In this paper, a solar energy powered gamma type SE has been optimized using Finite Physical Dimensions Thermodynamics (FPDT) method by multi-objective criteria. Genetic algorithm was used to get the Pareto frontier, and optimum points were obtained using the decision making methods of LINMAP and TOPSIS. The optimization results have been compared with those obtained using the ecological method. It was shown that the multi-objective optimization in this paper has a better balance among the optimizing criteria (maximum mechanical power, maximum thermal efficiency and minimum entropy generation flow). The effects of the hot source temperature and the total thermal conductance of the engine on the Pareto frontier have been also studied. This sensibility study shows that an increase in the hot reservoir temperature can increase the output mechanical power, the thermal efficiency of the engine, but also the entropy generation rate. In addition to this, an increase of the total thermal conductance of the engine can strongly increase the output mechanical power and only slightly increase the thermal efficiency. These results allow us to improve the engine performance after some modifications as geometrical dimensions (diameter, stroke, heat exchange surface, etc.) and physical parameters (temperature, thermal conductivity). (C) 2016 Published by Elsevier Ltd.