Convergent Dual Bounds Using an Aggregation of Set-Covering Constraints for Capacitated Problems
| hal.structure.identifier | Centre d'études et de recherche en informatique et communications [CEDRIC] | |
| dc.contributor.author | PORUMBEL, Daniel | |
| hal.structure.identifier | Reformulations based algorithms for Combinatorial Optimization [Realopt] | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | CLAUTIAUX, François | |
| dc.date.accessioned | 2024-04-04T03:11:05Z | |
| dc.date.available | 2024-04-04T03:11:05Z | |
| dc.date.issued | 2017 | |
| dc.identifier.issn | 1091-9856 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/193741 | |
| dc.description.abstractEn | Extended formulations are now widely used to solve hard combinatorial optimization problems. Such formulations have prohibitively-many variables and are generally solved via Column Generation (CG). CG algorithms are known to have frequent convergence issues, and, up to a sometimes large number of iterations, classical Lagrangian dual bounds may be weak. This paper is devoted to set-covering problems in which all elements to cover require a given resource consumption and all feasible configurations have to verify a resource constraint. We propose an iterative aggregation method for determining convergent dual bounds using the extended formulation of such problems. The set of dual variables is partitioned into k groups and all variables in each group are artificially linked using the following groupwise restriction: the dual values in a group have to follow a linear function of their corresponding resource consumptions. This leads to a restricted model of smaller dimension, with only 2k dual variables. The method starts with one group (k = 1) and iteratively splits the groups. Our algorithm has three advantages: (i) it produces good dual bounds even for low k values, (ii) it reduces the number of dual variables, and (iii) it may reduce the time needed to solve sub-problems, in particular when dynamic programming is used. We experimentally tested our approach on two variants of the cutting-stock problem: in many cases, the method produces near optimal dual bounds after a small number of iterations. Moreover the average computational effort to reach the optimum is reduced compared to a classical column generation algorithm. | |
| dc.language.iso | en | |
| dc.publisher | Institute for Operations Research and the Management Sciences (INFORMS) | |
| dc.title.en | Convergent Dual Bounds Using an Aggregation of Set-Covering Constraints for Capacitated Problems | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1287/ijoc.2016.0718 | |
| dc.subject.hal | Informatique [cs]/Recherche opérationnelle [cs.RO] | |
| bordeaux.journal | INFORMS Journal on Computing | |
| bordeaux.page | 15 | |
| bordeaux.volume | 29 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-01410195 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01410195v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=INFORMS%20Journal%20on%20Computing&rft.date=2017&rft.volume=29&rft.issue=1&rft.spage=15&rft.epage=15&rft.eissn=1091-9856&rft.issn=1091-9856&rft.au=PORUMBEL,%20Daniel&CLAUTIAUX,%20Fran%C3%A7ois&rft.genre=article |
Files in this item
| Files | Size | Format | View |
|---|---|---|---|
|
There are no files associated with this item. |
|||