## 1 Introduction
proposed a clustering vector-based forwarding algorithm (CVBF), which divided the network into multiple clusters, and each cluster transmitted data according to the vector (VBF) mechanism. However, in this strategy, the energy consumed by the boundary nodes of the cluster was much higher than that of other nodes. In addition, energy holes might exist in this algorithm. In [24], [PERSON] et al. proposed a three-dimensional geographic adaptive fidelity (BAGF) algorithm for the cluster-head (CH) under the background of an underwater environment to reduce the generation of energy holes. The BAGF algorithm selected the CH node according to its remaining energy. In [25], the authors proposed a fuzzy-based clustering strategy for the underwater acoustic sensor network (UWA-SN). Such a strategy inputted the remaining energy, distance between sensors and sinks, node density, and traffic load, together with link quality, into fuzzy logic units for cluster-head selection. In [26], [PERSON] et al. designed an improved clustering algorithm based on the particle swarm optimization algorithm, which can reduce network energy consumption and prolong network lifetime. In [27], [PERSON] et al. proposed a clustering mechanism based on the soft defined network, which selected CH nodes according to the energy threshold information broadcast between underwater nodes, and then connected un-CH nodes with CH nodes with the strongest signal strength. In [28], the authors introduced a Q-learning-based algorithm to calculate the reward function (to generate the highest reward) and selected the best multi-hop path. Such a reward was determined by the remaining energy of nodes in the Q-learning function and the depth difference between nodes. However, the proposed routing algorithm based on Q-Learning was not designed for the network topology based on clustering. In [29], a new UWSN routing protocol was proposed to deal with malicious attacks and improve the reliability of the network. In such a protocol, a multi-receiver network architecture and the cluster technology were adopted. In addition, the gateway identified and verified the cluster-header to ensure that all nodes in the cluster were valid. Such approach can provide a high data transmission rate and reduce energy consumption. In [30], a new hybrid clustering approach based on the fuzzy c-means technique was proposed, which adopted clustering technology to enhance the power utilization and optimize the network life-cycle. In [21], another cluster-based energy-efficient routing (CBE2R) approach was proposed. The messenger node was regarded as the cluster-head in the CBE2R routing approach and collected data from the anchor node through the relay node. The mobility of the messenger node was manipulated to optimize the network lifetime, as well as the consumed energy. In [31], the authors introduced a new protocol, named the distance and energy constrained K-means clustering scheme (DEKCS), for cluster-head selection. The potential cluster-head was selected according to the position of the potential head in the cluster. Such an algorithm dynamically updated the remaining energy threshold set for potential cluster-heads to ensure that the network completely ran out of energy before disconnecting. However, they did not consider the sparse area of sensor deployment, and the remaining energy had little influence on the selection of cluster-head. In DEKCS, the AUV was deployed on the water surface to receive and forward data. However, for underwater sensor-clustered networks, AUVs can be used to collect data from the network to reduce the transmission energy required to reach the remote base station [32; 33]. In this way, data collection via AUVs can significantly improve the lifetime of UWSNs [34]. This technique has also been used in the offshore energy industry [35].