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International Conference on Integration of Constraint Programming, Artificial Intelligence, and Operations Research

CPAIOR 2013: Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems pp 128–143Cite as

An MDD Approach to Multidimensional Bin Packing

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 7874)

Abstract

We investigate the application of multivalued decision diagrams (MDDs) to multidimensional bin packing problems. In these problems, each bin has a multidimensional capacity and each item has an associated multidimensional size. We develop several MDD representations for this problem, and explore different MDD construction methods including a new heuristic-driven depth-first compilation scheme. We also derive MDD restrictions and relaxations, using a novel application of a clustering algorithm to identify approximate equivalence classes among MDD nodes. Our experimental results show that these techniques can significantly outperform current CP and MIP solvers.

Keywords

  • Partial Solution
  • Constraint Satisfaction Problem
  • Binary Decision Diagram
  • Item Size
  • Feasible Instance

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This work was supported by the NSF under grant CMMI-1130012 and a Google Research Grant.

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  • DOI: 10.1007/978-3-642-38171-3_9
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References

  1. Andersen, H.R., Hadzic, T., Hooker, J.N., Tiedemann, P.: A constraint store based on multivalued decision diagrams. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 118–132. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  2. Behle, M.: On threshold BDDs and the optimal variable ordering problem. Journal of Combinatorial Optimization 16, 107–118 (2008)

    MathSciNet  CrossRef  Google Scholar 

  3. Bergman, D., Cire, A.A., van Hoeve, W.-J., Yunes, T.: BDD-based heuristics for binary optimization (submitted, 2013)

    Google Scholar 

  4. Bergman, D., van Hoeve, W.-J., Hooker, J.N.: Manipulating MDD relaxations for combinatorial optimization. In: Achterberg, T., Beck, J.C. (eds.) CPAIOR 2011. LNCS, vol. 6697, pp. 20–35. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  5. Bollig, B., Wegener, I.: Improving the variable ordering of OBDDs is NP-complete. IEEE Transactions on Computers 45(9), 993–1002 (1996)

    CrossRef  Google Scholar 

  6. Hadzic, T., Hooker, J.N., O’Sullivan, B., Tiedemann, P.: Approximate compilation of constraints into multivalued decision diagrams. In: Stuckey, P.J. (ed.) CP 2008. LNCS, vol. 5202, pp. 448–462. Springer, Heidelberg (2008)

    CrossRef  Google Scholar 

  7. Heckbert, P.: Color image quantization for frame buffer display. In: SIGGRAPH 1982, pp. 297–307. ACM, New York (1982)

    Google Scholar 

  8. Hoda, S., van Hoeve, W.-J., Hooker, J.N.: A systematic approach to MDD-based constraint programming. In: Cohen, D. (ed.) CP 2010. LNCS, vol. 6308, pp. 266–280. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  9. Knuth, D.E.: The Art of Computer Programming, vol. 4, fascicle 1: Bitwise Tricks & Techniques; Binary Decision Diagrams. Addison-Wesley (2009)

    Google Scholar 

  10. Lodi, A., Martello, S., Monaci, M.: Two-dimensional packing problems: A survey. European Journal of Operational Research 141(2), 241–252 (2002)

    MathSciNet  CrossRef  Google Scholar 

  11. Martello, S., Pisinger, D., Vigo, D.: The three-dimensional bin packing problem. Operations Research 48, 256–267 (2000)

    MathSciNet  CrossRef  Google Scholar 

  12. Schaus, P., Van Hentenryck, P., Monette, J.-N., Coffrin, C., Michel, L., Deville, Y.: Solving steel mill slab problems with constraint-based techniques: CP, LNS, and CBLS. Constraints 16(2), 125–147 (2011)

    MathSciNet  CrossRef  Google Scholar 

  13. Wegener, I.: Branching Programs and Binary Decision Diagrams: Theory and Applications. SIAM, Philadelphia (2000)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematical Sciences, Carnegie Mellon University, USA

    Brian Kell

  2. Tepper School of Business, Carnegie Mellon University, USA

    Willem-Jan van Hoeve

Authors
  1. Brian Kell
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  2. Willem-Jan van Hoeve
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Editor information

Editors and Affiliations

  1. Department of Computer Science, Cornell University, Ithaca, NY, USA

    Carla Gomes

  2. Thomas J. Watson Research Center, Yorktown Heights, NY, USA

    Meinolf Sellmann

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Kell, B., van Hoeve, WJ. (2013). An MDD Approach to Multidimensional Bin Packing. In: Gomes, C., Sellmann, M. (eds) Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems. CPAIOR 2013. Lecture Notes in Computer Science, vol 7874. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38171-3_9

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  • DOI: https://doi.org/10.1007/978-3-642-38171-3_9

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-38170-6

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