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A computational approach based on an innovative stochastic algorithm, namely, the particle swarm optimizer (PSO), is proposed for the solution of the inverse-scattering problem arising in microwave-imaging applications. The original inverse-scattering problem is reformulated in a global nonlinear optimization one by defining a suitable cost function, which is minimized through a customized PSO. In such a framework, this paper is aimed at assessing the effectiveness of the proposed approach in locating, shaping, and reconstructing the dielectric parameters of unknown two-dimensional scatterers. Such an analysis is carried out by comparing the performance of the PSO-based approach with other state-of-the-art methods (deterministic, as well as stochastic) in terms of retrieval accuracy, as well as from a computational point-of-view. Moreover, an integrated strategy (based on the combination of the PSO and the iterative multiscaling method) is proposed and analyzed to fully exploit complementary advantages of nonlinear optimization techniques and multiresolution approaches. Selected numerical experiments concerning dielectric scatterers different in shape, dimension, and dielectric profile, are performed starting from synthetic, as well as experimental inverse-scattering data.