Abstract: In order to improve the precision of solution, to avoid the premature convergence, various perturbation (mutation or jump) optimization approaches have been developed to realize the perturbation of the pBest or gBest, so as to enhance the search capability of the high-dimensional space and improve the performance of the PSO algorithm. To analyze the trajectory behavior of particles (search engine of PSO algorithm) under perturbation optimization approaches in a multi-dimensional space, a theoretic analysis of particles is presented by series and the convergence of particle trajectory under perturbation optimization approaches is proved. Lastly, an empirical analysis of stochastic particles is also presented based on the project scheduling problem in a multi-dimensional space, and the experimental results are provided to support the conclusions drawn from the theoretical ?ndings.