The main aim of this research article is a parametric demonstration of irreversible Stirling cryogenic refrigerator cycles that includes irreversibilities such as external and internal irreversibilities. In addition, through this study, finite heat capacities of external reservoirs are considered accordingly. To reach the addressed goal of this research, three objective functions that include the input power of the Stirling refrigerator, the coefficient of performance (COP) and cooling load (RL) have been involved in optimization process simultaneously. The first aforementioned objective function has to minimize; the rest objective functions, on the other hand, have to maximize in parallel optimization process. Developed multi objective evolutionary approaches (MOEAs) based on NSGA-II algorithm is implemented throughout this work. Moreover, cold-side’s effectiveness of the heat exchanger, hot-side’s effectiveness of the heat exchanger, heat source’s heat capacitance rate, heat sink’s capacitance rate, temperature ratio T h T c , temperature of cold side are assigned as decision variables for decision making procedure. To gain a robust decision, different decision making approaches that include TOPSIS, \LINMAP\ and fuzzy Bellman–Zadeh are used. Pareto optimal frontier was determined precisely and then three final outputs have been gained by means of the mentioned decision making approaches.