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 region approximately equals to a random weighted mean of the best positions found by an individual and its neighbors. This phenomenon is observed and verified from the trajectory profiles. The feasibility and capability of PPSO and SPPSO are tested on several high dimensional benchmark functions. They are also verified by applied to economic power dispatch problems with various kinds of cost functions as well as different constraints. Experimental results demonstrate that, for most of the problems, PPSO and SPPSO indeed can obtain better solutions than PSO.