## 2 Related Work
### Coverage Enhancement Method Based on Mobile Node Redeployment  
There are three main methods for redeploying mobile nodes: the virtual force method, the swarm intelligence method, and the MEP method. The virtual force algorithm (VFA) schedules sensors by simulating the interaction forces (including attraction and repulsion) between sensors, sensors and obstacles, and sensors and boundaries to achieve coverage enhancement. The method based on VFA is the most effective coverage enhancement strategy [23]. [PERSON] et al. [24] improved the virtual force algorithm by introducing geometric relationships to analyze the forces between nodes, greatly enhancing the coverage performance of the network. [PERSON] et al. [25] proposed a virtual force algorithm applied to 3D scenes. This method enhances coverage by scheduling node movements and avoids ineffective node movements through rigorous force analysis. The advantage of the virtual force algorithm and its improvement methods lies in their fast convergence speed. However, it is usually impossible to obtain the optimal distance threshold, resulting in redundant coverage of nodes and difficulty in achieving the best coverage enhancement effect. Swarm intelligence (SI) is another widely used optimization method in WSN coverage enhancement [26]. The method proposed by [PERSON] et al. [27] combines virtual forces with an ant-lion optimization algorithm, which accelerates convergence speed and improves optimization performance. The method they proposed can effectively enhance the coverage of the network. [PERSON] et al. [28] proposed a coverage enhancement method that combines game theory and the biological characteristics of vampire bats. This method transforms the coverage problem into a task allocation problem, which can optimize the coverage range and reduce deployment costs. [PERSON] et al. [29] improved the vampire bat algorithm and combined it with the virtual force algorithm. Their method can achieve coverage enhancement with less moving distance. The SI-based methods perform better in coverage enhancement than the algorithm based on virtual force. However, the SI method ignores moving energy consumption and energy balance. In recent years, MEP methods have been applied to address coverage enhancement problems. Early research on the MEP focused on how to determine the path with the worst network coverage without applying the MEP to coverage optimization [30; 31]. [PERSON] et al. [32] first applied the MEP method for coverage optimization. Their method achieves coverage enhancement by adding sensors on the MEP. [PERSON] et al. [33] used the PSO algorithm to search for the MEP and solve the coverage enhancement problem in DSNs. Both methods above can only schedule one sensor at a time, which is inefficient and prone to new coverage holes, resulting in limited coverage. The existing MEP-based methods have shown good results in improving coverage, but there are still problems with energy consumption, efficiency, and other aspects. As mentioned above, the current coverage enhancement algorithms mainly focus on two aspects: adjusting the sensing direction and redeploying mobile nodes. The method based on adjusting the sensing direction requires high-density sensors to achieve better results. The method based on mobile node redeployment requires a large number of mobile sensors, which will increase deployment costs. Moreover, the current research primarily focuses on optimizing coverage effectiveness, with little consideration given to the impact of mobile energy consumption on the network. Therefore, to solve the above problems, we comprehensively consider coverage optimization and energy balance, deploy stationary and mobile sensors in the network, and enhance coverage by rotating and moving nodes. On this basis, we studied the coverage enhancement problem of the sensing layer of the IoT, which consists of stationary and mobile directional sensors, and proposed a two-stage optimization method.