A simple way for parameter selection of standard particle swarm optimization

A simple way is proposed to estimate the non-negative real parameter tuple {?, c1, c2} of standard Particle Swarm Optimization algorithm using control theory. The distribution of complex characteristic roots on the convergence region of particles is studied by means of linear discrete-time system analysis method. It is pointed out that the critical factors affecting the modulus value and the phase angle of the complex characteristic roots are the maximum overshoot and angular frequency of damped oscillation. The way shows that the product of the maximum overshoot and the angular frequency of damped oscillation approximately equaling to 1 is the promising guideline for parameter selection in PSO when the angular frequency in the range of (0.65p, 0.35p). Based on this, widely used benchmark problems are employed in series experiments using a stochastic approximation technique, and the results are well back above deduction.