Cutting planes are essential for solving mixed-integer linear problems (MILPs), because they facilitate bound improvements on the optimal solution value. For selecting cuts, modern solvers rely on manually designed heuristics that are tuned to gauge the potential effectiveness of cuts. We show that a greedy selection rule explicitly looking ahead to select cuts that yield the best bound improvement delivers strong decisions for cut selection - but is too expensive to be deployed in practice. In response, we propose a new neural architecture (NeuralCut) for imitation learning on the lookahead expert. Our model outperforms standard baselines for cut selection on several synthetic MILP benchmarks. Experiments with a B&C solver for neural network verification further validate our approach, and exhibit the potential of learning methods in this setting.
翻译:剪切机对于解决混合整数线性问题至关重要,因为它们有助于在最佳解决方案值上实现约束性改进。 对于选择裁剪,现代溶剂依赖人工设计的超自然学,这些超自然学可以用来测量裁剪的潜在效果。 我们表明,贪婪的挑选规则明确着眼于选择能够产生最佳约束性改进的裁剪,可以作出强有力的裁剪选择,但实际上却太昂贵,无法实际应用。 作为回应,我们提议了一个新的神经结构(NeuralCut),用于模仿长相专家的学习。我们的模型超越了在几个合成MILP基准上削减选择的标准基线。与用于神经网络核查的B&C解析器的实验进一步证实了我们的做法,并展示了在这一环境中学习方法的潜力。