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Electromagnetic inverse scattering problems arise in several diagnostic applications, in which the objective is retrieving the physical and geometrical properties of the unknown targets under test starting from measured samples of the scattered electric field. Solving such problems is still a challenging task, due to the related ill-posedness and nonlinearity. In order to partially overcome such difficulties, the inverse scattering problem is often recast as a global optimization problem, which can be solved by using stochastic methods. In this paper a new approach, based on the Differential Evolution method and on an iterative multiscaling strategy is proposed. Some results, concerning the imaging of dielectric structures are reported and discussed.