Hybrid Algorithms for the Variable Sized Bin Packing Problem

Abstract

This paper deals with the so-called variable sized bin packing problem, which is a generalization of the one-dimensional bin packing problem in which a set of items with given weights have to be packed into a minimum-cost set of bins of variable sizes and costs. First we propose a heuristic and a beam search approach. Both algorithms are strongly based on dynamic programming procedures and lower bounding techniques. Second, we propose a variable neighborhood search approach where some neighborhoods are also based on dynamic programming. The best results are obtained by using the solutions provided by the proposed heuristic as starting solutions for variable neighborhood search. The results show that this algorithm is very competitive with current state-of-the-art approaches.

This work was supported by the binational grant Acciones Integradas ES16-2009 (Austria) and MEC HA2008-0005 (Spain), and by grant TIN2007-66523 (FORMALISM) of the Spanish government. In addition, Christian Blum acknowledges support from the Ramón y Cajal program of the Spanish Government of which he is a research fellow, and Hugo Hernández acknowledges support from the Catalan Government through an FI grant.