With the proposal of carbon neutrality goals, the necessity of reducing carbon in the aviation industry has become increasingly prominent. The advanced aero propulsion technology of adaptive cycle engines poses a new challenge to the traditional engine, which has received widespread attention and high expectations from people. Adaptive cycle engines can change the engine's thermal cycle through adjusting variable geometry schedules to improve engine efficiency, reduce fuel consumption, and increase aircraft cruise time under different missions. In this paper, the optimization variables, constraints, and optimization goals are proposed, and the mathematical performance optimization models of the adaptive cycle engine and the mixed flow turbofan engine are established. Compared with the traditional engines, the control laws of each variable geometry modulation are analyzed in terms of performance matching mechanism, and the regulation necessity of all the variable geometries is discussed. The optimal throttling characteristics lines of the adaptive cycle engine in different bypass modes are calculated by the particle swarm optimization method. The advantageous thrust ranges of the adaptive cycle engine in different operating modes are derived, and the design principles of split ratios is given according to the optimization resultsr.