Abstract: The particle swarm optimization (PSO) may be trapped in local optima and fail to converge to global optima, especially for multimodal and high-dimensional problems. To handle this problem, a stepwise learning strategy and a stepwise evaluation strategy are presented. The former makes each particle learn from only one particle's historical best information in each update progress in order to search in a potential area, and simplifies particles' update rules to easily control their convergence behaviors. The latter enables each particle to be evaluated in dimension-by-dimension order so as to step steadily toward the destination position, and settles non-separable problems by means of detecting relationships between dimensions. Application of the new PSO on several benchmark optimization problems shows a marked improvement in performance over six other recent variants of the PSO.