Optimization Problems and Resolution Methods for Node Placement in Wireless Mesh Networks

With the emergence of wireless networking paradigm, several optimization problems are showing their usefulness to the efficient design of such networks. These problem are related, among others, to optimizing network connectivity, coverage and stability. The resolution of these problems turns out to be crucial for optimized network performance. In the case of Wireless Mesh Networks (WMN), such problems include computing placement of nodes (mesh router nodes, gateways and distribution of mesh client notes), so that network performance is optimized. However, most optimization problems formulated for WMNs are variations of NP-hard optimization problems and are thus unlikely to be solvable in polynomial time. For instance, mesh router node placement belongs to the family of node placement problems, which are known for their hardness to solve to optimality. Therefore heuristics methods are used to near-optimally solve such problems. In this work we present some optimization problems in WMNs and different heuristic methods such as Local Search, Genetic Algorithms, Tabu Search for solving them near-optimally. We formulate the optimization problems using multi-objective optimization models. Thus, for the mesh router nodes placement, the bi-objective optimization problem is obtained 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. We also discuss on the suitability of using different resolution methods for solving optimization problems in WMNs.