Increase in intensive applications with different computational requirements, coupled with the unification of remote and diverse resources thanks to advances in the wide- area network technologies and the low cost of components, have encouraged the development of grid computing. To exploit the promising potentials of geographically distributed resources, effective and efficient mapping algorithms are fundamental. Since the problem of optimally mapping is NP-complete, the development of evolutionary techniques to find near-optimal solutions is welcome. In this paper a distributed system based on Differential Evolution is designed and implemented to face the mapping problem in a grid environment aiming at reducing the degree of use of the grid resources. This system is tested on some different resource allocation scenarios.