二次指派问题：Xia和Yuan的线性化比Adams和Johnson的线性化弱，一族割来缩小差距
The quadratic assignment problem: the linearization of Xia and Yuan is weaker than the linearization of Adams and Johnson and a family of cuts to narrow the gap
摘要：
二次指派问题是一个著名的最优化问题，有许多应用。解决它的一个常见策略是使用其线性化之一，然后应用混合整数线性规划方法工具箱。混合整数公式的质量的一个度量是其线性松弛的质量。本文比较了二次指派问题的两种线性化，证明了Adams和Johnson线性化的线性松弛包含在Xia和Yuan线性化的线性松弛中。我们还开发了一个分支和切割的方法，使用证明中获得的见解，通过一个新的家庭的削减称为ab-削减，提高了线性化的夏和袁。
英文摘要：
The quadratic assignment problem is a well-known optimization problem with numerous applications. A common strategy to solve it is to use one of its linearizations and then apply the toolbox of mixed integer linear programming methods. One measure of quality of a mixed integer formulation is the quality of its linear relaxation. In this paper, we compare two linearizations of the quadratic assignment problem and prove that the linear relaxation of the linearization of Adams and Johnson is contained in the linear relaxation of the linearization of Xia and Yuan. We furthermore develop a Branch and Cut approach using the insights obtained in the proof that enhances the linearization of Xia and Yuan via a new family of cuts called ab-cuts.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
