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Linear programming insights into solvable cases of the quadratic assignment problem

机译：线性规划对二次赋值问题可解情况的见解

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摘要

The quadratic assignment problem is an NP-hard discrete optimization program that has been extensively studied for over 50 years. It has a variety of applications in many fields, but has proven itself extremely challenging to solve. As a result, an area of research has been to identify special cases which admit efficient solution strategies. This paper examines four such cases, and shows how each can be explained in terms of the dual region to the continuous relaxation of a classical linear reformulation of the problem known as the level- 1 RLT representation. The explanations allow for simplifications and/or generalizations of the conditions defining the special cases.
机译：二次分配问题是NP-hard离散优化程序，已被广泛研究了50多年。它在许多领域都有各种各样的应用，但是事实证明，解决起来非常困难。结果，研究领域是确定允许有效解决方案策略的特殊情况。本文研究了四个这样的情况，并说明了如何用双重区域来解释经典线性重构问题的连续区域，即所谓的1级RLT表示。这些解释允许对定义特殊情况的条件进行简化和/或概括。

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