Parameter selection, analysis and evaluation of an improved particle swarm optimizer with leadership

This paper introduces an improved particle swarm optimizer with leadership (PSO-L), inspired by the effect of individual experience to group in nature. Firstly, the stability analysis of an individual particle is undertaken, using Lyapunov theory. The obtained results offer a more stringent convergence condition on parameter selection in comparison with the existing results. Next, based on the convergence condition, the method PSO-L is proposed. In the method, to ensure that the swarm converges to the global optimum solution rapidly, a particle is selected as the leader of the swarm during the exploration search. And the parameter values of the leader particle in iteration are selected according to the obtained convergence condition. Then, the effect of the convergence condition to single particle’s trajectory is demonstrated. And five benchmark functions are used to verify the feasibility of the improved method, compared with two famous PSO methods. Finally, an application example is given to show the improved performance of the method.