In a wireless sensor network (WSN), the energy hole problem is a key factor which affects the lifetime of the networks. In a WSN with circular multi-hop deployment (modeled as concentric coronas), sensors in one corona have the same transmission range termed as the transmission range of this corona, and different coronas have different transmission ranges, which compose a list termed as transmission range list. Based on our improved corona model with levels, we propose that a right transmission

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... range of each corona is the decision factor for optimizing network lifetime after nodes deployment. We prove that searching optimal transmission range lists is a multi-objective optimization problem (MOP), which is NP hard. We propose a centralized algorithm and a distributed algorithm to build the transmission range list for different node distributions. The two algorithms can not only reduce the searching complexity but also obtain results approximated to the optimal solution. Furthermore, the simulation results indicate that the network lifetime under our solution approximates to that ensured by the optimal list. Compared with existing algorithms, our solution can make the network lifetime be extended more than two times longer.