Tree-decomposition based heuristics for the two-dimensional bin packing problem with conflicts

Authors:
Ali Khanafer;François Clautiaux;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 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

This paper deals with the two-dimensional bin packing problem with conflicts (BPC-2D). Given a finite set of rectangular items, an unlimited number of rectangular bins and a conflict graph, the goal is to find a conflict-free packing of the items minimizing the number of bins used. In this paper, we propose a new framework based on a tree-decomposition for solving this problem. It proceeds by decomposing a BPC-2D instance into subproblems to be solved independently. Applying this decomposition method is not straightforward, since merging partial solutions is hard. Several heuristic strategies are proposed to make an effective use of the decomposition. Computational experiments show the practical effectiveness of our approach.