This paper presents a multiobjective model for the simultaneous optimization of the number of relays and the energy dissipation when deploying a wireless sensor networks to monitor specific locations in an area. In order to solve the model, a hybrid evolutionary algorithm with two local searches is proposed an implemented. As the algorithm returns a set of efficient solutions, the tradeoff among placements in their number of relays with their energy dissipation is explored. The evaluation shows that the energy can be diminished greatly by choosing not the most efficient placement in terms of number of relays but other placement with more relays. In our experiments, it was found that the solution with one or two more relay sensors than the efficient placement helped greatly in diminishing the energy. The proposed algorithm also showed better approximations than an approximation problem in the literature to the minimal number of relays.
