Speeding up the solution of the site and power assignment problem in wireless networks

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.