## 3 Standard Particle Swarm Optimization  
Standard article swarm optimization (SPSO) is inspired by the behavior of bird flocking and fish schooling to find a place with enough food [28]. Algorithm 1 describes the process of SPSO. This algorithm starts by randomly generating the populations based on the swarm size parameter. The population consists of \(N\) particles in which each particle \(i\) acts as the representation of potential solutions to the given problem. A particle is represented by the vector \(x_{i}\) in the decision space. Each particle has its position (\(x\)) and velocity (\(v\)). Position represents the flying direction, and velocity relates to the step of the particle. The cooperation between particles achieves optimization. The particle closest to the objective is called the success particle. The success particle will influence the behavior of other particles. They will adjust their positions (\(x_{i}\)) toward the global optimum. Two factors affect the position of the particle. First, the best position visited by itself called personal best (\(Pbest_{i}\)), and second, the best position visited by the particles overall, known as the global best (\(Gbest_{i}\)). After the population is successfully created, for the following iterations, each particle will apply the following operations:First, update the velocity to define the amount of change applied to the particle as formulated in Equation (1). \[v_{i+1}=\omega v_{i}+C_{1}R_{1}*(\textit{Pbest}_{i}-x_{i})+C_{2}R_{2}*(\textit{ Gbest}_{i}-x_{i}) \tag{1}\]  
where \(v_{i+1}\) is a new velocity, and \(v_{i}\) is current or initialized velocities. Initialized velocity means that \(v_{i}\) is assigned as a random number between 0 and 1 alongside the generation of the population. \(C_{1}\) and \(C_{2}\) represent the constant variables that are well known as cognitive learning factors and social learning factors. \(R_{1}\) and \(R_{2}\) are random variables in the range of [0,1]. \(\textit{Pbest}_{i}\) is the best position visited by particle \(i\). \(\textit{Gbest}_{i}\) is the best position visited by overall particle. \(x_{i}\) is the current position of particle, whereas \(\omega\) is an inertia weight (see Equation (2)), where \(\omega_{t}\) is inertia weight of current iteration \(t\), \(\omega_{max}\) is maximum inertia value equal to 0.9, \(\omega_{min}\) is minimum inertia value equal to 0.4, and \(T_{max}\) is the maximum iteration. Inertia weight controls the momentum of the particle by weighting the contribution of the previous velocity, controlling the extent to which the previous flight direction will influence the new velocity. Inertia weight is critical in ensuring convergent behavior as formulated in Equation (2). \[\omega_{t}=\omega_{max}+\frac{(\omega_{max}-\omega_{min})*t}{T_{max}} \tag{2}\]  
Second, the position of the particle is updated as notated in Equation (3), where \(x_{i+1}\) is a new position of the particle, \(x_{i}\) is the last position, and \(v_{i}\) is the current velocity of the particle. \[x_{i+1}=x_{i}+v_{i} \tag{3}\]  
Each particle will update their personal best solution if \(x_{i}<\textit{Pbest}_{i}\) then \(\textit{Pbest}_{i}=x_{i}\) and the global best will be updated if \(x_{i}<\textit{Gbest}_{i}\), then \(\textit{Gbest}_{i}=x_{i}\).