In real life we are often confronted with dynamic optimization problems whose optima change over time. These problems challenge traditional optimization methods as well as conventional evolutionary optimization algorithms. In this paper, we propose an evolutionary model that combines the differential evolution algorithm with cellular automata to address dynamic optimization problems. In the proposed model, called CellularDE, a cellular automaton partitions the search space into cells. Individuals in each cell, which implicitly create a subpopulation, are evolved by the differential evolution algorithm to find the local optimum in the cell neighborhood. Experimental results on the moving peaks benchmark show that CellularDE outperforms DynDE, cellular PSO, FMSO, and mQSO in most tested dynamic environments.