Abstract
The 2-constraint bin packing problem consists in packing a given number of items, each one characterised by two different but not related dimensions, into the minimum number of bins in such a way to do not exceed the capacity of the bins in either dimension. The development of the heuristics for this problem is challenged by the need of a proper definition of the criterion for evaluating the feasibility of the two capacity constraints on the two different dimensions. In this paper, we propose a computational evaluation of several criteria, and two simple but effective algorithms—a greedy and neighbourhood search algorithms—for solving the 2-constraint bin packing problem. An extensive computational analysis supports our main claim.
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Alves, C., de Carvalho, J.V., Clautiaux, F., Rietz, J.: Multidimensional dual-feasible functions and fast lower bounds for the vector packing problem. Eur. J. Oper. Res. 233(1), 43–63 (2014)
Aringhieri, R.: Composing medical crews with equity and efficiency. Cent. Eur. J. Oper. Res. 17(3), 343–357 (2009)
Aringhieri, R., Dell’Amico, M.: Comparing metaheuristic algorithms for sonet network design problems. J. Heuristics 11(1), 35–57 (2005a)
Aringhieri, R., Dell’Amico, M.: Solution of the SONET ring assignment problem with capacity constraints. In: Rego, C., Alidaee, B. (eds.) Metaheuristic Optimization via Memory and Evolution. Tabu Search and Scatter Search, pp. 93–116. Kluwer, Dordrecht (2005b)
Aringhieri, R., Landa, P., Soriano, P., Tànfani, E., Testi, A.: A two level metaheuristic for the operating room scheduling and assignment problem. Comput. Oper. Res. 54, 21–34 (2015)
Aringhieri, R., Bruglieri, M., Malucelli, F., Nonato, M.: A special vrp arising in the optimization of waste disposal: a real case. Transp. Sci. (2016). http://hdl.handle.net/2318/1596992
Billaut, J.C., Della Croce, F., Grosso, A.: A single machine scheduling problem with two-dimensional vector packing constraints. Eur. J. Oper. Res. 243(1), 75–81 (2015)
Caprara, A., Toth, P.: Lower bounds and algorithms for the 2-dimensional vector packing problem. Discret. Appl. Math. 111(3), 231–262 (2001)
Della Croce, F., Ghirardi, M., Tadei, R.: Recovering beam search: enhancing the beam search approach for combinatorial optimization problems. J. Heuristics 10, 1089 (2004)
Garey, M., Graham, R., Johnson, D., Yao, A.: Resource constrained scheduling as generalized bin packing. J. Comb. Theory Ser. A 21(3), 257–298 (1976)
Gendreau, M., Hertz, A., Laporte, G.: A tabu search heuristic for the vehicle routing problem. Manag. Sci. 40(10), 1276–1290 (1994)
Guazzone, M., Anglano, C., Aringhieri, R., Sereno, M.: Distributed coalition formation in energy-aware cloud federations: a game-theoretic approach (extended version). CoRR abs/1309.2444 (2013). http://arxiv.org/abs/1309.2444
Kellerer, H., Kotov, V.: An approximation algorithm with absolute worst-case performance ratio 2 for two-dimensional vector packing. Oper. Res. Lett. 31(1), 35–41 (2003)
Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack Problems. Springer, Berlin (2004)
Martello, S., Toth, P.: Knapsack problems: algorithms and computer implementations. In: Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley, New York (1990)
Monaci, M., Toth, P.: A set-covering-based heuristic approach for bin-packing problems. INFORMS J. Comput. 18(1), 71–85 (2006)
Shachnai, H., Tamir, T.: Approximation schemes for generalized two-dimensional vector packing with application to data placement. J. Discret. Algorithms 10(1), 35–48 (2012)
Spieksma, F.C.: Branch-and-bound algorithm for the two-dimensional vector packing problem. Comput. Oper. Res. 21(1), 19–25 (1994)
Wilcox, D., McNabb, A., Seppi, K.: Solving virtual machine packing with a reordering grouping genetic algorithm. In: 2011 IEEE Congress of Evolutionary Computation (CEC 2011), pp. 362–369 (2011)
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The authors would thank the students Gianluca Bortignon and Federico Iannicelli for running part of the computational tests.
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Aringhieri, R., Duma, D., Grosso, A. et al. Simple but effective heuristics for the 2-constraint bin packing problem. J Heuristics 24, 345–357 (2018). https://doi.org/10.1007/s10732-017-9326-0
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DOI: https://doi.org/10.1007/s10732-017-9326-0