## 2 Related Work  
In UACNs, underwater routing protocols can select appropriate paths for data transmission between underwater nodes by considering the characteristics of the underwater acoustic channel and the network topology [18]. Routing protocols are primarily classified into two categories, non-cross-layer routing and cross-layer routing which depends on the involvement of parameters from other layers of the network stack [19]. These parameters include node buffer states, receiver SNR, transmission power, and transmission rates. Traditional non-cross-layer routing implements specific standards and rules only within network layers, with no interaction between layers. One classic example is the Vector-Based Forwarding (VBF) routing protocol, which relies on three-dimensional coordinate information for data transmission [20]. VBF uses source-destination vectors as axes to directionally forward packets within a limited-radius communication pipe, in contrast to the flooding approach. However, in a network with sparsely distributed nodes, the forwarding node may not be able to find the next hop node within the communication range of the pipe. To solve this problem, researchers have also proposed two improved routing protocols based on VBF: the HHVBF (Hop-by-Hop VBF) routing protocol [21] and VBVA (Vector-Based Void Avoidance) routing protocol [22]. HHVBF employs a hop-by-hop forwarding strategy that allows each node to maintain a virtual routing pipeline pointing to the destination node. VBVA combines vector shifting and backpressure mechanisms to avoid convex and concave voids in the network. QELAR [23] employs Q-learning for the first time in distributed routing protocols in underwater sensor networks. It integrates the residual energy of each node and the average residual energy of neighboring nodes into the design of the reward function to select an optimally energy-efficient transmission path. Experiments show that the lifetime of QELAR is on average 20% longer than that of VBF. However, the design of the protocol focuses only on the energy of the nodes and does not consider other factors that may affect the routing. The objective of cross-layer routing protocols is to enhance the overall performance of routing protocols through the implementation of effective information-sharing mechanisms while maintaining the hierarchical structure of the network stack [24]. GEDAR [25] is an opportunistic routing protocol that employs the concept of clustering, which focuses on determining the next hop forwarding node by calculating the priority of the derived cluster. The priority calculation incorporates both the distance between nodes and the packet error rate. The sending node then forwards the packet to the cluster of nodes with the highest priority. However, the protocol does not fully consider the congestion state of the nodes during packet forwarding, which may result in higher end-to-end delay and energy consumption. In [15], a congestion avoidance routing protocol, RCAR, is proposed. The reward function takes into account the congestion level and the residual energy of the nodes, allowing for the avoidance of congested regions during packet forwarding. Furthermore, RCAR introduces an MAC layer-based handshake mechanism for updating information, which ensures that the optimal transmission path is selected. Although RCAR is a cross-layer routing protocol, it primarily concentrates on the design of the network layer and data link layer, with minimal consideration of how certain factors in the physical layer impact the protocol's performance. MOR [26] is a cross-layer routing protocol proposed by [PERSON] et al. The protocol considers four key performance indicators, energy consumption, end-to-end delay, link quality, and link congestion, and uses the non-dominated sorting genetic algorithm II (NSGA-II) to find the optimal routing path. The effectiveness of MOR in reducing energy consumption, decreasing end-to-end delay, and improving packet transmission rate is verified by experiments.