Problem of Optimal Positioning of Routers in a WSAN

Indoor deployment of Wireless Sensor and Actor Networks represents a challenge for designers; requires extensive experience on this field and usually several iterations of trial and error to find an optimal design. As part of a collaborative research project, we are developing a tool that suggests the optimal design of a WSAN; taking into account the number of routers, fault tolerance and energy consumption. One of the main problems that face the development of that tool is, given the candidate positions that can take the routers, to find the optimal positioning based on the optimization criteria. In this paper is formally defined the problem and is classified according to its computational complexity in NP-Hard. Based on the problem complexity and the state of art, we decide to study the feasibility of solving it with an evolutionary approach. Using jMetal framework, we compare the behavior of four evolutionary algorithms solving the proposed problem: NSGAII, SPEA2, PAES and PESAII. As quality indicators we use Hypervolume and Epsilon.