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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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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

  • Online ISBN: 978-3-642-38171-3

  • eBook Packages: Computer ScienceComputer Science (R0)