Internal combustion engines (ICEs) have harmful effects on the environment in terms of emissions. According to present emission regulations, reducing NOx emissions came into prominence. One of the techniques of reducing NOx emissions is implementation of Miller Cycle to the engine. A comparative performance analysis and optimization based on the non-dimensional power output and thermal efficiency criteria have been performed for an irreversible Dual-Miller Cycle. The effect of the design parameters such as cycle compression ratio, cut-off ratio and Miller cycle ratio of the cycle have also been investigated on the basis of having the internal irreversibility with assuming the working fluid is an ideal gas with constant specific heat. Performance analysis has been also extended to the Otto-Miller and Diesel-Miller cycles which may be considered as two special cases of the Dual-Miller cycle. The analysis and optimization study carried out in this work are hoped to provide guidelines for optimal design in terms of power output and thermal efficiency for internal combustion engines.