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This paper proposes a modification of Differential Evolution (DE) schemes. During the offspring generation, a local search is applied, with a certain probability to the scale factor in order to generate an offspring with high performance. In a memetic fashion, the main idea in this paper is that the application of a different perspective in the search of a DE can assist the evolutionary framework and prevent the undesired effect of stagnation which DE is subject to. Two local search algorithms have been tested for this purpose and an application to the individual with the best performance has been proposed. The resulting algorithms seem to significantly enhance the performance of a standard DE scheme over a broad set of test problems. Numerical results show that the modified algorithm is very efficient with respect to a standard DE in terms of final solution detected, convergence speed and robustness.