## 4 Proposed Method
### Coverage Hole Repair Based on Mobile Node Redeployment
#### 4.2.2 Calculate the Number of Mobile Sensors Required
Coverage rate, redundancy rate, coverage efficiency, and moving distance are important evaluation indicators for the coverage enhancement process. The performance of the proposed algorithm in these four indicators is compared with VB-IVFA [29], VF-IALO [27], and MEP-PSO [33] algorithms. This study used a directed sensing model, while the VB-IVFA and VF-IALO algorithms used an omnidirectional sensing model, so direct comparison cannot be made. We modified the VB-IVFA and VF-IALO algorithms using a method from reference [12] to make them applicable to directed sensor networks. The simulation parameters of each algorithm are shown in Table 1. \begin{table}
\begin{tabular}{c c} \hline \hline  & 100 m \(\times\) 100 m \\ Region of Interest (ROI) & 200 m \(\times\) 200 m \\  & 300 m \(\times\) 300 m \\ \hline Number of stationary sensors (\(n_{s}\)) & [50, 500] \\ Number of mobile sensors (\(n_{m}\)) & [50, 500] \\ Sensing angles (\(\alpha\)) & [\(\pi/3,\pi\)] \\ Sensing radius (\(R_{s}\)) & 10 m \\ Communication radius (\(R_{c}\)) & 20 m \\ Distance threshold of virtual force & 12.47 m \\ \hline \multirow{2}{*}{VB-IVFA} & Maximum number of & 60 \\  & Maximum single step size & 0.5 m/iter \\ \hline \multirow{3}{*}{VF-IALO} & Maximum number of & 50 \\  & iterations & 30 \\ \hline \multirow{3}{*}{MEP-PSO} & Maximum number of & 50 \\  & iterations & 30 \\ \cline{1-1}  & Maximum number of & 50 \\ \cline{1-1}  & iterations & 50 \\ \cline{1-1}  & Maximum single step size & 0.5 m/iter \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Simulation parameters. The maximum number of iterations (\(T_{\max}\)), maximum step size (\(MaxStep\)), and population size (\(P\)) are key parameters of the proposed algorithm, which determine the position and moving distance of the sensor. We referred to the methods in references [27; 29] and set \(MaxStep\) to 0.5 m/iter, \(P\) to 30. The setting of the maximum number of iterations is very important. If \(T_{\max}\) is too large, it will slow down the running speed, and if it is too small, it will not be able to search for the optimal solution. In this section, we experimentally verify the impact of different \(T_{\max}\) values on coverage rate (COVR). As shown in Table 2, as \(T_{\max}\) increases, COVR is optimized, but when \(T_{\max}\) exceeds 50, the optimization effect actually decreases. According to the experimental results, the algorithm performs best when \(T_{\max}\) is 50. Therefore, we set the maximum number of iterations to 50. Figure 5 shows a visual example of executing the proposed method. In this simulation experiment, stationary and mobile sensors were randomly deployed in an ROI of size 200 m \(\times\) 200 m. The gray sector in Figure 5 represents the stationary sensor, while the blue sector represents the moving sensor. The green curve represents the MEP that was searched for. Figure 5a shows the initial state of the sensor. Figure 5b shows the result of adjusting the sensing direction. The result of one iteration of the algorithm is shown in Figure 5c. The final result after the iteration is shown in Figure 5d. \begin{table}
\begin{tabular}{c c c c c c c} \hline  & \(T_{\max}\) = 10 & \(T_{\max}\) = 30 & \(T_{\max}\) = 50 & \(T_{\max}\) = 70 & \(T_{\max}\) = 90 & \(T_{\max}\) = 100 \\ \hline \multirow{3}{*}{COVR} & ROI1 & 95.39\% & 95.47\% & 95.56\% & 95.51\% & 95.43\% & 95.36\% \\  & ROI2 & 94.96\% & 95.67\% & 95.85\% & 95.79\% & 95.75\% & 95.70\% \\  & ROI3 & 95.03\% & 95.15\% & 95.23\% & 95.12\% & 95.05\% & 94.91\% \\ \hline \end{tabular}
\end{table} 
Table 2: The impact of \(T_{\max}\) on coverage rate. Figure 5: Visualization of the proposed method. (**a**) Initial status. (**b**) Result of adjusting the sensing direction algorithm. (**c**) The result of executing an iteration. (**d**) Final result. ### Comparison of Coverage Rate

Coverage is an important performance indicator for measuring the effectiveness of coverage enhancement. To verify the performance of the proposed method in terms of coverage, we designed three sets of simulation experiments.