Cutting plane methods play a significant role in modern solvers for tackling mixed-integer programming (MIP) problems. Proper selection of cuts would remove infeasible solutions in the early stage, thus largely reducing the computational burden without hurting the solution accuracy. However, the major cut selection approaches heavily rely on heuristics, which strongly depend on the specific problem at hand and thus limit their generalization capability. In this paper, we propose a data-driven and generalizable cut selection approach, named Cut Ranking, in the settings of multiple instance learning. To measure the quality of the candidate cuts, a scoring function, which takes the instance-specific cut features as inputs, is trained and applied in cut ranking and selection. In order to evaluate our method, we conduct extensive experiments on both synthetic datasets and real-world datasets. Compared with commonly used heuristics for cut selection, the learning-based policy has shown to be more effective, and is capable of generalizing over multiple problems with different properties. Cut Ranking has been deployed in an industrial solver for large-scale MIPs. In the online A/B testing of the product planning problems with more than $10^7$ variables and constraints daily, Cut Ranking has achieved the average speedup ratio of 12.42% over the production solver without any accuracy loss of solution.
翻译:正确选择削减将消除早期的不可行解决方案,从而大大减轻计算负担,同时又不影响解决方案的准确性。然而,主要削减选择方法严重依赖疲劳症,这在很大程度上取决于手头的具体问题,从而限制了其概括化能力。在本文件中,我们提议了一种数据驱动和可普遍适用的削减选择方法,在多个实例学习的环境下采用名为“切分分”的多重实例学习模式。为了衡量候选人裁员的质量,一种评分功能,以具体实例的截断特征作为投入,在削减排名和选择中进行培训和应用。为了评估我们的方法,我们在合成数据集和现实世界数据集方面进行了广泛的实验。与通常使用的裁员偏重论相比,基于学习的政策已经证明更为有效,并且能够对不同属性的多重问题进行概括化。在大规模MIP的工业解决方案中,将评分功能作为特有的裁分功能作为投入,在削减等级和选择中应用。在网上A/B级测试中,对合成数据集和现实世界数据集进行了广泛的实验。在产品规划速度方面,没有超过10比10的年平均水平,而是对产品平均损失率率率率进行了超过12年的计算。