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An experimental comparison of some heuristics for cardinality constrained bin packing problem

Remic Maja, Žerovnik Gašper and Žerovnik Janez
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Remic Maja: University of Ljubljana, Ljubljana, Slovenia
Žerovnik Gašper: Reactor Physics Division, Jožef Stefan Institute, Ljubljana, Slovenia
Žerovnik Janez: Faculty for Mechanical Engineering, University of Ljubljana, Ljubljana, Slovenia

Business Systems Research, 2012, vol. 3, issue 2, 57-63

Abstract: Background: Bin packing is an NPhard optimization problem of packing items of given sizes into minimum number of capacitylimited bins. Besides the basic problem, numerous other variants of bin packing exist. The cardinality constrained bin packing adds an additional constraint that the number of items in a bin must not exceed a given limit Nmax. Objectives: Goal of the paper is to present a preliminary experimental study which demostrates adaptations of the new algorithms to the general cardinality constrained bin packing problem. Methods/Approach: Straightforward modifications of First Fit Decreasing (FFD), Refined First Fit (RFF) and the algorithm by Zhang et al. for the bin packing problem are compared to four cardinality constrained bin packing problem specific algorithms on random lists of items with 0%, 10%, 30% and 50% of large items. The behaviour of all algorithms when cardinality constraint Nmax increases is also studied. Results: Results show that all specific algorithms outperform the general algorithms on lists with low percentage of big items. Conclusions: One of the specific algorithms performs better or equally well even on lists with high percentage of big items and is therefore of significant interest. The behaviour when Nmax increases shows that specific algorithms can be used for solving the general bin packing problem as well.

Keywords: cardinality constrained bin packing problem heuristics; approximation algorithm (search for similar items in EconPapers)
Date: 2012
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DOI: 10.2478/v10305-012-0013-1

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