Most of multi-objective particle swarm optimization algorithms (MOPSO) require non-dominated sorting of the population. It will consume a large proportion of time in the whole optimization process. To achieve real-time multi-objective optimization, this paper proposes a set of fast non-dominated sorting algorithm for two-objective and three-objective and many-objective optimization problems, respectively. The sorting algorithms utilize the transitivity of comparison and elaborate data structure to reduce needless comparison computations. Time complexity analysis of the sorting algorithms proves their efficiency. Experimental analysis and comparison study also show that MOPSO based fast non-dominated sorting performs better than the original MOPSO in running efficiency.