## 2 Methodology
### Particle Swarm Optimization Algorithm  
[PERSON] and [PERSON] (2011) have founded the theory of Particle Swarm Optimization (PSO). This method is based on stochastic optimization and the social behavior of bird flock or fish school. Each particle plays an important role in the use of Particle Swarm Optimization method. The particles will associate together after that they look for the best solution or fitness function value. The fitness function value is called as \(P_{best}\). The fitness function value will correspond to the best location (\(L_{best}\)). Especially, a particle takes all of the topological neighbors. In this case, the best value will be a global best value and it is known as \(G_{best}\) (Figure 3) ([PERSON] et al., 2016). Where:  
\(X_{i}^{k}\) is the current position;  
\(X_{i}^{k+1}\) is the modified position;  
\(V_{i}^{k}\) is the current velocity;  
\(V_{i}^{k+1}\) is the modified velocity;  
\(V_{i}^{P_{best}}\) is the velocity of \(P_{best}\); and,  
\(V_{i}^{G_{best}}\) is the velocity of \(G_{best}\). The Particle Swarm Optimization (PSO), which is known as an evolutionary computation algorithm, is different from other one such as Genetic Algorithms (GAs). The search space of PSO algorithm is carried out by a population. The simulation of bird flock or fish school behavior is known as PSO method. The discovery and previous experience of bird flock behavior in the finding food have made an effective evolutionary computation algorithm, like the PSO method. So, _particle_ particle is called as each companion in the population, which is called _swarm_ swarm. Swarm is assumed to 'fly' over the search space in order to find promising regions of the landscape. Each particle is allocated with a random velocity initially and its location is adjusted according to its own previous best (\(P_{best}\)) and the global best (\(G_{best}\)). On the other hand, the velocity change is weighted by random terms with separate random numbers being generated for acceleration toward the two best solutions (\(P_{best}\) and \(G_{best}\)). The procedures of PSO algorithm have been showed in Figure 4.  
Figure 3: The modification of a searching points by Particle Swarm Optimization (PSO) ([PERSON] et al., 2016). Initialization process: Generate a population of particles and allocate a velocity to each particle randomly. * \(\mathcal{O}\) Evaluation process: Update the best locations of particles and calculate the optimization fitness function. * Velocity and location update: Change the location of each particle by means of updating its own velocity as well as the particle will be adjusted dramatically. * The updating process of velocity and location at each particle can be realized through Equations (1) and (2). \[V_{int}^{k+1}=w.V_{im}^{k}+c_{1}.r_{1}.(P_{best,im}^{k}-X_{im}^{k})+c_{2}.r_{2}. (G_{best,im}^{k}-X_{in}^{k}) \tag{1}\]  
\[X_{im}^{k+1}=X_{im}^{k}+V_{im}^{k+1} \tag{2}\]  
Figure 4: Procedures of the Particle Swarm Optimization [24]. where:  
\(i=1\), 2,..., \(n\); and \(m=1\), 2,..., \(d\);  
\(n\) is the number of particles in the group;  
\(d\) is the dimension of the group;  
\(k\) is the number of iterations of the current particle;  
\(w\) is the inertia weight factor;  
\(P_{best}\) is the previous best;  
\(G_{best}\) is the global best;  
\(X\) is the location of the particle;  
\(V\) is the velocity of the particle;  
\(c_{1}\), \(c_{2}\) are the acceleration coefficients; and,  
\(r_{1}\), \(r_{2}\) are the random numbers between 0 and 1. The assumption is a basic definition of Particle Swarm Optimization (PSO). In PSO algorithm, a flock of particles are put into the d-dimensional search space with randomly in order to choose velocities and positions that are known as their best values (\(P_{best}\)) and the position in the d-dimensional space. Furthermore, the velocity of each particle is adjusted according to its own flying experience and the other particle's flying experience.