The min-conflict packing problem

Authors:
Ali Khanafer;François Clautiaux;Saïd Hanafi;El-Ghazali Talbi
Affiliations:
Université des Sciences et Technologies de Lille, LIFL CNRS UMR 8022, INRIA Lille - Nord Europe, Bítiment INRIA, Parc de la Haute Borne, 59655 Villeneuve d'Ascq, France;Université des Sciences et Technologies de Lille, LIFL CNRS UMR 8022, INRIA Lille - Nord Europe, Bítiment INRIA, Parc de la Haute Borne, 59655 Villeneuve d'Ascq, France;Université de Valenciennes et du Hainaut-Cambrésis, LAMIH CNRS FRE 3304, Le Mont Houy - ISTV2, 59313 Valenciennes Cedex 9, France;Université des Sciences et Technologies de Lille, LIFL CNRS UMR 8022, INRIA Lille - Nord Europe, Bítiment INRIA, Parc de la Haute Borne, 59655 Villeneuve d'Ascq, France
Venue:
Computers and Operations Research
Year:
2012

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Abstract

In the classical bin-packing problem with conflicts (BPC), the goal is to minimize the number of bins used to pack a set of items subject to disjunction constraints. In this paper, we study a new version of BPC: the min-conflict packing problem (MCBP), in which we minimize the number of violated conflicts when the number of bins is fixed. In order to find a tradeoff between the number of bins used and the violation of the conflict constraints, we also consider a bi-objective version of this problem. We show that the special structure of its Pareto front allows to reformulate the problem as a small set of MCBP. We solved these two problems through heuristics, column-generation methods, and a tabu search. Computational experiments are reported to assess the quality of our methods.