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The Differential Evolution (DE) algorithm was initially proposed for continuous numerical optimization, but it has been applied with success in many combinatorial optimization problems, particularly permutation-based integer combinatorial problems. In this paper, a new and general approach for combinatorial optimization is proposed using the Differential Evolution algorithm. The proposed approach aims at preserving its interesting search mechanism for discrete domains, by defining the difference between two candidate solutions as a differential list of movements in the search space. Thus, a more meaningful and general differential mutation operator for the context of combinatorial optimization problems can be produced. We discuss three alternatives for using the differential list of movements within the differential mutation operation. We present results on instances of the Traveling Salesman Problem (TSP) and the N-Queen Problem (NQP) to illustrate the adequacy of the proposed approach for combinatorial optimization.