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Branch-and-Check with Explanations for the Vehicle Routing Problem with Time Windows

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Principles and Practice of Constraint Programming (CP 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10416))

Abstract

This paper proposes the framework of branch-and-check with explanations (BCE), a branch-and-check method where combinatorial cuts are found by general-purpose conflict analysis, rather than by specialized separation algorithms. Specifically, the method features a master problem that ignores combinatorial constraints, and a feasibility subproblem that uses propagation to check the feasibility of these constraints and performs conflict analysis to derive nogood cuts. The BCE method also leverages conflict-based branching rules and strengthens cuts in a post-processing step. Experimental results on the Vehicle Routing Problem with Time Windows show that BCE is a potential alternative to branch-and-cut. In particular, BCE dominates branch-and-cut, both in proving optimality and in finding high-quality solutions quickly.

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Authors and Affiliations

  1. CSIRO Data61, Eveleigh, NSW, 2015, Australia

    Edward Lam

  2. University of Melbourne, Parkville, VIC, 3010, Australia

    Edward Lam

  3. University of Michigan, Ann Arbor, MI, 48109-2117, USA

    Pascal Van Hentenryck

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  1. Edward Lam
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  2. Pascal Van Hentenryck
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Correspondence to Edward Lam .

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Editors and Affiliations

  1. University of Toronto, Toronto, Ontario, Canada

    J. Christopher Beck

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Lam, E., Van Hentenryck, P. (2017). Branch-and-Check with Explanations for the Vehicle Routing Problem with Time Windows. In: Beck, J. (eds) Principles and Practice of Constraint Programming. CP 2017. Lecture Notes in Computer Science(), vol 10416. Springer, Cham. https://doi.org/10.1007/978-3-319-66158-2_37

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  • DOI: https://doi.org/10.1007/978-3-319-66158-2_37

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  • Print ISBN: 978-3-319-66157-5

  • Online ISBN: 978-3-319-66158-2

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