Abstract: Dynamic multi-objective optimization problems (DMOPs) often involve incommensurable, competing and varying objectives with time, and the number of their optimal solutions is usually infinite. Thus how to find a sufficient number of uniformly distributed and representative Pareto optimal solutions under the condition of the continuously changing time for the decision maker is very important. In this paper, the continuously changing time period of DMOPs is divided into several random subperiods. In each subperiod, the dynamic multi-objective optimization problem is approximated by a static multi-objective optimization problem. At the same time, the static rank variance and the static density variance of the population is defined in each subperiod. Then, by using the static rank variance and the static density variance of the population, the dynamic multi-objective optimization problem with random objective functions is transformed into a bi-objective static optimization problem. A new dynamic multi-objective optimization evolutionary algorithm is proposed based on a new self-check operator which can automatically check out the time variation and its convergence is proved. The simulations are made and the results demonstrate the effectiveness of the proposed algorithm.