Abstract: The loss of population diversity is an important reason which leads to the premature convergence of the PSO algorithm Therefore, the stability of the PSO algorithm based on the linear time-invariant discrete system was analyzed theoretically and the possible reasons of the lack of the population diversity were discussed in this paper. Based on the stability of the algorithm, an improved PSO algorithm was presented in which the inertia weight factor value is got randourly within a certain range and the leaning factor value is a constant. In the algorithm the population diversity can be maintained by the character that the particle speed has certain probability. The simulation experiments of three constraint optimization problems show that the algorithm has great probability to jump out of local extremum,and avoids the precocious premature convergence effectively.

Key words: PSO algorithm, Linear timcinvariant discrete systems, Stability analysis, Premature convergence, Population diversity