论文标题
整数编程中的连续切割平面算法
Continuous cutting plane algorithms in integer programming
论文作者
论文摘要
混合企业线性程序（MILP）的切割平面通常是通过迭代解决优化问题（即所谓的分离）来计算的。取而代之的是，我们将找到良好的切割平面作为连续优化问题而不是权重的问题的问题重新构架，以参数为有效不平等的家族。这个问题也可以解释为优化神经网络，以在亚addive函数上解决优化问题，我们称之为MILP的亚addivity Primal问题。为此，我们提出了一种混凝土的两步算法，并在优化多种类MILP的广义Gomory混合成员不平等时，证明了经验收益。可以在https://github.com/dchetelat/subadditive上找到重现实验的代码。
Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous optimization problem over weights parametrizing families of valid inequalities. This problem can also be interpreted as optimizing a neural network to solve an optimization problem over subadditive functions, which we call the subadditive primal problem of the MILP. To do so, we propose a concrete two-step algorithm, and demonstrate empirical gains when optimizing generalized Gomory mixed-integer inequalities over various classes of MILPs. Code for reproducing the experiments can be found at https://github.com/dchetelat/subadditive.
