This paper addresses the optimal design of wireless networks through the site and power assignment problem. Given a set of candidate transmitters, this problem involves choosing optimal transmitter locations and powers to provide service coverage over a target area. In the modern context of increasing traffic, establishing suitable locations and power emissions for the transmitters in wireless networks is a relevant and challenging task due to heavy radio spectrum congestion. Traditional network design formulations are very ill-conditioned and suffer from numerical inaccuracies and limited applicability to large-scale practical scenarios. Our contribution consists of speeding up the solution of the problem under consideration by addressing its drawbacks from a modeling point of view. We propose valid cutting planes and various presolve operations to reduce the problem size and strengthen existing formulations, along with a reduction scheme based on reduced cost fixing to reduce the sources of numerical inaccuracies. Our proposals prove effective, allowing us to achieve optimality on large-scale instances obtained from a real 4G LTE network in solution times aligning well with planning windows.

翻译：摘要：本文通过站点与功率分配问题研究无线网络的最优设计。给定一组候选发射机，该问题涉及选择最优发射机位置和功率，以在目标区域提供服务覆盖。在当前流量持续增长的背景下，由于无线电频谱严重拥塞，为无线网络中的发射机确定合适的位置和功率发射是一项重要且具有挑战性的任务。传统网络设计方案具有很强的病态性，存在数值不精确问题，且难以适用于大规模实际场景。本文的贡献在于从建模角度解决上述缺陷，从而加快所研究问题的求解速度。我们提出有效的割平面和多种预处理操作以减小问题规模并强化现有模型，同时引入基于简化成本固定的缩减方案来减少数值不精确的来源。实验证明，我们的方法行之有效，能够在与实际规划窗口相匹配的求解时间内，对来自真实4G LTE网络的大规模实例实现最优解。