## 6 Proposed Approach
### Multi-Objective Area Coverage Optimization Based on IAPSO  
Let there are \(n\) directional sensor nodes randomly deployed in the monitoring area, and the position of them are fixed. To improve coverage quality, the improved adaptive particle swarm optimization (IAPSO) algorithm is utilized to improve coverage ratio and reduce redundancy ratio by solving a multi-objective area coverage optimization model. In each iteration, the position and velocity update using Equations (18) and (19). The pseudo code of the proposed multi-objective area coverage optimization algorithm based on IAPSO (IAPSO-MOACO) is shown in Algorithm 3. ```
1:\(\omega_{\max}\), \(t\), \(\omega_{\max}\), \(t\), \(\omega_{\min}\), \(t\), \(\omega_{\max}\), \(t\)


```
1:Sensor nodes group: \(s=\left\{s_{1},s_{2},...,s_{n}\right\}\) Predefined swarm size: \(num\) Number of dimensions of particles: \(D_{1}=n\) Largest number of iterations: _maxnumber_ Output: Coverage ratio and redundancy ratio: _CoverageRatio, RedundancyRatio_
```
```
1:Initialize particle \(P_{1i},\forall i,j,1\leq i\leq num,1\leq j\leq D_{1}=n\), \(X_{1i,j}\left(0\right)=\left(x_{1i,j}\left(0\right),y_{1i,j}\left(0\right)\right)\)
2:for\(i=1\) to numdo
3: (1) Calculate \(Fitness1\left(P_{1i}\right)\), Using Equation (12)
4: (2) \(P_{1 besti}=P_{1i}\)
5:endfor
6:\(G_{1 best}=\left\{P_{1 besti}|Fitness1\left(P_{1 besti}\right)=\min\left(Fitness \left(P_{1 besti}\right),\forall i,1\leq i\leq num\right)\right\}\)
7:for\(t=1\) to maxnumberdo
8:for\(i=1\) to numdo
9: (1) Update velocity and position of \(P_{1i}\) using Equations (18) and (19)
10: (2) Calculate \(Fitness1\left(P_{1i}\right)\), update \(P_{1 besti}\) and \(G_{1 besti}\)
11: (3) Calculate the coverage ratio and redundancy ratio using Equations (10) and (11)
12:endfor
13:endfor
```

**Algorithm 3**Multi-objective area coverage optimization algorithm based on IAPSO

### Cluster Head Selection Optimization Based on IAPSO

To achieve energy consumption balance, the improved adaptive particle swarm optimization (IAPSO) algorithm is utilized to select optimal cluster head group by solving cluster head selection optimization model. In each iteration, the position and velocity update using Equations (18) and (19). The pseudo code of the proposed cluster head selection optimization algorithm based on IAPSO (IAPSO-CHSO) is shown in Algorithm 4. ```
1:Input: Sensor nodes group: \(s=\left\{s_{1},s_{2},...,s_{n}\right\}\) Predefined swarm size: \(num\) Number of dimensions of particles: \(D_{2}=k\) Largest number of iterations: \(m_{2}=k\)
2:Output: Cluster head group: \(CH=\left\{CH_{1},CH_{2},...,CH_{k}\right\}\)
3:Initialize particle \(P_{2i},\forall i,j,1\leq i\leq num,1\leq j\leq D_{2}=k\), \(X_{2i,j}\left(0\right)=\left(x_{2i,j}\left(0\right),y_{2i,j}\left(0\right)\right)\)
4:for\(i=1\) to numdo
5: (1) Calculate \(Fitness2\left(P_{2i}\right)\), Using Equation (15)
6: (2) \(P_{2 besti}=P_{2i}\)
7:endfor
8:\(G_{2 best}=\left\{P_{2 besti}|Fitness2\left(P_{2 besti}\right)=\min\left(Fitness2 \left(P_{2 besti}\right),\forall i,1\leq i\leq num\right)\right\}\)
9:for\(t=1\) to maxnumberdo
10:for\(i=1\) to numdo
11: (1) Update velocity and position of \(P_{2i}\) using Equations (18) and (19)
12: (2) Calculate \(Fitness2\left(P_{2i}\right)\), update \(P_{2 besti}\) and \(G_{2 besti}\)
13: (3) Output the optimal cluster heads group \(G_{2 besti}\)
14:endfor
```

**Algorithm 4**Cluster head selection optimization algorithm based on IAPSO

Algorithm 4 shows the process of cluster head selection optimization by iteration. Firstly, randomly deployed sensor nodes group, predefined swarm size, number of dimensions of particles, and largestnumber of iterations are initialized. Then the fitness function values of cluster head selection optimization are calculated by using Equation (15), and the personal best and global best are derived. With the particle constantly search for the better personal best, the fitness function values gradually tend to be best. Finally, cluster head group are derived.