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Lifetime is a critical issue at wireless sensor networks (WSNs). Partitioning the set of sensors into several covers over all targets and enabling the covers by turns can effectively extend the lifetime. The problem formulation regarding optimization of sensor partition commonly assumes static networks; however, the composition and topology of real-world WSNs can vary with time due to hardware failure or communication error. This study considers extending the lifetime of dynamic WSNs; specifically, some sensors may fail or recover during the lifetime. In addition, we propose two genetic algorithms (GAs) to deal with this dynamic optimization problem. A series of simulations was conducted to examine the performance of the proposed algorithms. The simulation results validate the effectiveness of the GAs on extending the lifetime under dynamic network environment.