Two variants of particle swarm optimization, called personal best PSO(PPSO) and simplified PPSO(SPPSO), are proposed. Empirical studies demonstrate that PPSO usually outperforms PSO both in computation quality and onvergent speed. Moreover, without incurring any new computational and logical operations, PPSO and SPPSO are simple and easy to implement. A first-order difference equation is developed to characterize the behaviors of PPSO and SPPSO. Theoretical analysis depicted that a particle stochastically moves within a region in real space. On each dimension, the center of the...