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A genetically optimized technique that fully automates the potentially laborious allocation of the auxiliary monopoles for the method of auxiliary sources (MAS) is presented for the problem of electromagnetic (EM) scattering by isotropic dielectric cylinders with various cross sections. The proposed technique uses as input information not only the geometry of the scatterer but also the exciting field and the material properties of the cylinders are implicitly taking part in the optimization procedure. The resulting auxiliary surfaces, where the simulating monopoles are situated, are appropriately adapted to the original boundary surface and the MAS modeling is greatly facilitated. In addition, certain considerations are taken into account in order to avoid undesirable numerical dependencies between the fictitious monopoles. Finally, the accuracy of the numerical method combined with overdetermined systems of equations is examined for isotropic cylinders of various geometries and dielectric characteristics.