Cutting plane methods are a fundamental approach for solving integer linear programs (ILPs). In each iteration of such methods, additional linear constraints (cuts) are introduced to the constraint set with the aim of excluding the previous fractional optimal solution while not affecting the optimal integer solution. In this work, we explore a novel approach within cutting plane methods: instead of only adding new cuts, we also consider the removal of previous cuts introduced at any of the preceding iterations of the method under a learnable parametric criteria. We demonstrate that in fundamental combinatorial optimization settings such cut removal policies can lead to significant improvements over both human-based and machine learning-guided cut addition policies even when implemented with simple models.

翻译：割平面方法是求解整数线性规划问题的基本方法。在此类方法的每次迭代中，会向约束集中引入额外的线性约束（割平面），旨在排除先前的小数最优解，同时不影响最优整数解。本文探索了割平面方法中的一种新思路：除了添加新割平面外，我们还考虑在可学习的参数化准则下，移除该方法在前序任意迭代中引入的已有割平面。我们证明，在基础的组合优化场景中，即使采用简单模型实现，这种割平面移除策略相较于基于人工规则和机器学习引导的割平面添加策略仍能带来显著改进。