Fractional-order particle swarm optimization

By introducing the fractional-order difference into the updating formulas of the velocity and position, fractional-order particle swarm optimization algorithm is proposed. The effects on the convergence rate and accuracy are analyzed, by introducing fractional-orders in the updating formulas for the velocity and position. Moreover, the linear increasing methods to adjust the fractional-orders are proposed. Compared with the standard particle swarm optimization algorithm, the higher convergence rate is achieving to improve the accuracy of the optimal result. Finally, five standard functions are tested, and the results of the numerical experiments illustrate the effectiveness of the fractional-order particle swarm optimization.