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In this work, we present genetic algorithm based approach for the design of asymmetric Bragg mirrors for the microcavity organic light emitting diodes (OLEDs) applications. The phase shift of the Bragg mirror is calculated using the matrix formulation for light propagation through a thin film multilayer. The objective function to be minimized is the wavelength shift in Ag/Alq3/TPD/ITO/Bragg mirror/glass device, where ITO is indium tin oxide, AIq3 is tris (8-hydroxyquinoline) aluminum, and TPD is N,N'-disphenyl-N,N'-bis(3-methylphenyl)-1,1'-disphenyl-4,4'-diamine, which are commonly used emitting and hole transport materials. We have considered TiO2/SiO2 and Si3N4/SiO2 Bragg mirrors, where thickness of each layer in the mirror is determined by minimizing the emission wavelength shift using a genetic algorithm. Simulation results show that the use of asymmetric Bragg mirrors may enable reduction of the emission wavelength shift in organic microcavity devices.