Current research on energy consumption of underwater acoustic networks does not include the extra energy consumption from retransmissions for data sending failure. In this paper the optimal routing paths that minimize the total energy consumption for a given target signal-to-noise ratio ( SNR) for reliable multi-hop underwater acoustic networks were considered. A reliable network energy model was established, and an empirical closed-form expression of the optimal frequency-distance relationship was derived through the method of curve fitting to simplify the energy model. Then the energy efficient routing paths for both variable transmission power( VTP)and fixed transmission power (FTP)schemes were investigated. It is shown that the total energy consumption of the network is minimized only if all the hop distances are equal for a linear multi-hop network. In the case of equispaced relays,the analytical results on the optimal number of hops and the optimal distance that minimize the total energy consumption were also provided. Simulation results verified the correctness of this theory.%目前对水声网络能耗的研究并未考虑因数据发送失败而引起的数据重发导致的额外的能耗.研究在给定接收信噪比条件下可靠通信的多跳水声网络能量最小路径问题.首先建立了可靠通信的网络能量模型,通过曲线拟合的方法得到最优频率-距离关系的近似表达,以简化能耗模型；然后分析了可变发送功率和固定发送功率两种模式下的能量最小路径,从理论上证明了直线等距网络的总能耗最小,并给出了直线等距网络最优跳数和最优距离的求解方法.仿真结果验证了该理论的正确性.
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