## 4 Proposed Method
### Coverage Hole Repair Based on Mobile Node Redeployment
#### 4.2.1 Repair Path Search Method Based on MEP-ISSA  
According to the previous analysis, the MEP is the area with the worst coverage performance in the ROI. When repairing coverage holes, we prioritize selecting holes on the repair path to achieve maximum coverage performance improvement. Therefore, the MEP can be used as a repair path and the improved sparrow search algorithm (ISSA) can be used to search for this path. The sparrow search algorithm (SSA) [34] is a swarm intelligence method for learning sparrow foraging and anti-predation biological behaviors. The SSA has the characteristics of low algorithm complexity and strong robustness, making it highly suitable for solving optimization problems. There are three types of sparrows in the population: explorers, followers, and observers [35]. Explorers are leaders in foraging, possessing high energy reserves and providing followers with areas and directions for foraging. Followers always follow explorers with higher energy. Observers are randomly selected from explorers and followers, and evacuate to a safe area upon discovering danger. The steps of the SSA algorithm are as follows:  
1. Initialize the population and related parameters, and calculate the fitness value of the initial population. 2. Update the explorer position as shown in Formula (23): \[x_{ij}^{t+1}=\left\{ \begin{array}{l}x_{ij}^{t}\cdot\exp\left(\frac{-i}{\pi t} \right),R<ST\\ x_{ij}^{t}+Q,R\geq ST\end{array} \right.\] (24) where \(t\) and \(T\) represent the current iteration and the maximum number of iterations, respectively. \(x_{ij}^{t}\) represents the position of the sparrow at the \(t^{th}\) iteration. \(\alpha\) and \(Q\) are two random numbers. \(R\) is the warning value and \(ST\) is the safety threshold. 3. Update the follower position as shown in Formula (24): \[x_{ij}^{t+1}=\left\{ \begin{array}{l}Q\cdot\exp\left(\frac{x_{w}^{t}-x_{ij}^{ t}}{i^{2}}\right),i<n/2\\ x_{P}^{t+1}+\left|x_{ij}^{t}-x_{P}^{t+1}\right|\cdot A^{+}\cdot L,i\leq n/2 \end{array} \right.\] (25) where \(x_{P}^{t}\) represents the location of the optimal explorer. \(x_{w}^{t}\) represents the worst individual in the \(t^{th}\) iteration. \(A^{+}\) and \(L\) are two \(1\times d\) matrices. 4. Update the position of the sparrow that is aware of the danger, as shown in Formula (25): \[x_{ij}^{t+1}=\left\{ \begin{array}{l}x_{b}^{t}+\beta\cdot\left|x_{ij}^{t}-x_ {b}^{t}\right|,f_{i}>f_{g}\\ x_{ij}^{t}+K\left(\frac{\left|x_{ij}^{t}-x_{w}^{t}\right|}{(f_{i}-f_{w})+ \varepsilon}\right),f_{i}=f_{g}\end{array} \right.\] (26) where \(K\), \(\beta\), and \(\varepsilon\) are random numbers. \(x_{b}^{t}\) represents the worst individual in the \(t^{th}\) iteration. \(f_{i}\) is the fitness value of the current individual. \(f_{g}\) and \(f_{w}\) are the current maximum and minimum fitness values, respectively. 5. Check whether the stop condition is met. If yes, output the optimal sparrow position. Otherwise, return to Step 2. The SSA has certain advantages in solving optimization problems, but there are still limitations that most swarm intelligence algorithms have, for example, local optima and algorithm search speed problems. We made the following improvements to address these issues. 1. Population update mechanism  
Being trapped in local optima seriously affects the speed and accuracy of the SSA in solving optimization problems. The imbalance of population proportion is an important reason for local optima. Most followers follow the explorer with the highest energy to update their positions. Therefore, if an explorer is always in the local optimum position, it will cause the entire population to be unable to find the global optimum position. To solve this problem, we design update strategies for explorers and followers to enhance the algorithm's ability to escape local optima, thereby improving the speed and accuracy of the algorithm. 2. Cauchy mutation and reverse learning  
We combine Cauchy mutation with reverse learning methods to improve the problems of local optima.