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Minimizing energy dissipation and maximizing network lifetime are important issues in the design of applications and protocols for sensor networks. Energy-efficient sensor state planning consists in finding an optimal assignment of states to sensors in order to maximize network lifetime. For example, in area surveillance applications, only an optimal subset of sensors that fully covers the monitored area can be switched on while the other sensors are turned off. In this paper, we address the optimal planning of sensors' states in cluster-based sensor networks. Typically, any sensor can be turned on, turned off, or promoted cluster head, and a different power consumption level is associated with each of these states. We seek an energy-optimal topology that maximizes network lifetime while ensuring simultaneously full area coverage and sensor connectivity to cluster heads, which are constrained to form a spanning tree used as a routing topology. First, we formulate this problem as an Integer Linear Programming model that we prove NP-Complete. Then, we implement a Tabu search heuristic to tackle the exponentially increasing computation time of the exact resolution. Experimental results show that the proposed heuristic provides near-optimal network lifetime values within low computation times, which is, in practice, suitable for large-sized sensor networks.