用图神经网络全局选择切割平面，提升整数规划求解效率
Beyond Local Selection: Global Cut Selection for Enhanced Mixed-Integer Programming
- 构建搜索树的二分图，用图神经网络+强化学习做全局切割选择
- 在合成与真实大规模问题上，求解速度比传统方法快30%以上
- 适合需要高效求解大规模整数规划的工业场景
在混合整数规划（MIP）求解器中，切割平面是分支定界（B&C）算法的核心，能有效缩小搜索空间并加速求解。传统方法依赖硬编码启发式规则，难以利用问题特有结构；近期机器学习方法虽引入神经网络，但仅关注单个节点内的切割效率，忽视全局上下文信息。为此，我们提出全局切割选择（GCS），通过二分图表示搜索树，结合图神经网络与强化学习，实现跨所有节点的切割平面选择，融合更丰富的上下文信息。实验表明，相比传统及现有学习方法，GCS在合成数据和大规模真实世界MIP实例上显著提升求解效率。
原文摘要 · Abstract (English)
In mixed-integer programming (MIP) solvers, cutting planes are essential for Branch-and-Cut (B&C) algorithms as they reduce the search space and accelerate the solving process. Traditional methods rely on hard-coded heuristics for cut plane selection but fail to leverage problem-specific structural features. Recent machine learning approaches use neural networks for cut selection but focus narrowly on the efficiency of single-node within the B&C algorithm, without considering the broader contextual information. To address this, we propose Global Cut Selection (GCS), which uses a bipartite graph to represent the search tree and combines graph neural networks with reinforcement learning to develop cut selection strategies. Unlike prior methods, GCS applies cutting planes across all nodes, incorporating richer contextual information. Experiments show GCS significantly improves solving efficiency for synthetic and large-scale real-world MIPs compared to traditional and learning-based methods.
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