Particle Swarm Optimizer with Integral Controller

The evolutionary equations of PSO are second-order discrete time linear stochastic system. It can be regarded as a control plant, and introducing a controller to regulate the dynamic evolutionary behaviors of PSO. In the paper, z-transformation is used to evolutionary equations, and the system structure diagram is obtained. Then, an integral controller is introduced to PSO to give an integral-PSO algorithm. Meanwhile, the integral-PSO is analyzed through the support set of sample space of particles and linear system theory for the convergence conditions and diversity of particles. Finally, the simulation results for the test functions are given to show that the integral-PSO is more efficiency than the original PSO