Using rank-1 lift-and-project closures to generate cuts for 0-1 MIPs, a computational investigation

Pierre Bonami; Michel Minoux

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DOI : 10.1016/j.disopt.2005.08.006

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Discrete Optimization 2, 4 (2005) 288-307

Using rank-1 lift-and-project closures to generate cuts for 0-1 MIPs, a computational investigation

Pierre Bonami ¹, Michel Minoux ²

(24/10/2005)

Various techniques for building relaxations and generating valid inequalities for pure or mixed integer programming problems without special structure are reviewed and compared computationally. Besides classical techniques such as Gomory cuts, Mixed Integer Rounding cuts, lift-and-project and reformulation–linearization techniques, a new variant is also investigated: the use of the relaxation corresponding to the intersection of simple disjunction polyhedra (i.e. the so-called elementary closure of lift-and-project cuts). Systematic comparative computational results are reported on series of test problems including multidimensional knapsack problems (MKP) and MIPLIB test problems. From the results obtained, the relaxation based on the elementary closure of lift-and-project cuts appears to be one of the most promising.

1 :	Laboratoire d'informatique Fondamentale de Marseille (LIF)

	CNRS : UMR6166 – Université de la Méditerranée - Aix-Marseille II – Université de Provence - Aix-Marseille I

2 :	Laboratoire d'Informatique de Paris 6 (LIP6)

	CNRS : UMR7606 – Université Pierre et Marie Curie [UPMC] - Paris VI

Domaine

Informatique/Recherche opérationnelle

Mathématiques/Optimisation et contrôle

Mots Clés : Mixed integer programming – Cutting-planes – Lift-and-project – rank-1 closures


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Soumis le : Samedi 3 Octobre 2009, 11:39:57
Dernière modification le : Samedi 3 Octobre 2009, 11:39:57