## 1 Introduction  
Due to the large area of oceans (i.e., occupying nearly 71% of Earth's surface), many nations have proposed their respective marine development strategies, which intensively requires underwater exploration for oceans. Unlike other typical wired and wireless networks [1; 2; 3; 4; 5; 6], underwater wireless sensor networks, adopting diverse underwater wireless communication technologies (e.g., underwater wireless acoustic communication), are considered essential in realizing underwater monitor and exploration, such as auxiliary navigation, ecological observation, resource development, and ship detection, in the underwater circumstances [7; 8].However, because of the significant limitations of underwater acoustic systems in bandwidth and data-rate, optical waves [9] were introduced into underwater wireless communication, also known as underwater wireless optical communication (UWOC) [10; 11; 12; 13; 14], to provide low-delay and high-speed underwater data delivery. In addition, UWOC has the advantages of high confidentiality and strong anti-interference ability, although the characteristics of optical waves limit their transmission range. Bycombining the characteristics of acoustic and optical waves, hybrid acoustic-optical communication is considered another solution to underwater wireless communication [15; 16; 17]. In all the above underwater wireless communication technologies that can be employed to construct underwater wireless sensor networks (UWSNs), efficient routing algorithms are highly desirable. As the energy supply of sensor nodes is always restricted as they can hardly be replaced or charged, especially in the underwater environment, energy consumption is always an important concern in designing routing algorithms for UWSNs. Thus, energy efficiency becomes one of the most momentous indices to evaluate their performance [18]. As data transmission consumes most of the energy at each sensor node [16], reducing the transmission power or times can effectively help reduce energy consumption. The clustered routing technique has been employed as a promising candidate technology to save energy consumption and prolong the lifetime of wireless sensor networks (WSNs) [19; 20]. By dividing the network sensor nodes into several clusters, the nodes of each cluster gather data to the cluster-head, which helps these nodes minimize their transmission power due to their proximity to the cluster-head, and thus reduces the energy consumption with the prolonged network life of the network. In addition, the cluster-head also helps avoid redundant data transmission by removing duplicate data and transmitting it to the base station. The selection of cluster-heads in traditional sensor networks is sorted into two types: centralized and distributed selection approaches. The former approaches employ the base station for cluster-head selection, while the latter are self-organized. Distributed approaches include low-energy adaptive clustering hierarchy (LEACH) [19], hybrid energy-saving distributed clustering (HEED) [20], and distributed underwater clustering (DUC) approaches [21].In addition, the machine learning technique was also employed to select cluster-heads according to specified criteria [15]. All these techniques have extensively been employed in WSNs and the Internet of Things. Recently, much research attention has been focused on designing energy-efficient clustering algorithms for underwater wireless communication (UWC). In [22], [PERSON] et al. proposed an algorithm to designate the node with the highest remaining energy in a cluster as the cluster-head for UWC. In such an algorithm, non-head nodes entered sleep mode after sending data to the designated cluster-head, when the cluster-head aggregated and forwarded the received data to autonomous underwater vehicles (AUVs). In this way, the energy consumed by non-head nodes may be balanced. However, there was no specific clustering method in the approach, and its performance was affected by the AUVs' located site. In [23], [PERSON] et al.