A Simple and Effective Decomposition for the Multidimensional Binpacking Constraint

  • Stefano Gualandi
  • Michele Lombardi
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8124)

Abstract

The multibin_packing constraint captures a fundamental substructure of many assignment problems, where a set of items, each with a fixed number of dimensions, must be assigned to a number of bins with limited capacities. In this work we propose a simple decomposition for multibin_packing that uses a bin_packing constraint for each dimension, a set of all_different constraints automatically derived from a conflict graph, plus two alternative symmetry breaking approaches. Despite its simplicity, the proposed decomposition is very effective on a number of instances recently proposed in the literature.

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References

  1. 1.
    Beldiceanu, N., Carlsson, M., Rampon, J.X.: Global constraint catalog. SICS Research Report (2005)Google Scholar
  2. 2.
    Kell, B., van Hoeve, W.-J.: An MDD approach to multidimensional bin packing. In: Gomes, C., Sellmann, M. (eds.) CPAIOR 2013. LNCS, vol. 7874, pp. 128–143. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  3. 3.
    Garey, M.R., Johnson, D.S.: Computers and intractability. Freeman, New York (1979)MATHGoogle Scholar
  4. 4.
    Gecode Team. Gecode: Generic constraint development environment (2013), http://www.gecode.org
  5. 5.
    Martello, S., Toth, P.: Knapsack problems: algorithms and computer implementations. John Wiley & Sons, Inc. (1990)Google Scholar
  6. 6.
    Mehta, D., O’Sullivan, B., Simonis, H.: Comparing solution methods for the machine reassignment problem. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 782–797. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  7. 7.
    Östergård, P.R.J.: A fast algorithm for the maximum clique problem. Discrete Applied Mathematics 120(1), 197–207 (2002)MathSciNetCrossRefMATHGoogle Scholar
  8. 8.
    Rossi, F., Van Beek, P., Walsh, T.: Handbook of constraint programming. Elsevier Science (2006)Google Scholar
  9. 9.
    Schaus, P., Régin, J.-C., Van Schaeren, R., Dullaert, W., Raa, B.: Cardinality reasoning for bin-packing constraint: Application to a tank allocation problem. In: Milano, M. (ed.) CP 2012. LNCS, vol. 7514, pp. 815–822. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  10. 10.
    Shaw, P.: A constraint for bin packing. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 648–662. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Trick, M.A.: A dynamic programming approach for consistency and propagation for knapsack constraints. Annals of Operations Research 118(1), 73–84 (2003)MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Stefano Gualandi
    • 1
  • Michele Lombardi
    • 2
  1. 1.Dipartimento di MatematicaUniversità di PaviaItaly
  2. 2.Dipartimento di Informatica: Scienza ed IngegneriaUniversità di BolognaItaly

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