The min-conflict packing problem

Ali Khanafer (1) , François Clautiaux (1, 2) , Said Hanafi (3) , El-Ghazali Talbi (1)

1 DOLPHIN - Parallel Cooperative Multi-criteria Optimization
2 LIFL - Laboratoire d'Informatique Fondamentale de Lille
3 LAMIH - Laboratoire d'Automatique, de Mécanique et d'Informatique industrielles et Humaines - UMR 8201

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.

Domaines: Recherche opérationnelle [math.OC]

Ali Khanafer, François Clautiaux, Said Hanafi, El-Ghazali Talbi. The min-conflict packing problem. Computers and Operations Research, 2011, 39 (9), pp.2122-2132. ⟨10.1016/j.cor.2011.10.021⟩. ⟨hal-00638177⟩