The determination of a topology that extends the network lifetime is a major challenge in the area of wireless sensor networks (WSNs). In this paper we present the dynamic coverage problem (DCP), applying it to network-design purposes. In the context of WSNs, we have to find a configuration that maintains the coverage of the monitoring area, accomplishes the management of the network resources and minimizes the energy consumption. This work presents an integer linear programming formulation and an evolutionary algorithm for this combinatorial problem. We report computational results and comparisons between solutions for the proposed model and our evolutionary approach.