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：剪切平面选择是所有现代混合整数线性编程求解器中使用的子例,目标是选择一组生成的剪切,以产生最佳求解性能。 这些解算器拥有数以百万计的参数组合, 也是极佳的参数调制对象。 剪切选择评分规则通常是不同测量的加权总和, 其中加权是参数。 我们提出了一个混合整数线性程序以及无限多全家庭有效切分数的参数组合。 其中一些剪切可以在应用后直接产生整数最佳解决方案, 而另一些则无法这样做, 即使应用了无限数量。 我们展示了特定的剪切分选择规则规则, 参数空间的任何定数网格搜索都会错过所有参数值, 选择整数最优的剪切值, 问题很多。 我们提议对现有的图动神经神经网络的设计进行修改, 以学习剪切规则参数。 我们提出了一个强化的学习框架, 用于选择削减, 并培训我们的设计, 使用MIPLIB 2017 和 神经网络核查数据集。 我们的框架和设计显示, 适应性剪裁选择会大大改进所有参数- 将大大改进了所有参数的功能, 正在改进一个不同的操作。