Abstract: The effectiveness of a cluster-based distributed sensor network, to a large extent, depends on the coverage provided by the sensor nodes. To activate only the necessary number of sensor nodes at any particular moment is an efficient way to save the overall energy. However, this is an NP-complete problem because of the high-density deployment of wireless sensor networks. In this paper, a novel searching algorithm based on improved NSGA-II (elitist nondominated sorting genetic algorithm) is proposed to select an optimal cover set. In contrast to the binary detection model used in the previous work, a probabilistic detection model is adopted in combination with the detection error range and coverage threshold. With the full network coverage being guaranteed, a number of nodes are made into dormancy mode to save energy. The circulated combination and delete operators are proposed to enhance the search capability. Extensive simulation results are presented to demonstrate the effectiveness of our approach.