Convergent Dual Bounds Using an Aggregation of Set-Covering Constraints for Capacitated Problems
| hal.structure.identifier | Laboratoire de Génie Informatique et d'Automatique de l'Artois [LGI2A] | |
| dc.contributor.author | PORUMBEL, Daniel Cosmin | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| hal.structure.identifier | Reformulations based algorithms for Combinatorial Optimization [Realopt] | |
| dc.contributor.author | CLAUTIAUX, François | |
| dc.date.accessioned | 2024-04-04T02:20:41Z | |
| dc.date.available | 2024-04-04T02:20:41Z | |
| dc.date.created | 2013-12-13 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189513 | |
| 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 \emph{resource consumption} and all feasible configurations have to verify a \emph{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.title.en | Convergent Dual Bounds Using an Aggregation of Set-Covering Constraints for Capacitated Problems | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Informatique [cs]/Recherche opérationnelle [cs.RO] | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-00747375 | |
| hal.version | 1 | |
| hal.audience | Non spécifiée | |
| dc.subject.it | column generation | |
| dc.subject.it | duality | |
| dc.subject.it | aggregation | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00747375v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=PORUMBEL,%20Daniel%20Cosmin&CLAUTIAUX,%20Fran%C3%A7ois&rft.genre=preprint |
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