A Local Search Framework for Compiling Relaxed Decision Diagrams

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10848)


This paper presents a local search framework for constructing and improving relaxed decision diagrams (DDs). The framework consists of a set of elementary DD manipulation operations including a redirect operation introduced in this paper and a general algorithmic scheme. We show that the framework can be used to reproduce several standard DD compilation schemes and to create new compilation and improvement strategies. In computational experiments for the 0–1 knapsack problem, the multidimensional knapsack problem and the set covering problem we compare different compilation methods. It turns out that a new strategy based on the local search framework consistently yields better bounds, in many cases far better bounds, for limited-width DDs than previously published heuristic strategies.


  1. 1.
    Aarts, E., Lenstra, J.K. (eds.): Local Search in Combinatorial Optimization, 1st edn. Wiley, New York (1997)zbMATHGoogle Scholar
  2. 2.
    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). Scholar
  3. 3.
    Bergman, D., Cire, A.A.: Theoretical insights and algorithmic tools for decision diagram-based optimization. Constraints 21, 533–556 (2016)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bergman, D., Cire, A.A., van Hoeve, W.-J., Hooker, J.N.: Variable ordering for the application of BDDs to the maximum independent set problem. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds.) CPAIOR 2012. LNCS, vol. 7298, pp. 34–49. Springer, Heidelberg (2012). Scholar
  5. 5.
    Bergman, D., Cire, A.A., van Hoeve, W.J., Hooker, J.N.: Discrete optimization with decision diagrams. INFORMS J. Comput. 28(1), 47–66 (2016)MathSciNetCrossRefGoogle Scholar
  6. 6.
    Bergman, D., Cire, A.A., van Hoeve, W.J., Hooker, J.: Decision Diagrams for Optimization. Artificial Intelligence: Foundations, Theory, and Algorithms. Springer, Cham (2016). Scholar
  7. 7.
    Bergman, D., Cire, A.A.: On finding the optimal BDD relaxation. In: Salvagnin, D., Lombardi, M. (eds.) CPAIOR 2017. LNCS, vol. 10335, pp. 41–50. Springer, Cham (2017). Scholar
  8. 8.
    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). Scholar
  9. 9.
    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). Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institute of Information Systems and ORMartin Luther University Halle-WittenbergHalleGermany
  2. 2.Department of ManagementUniversity of Toronto ScarboroughTorontoCanada
  3. 3.CIRRELT, École Polytechnique de MontréalMontrealCanada

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