Cutting planes are a crucial component of state-of-the-art mixed-integer programming solvers, with the choice of which subset of cuts to add being vital for solver performance. We propose new distance-based measures to qualify the value of a cut by quantifying the extent to which it separates relevant parts of the relaxed feasible set. For this purpose, we use the analytic centers of the relaxation polytope or of its optimal face, as well as alternative optimal solutions of the linear programming relaxation. We assess the impact of the choice of distance measure on root node performance and throughout the whole branch-and-bound tree, comparing our measures against those prevalent in the literature. Finally, by a multi-output regression, we predict the relative performance of each measure, using static features readily available before the separation process. Our results indicate that analytic center-based methods help to significantly reduce the number of branch-and-bound nodes needed to explore the search space and that our multiregression approach can further improve on any individual method.

翻译：割平面是先进混合整数规划求解器的关键组成部分，选择添加哪些割平面子集对求解器性能至关重要。我们提出新的基于距离的度量方法，通过量化割平面分离松弛可行集相关部分的程度来评估其价值。为此，我们利用松弛多面体或其最优面的解析中心，以及线性规划松弛的替代最优解。我们评估了距离度量选择对根节点性能及整个分支定界树的影响，并将我们的度量与文献中常见度量进行了比较。最后，通过多输出回归，我们利用分离过程之前即可获得的静态特征预测每种度量的相对性能。结果表明，基于解析中心的方法有助于显著减少探索搜索空间所需的分支定界节点数量，且我们的多回归方法能够进一步优化任何单一方法的性能。