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The paper focuses on design and optimization of metallo-dielectric periodic structures with simultaneous electromagnetic band gap (EBG) and artificial magnetic conductor (AMC) behavior in the required frequency band. Three variants of mushroom structures were studied to fulfill the requirements: the two-layer one with simple square metallic patch, the two-layer one with metallic patch of complex shape and the three-layer one with simple square metallic patch at the top and the bottom layer. The structures were tuned using particle swarm optimization (PSO) algorithm implemented in Matlab in connection with CST Microwave Studio (CST MWS) for full-wave dispersion diagram and reflection phase diagram computation. The obtained results were verified by Ansoft's High Frequency Structure Simulator (HFSS).