# A Comparison of Models for Uncertain Network Design

## TL;DR

This paper compares different uncertainty modeling approaches in a telecommunications network design problem, revealing that robust optimization with polyhedral sets may be less efficient than simpler stochastic models in real-world scenarios.

## Contribution

It provides a practical comparison of uncertainty sets in network design, highlighting the effectiveness of different models using real-world data.

## Key findings

- Robust optimization with polyhedral sets may be less efficient than stochastic models.
- Discrete and mean-based models perform competitively in real-world data.
- The study challenges current trends favoring polyhedral uncertainty sets.

## Abstract

To solve a real-world problem, the modeler usually needs to make a trade-off between model complexity and usefulness. This is also true for robust optimization, where a wide range of models for uncertainty, so-called uncertainty sets, have been proposed. However, while these sets have been mainly studied from a theoretical perspective, there is little research comparing different sets regarding their usefulness for a real-world problem. In this paper we consider a network design problem in a telecommunications context. We need to invest into the infrastructure, such that there is sufficient capacity for future demand which is not known with certainty. There is a penalty for an unsatisfied realized demand, which needs to be outsourced. We consider three approaches to model demand: using a discrete uncertainty set, using a polyhedral uncertainty set, and using the mean of a per-commodity fitted zero-inflated uniform distribution. While the first two models are used as part of a robust optimization setting, the last model represents a simple stochastic optimization setting. We compare these approaches on an efficiency frontier real-world data taken from the online library SNDlib and observe that, contrary to current research trends, robust optimization using the polyhedral uncertainty set may result in less efficient solutions.