A Study on the Performance of Search Methods for Mesh Router Nodes Placement Problem

Node placement problems have been long investigated in the optimization field due to numerous applications in facility location, logistics, services, etc. Such problems are attracting again the attention of researchers now from the networking domain, and more especially from Wireless Mesh Networks (WMNs) field. Indeed, the placement of mesh routers nodes appears to be crucial for the performance and operability of WMNs, in terms of network connectivity and stability. However, node placement problems are known for their hardness for solving them to optimality, and therefore heuristics methods are used to near-optimally solve such problems. In this work we evaluate the performance of different heuristic methods in order to judge on their suitability of solving mesh router nodes problem. We have selected methods from two different families, namely, local search methods (Hill Climbing and Simulated Annealing) and population-based methods (Genetic Algorithms). The former are known for their capability to exploit the solution space by constructing a path of visited solutions, while the later use a population of individuals aiming to largely explore the solution space. In both cases, a bi-objective optimization consisting in the maximization of the size of the giant component in the mesh routers network (for measuring network connectivity) and that of user coverage are considered. In the experimental evaluation, we have used a benchmark of instances -- varying from small to large size -- generated using different distributions of mesh node clients (Uniform, Normal, Exponential and Weibull).