Abstarct: In this study, focusing on the Alpha-type Stirling Engine, the variable compression ratio mode is designed. The design variables of the problem are determined according to the geometry of the engine and how to change its structure, and to solve the optimization problem, the PSO and ALO algorithm are used and their results are compared with each other. Matlab software has also been used to write the program of two algorithms. The results of this research consist of two parts, so that initially the only design variables are the displacement of the hinge o in the direction of x and y (the concept of variable Compression ratio) and using the two optimization algorithms mentioned, the optimal output work is obtained. In the second part of the studies of this research, all the geometric parameters of the engine are optimized. The results of this study indicate that the output of the engine is higher than the main engine in the ratio of constant Compression ratio. Thus, the output work in this case increases by approximately 0.06%. It was also observed that the output work optimized by the ALO algorithm is somewhat better than the PSO algorithm. In the end, the results showed that in the case of optimizing all the geometric parameters of the motor, including moving the hinge o in the direction of x and y, the output work is approximately 2.5 times the work of the main motor.