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.
Coffman, E. G, Garey, M. R, Johnson, D. S. (1997), "Approximation algorithms for binpacking: A survey", in Hochbaum, D. (Ed.), Approximation Algorithms for NPHard Problems, PWS, Boston, pp. 4693.
Kellerer, H, Pferschy, U. (1999), "Cardinality constrained bin-packing problems", Annals of Operations Research, Vol. 92, No. 0, pp. 335-348.
Korte, B, Vygen, J. (2000), Combinatorial Optimization, Theory and Algorithms, Berlin, Springer.
Krause, K. L, Shen, V. Y, Schwetman, H. D. (1975), "Analysis of several task-scheduling algorithms for a model of multiprogramming computer systems", Journal of ACM, Vol. 22, No. 4, pp. 522-550.
Milnes, A. G. (2002), "Guide to the documentation of 25 year of geoscientific research (1976-2000)", Technical Report, No. 02-18, Swedish Nuclear Fuel and Waste Management Co., Sweden, Stockholm, March 2002.
Yao, A. C. (1980), "New algorithms for bin packing", Journal of the ACM, Vol. 27, No. 2, pp. 207-227.
Zhang, G, Cai, X, Wong, C. K. (2000), "Lineartimeapproximation algorithms for bin packing", Operations Research Letters, Vol. 26, No. 5, pp. 217222.
Železnik, N, et al. (2004), "Program razgradnje NEK in odlaganja NSRAO in IJG" ("Program of NPP Krško Decommissioning and SF & LILW Disposal"), Study, No. T-1123-03, Agency for Radwaste Management, Ljubljana, Slovenia, and Agency for Hazardous Waste, Zagreb, Croatia.
Žerovnik, G, Snoj, L, Ravnik, M. (2009), "Optimization of Spent Nuclear Fuel Filling in Canisters for Deep Repository", Nuclear Science and Engineering, Vol. 163, No. 2, pp. 183-190.
Žerovnik, G, Žerovnik, J. (2011), "Constructive heuristics for the canister filling problem", Central European Journal of Operations Research, Vol. 19, No. 3, pp. 371-389.