Wireless sensor nodes are mostly battery operated, tiny in size, and deployed in some specified area. The limited capacity of the battery power hinders the performance of the node as well as of the network. This requires efficient management of battery power for optimal utilization of the sensor network technology. In this work we propose a novel method to extend the life time of the sensor network by organizing the sensors into a maximal number of non-disjoint set covers with non-uniform sensing ranges. Sensors present in one set cover remain active at any instant of time while other sensors are in sleep mode, so they consume negligible battery power. Each set cover is activated successively, thereby increasing the total lifetime of the network. Each sensor can move towards the center of the set of nodes it covers to further reduce the sensing range and further diminishes the consumption of energy. It is observed through extensive simulation work that the network lifetime can be increased by adjusting their sensing ranges as compared to sensors with fixed sensing ranges. This method employs genetic algorithm (GA) and greedy heuristic approach to determine optimal sensing range for efficient energy management in sensor network. Simulation results show its efficiency over the fixed-range strategies.