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

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Remic M., Žerovnik G., Žerovnik J.
Business Systems Research Journal
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2012
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vol. 3
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issue 2
57-63
EN
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.
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An approximation algorithm for multi-unit auctions: numerical and subject experiments

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TAKAHASHI S., IZUNAGA Y., WATANABE N.
Operations Research and Decisions
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2018
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vol. 28
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issue 1
95-115
EN
In multi-unit auctions for a single item, the Vickrey–Clarke–Groves mechanism (VCG) attains allocative efficiency but suffers from its computational complexity. Takahashi and Shigeno thus proposed a greedy based approximation algorithm (GBA). In a subject experiment there was truly a difference in efficiency rate but no significant difference in seller’s revenue between GBA and VCG. It is not clear in theory whether each bidder will submit his or her true unit valuations in GBA. We show, however, that in a subject experiment there was no significant difference in the number of bids that obey “almost” truth-telling between GBA and VCG. As for individual bidding behavior, GBA and VCG show a sharp contrast when a human bidder competes against machine bidders; underbidding was observed in GBA, while overbidding was observed in VCG. Some results in a numerical experiment are also provided prior to reporting those observations.
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