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In this study, a synthesis framework for designing artificial electromagnetic materials with periodic repetitions and desired constitutive parameters is proposed. The framework is based on a homogenized material model and its numerical solution via COMSOL. Material model results are shown to agree well with mixing formulas and existing models in the literature. Design results show that the GA based framework is capable of designing material compositions of a periodically repeated unit cell to achieve desired electromagnetic material properties. An array configuration of the unit cell design was fabricated. Future work comprises material measurements, extension of the framework to 3D structures, and its application to the design of magnetic photonic crystals.