Towards an accurate solution of wireless network design problems

TL;DR

This paper investigates the numerical challenges in wireless network design optimization models and explores how recent advances in exact algorithms over rational numbers can improve solution accuracy.

Contribution

It introduces a novel approach using recent exact solution algorithms to address numerical instability issues in wireless network design models.

Findings

Identifies sources of numerical instability in existing models.

Demonstrates the effectiveness of rational number algorithms in improving solution reliability.

Provides insights into potential improvements for solving complex wireless network problems.

Abstract

The optimal design of wireless networks has been widely studied in the literature and many optimization models have been proposed over the years. However, most models directly include the signal-to-interference ratios representing service coverage conditions. This leads to mixed-integer linear programs with constraint matrices containing tiny coefficients that vary widely in their order of magnitude. These formulations are known to be challenging even for state-of-the-art solvers: the standard numerical precision supported by these solvers is usually not sufficient to reliably guarantee feasible solutions. Service coverage errors are thus commonly present. Though these numerical issues are known and become evident even for small-sized instances, just a very limited number of papers has tried to tackle them, by mainly investigating alternative non-compact formulations in which the sources of numerical instabilities are eliminated. In this work, we explore a new approach by investigating how recent advances in exact solution algorithms for linear and mixed-integer programs over the rational numbers can be applied to analyze and tackle the numerical difficulties arising in wireless network design models.