Cutting plane selection is a subroutine used in all modern mixed-integer linear programming solvers with the goal of selecting a subset of generated cuts that induce optimal solver performance. These solvers have millions of parameter combinations, and so are excellent candidates for parameter tuning. Cut selection scoring rules are usually weighted sums of different measurements, where the weights are parameters. We present a parametric family of mixed-integer linear programs together with infinitely many family-wide valid cuts. Some of these cuts can induce integer optimal solutions directly after being applied, while others fail to do so even if an infinite amount are applied. We show for a specific cut selection rule, that any finite grid search of the parameter space will always miss all parameter values, which select integer optimal inducing cuts in an infinite amount of our problems. We propose a variation on the design of existing graph convolutional neural networks, adapting them to learn cut selection rule parameters. We present a reinforcement learning framework for selecting cuts, and train our design using said framework over MIPLIB 2017 and a neural network verification data set. Our framework and design show that adaptive cut selection does substantially improve performance over a diverse set of instances, but that finding a single function describing such a rule is difficult. Code for reproducing all experiments is available at https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP.

翻译：切割平面选择是现代混合整数线性规划求解器中使用的子程序，旨在从生成的割集中选择能带来最优求解器性能的子集。这些求解器拥有数百万种参数组合，因此是参数调优的绝佳对象。割选择评分规则通常是不同度量指标的加权和，其中权重为参数。我们提出了一族参数化的混合整数线性规划问题，并附带了无限多个该族通用的有效割。其中一些割在应用后能直接诱导出整数最优解，而另一些即使应用无限多个也无法做到。我们针对特定割选择规则证明：参数空间的任何有限网格搜索都无法捕捉到所有能在我方无限个问题中选出诱导整数最优割的参数值。我们提出一种基于现有图卷积神经网络的变体设计，使其适应于学习割选择规则参数。我们提出一个用于选择割的强化学习框架，并通过该框架在MIPLIB 2017数据集和神经网络验证数据集上训练我们的设计。我们的框架和设计表明，自适应切选择确实能在多样化的实例集合上显著提升性能，但寻找能描述此类规则的单一函数十分困难。所有实验的复现代码可在 https://github.com/Opt-Mucca/Adaptive-Cutsel-MILP 获取。