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Improving the Filtering of Branch-and-Bound MDD Solver

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2021)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 12735))

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Abstract

This paper presents and evaluates two pruning techniques to reinforce the efficiency of constraint optimization solvers based on multi-valued decision-diagrams (MDD). It adopts the branch-and-bound framework proposed by Bergman et al. in 2016 to solve dynamic programs to optimality. In particular, our paper presents and evaluates the effectiveness of the local-bound (LocB) and rough upper-bound pruning (RUB). LocB is a new and effective rule that leverages the approximate MDD structure to avoid the exploration of non-interesting nodes. RUB is a rule to reduce the search space during the development of bounded-width-MDDs. The experimental study we conducted on the Maximum Independent Set Problem (MISP), Maximum Cut Problem (MCP), Maximum 2 Satisfiability (MAX2SAT) and the Traveling Salesman Problem with Time Windows (TSPTW) shows evidence indicating that rough-upper-bound and local-bound pruning have a high impact on optimization solvers based on branch-and-bound with MDDs. In particular, it shows that RUB delivers excellent results but requires some effort when defining the model. Also, it shows that LocB provides a significant improvement automatically; without necessitating any user-supplied information. Finally, it also shows that rough-upper-bound and local-bound pruning are not mutually exclusive, and their combined benefit supersedes the individual benefit of using each technique.

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Notes

  1. 1.

    https://github.com/xgillard/ddo.

  2. 2.

    An incremental refinement a.k.a. construction by separation procedure is detailed in [11, pp. 51–52] but we will not cover it here for the sake of conciseness.

  3. 3.

    Consequently, it also suffers from a potentially exponential time requirement in the worst case. Indeed, time is constant in the final number of nodes (unless the transition functions themselves are exponential in the input).

  4. 4.

    The very definition of these operators is problem-specific. However, [22] formally defines the conditions that are necessary to correctness.

  5. 5.

    https://github.com/xgillard/ddo.

  6. 6.

    Available online at: http://hdl.handle.net/2078.1/245322.

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Authors and Affiliations

  1. Université Catholique de Louvain, Ottignies-Louvain-la-Neuve, Belgium

    Xavier Gillard, Vianney Coppé & Pierre Schaus

  2. Rotman School of Management, University of Toronto Scarborough, Toronto, Canada

    André Augusto Cire

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  1. Xavier Gillard
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  2. Vianney Coppé
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  3. Pierre Schaus
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  4. André Augusto Cire
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Correspondence to Xavier Gillard .

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  1. Monash University, Melbourne, VIC, Australia

    Peter J. Stuckey

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Gillard, X., Coppé, V., Schaus, P., Cire, A.A. (2021). Improving the Filtering of Branch-and-Bound MDD Solver. In: Stuckey, P.J. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2021. Lecture Notes in Computer Science(), vol 12735. Springer, Cham. https://doi.org/10.1007/978-3-030-78230-6_15

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  • DOI: https://doi.org/10.1007/978-3-030-78230-6_15

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