英文文献：GUB Covers and Power-Indexed Formulations for Wireless Network Design-GUB涵盖了用于无线网络设计的功率索引公式
英文文献作者：Fabio D'Andreagiovanni,Carlo Mannino,Antonio Sassano
英文文献摘要：
Wireless networks have shown a rapid growth over the past two decades and now play a key role in new generation telecommunications networks. The physical medium of wireless networks is the radio spectrum, a scarce resource which is becoming extremely congested and needs to be allocated in more effective ways. Since the early 1980s several optimization models have been developed to design wireless networks. In this paper we propose a pure 0-1 formulation which is able to model a very general situation in which both emission powers and operating frequencies can be optimized. In contrast with the classical mixed integer formulation, where powers are represented by continuous variables, we consider only a finite set of transmitting powers. The ensuing model has two major advantages: it better fits the usual practice and minimizes the numerical problems produced by the interaction of continuous and 0-1 decision variables. A crucial ingredient of our approach is an effective basic formulation for the single knapsack problem representing the coverage condition of a receiver. This formulation is based on the well-known lifted GUB cover inequalities introduced by Wolsey and its core is a slight extension of the exact formulation proposed by Wolsey for the GUB knapsack polytope with two GUB constraints. In the specific framework of our real-life problem the two GUB constraints case corresponds to the very common situation in which only one major interferer is present. The effectiveness of such formulation is assessed by comprehensive computational results.

无线网络在过去二十年中迅速发展，现在在新一代电信网络中发挥着关键作用。无线网络的物理媒介是无线电频谱，这是一种日益拥挤的稀缺资源，需要以更有效的方式分配。自1980年代早期以来，已经发展了若干优化模型来设计无线网络。在本文中，我们提出了一个纯0-1公式，它能够模拟一个非常普遍的情况，即发射功率和工作频率都可以优化。与经典的幂用连续变量表示的混合整数公式不同，我们只考虑有限的幂传递集合。随后的模型有两个主要的优点:它更好地适合通常的实践和最小化由连续和0-1决策变量的相互作用产生的数值问题。我们的方法的一个关键组成部分是一个有效的基本公式的单背包问题表示的覆盖条件的接收器。该公式基于Wolsey引入的著名的解除GUB覆盖不等式，其核心是对Wolsey提出的具有两个GUB约束的GUB背包多边形精确公式的轻微扩展。在我们实际问题的特定框架中，两个GUB约束情况对应于只有一个主要干扰存在的非常常见的情况。综合计算结果评价了该公式的有效性。