A new third order particle swarm optimization and applications to test various functions

The particle swarm optimization is one of well known algorithms in the world with its performance and easy implementation. This algorithm is used for finding optimal values or regions of multi-dimensional spaces throughout the interaction of each particle positions and its values. Originally, the PSO has two factors such as position and velocity vectors which are sources for next positions of particles, respectively. However, in order to reach optimal regions quickly, accurately and even closely, we present a new third order particle swarm optimization which has three vectors: i.e. a position vector, a velocity vector and an acceleration vector. From the proposed PSO, we obtain a third order difference equation and we will derive the convergence region for four parameters from the equation. By setting four appropriate parameters near the convergence region with the proposed PSO algorithm, we test 2 benchmark functions with it and make comparison between the new third order PSO and the variant of the original PSO. Results from simulations clearly show that the proposed algorithm has better performance and faster convergence speed rather than the original PSO.