干货 | 10分钟掌握branch and cut（分支剪界）算法原理附带C++求解TSP问题代码

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于 2019-08-13 10:50:00 发布 · 3.7k 阅读

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本文介绍了分支剪界（Branch and Cut）算法，它是求解整数线性规划（ILPs）的一种方法，通过结合分支定界（Branch and Bound）和切割平面（Cutting Planes）来提高效率。文章详细阐述了算法原理，通过举例和伪代码说明了如何在求解过程中使用切割平面来收紧线性规划松弛模型的解空间，从而加速收敛。

00 前言

branch and cut其实还是和branch and bound脱离不了干系的。所以，在开始本节的学习之前，请大家还是要务必掌握branch and bound算法的原理。

01 应用背景

Branch and cut is a method of combinatorial optimization for solving integer linear programs (ILPs), that is, linear programming (LP) problems where some or all the unknowns are restricted to integer values. Branch and cut involves running a branch and bound algorithm and using cutting planes to tighten the linear programming relaxations. Note that if cuts are only used to tighten the initial LP relaxation, the algorithm is called cut and branch.[1]