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

  • Edward LamEmail author
  • Pascal Van Hentenryck
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10416)


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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© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.CSIRO Data61EveleighAustralia
  2. 2.University of MelbourneParkvilleAustralia
  3. 3.University of MichiganAnn ArborUSA

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