Development of Third Order Particle Swarm Optimization and Verification of its Performance with Various Test 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-dimension 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 of next positions for 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 which Its performance behavior is far different from original with its convergence regions. By setting four appropriate parameters near or out of the convergence region with the proposed PSO algorithm, we test various basic 6 benchmark functions and make comparison between the new third order PSO and in terms 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.