论文标题
学习使用当地削减
Learning to Use Local Cuts
论文作者
论文摘要
现代求解器中的一个重要组成部分(线性)程序(MIPS)是分离其他不平等(切割平面),以拧紧线性编程放松。当将切割平面方法集成到分支结合(B&B)求解器中时,需要各种算法决策,因为鉴于削减的效率与成本之间总是存在权衡,因为它们倾向于减慢放松的解决方案时间。最关键的问题之一是:是否应该仅在根部或本地生成剪切?我们通过一种机器学习方法来解决这个问题,我们训练回归森林,以预测使用本地切割提供的加速(或减速)。我们通过公开实施证明,这有助于在一般MIP实例的公共测试集上提高FICO XPRESS MIP求解器的性能。我们进一步报告了Xpress内部实施实施对大型,多样化的现实世界行业MIP的影响。
An essential component in modern solvers for mixed-integer (linear) programs (MIPs) is the separation of additional inequalities (cutting planes) to tighten the linear programming relaxation. Various algorithmic decisions are necessary when integrating cutting plane methods into a branch-and-bound (B&B) solver as there is always the trade-off between the efficiency of the cuts and their costs, given that they tend to slow down the solution time of the relaxation. One of the most crucial questions is: Should cuts only be generated globally at the root or also locally at nodes of the tree? We address this question by a machine learning approach for which we train a regression forest to predict the speed-up (or slow-down) provided by using local cuts. We demonstrate with an open implementation that this helps to improve the performance of the FICO Xpress MIP solver on a public test set of general MIP instances. We further report on the impact of a practical implementation inside Xpress on a large, diverse set of real-world industry MIPs.