This article studies the effect of partial coverage to extend the lifetime of wireless sensor networks and introduces a hybrid exact solution strategy that efficiently maximizes network lifetime. We consider a set of sensors used to provide coverage of discrete targets and transfer the information to the sink node via multi-hop wireless communication. An active sensor has one of the two roles: it is a source when it senses and transfers data; it is a relay if it only transfers data. Network lifetime is extended through the use of covers representing sensors role allocation and network topology. A hybrid column generation is used to identify the optimal operation schedules and roles allocation that maximize network lifetime. A constraint programming strategy is provided to identify profitable network configurations leading to extend network lifetime and to prove optimality of the solutions found. Moreover, an evolutionary algorithm is proposed to boost up the solution process and accelerate convergence. Extensive computational results demonstrate the effectiveness of the proposed approach.