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Phaseless data are used to evaluate the application of an electromagnetic inverse-scattering-based procedure for the detection of cylindrical inhomogeneities, which are schematized as multilayer infinite dielectric cylinders with elliptic cross sections. The electromagnetic inverse problem is recast as a global optimization problem and iteratively solved by an efficient memetic algorithm, which combines deterministic and stochastic concepts. Moreover, a recursive analytical procedure is used for the forward-scattering computation. The possibility of localizing and reconstructing the scatterers by using phaseless input data, which would greatly simplify the design of the imaging apparatus, is evaluated both with reference to synthetically produced data and by means of experimental data obtained by a microwave tomograph.