Model reduction, which aims to learn a simpler model of the original mixed integer linear programming (MILP), can solve large-scale MILP problems much faster. Most existing model reduction methods are based on variable reduction, which predicts a solution value for a subset of variables. From a dual perspective, constraint reduction that transforms a subset of inequality constraints into equalities can also reduce the complexity of MILP, but has been largely ignored. Therefore, this paper proposes a novel constraint-based model reduction approach for the MILP. Constraint-based MILP reduction has two challenges: 1) which inequality constraints are critical such that reducing them can accelerate MILP solving while preserving feasibility, and 2) how to predict these critical constraints efficiently. To identify critical constraints, we first label these tight-constraints at the optimal solution as potential critical constraints and design a heuristic rule to select a subset of critical tight-constraints. To learn the critical tight-constraints, we propose a multi-modal representation technique that leverages information from both instance-level and abstract-level MILP formulations. The experimental results show that, compared to the state-of-the-art methods, our method improves the quality of the solution by over 50\% and reduces the computation time by 17.47\%.

翻译：模型降维旨在学习原始混合整数线性规划（MILP）的简化模型，从而显著加速大规模MILP问题的求解。现有降维方法大多基于变量约简，即预测部分变量的解值。从对偶视角看，将部分不等式约束转化为等式约束的约束约简同样能降低MILP复杂度，但长期被忽视。为此，本文提出一种基于约束的MILP模型降维新方法。约束式MILP降维面临两大挑战：1）如何识别关键不等式约束，使其约简在保持可行性的同时加速求解；2）如何高效预测这些关键约束。为识别关键约束，我们首先将最优解处的紧约束标记为潜在关键约束，并设计启发式规则筛选关键紧约束子集。为学习关键紧约束，我们提出多模态表示技术，综合利用MILP问题实例级与抽象级表述信息。实验结果表明：相较于现有最优方法，本方法将解的质量提升超50%，计算时间降低17.47%。