In the case of particle swarm optimization, this paper mainly analyzes and discusses the mathematical model and the analysis on searching for the global optimum region. Firstly, the global optimum region $Theta$ is defined and calculated in the convergence step and the divergence step. Furthermore, the rate $mu$ of locating into the global optimum region is mathematically related to the number of particles, the number of generations, the fitness landscape, the ratio between exploration ability and exploitation ability, etc. Simulation results on Schaffer f6 function can help to understand the obtained results. Finally, those corresponding results and several remarks in the paper are helpful for the tradeoff between exploration ability and exploitation ability, together with the suitable searching strategy of particle swarm optimization algorithm.
