Abstract: Particle swarm optimizer (PSO), a swarm intelligence based optimization technique, is described by a general formula in terms of iterations in the paper. Based on the general formula, its optimization mechanism is analyzed and the general mathematic description of particle's maximum covering space is deduced according to the current social information and personal experience. Furthermore, the general formula is illustrated as the weighted summation of historical position states, so as to prove that in terms of cumulative iterations, parameters of PSO have an inherent forgetting characteristic in probability, moreover the searching mechanisms of canonical PSO and Barebones particle swarm are almost the same. From the perspective of information propagation, the strategy of PSO is a weighted summation of the historical information, which has the forgetting characteristic in probability. Some important properties of canonical PSO, such as forgetting characteristic, similarity between canonical PSO and BBPS, etc, are explained by the results of the research in this paper.