Algorithms for the Bin Packing Problem with Overlapping Items

Aristide Grange (1) , Imed Kacem (1) , Sébastien Martin (1)

1 LCOMS - Laboratoire de Conception, Optimisation et Modélisation des Systèmes

We introduce the strongly NP-hard pagination problem, an extension of BIN PACKING where packing together two items may make them occupy less volume than the sum of their individual sizes. To achieve this property, an item is defined as a finite set of symbols from a given alphabet. While, in BIN PACKING, any two such sets would be disjoint, in PAGINATION, they can share zero, one or more symbols. After formulating the problem as an integer linear program, we try to approximate its solutions with several families of algorithms: from straightforward adaptations of classical BIN PACKING heuristics, to dedicated algorithms (greedy and non-greedy), to standard and grouping genetic algorithms. All of them are studied first theoretically, then experimentally on an extensive random test set. Based upon these data, we propose a predictive measure of the difficulty of a given instance, and finally recommend which algorithm should be used in which case, depending on either time constraints or quality requirements.

Mots clés: Optimization; Bin packing; Virtual-Machine Packing; Integer linear programming; Heuristics; Genetic algorithms

Domaines: Mathématique discrète [cs.DM]; Recherche opérationnelle [math.OC]; Base de données [cs.DB]; Algorithme et structure de données [cs.DS]

Aristide Grange, Imed Kacem, Sébastien Martin. Algorithms for the Bin Packing Problem with Overlapping Items. 2016. ⟨hal-01312527v2⟩