Solving the two-dimensional bin packing problem with a probabilistic multi-start heuristic

Authors:
Lukas Baumgartner;Verena Schmid;Christian Blum
Affiliations:
Department of Business Administration, Universität Wien, Vienna, Austria;Department of Business Administration, Universität Wien, Vienna, Austria;ALBCOM Research Group, Universitat Politècnica de Catalunya, Barcelona, Spain
Venue:
LION'05 Proceedings of the 5th international conference on Learning and Intelligent Optimization
Year:
2011

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Abstract

The two-dimensional bin packing problem (2BP) consists in packing a set of rectangular items into rectangular, equally-sized bins. The problem is NP-hard and has a multitude of real world applications. We consider the case where the items are oriented and guillotine cutting is free. In this paper we first present a review of well-know heuristics for the 2BP and then propose a new ILP model for the problem. Moreover, we develop a multi-start algorithm based on a probabilistic version of the LGFi heuristic from the literature. Results are compared to other well-known heuristics, using data sets provided in the literature. The obtained experimental results show that the proposed algorithm returns excellent solutions. With an average percentage deviation of 1.8% from the best know lower bounds it outperformes the other algorithms by 1.1%−5.7%. Also for 3 of the 500 instances we tested a new upper bound was found.