Contents I. Introduction
Particle swarm optimizer (PSO) is an evolutionary algorithm, introduced by Kennedy and Eberhart in [1] and [2]. The algorithm derives from the behavior of social animals like bird flocking and fish schooling. The algorithm contains a swarm of particles, which are randomly initialized in an ndimensional search space. Each particle has a velocity vector and a position vector. During the each generation, each particle update its velocity and position by learning from the particle's own best position and the historically best solution of the whole swarm. The two vectors of each particle are updated using the following equations:\begin{align*} V_{i}(t+1)&=\omega \cdot V_{i}(t)+c_{1}\cdot r_{1}(pBest_{i}-X_{i}(t)) {\tag{1}} \\ &\qquad \ +c_{2}\cdot r_{2}\cdot(gBest-X_{i}(t))\\ X_{i}(t+1)&=X_{i}(t)+V_{i}(t+1) {\tag{2}} \end{align*} where pBestiis the i-th particle own historically best position, gBest is the historically best solution of the whole swarm. and are two parameters called learning factors, which keep a delicate balance between pBestiand gBest. and are random numbers uniformly distributed in [0, 1]. is a parameter called the inertia weight.
