  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.
