A modern wireless network can be neither successfully deployed nor successfully expanded without proper planning. In this paper we consider the wireless mesh network (WMN) planning problem where not much work has been done. We propose a more realistic multi-objective approach to model this problem where the two conflicting objectives of total deployment cost and network throughput are to be optimized while guaranteeing full coverage to all mesh clients. Previous contributions have mainly formulated and solved this problem by using single-objective integer linear programming formulations and exact methods. The main limitation of these approaches resides in their restriction to small sized instances. We propose a population-based meta-heuristic algorithm to solve the problem. This algorithm produces a set of good planning solutions for real-size networks thus enlarging the decision perspective of a network planner. We also discuss the effect of different parameters on the characteristics of the solutions.