In this research work, a connectionist investigation of irreversible Stirling heat pump cycles that includes both internal and external irreversibilities together finite heat capacities of external reservoirs was carried out. Finite temperature difference between the external fluids and the working fluids through the heat sink and heat source causes an external irreversibility. On the other hand, regenerative heat loss and entropy generation through the cycle are the main source of the internal irreversibilities generation. Three objective functions including the heating load (RH) and coefficient of performance (COP) have been considered simultaneously maximized, on the other hand at the same time the input power of the Stirling heat pump is minimized. To assess this idea, Multi-objective optimization approach be founded on NSGA-II method has been utilized which following variables have been considered as decision variables such as 1 – the effectiveness of the hot-side heat exchanger, 2 – the performance of the cold-side heat exchanger, 3 – the rate of heat capacitance through the heat sink, temperature ratio ( T h T c ), 4 – rate of the heat capacitance through the heat source and 5-temperature of cold side. By applying addressed multi-objective optimization approach, Pareto optimal frontier determined and utilizing different decision-making techniques that includes the LINMAP, \TOPSIS\ and fuzzy Bellman–Zadeh approaches help us to figure out a final optimal solution.