Hybrid Stages Particle Swarm Optimization Learning Fuzzy Modeling Systems Design

An innovative hybrid stages particle swarm optimization (HSPSO) learning method, contains fuzzy c-mean (FCM) clustering, particle swarm optimization (PSO) and recursive least-squares, is developed to generate evolutional fuzzy modeling systems to approach three different nonlinear functions. In spite of the adaptive ability of PSO algorithm, its training result is not desirable for the reason of incomplete learning cycles. To actually approximate the desired output of the nonlinear function, the input-output training data is first clustered by FCM algorithm, and then some favorable features of training data will be got as initial population of the PSO. Finally, both recursive leastsquares and PSO are utilized to quickly regulate adjustable parameters to construct desired fuzzy modeling systems. After the procedure of the FCM, small initial swarms of PSO are not got by random process but direct selected from training patterns. Therefore, the proposed HSPSO-based fuzzy modeling system with small numbers of fuzzy rules and necessary initial population sizes is enough to approach high accuracy within a short training time. Simulation results compared with the standard PSO and other popular methods demonstrate the efficiency of the proposed fuzzy model systems.