## 1 Introduction  
The development of the maritime Internet of Things (IoT) facilitates various maritime activities of humans more frequently and greatly promotes the development of the maritime economy. The surging demand for wireless communication puts great pressure on maritime wireless communication systems for the next generation of wireless communication technologies (such as beyond Fifth-Generation (5G) and Six-Generation (6G)) [1, 2]. However, maritime wireless communication technology is relatively behind compared with that for land [3]. For example, the maritime wireless communication system lacks the construction conditions of communication facilities (such as base stations), and the maritime spectrum resources are scarce [4]. Besides, complex sea surface changes (such as wave motion and evaporation duct) make the maritime wireless communication environment unstable [5]. Hence, it is of great significance to research the maritime IoT to realize flexible, efficient, and reliable transmission. In the maritime IoT system, buoys embedded with a variety of sensors are usually deployed on the sea surface to monitor the maritime environment. However, these buoys are generally out of the service coverage of the offshore base stations (OBSs). Although monitoring data can be transmitted through the multi-hop network formed by buoys and ships, the connectivity of the network will be seriously damaged when nodes in the network fail [6]. Satellite communication could mitigate the issue of network failure, but it has fatal drawbacks in terms of high delay, low-link reliability, and high cost [7]. The unmanned-aerial-vehicle (UAV)-assisted maritime communication system is regarded as a promising solution to deal with the high delay and low reliability. The UAV as the aerial mobile base station has the following advantages in assisting maritime wireless communication. On the one hand, the high maneuverability of the UAV makes it easier to establish line-of-sight (LoS) communication link between UAVs and buoys and also allows them to flexibly approach buoys to enhance the communication links [8]. Hence, the UAV can better adapt to the complex maritime wireless communication environment and is very suitable for emergency communication scenarios. On the other hand, the UAV usually has the advantages of a small size, low cost, and easy control [9]. The application of UAVs can reduce the risk of manual operation in some dangerous maritime environments. The above advantages also make UAVs have high concealment and be widely used in maritime military activities. However, the size of the batteries embedded in UAVs and buoys is limited. It will affect the efficiency of UAV's mission execution, if UAVs frequently return to the charging area. Moreover, frequent battery replacement will increase the maintenance cost of buoys, and in fact, it difficult to achieve due to the bad condition of the sea environment. Hence, the performance of UAV-assisted maritime wireless communication is severely limited by the energy consumption of UAVs and buoys [10]. The energy consumption disadvantage could be compensated by multi-UAV cooperative data transmission. The multi-UAV communication system has a wider communication range and a shorter transmission distance, which can reduce the communication delay and improve the energy efficiency [11]. In the multi-UAV communication system, UAVs need to collect the data cached in buoys and offload the data to the OBS. In this process, the UAV will be far away from the OBS, which may make it take a long time to offload the data. Hence, it is important to design the trajectories of multiple UAVs to ensure the data transmission requirement under the condition of limited energy and shorten the mission completion time of data collection and data offloading. Recently, there has been extensive research work focused on the multi-UAV-assisted wireless communication scenarios. [PERSON] et al.