Abstract A solar-powered high temperature differential Stirling engine has been considered for optimization with multiple criteria. A mathematical model based on the finite-time thermodynamics has been developed so that the output power and thermal efficiency and the rate of entropy generation of the solar Stirling system with finite rate of heat transfer, regenerative heat loss, conductive thermal bridging loss and finite regeneration process time are obtained. Furthermore, imperfect performance of the dish collector and convective/radiative heat transfer mechanisms at the hot end as well as the convective heat transfer at the heat sink of the engine are considered in the developed model. Three objective functions including the output power and overall thermal efficiency have been considered simultaneously for maximization and the rate of entropy generation of the Stirling engine are minimized at the same time. Multi-objective evolutionary algorithms (MOEAs) based on NSGA-II algorithm has been employed while the Effectiveness’s of regenerator, the Effectiveness’s of the low temperature heat exchanger, the Effectiveness’s of the high temperature heat exchanger, heat capacitance rate of the heat sink, heat capacitance rate of the heat source, temperatures of the working fluid in the high temperature isothermal process and temperatures of the working fluid in the low temperature isothermal process are considered as decision variables. Pareto optimal frontier has been obtained and a final optimal solution has been selected using various decision-making approaches including the fuzzy Bellman–Zadeh, LINMAP and TOPSIS methods.