Abstract: The irreversible problems of heat leakage, heat recovery loss and various mechanical friction loss between the cold and heat sources in the dish Stirling system are considered. Firstly, the efficiency, output power and pressure drop of the system are analyzed by finite time thermodynamics. Secondly, an improved fast non dominated sorting genetic algorithm is proposed to improve the multi-objective fast non dominated sorting genetic algorithm by introducing selection operator and elite retention strategy. Finally, the improved algorithm is used to optimize the power voltage drop, efficiency voltage drop and power efficiency voltage drop of the system with two objectives and three objectives respectively, and the distribution of 11 decision variables in the optimization process is analyzed. The final optimal solution is selected from the available solutions of Pareto boundary by TOPSIS decision method. The results show that the Pareto optimal solution obtained by the multi-objective optimization is evenly distributed, and the optimal solution is more practical, and the structural parameters such as the engine speed, the average cycle pressure of the engine, the number of regenerator grids, the piston diameter and so on have high sensitivity, which provides theoretical basis for the improvement of Stirling engine.