Data availability: No data was used for the research described in the article. The primary objective of the current study is to demonstrate the multi-objective, ecological optimization of an irreversible Stirling cycle-based cryogenic refrigerator. The novelty of the work lies in the ecological optimization of the system, where irreversibilities are considered during the study and the thermal reservoirs have finite energy. The heat source and heat sink exchange energy with the working fluid and respective thermodynamic processes are carried out. The aim is to maximize the ecological objective function and the ecological coefficient of performance, and the effect of design variables on the objective function is investigated. The heat sink capacitance rate, temperature ratio, heat source, and sink capacitance rates, and effectiveness of the hot and cold side heat exchangers are regarded as the design variables. A heat transfer search algorithm is used to optimize the objective functions, and multiple optimal solutions are presented using the Pareto optimal curve. The multi-criteria decision technique TOPSIS is employed to select the ideal solution. For an ideal point selected through TOPSIS, the system works at an optimum ECF and ECOP of 787 W and 5.9, respectively. The ECOP of the system for the current study is 1.81 times and 4.03 times higher than the existing literature. However, the maximum ECF of 1797 W and maximum COP of 17.2 can be obtained for the given constraints of design variables.