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This paper proposes a new evolutionary approach to multiobjective optimization problems - the dynamic multiobjective evolutionary algorithm (DMOEA). In DMOEA, a novel cell-based rank and density estimation strategy is proposed to efficiently compute dominance and diversity information when the population size varies dynamically. In addition, a population growing and declining strategies are designed to determine if an individual will survive or be eliminated based on some qualitative indicators. Meanwhile, an objective space compression strategy is devised to continuously refine the quality of the resulting Pareto front. By examining the selected performance metrics on three recently designed benchmark functions, DMOEA is found to be competitive with or even superior to five state-of-the-art MOEAs in terms of maintaining the diversity of the individuals along the tradeoff surface, tending to extend the Pareto front to new areas, and finding a well-approximated Pareto optimal front. Moreover, DMOEA is evaluated by using different parameter settings on the chosen test functions to verify its robustness of converging to an optimal population size, if it exists. Simulations show that DMOEA has the potential of autonomously determining the optimal population size, which is found insensitive to the initial population size chosen.