## 4 Proposed Method
### Sensing Direction Adjustment Method Based on IPSO  
Particle swarm optimization (PSO) is a global optimization algorithm with few parameters, single rules, and sensitive and fast convergence ability. In most cases, PSO has a faster convergence speed than evolutionary algorithms. Due to the excellent ability of PSO to search for approximate optimal solutions, this paper adopts PSO to solve the optimal sensing direction of sensors. The speed and position update rules are the core of PSO, and each particle is a potential solution. Individual and global optimal values are searched for in the search space by iteratively updating speed and location.  
Inertia weight is an essential parameter in the formula of velocity and position. In traditional PSO, the inertia weight is a fixed constant, which means the local search ability of the algorithm is weak and it is easy to fall into a local optimum. To solve this problem, we use a nonlinear dynamic adjustment method with random factors to improve the inertia weight. The improved inertia weight is a dynamically adjusted value that can avoid getting stuck in local optima.  
In addition, to improve the global search capability of PSO, we introduce the Cauchy mutation operator. Cauchy mutation is an adaptive mutation optimization method that can increase the population diversity of PSO through mutation operations, thereby improving the global search ability.  
In a randomly deployed network, the control center (base station) collects the location information of all nodes. We can adjust the sensing direction of nodes by running the IPSO algorithm in the base station before starting the sensing task. We take the effective coverage area and redundant area of the sensor as the optimization objectives, then use an improved multi-objective particle swarm algorithm to solve the objective function.  
\[f_{5} =\max(A_{E}(s_{i})) \tag{21}\] \[f_{6} =\min(A_{O}(s_{i}))\] (22) \[A_{E}(s_{i}) =A(s_{i})-A_{O}(s_{i}) \tag{23}\]  
We will obtain a solution with the maximum effective coverage area from the search space as the set of sensing directions for sensors in the network. Stationary sensors rotate  
Figure 1: Basic process of the proposed method.  
and adjust their sensing direction based on information from the control center. After a rotation operation, the stationary sensor sends the current position information to the base station. If the expected goal is still not achieved after completing the subsequent steps, the IPSO algorithm will be rerun based on the current position to find a new optimal set of sensing directions. The pseudocode of the sensing direction adjustment method is shown in Algorithm 1.  
```
Input:\(S^{\prime},\ \beta_{0},\ N_{\mathit{iwr}},\ P\) Output: optimal subset \(S_{opt},\beta_{t}\)
1:for\(s_{i}\in S^{\prime}\)do
2: Initial direction as the initial population position \(\beta_{0}\)
3: Initialize the population P
4: Calculate fitness value
5:\(\mathit{g.best}\gets 0,\mathit{p.best}\gets 0\)
6: Generate \(\mathit{g.best}\)
7:While failure to meet termination conditions do
8:for each individual do
9: Calculate fitness value \(\mathit{f.current}\)
10:if\(\mathit{f.current}>\mathit{p.best}\)then
11:\(\mathit{p.best}\gets\mathit{f.current}\)
12:if\(\mathit{p.best}>\mathit{g.best}\)then
13:\(\mathit{g.best}\gets\mathit{p.current}\)
14: Update individual(velocity and position)
15: Get the best work direction \(\beta_{t}\leftarrow\mathit{g.best}\)
16: Output the set of optimal working directions \(S_{opt}\)
```  
**Algorithm 1** Sensing direction adjustment method