The paper proposes a new approach to minimize the number of relays while maximizing the lifetime of underwater acoustic sensor networks (UASNs). This involves formulating the relay node placement (RNP) problem as a multi-objective optimization problem and employing the multi-objective lexico-graphic method (MOLM) to solve it. To achieve the optimal solution, the MOLM consists of two steps. First, the problem of lifetime maximization is tackled to find RNP solutions. This transforms the RNP into a non-convex optimization problem which is then converted into a convex programming equivalent. The proposed method has the same computational complexity as previous relay-node adjustment (RA) and difference convex algorithm (DCA) methods. The second step introduces a novel relay node selection to reach the optimal number of relays. Simulation results demonstrate that it has superior network lifetime and efficiency compared to RA and DCA.

翻译：论文提出了一种新方法，旨在最小化中继节点数量的同时最大化水下声学传感器网络（UASNs）的寿命。该方法将中继节点部署（RNP）问题建模为多目标优化问题，并采用多目标词典序方法（MOLM）进行求解。为实现最优解，MOLM包含两个步骤：首先，通过解决寿命最大化问题来寻找RNP方案，该步骤将RNP转化为非凸优化问题，进而转换为等价的凸规划问题。所提方法计算复杂度与现有中继节点调整（RA）算法和差分凸函数算法（DCA）相同。第二步引入了一种新颖的中继节点选择策略，以确定最优中继数量。仿真结果表明，与RA和DCA相比，该方法在网络寿命和效率方面具有显著优势。