# Nonlinear Negotiation Approaches for Complex-Network Optimization: A Study Inspired by Wi-Fi Channel Assignment

## TL;DR

This paper models Wi-Fi channel assignment as a graph coloring problem and compares nonlinear negotiation techniques, finding that simulated annealing outperforms particle swarm optimization in complex scenarios with faster runtimes.

## Contribution

It introduces a novel application of negotiation techniques to Wi-Fi channel assignment modeled as a graph coloring problem, demonstrating superior performance of simulated annealing.

## Key findings

- Simulated annealer outperforms particle swarm optimizer in complex scenarios.
- Annealer achieves better results with lower computational time.
- Network layout properties influence the performance gains of annealing.

## Abstract

At the present time, Wi-Fi networks are everywhere. They operate in unlicensed radio-frequency spectrum bands (divided in channels), which are highly congested. The purpose of this paper is to tackle the problem of channel assignment in Wi-Fi networks. To this end, we have modeled the networks as multilayer graphs, in a way that frequency channel assignment becomes a graph coloring problem. For a high number and variety of scenarios, we have solved the problem with two different automated negotiation techniques: a hill-climber and a simulated annealer. As an upper bound reference for the performance of these two techniques, we have also solved the problem using a particle swarm optimizer. Results show that the annealer negotiator behaves as the best choice because it is able to obtain even better results than the particle swarm optimizer in the most complex scenarios under study, with running times one order of magnitude below. Finally, we study how different properties of the network layout affect to the performance gain that the annealer is able to obtain with respect to the particle swarm optimizer.