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.
CITATION STYLE
Lam, E., & Van Hentenryck, P. (2017). Branch-and-check with explanations for the vehicle routing problem with time windows. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10416 LNCS, pp. 579–595). Springer Verlag. https://doi.org/10.1007/978-3-319-66158-2_37
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