Abstract
We introduce a constraint for one-dimensional bin packing. This constraint uses propagation rules incorporating knapsack-based reasoning, as well as a lower bound on the number of bins needed. We show that this constraint can significantly reduce search on bin packing problems. We also demonstrate that when coupled with a standard bin packing search strategy, our constraint can be a competitive alternative to established operations research bin packing algorithms.
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References
Valerio de Carvalho, J.: Exact solution of bin-packing problems using column generation and branch-and-bound. Annals of Operations Research 86, 629–659 (1999)
Coffman Jr., E.G., Garey, M.R., Johnson, D.S.: Approximation algorithms for bin packing: A survery. In: Hochbaum, D. (ed.) Appoximation algorithms for NP-Hard Problems, pp. 46–93. PWS Publishing, Boston (1996)
Falkenauer, E.: A hybrid grouping genetic algorithm for bin packing. Journal of Heuristics 2, 5–30 (1996)
Friesen, D.K., Langston, M.A.: Variable sized bin packing. SIAM Journal on Computing 15, 222–230 (1986)
Gent, I., Walsh, T.: From approximate to optimal solutions: Constructing pruning and propagation rules. In: Proceedings of the 15th IJCAI (1997)
Gent, I.P.: Heuristic solution of open bin packing problems. Journal of Heuristics 3, 299–304 (1998)
ILOG S.A., Gentilly, France. ILOG Solver 6.0. User Manual (September 2003)
Johnson, D.S.: Fast algorithms for bin packing. Journal of Computer and System Sciences 8, 272–314 (1974)
Kellerer, H., Pferschy, U., Pisinger, D.: Knapsack Problems. Springer, Heidelberg (2004)
Korf, R.: A new algorithm for optimal bin packing. In: Proceedings of 18th AAAI, pp. 731–736 (2002)
Korf, R.: An improved algorithm for optimal bin packing. In: Proceedings of the 18th IJCAI, pp. 1252–1258 (2003)
Martello, S., Toth, P.: Knapsack problems. Wiley, Chichester (1990)
Martello, S., Toth, P.: Lower bounds and reduction procedures for the bin packing problem. Discrete and Applied Mathematics 28(1), 59–70 (1990)
Régin, J.-C.: A filtering algorithm for constraints of difference in CSPs. In: Proceedings of the 12th AAAI. American Association for Artificial Intelligence, pp. 362–367. AAAI Press / The MIT Press (1994)
Scholl, A., Klein, R., Jürgens, C.: BISON: A fast hybrid procedure for exactly solving the one-dimensional bin packing problem. Computers & Operations Research 24, 627–645 (1997)
Sellmann, M.: Approximated consistency for knapsack constraints. In: Rossi, F. (ed.) CP 2003. LNCS, vol. 2833, pp. 679–693. Springer, Heidelberg (2003)
Trick, M.: A dynamic programming approach for consistency and propagation for knapsack constraints. In: Proceedings of CP-AI-OR 2001 (2001)
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Shaw, P. (2004). A Constraint for Bin Packing. In: Wallace, M. (eds) Principles and Practice of Constraint Programming – CP 2004. CP 2004. Lecture Notes in Computer Science, vol 3258. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30201-8_47
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DOI: https://doi.org/10.1007/978-3-540-30201-8_47
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23241-4
Online ISBN: 978-3-540-30201-8
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