Behavior Analyzing And Applicative Example Of Particle Swarm Optimization Algorithm

Particle Swarm Optimization (PSO) algorithm is a global optimization algorithm presented in the past decade. PSO is easy to be understood and realized on the computer, so it attracted attention of researchers in different fields and the research regarding its theory and application has gained primary achievements. Since it is a new method, some fundamental behavior is still not clear. In the application area, to combine it with local optimization algorithm, is still waiting for further study. After analyzing the situation of PSO research, this wok devoted on the aspects:1. The background of PSO and the connections and differences between PSO and other methods were analyzed in detail. Moreover, the fundamental recursive equation, procedure and structure, the influence of parameter to PSO efficiency, and topological structure research were reviewed. Based on some simplified models, the track of particle movement was achieved and its convergence was analyzed. All the possible algorithm models in general conditions have been considered, and parameter choice and convergence speed of these different algorithm were investigated.2. Three different improved algorithms were proposed. First is PSO based on chaos search for optimizing system parameter. Optimum System parameter could be attained utilizing ergodicity of chaos which improves efficiency of algorithm. Second is a hybrid algorithm of PSO and Broyden-Fletcher-Goldfarb-Shanno(BFGS), which combines global search with gradient search, and that convergence speed is faster than conventional PSO method. Third, a novel algorithm based on Rotate Surface Transformation(RST) was proposed. PSO is easy to be trapped into local minima in optimizing multimodal function, and RST will help the search to escape from local minima, by transforming local minima to global maximum without changing the values of function where they are lower than local minima. The improved algorithm converges faster and more stable than conventional PSO.3. Research on PSO mechanism was conducted. Fokker -Planck equation and Langevin equation of nonequilibrium thermodynamic were employed to analyze the behavior of particle. Recursive equation of PSO algorithm was reconstructed into a form of Langevin equation after a series of simplification, and thencorresponding Fokker-Planck equation of this system was constructed. From the solution of Fokker -Planck equantion, joint distribution of system evolving with time could be worked out. Finally, through analogizing PSO and multiparticle system, a new swarm algorithm was proposed in which the number of intermediate variables was reduced in comparing with conventional PSO.4. Three practical applications were designed. (1) estimating modal parameter of Markov random field, (2) problem of nonlinear system optimal control, (3) problem of classification of toxicity of amines. Key of the three problems is to change these problems into optimization problem, then they could be solved by PSO. The problem of estimating modal parameter of Markov random field could be converted into multimodal function optimization problem by maximum pseudolikelihood. By discretzing System equation and object functional, optimal control problem is changed into function optimization. Finally, the training of neural network for classification of amines was changed into function optimization problem through fitness function. Finally, the whole research contents were summarized, and further researchdirections were indicated.