Abstract: The current work is applied optimization process with multi objective on the solar-powered Stirling engine with high temperature differential. On the basis of finite –time thermodynamic, new mathematical approach was evolved. Furthermore, thermal efficiency of the solar Stirling system with rate of finite heat transfer, regenerative heat loss, the output power, finite regeneration process time and conductive thermal bridging loss are specified. The power output and thermal efficiency and entransy loss rate are specified at Maximum condition for a dish-Stirling system and entropy generation's rate in the engine Minimized by carrying out thermodynamic analysis and NSGAǁ approach. Three well known decision making methods are carried out to indicate optimum values of outputs obtained with optimization process. Finally, with the aim of error analysis the error of the aforementioned results are determined.