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Cutting planes are a crucial component of state-of-the-art mixed-integerprogramming solvers, with the choice of which subset of cuts to add being vitalfor solver performance. We propose new distance-based measures to qualify thevalue of a cut by quantifying the extent to which it separates relevant partsof the relaxed feasible set. For this purpose, we use the analytic centers ofthe relaxation polytope or of its optimal face, as well as alternative optimalsolutions of the linear programming relaxation. We assess the impact of thechoice of distance measure on root node performance and throughout the wholebranch-and-bound tree, comparing our measures against those prevalent in theliterature. Finally, by a multi-output regression, we predict the relativeperformance of each measure, using static features readily available before theseparation process. Our results indicate that analytic center-based methodshelp to significantly reduce the number of branch-and-bound nodes needed toexplore the search space and that our multiregression approach can furtherimprove on any individual method.

Cutting Plane Selection with Analytic Centers and Multiregression