Particle Swarm Optimization - Stochastic Trajectory Analysis and Parameter Selection
Ming Yan Jiang, Yadav B.P, S. Y. · 2007
The stochastic process theory is applied to analyze the particle swarm optimization algorithm determined by five-dimensional real-value parameter tuple { , c1, c2, a, b}, considering the randomness thoroughly. Specifically speaking, stochastic convergence analysis is conducted on PSO algorithm when it is in stagnation phase, and the convergent properties of expectation and variance sequence of particle's position are studied. The analysis results determines corresponding parameter ranges, both in formular and graphical form. This result is helpful to understand the mechanism of PSO algorithm and select appropriate parameters to make PSO algorithm more powerful. After the theoretical stochastic convergence analysis of PSO algorithm in stagnation phase, parameter selection guidelines are discussed, and a set of suggested parameters { =0.715, c1=c2=1.7} is given, which is compared against other three sets of parameters which are proposed in literatures. Experimental result shows that the PSO algorithm using our suggested parameters can achieve robust performance, but the time expires before reaching optimal area is longer than PSO algorithm using other suggested parameters.