Cutting planes (cuts) play an important role in solving mixed-integer linear programs (MILPs), as they significantly tighten the dual bounds and improve the solving performance. A key problem for cuts is when to stop cuts generation, which is important for the efficiency of solving MILPs. However, many modern MILP solvers employ hard-coded heuristics to tackle this problem, which tends to neglect underlying patterns among MILPs from certain applications. To address this challenge, we formulate the cuts generation stopping problem as a reinforcement learning problem and propose a novel hybrid graph representation model (HYGRO) to learn effective stopping strategies. An appealing feature of HYGRO is that it can effectively capture both the dynamic and static features of MILPs, enabling dynamic decision-making for the stopping strategies. To the best of our knowledge, HYGRO is the first data-driven method to tackle the cuts generation stopping problem. By integrating our approach with modern solvers, experiments demonstrate that HYGRO significantly improves the efficiency of solving MILPs compared to competitive baselines, achieving up to 31% improvement.

翻译：切割平面（cuts）在求解混合整数线性规划（MILPs）中扮演着重要角色，因为它们能显著收紧对偶界并提升求解性能。切割生成的一个关键问题在于何时停止，这对MILPs的求解效率至关重要。然而，许多现代MILP求解器采用硬编码启发式方法处理该问题，往往忽略了特定应用场景中MILPs的潜在模式。为应对这一挑战，我们将切割生成停止问题建模为强化学习问题，并提出一种新型混合图表示模型（HYGRO）以学习有效的停止策略。HYGRO的一个显著优势是能有效捕捉MILPs的动态与静态特征，从而实现对停止策略的动态决策。据我们所知，HYGRO是首个解决切割生成停止问题的数据驱动方法。通过将我们的方法集成到现代求解器中，实验表明，与竞争性基线相比，HYGRO显著提升了MILPs的求解效率，最高可提升31%。