Volume 52, Number 2, April–June 2018
|Page(s)||391 - 414|
|Published online||22 June 2018|
A theoretical and experimental study of fast lower bounds for the two-dimensional bin packing problem
Sorbonne universités, Université de technologie de Compiègne, CNRS, Heudiasyc UMR 7253, CS 60 319,
2 Department of Mechanical and Industrial Engineering, College of Engineering, Qatar University, Doha, Qatar
* e-mail: firstname.lastname@example.org
Accepted: 16 March 2017
We address the two-dimensional bin packing problem with fixed orientation. This problem requires packing a set of small rectangular items into a minimum number of standard two-dimensional bins. It is a notoriously intractable combinatorial optimization problem and has numerous applications in packing and cutting. The contribution of this paper is twofold. First, we propose a comprehensive theoretical analysis of lower bounds and we elucidate dominance relationships. We show that a previously presented dominance result is incorrect. Second, we present the results of an extensive computational study that was carried out, on a large set of 500 benchmark instances, to assess the empirical performance of the lower bounds. We found that the so-called Carlier-Clautiaux-Moukrim lower bounds exhibits an excellent relative performance and yields the tightest value for all of the benchmark instances.
Mathematics Subject Classification: 90-08
Key words: Two-dimensional bin packing / lower bounds / dual feasible functions / dominance results
© EDP Sciences, ROADEF, SMAI 2018
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