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Information Technology Journal
Year: 2013  |  Volume: 12  |  Issue: 8  |  Page No.: 1480 - 1490

Convergence and Spectral Radius Analysis and Parameter Selection for the Particle Swarm Optimization Algorithm Based on the Stochastic Process

Long-Hua Ma, Ming Xu, Meng Shao and Zhe-Ming Lu    

Abstract: Randomness and parameter selection in the Particle Swarm Optimization (PSO) algorithm had great influence on its performance. This study presented a formal convergence and spectral radius analysis of the standard PSO algorithm model, where some of the parameters were stochastic. Based on the analysis of the relationship of {ω, c1, c2}, a sufficient condition was given to guarantee that the PSO algorithm was mean-square convergent, using the stochastic process theory. Then, the mean spectral radius was constructed. According to the relationship between the spectral radius and the convergent speed, it was shown that, a small spectral radius lead to a faster convergent speed than a big one. By optimizing the mean spectral radius of the PSO algorithm in the mean-square convergent region, a minimum spectral radius and corresponding parameter selection guidelines were derived to guarantee that the PSO algorithm was mean-square convergent and had a fast convergent speed in the stochastic sense. Finally, one parameter selection {c1 = c2 = 2, ω = 0.4222} was proposed. with the parameter, the study gave examples whose performance on benchmark functions were superior to previously published results.

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