Algorithm 4: Cluster head selection optimization algorithm based on IAPSO

Input: Sensor nodes group: $s=\left\{s_1,s_2,\dots ,s_n\right\}$

Predefined swarm size: $num$

Number of dimensions of particles: $D_2=k$

Largest number of iterations: maxnumber

Output: Cluster head group: $CH=\left\{C{H}_1,C{H}_2,\dots ,C{H}_k\right\}$

1: Initialize particle $P_{2i},\forall i,j,1\le i\le num,1\le j\le D_2=k$, $X_{2i,j}\left(0\right)=\left(x_{2i,j}\left(0\right),y_{2i,j}\left(0\right)\right)$

2: for $i=1$ $to$ $num$ do

3:       (1) Calculate $Fitness2\left(P_{2i}\right)$, Using Equation (15)

4:       (2) $P_{2besti}=P_{2i}$

5: end for

6: $G_{2best}=\left\{P_{2besti}|Fitness2\left(P_{2besti}\right)=min\left(Fitness2\left(P_{2besti}\right),\forall i,1\le i\le num\right)\right\}$

7: for $t=1$ $to$ $maxnumber$ do

8:       for $i=1$ $to$ $num$ do

9:             (1) Update velocity and position of $P_{2i}$ using Equations (18) and (19)

10:           (2) Calculate $Fitness2\left(P_{2i}\right)$, update $P_{2besti}$ and $G_{2besti}$

11:           (3) Output the optimal cluster heads group $G_{2besti}$

12:      end for

13: end for