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Laboratoire d'informatique fondamentale de Marseille UMR 6166 - CNRS, Université de la Méditerranée, Université de Provence |
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Laboratoire d'informatique fondamentale de Marseille UMR 6166 - CNRS, Université de la Méditerranée, Université de Provence |
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| HAL: hal-00421752, version 1 |
| DOI: 10.1007/s10107-006-0051-y |
| Detailed view |  Export this paper |
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| Mathematical Programming, Series A 113, 2 (2008) 241-257 |
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| Projected Chvátal–Gomory cuts for mixed integer linear programs |
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| Pierre Bonami 1Gérard Cornuéjols 1, 2 |
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| (2008-06-02) |
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| Recent experiments by Fischetti and Lodi show that the first Chvátal closure of a pure integer linear program (ILP) often gives a surprisingly tight approximation of the integer hull. They optimize over the first Chvátal closure by modeling the Chvátal–Gomory (CG) separation problem as a mixed integer linear program (MILP) which is then solved by a general- purpose MILP solver. Unfortunately, this approach does not extend immediately to the Gomory mixed integer (GMI) closure of an MILP, since the GMI separation problem involves the solution of a nonlinear mixed integer program or a parametric MILP. In this paper we introduce a projected version of the CG cuts, and study their practical effectiveness for MILP problems. The idea is to project first the linear programming relaxation of the MILP at hand onto the space of the integer variables, and then to derive Chvátal–Gomory cuts for the projected polyhedron. Though theoretically dominated by GMI cuts, projected CG cuts have the advantage of producing a separation model very similar to the one introduced by Fischetti and Lodi, which can typically be solved in a reasonable amount of computing time. |
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| 1: | Laboratoire d'informatique Fondamentale de Marseille (LIF) |
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CNRS : UMR6166 – Université de la Méditerranée - Aix-Marseille II – Université de Provence - Aix-Marseille I |
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| 2: | Tepper School of Business |
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Carnegie Mellon University |
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| 3: | IBM Watson Research Center |
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IBM |
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| 4: | Dipartimento di Ingegneria de l'Informazione [Padova] (DEI) |
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Università degli studi di Padova |
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| 5: | Dipartimento di Elettronica, Informatica e Sistemistica (DEIS) |
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University of Bologna |
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| Subject | : | Computer Science/Operations Research Mathematics/Optimization and Control |
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| Mixed integer linear program - Chvátal–Gomory cut - Separation problem - Projected polyhedron |
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| hal-00421752, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00421752 | |
| oai:hal.archives-ouvertes.fr:hal-00421752 | |
| From: Pierre Bonami | |
| Submitted on: Saturday, 3 October 2009 11:58:42 | |
| Updated on: Saturday, 3 October 2009 12:32:24 | |
