The design of a wireless mesh network is usually posed as a multi-objective optimization problem. In this paper, we consider the planning of a wireless mesh network in a rural region where the network coverage and the cost of the architecture must be optimized. In addition, mesh routers are heterogeneous, meaning that they may have different transmission ranges. In the network model, we assume that the region to serve is divided into a set of small zones of various types, including cost-effective locations and zones of interest for which the coverage is mandatory. The objective is then to minimize the number of routers, their types and locations which maximize the coverage percentage of mandatory zones in terms of coverage while minimizing the overall cost of the architecture. To achieve this, we propose three multi-objective approaches. We test the proposed approaches on several random topologies. The min-max regret metric is used to appreciate the quality of solutions of the Pareto front of different approaches.