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On Finding the Optimal BDD Relaxation

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Integration of AI and OR Techniques in Constraint Programming (CPAIOR 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10335))

Abstract

This paper presents an optimization model for identifying limited-width relaxed binary decision diagrams (BDDs) with tightest possible relaxation bounds. The model developed is a network design model and is used to identify which nodes and arcs should be in a relaxed BDD so that the objective function bound is as close to the optimal value as possible. The model is presented specifically for the 0–1 knapsack problem, but can be extended to other problem classes that have been investigated in the stream of research on using decision diagrams for combinatorial optimization problems. Preliminary experimental results indicate that the bounds provided by the relaxed BDDs are far superior to the bounds achieved by relaxed BDDs constructed via previously published compilation algorithms.

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Author information

Authors and Affiliations

  1. Department of Operations and Information Management, University of Connecticut, Mansfield, USA

    David Bergman

  2. Department of Management, University of Toronto Scarborough, Toronto, USA

    Andre Augusto Cire

Authors
  1. David Bergman
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  2. Andre Augusto Cire
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Correspondence to Andre Augusto Cire .

Editor information

Editors and Affiliations

  1. University of Padua, Padua, Italy

    Domenico Salvagnin

  2. University of Bologna, Bologna, Italy

    Michele Lombardi

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Bergman, D., Cire, A.A. (2017). On Finding the Optimal BDD Relaxation. In: Salvagnin, D., Lombardi, M. (eds) Integration of AI and OR Techniques in Constraint Programming. CPAIOR 2017. Lecture Notes in Computer Science(), vol 10335. Springer, Cham. https://doi.org/10.1007/978-3-319-59776-8_4

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  • DOI: https://doi.org/10.1007/978-3-319-59776-8_4

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-59775-1

  • Online ISBN: 978-3-319-59776-8

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