Cut generation and lifting are key components for the performance of state-of-the-art mathematical programming solvers. This work proposes a new general cut-and-lift procedure that exploits the combinatorial structure of 0–1 problems via a binary decision diagram (BDD) encoding of their constraints. We present a general framework that can be applied to a wide range of binary optimization problems and show its applicability for second-order conic inequalities. We identify conditions for which our lifted inequalities are facet-defining and derive a new BDD-based cut generation linear program. Such a model serves as a basis for a max-flow combinatorial algorithm over the BDD that can be applied to derive valid cuts more efficiently. Our numerical results show encouraging performance when incorporated into a state-of-the-art mathematical programming solver, significantly reducing the root node gap, increasing the number of problems solved, and reducing the run-time by a factor of three on average.

切割生成和提升是最先进的数学规划求解器性能的关键组成部分。这项工作提出了一种新的通用剪切和提升程序，该程序通过对其约束的二元决策图 (BDD) 编码来利用 0-1 问题的组合结构。我们提出了一个通用框架，可以应用于广泛的二元优化问题，并展示其对二阶圆锥不等式的适用性。我们确定了我们解除的不等式定义方面的条件，并推导出一个新的基于 BDD 的切割生成线性程序。这样的模型作为 BDD 上最大流组合算法的基础，可用于更有效地推导出有效切割。