## 3 Materials and Methods
### Particle Swarm Optimization Methods (PSO)  
In 1995, [PERSON] and [PERSON] released the first version of the particle swarm optimization (PSO) technique. PSO techniques are population-based optimization algorithms that guide particle search for universally optimal solutions by simulating interactions between flocks of birds and schools of fish. PSO, an unsupervised algorithm, is used to find more efficient ways to extract features. PSO involves group members interacting with one another. Based on their individual research and the group's collective data, each member modifies the group's course. When using PSO to solve an optimization problem, a swarm of computer parts called particles scour the solution space in search of the best solution [30]. The PSO algorithm starts with a population of random particles (swarms) and then updates generations to look for the best answer. The present position and velocity vectors are connected to each particle. These vectors are the same dimension as the search space in terms of size. The two best values are updated for each particle in every iteration. The best fitness value is found in the swarm, and the other is which stores the fitness value of the greatest fitness solution [31]. However, [PERSON] and his co-authors defined PSO as having the three simple behaviors of separation, alignment, and cohesion (Figure 3a-c, respectively). Separation is the behavior of avoiding the crowded local flock mates, whereas alignment is the behavior of moving in the general direction of the local flock mates. The PSO algorithm's formulas are as follows [32], and cohesion is the behavior of moving toward the median position. \[\text{vid}\;\text{t}+1=\text{vt}\;\text{td}+\;\text{c}\;1.\;\text{rand}-(0,1).( \text{pt}\;\text{td}-\text{xttd})+\;\text{c}\;2.\;\text{rand}\;-(0\,,1).(\text{ ptgd}-\text{xttd}) \tag{2}\]  
\[\text{xid}\;\text{t}+1=\;\text{xtid}+\;\text{vidt}+1 \tag{3}\]  
Note: where, respectively, vt id and xt id represent particle position and velocity, it is the particle index;t which is the iteration number, and d is the dimension of the search space. When flying toward the most ideal individual particle and the ideal particle overall, c1 and c2 stand for the speed that controls the length of the flight. Pi is the highest position that a particle has yet attained. The best position determined by the particle's neighbors is I and pg. I. Rand (0, 1) represents the values at random between 0 and 1. The differences between the population's all-time best (ptgd) and exploration happen when the difference between the position of the previous particle (xtid) and the position of the best particle (ptid) is large. When these two value systems are small, there is exploitation. In addition, at the first step, the population is implemented through the PSO algorithm and then the second step involves determining each particle's fitness values which are updating the global and individual tests, then updating the position and velocity of the particles. Up until the termination, the condition is met, and steps two through four are repeated. The output of the PSO algorithm over iterations is shown in Figure 4. To find the best solution in the first iteration, all particles dispersed (exploration) and also every particle is assessed. The ideal answers are discovered regarding swarm members' neighborhood configuration, and their individual and collective best particles are updated. Convergence would be reached by trying to move all the particles toward the one with the best solution [32]. Figure 4: Over iterations, particle swarm optimization tends toward global optimums. Figure 3: **(a)** A separation behavior in which particles try to avoid coming into contact with one another. **(b)** Alignment. behavior, where particles move themselves with the leader of their local flock while keeping their relative velocities constant. **(c)** Cohesion. behavior, where particles tend to move to where their neighbors in the flock are.