEntity: Dates: – D: 16 M: 05 Text: May2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 03772217 Numbering: – Type: volume Value: 331 – Type: issue Value: 1 Titles: – TitleFull: European Journal of Operational Research Type: main |
| ResultId | 1 |