  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.
