In this paper, we propose a cutting plane algorithm based on DC (Difference-of-Convex) programming and DC cut for globally solving Mixed-Binary Linear Program (MBLP). We first use a classical DC programming formulation via the exact penalization to formulate MBLP as a DC program, which can be solved by DCA algorithm. Then, we focus on the construction of DC cuts, which serves either as a local cut (namely type-I DC cut) at feasible local minimizer of MBLP, or as a global cut (namely type-II DC cut) at infeasible local minimizer of MBLP if some particular assumptions are verified. Otherwise, the constructibility of DC cut is still unclear, and we propose to use classical global cuts (such as the Lift-and-Project cut) instead. Combining DC cut and classical global cuts, a cutting plane algorithm, namely DCCUT, is established for globally solving MBLP. The convergence theorem of DCCUT is proved. Restarting DCA in DCCUT helps to quickly update the upper bound solution and to introduce more DC cuts for lower bound improvement. A variant of DCCUT by introducing more classical global cuts in each iteration is proposed, and parallel versions of DCCUT and its variant are also designed which use the power of multiple processors for better performance. Numerical simulations of DCCUT type algorithms comparing with the classical cutting plane algorithm using Lift-and-Project cuts are reported. Tests on some specific samples and the MIPLIB 2017 benchmark dataset demonstrate the benefits of DC cut and good performance of DCCUT algorithms.

中文翻译：

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混合二进制线性程序的凸差切割平面算法

在本文中，我们提出了一种基于DC（凸差）编程和DC Cut的割平面算法，用于全局求解混合二进制线性程序（MBLP）。我们首先通过精确的惩罚使用经典的DC编程公式，将MBLP公式化为DC程序，这可以通过DCA算法解决。然后，我们集中讨论DC剪切的构建，该DC剪切在MBLP的可行局部最小化器中用作局部剪切（即I型DC剪切），或者在不可行的局部最小化器中用作全局剪切（即II型DC剪切）。如果验证了某些特定的假设，则MBLP的大小。否则，DC切割的可构造性仍不清楚，我们建议改用经典的全局切割（例如“ Lift-and-Project”切割）。结合了DC切割和经典的全局切割，这是一种切割平面算法，即DCCUT，为全球解决MBLP而建立。证明了DCCUT的收敛定理。在DCCUT中重新启动DCA有助于快速更新上限解决方案，并引入更多的DC削减以改善下限。通过在每次迭代中引入更多经典的全局切割，提出了DCCUT的变体，并且还设计了并行版本的DCCUT及其变体，它使用多个处理器的功能来获得更好的性能。报告了DCCUT类型算法与使用“提升并投影”切割的经典切割平面算法相比的数值模拟。对某些特定样本和MIPLIB 2017基准数据集的测试证明了DC Cut的好处和DCCUT算法的良好性能。在DCCUT中重新启动DCA有助于快速更新上限解决方案，并引入更多的DC削减以改善下限。通过在每次迭代中引入更多经典的全局切割，提出了DCCUT的变体，并且还设计了并行版本的DCCUT及其变体，它使用多个处理器的功能来获得更好的性能。报告了DCCUT类型算法与使用“提升并投影”切割的经典切割平面算法相比的数值模拟。对某些特定样本和MIPLIB 2017基准数据集的测试证明了DC Cut的好处和DCCUT算法的良好性能。在DCCUT中重新启动DCA有助于快速更新上限解决方案，并引入更多的DC削减以改善下限。通过在每次迭代中引入更多经典的全局切割，提出了DCCUT的变体，并且还设计了并行版本的DCCUT及其变体，它使用多个处理器的功能来获得更好的性能。报告了DCCUT类型算法与使用“提升并投影”切割的经典切割平面算法相比的数值模拟。对一些特定样本和MIPLIB 2017基准数据集的测试证明了DC削减的好处和DCCUT算法的良好性能。同时还设计了并行版本的DCCUT及其变体，它们使用多个处理器的功能来获得更好的性能。报告了DCCUT类型算法与使用“提升并投影”切割的经典切割平面算法相比的数值模拟。对一些特定样本和MIPLIB 2017基准数据集的测试证明了DC削减的好处和DCCUT算法的良好性能。同时还设计了并行版本的DCCUT及其变体，它们使用多个处理器的功能来获得更好的性能。报告了DCCUT类型算法与使用“提升并投影”切割的经典切割平面算法相比的数值模拟。对一些特定样本和MIPLIB 2017基准数据集的测试证明了DC削减的好处和DCCUT算法的良好性能。