Abstract
An experimental comparison of some heuristics for cardinality constrained bin packing problem 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.
Highlights
The cardinality constrained bin packing problem can be described as follows: A list I of n items with specified size xi has to be arranged into bins of limited capacity Cmax and maximum number of items per bin Nmax to minimize m, the number of bins used
The new heuristics were compared against an obvious adaptation of the first fit decreasing (FFD) algorithm and were proven to clearly outperform the First Fit Decreasing (FFD) algorithm on the datasets of interest
It is well known that FFD algorithm is a good approximation algorithm for the general bin packing problem (more precisely, it is well known (Korte and Vygen, 2000) that FFD always gives a solution with at most 11/9 OPT(I) + C bins, where OPT(I) stands for the value of the optimal solution)
Summary
The cardinality constrained bin packing problem can be described as follows: A list I of n items with specified size (or weight/volume/etc.) xi has to be arranged into bins of limited capacity Cmax and maximum number of items per bin (cardinality constraint) Nmax to minimize m, the number of bins used. Swedish concept of deep repository in hard rock (Milnes, 2002) is currently seriously regarded in Slovenia as an option for nuclear power plant Krško decommissioning program (Železnik, et al, 2004) Motivated by this application, several heuristics for the cardinality constrained bin packing problem with Nmax =4 were designed in Žerovnik and Žerovnik (2011). A preliminary experimental study is presented in this report which shows that the obvious adaptations of the new algorithms are competitive on the general cardinality constrained bin packing problem. 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. The behaviour when Nmax increases shows that specific algorithms can be used for solving the general bin packing problem as well
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