Fuel cells are chemical energy converted to electric energy, which is today a new technology in energy production. Among the existing fuel cells, solid fuel oxide cells have a high potential for use in synthetic and combined production systems due to their high temperature (700–1000°C). The solid oxide fuel cell (SOFC) output acts as a high-temperature source, which can be used for heat engines such as the Stirling engine as a high-temperature heat source. A hybrid system including solid oxide fuel cell and Stirling engine and reverse osmosis desalinating is a cogeneration plant. This system includes two parts for power generation; the first part is power generated in the SOFC, and the second part is that with use of heat rejection of solid oxide fuel cell to generate power in the Stirling engine. Also, due to the water critical situation in the world and the need for freshwater, it is very common to use desalination systems. In this study, important goals such as power density and exergy destruction, and exergy efficiency, have been investigated. In general, the performance of the hybrid system has been investigated. Firstly, a thermodynamic analysis for all components of the system and then multi-objective optimization performed for several objective functions include exergy destruction density, exergy efficiency, fuel cell power and freshwater production rate. The present optimization is performed for two overall purposes; the first purpose is to improve fuel cell output power, exergy efficiency and exergy destruction density, and the second purpose is to improve the exergy efficiency, the amount of freshwater production and exergy destruction density. In this optimization, three robust decision-making methods TOPSIS, LINMAP and FUZZY are used. Two scenarios are presented; the first scenario is covering power, exergy efficiency and exergy destruction density. The output power and exergy efficiency, and exergy destruction density, have optimum values in the TOPSIS method’s results. The values are 939.393 (kW), 0.838 and 1139.85 (w/m2) respectively. In the second scenario that includes the freshwater production rate, the exergy destruction density and exergy efficiency, three objective functions are at their peak in the FUZZY results, which are 5.697 (kg/s), 7561.192 (w/m2) and 0.7421 respectively.
