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Decision Diagrams and Dynamic Programming

  • Conference paper
Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CPAIOR 2013)

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

Abstract

Binary and multivalued decision diagrams are closely related to dynamic programming (DP) but differ in some important ways. This paper makes the relationship more precise by interpreting the DP state transition graph as a weighted decision diagram and incorporating the state-dependent costs of DP into the theory of decision diagrams. It generalizes a well-known uniqueness theorem by showing that, for a given optimization problem and variable ordering, there is a unique reduced weighted decision diagram with “canonical” edge costs. This can lead to simplification of DP models by transforming the costs to canonical costs and reducing the diagram, as illustrated by a standard inventory management problem. The paper then extends the relationship between decision diagrams and DP by introducing the concept of nonserial decision diagrams as a counterpart of nonserial dynamic programming.

Partial support from NSF grant CMMI-1130012 and AFOSR grant FA-95501110180.

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Authors and Affiliations

  1. Carnegie Mellon University, USA

    John N. Hooker

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  1. John N. Hooker
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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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Hooker, J.N. (2013). Decision Diagrams and Dynamic Programming. 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_7

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  • DOI: https://doi.org/10.1007/978-3-642-38171-3_7

  • 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)

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