This study represents the results of the analysis and optimization of an integrated system for cogenerating electricity and freshwater. This setup consists of a Solid Oxide Fuel cell (SOFC) for producing electricity. Unburned fuel of the SOFC is burned in the afterburner to increase the temperature of the SOFC's outlet gasses and operate a Gas turbine (GT) to produce additional power and operate the air compressor. At the bottom of this cycle, a combined setup of a Multi-Effect Desalination (MED) and Reverse Osmosis (RO) is considered to produce freshwater from the unused heat capacity of the GT's exhaust gasses. Also, a Stirling engine is used in the fuel supply line to increase the fuel's temperature. Using LNG and the Stirling engine will replace the fuel compressor with a pump which increases the system performance and eliminates the need for the expansion valve. To study the system performance a mathematical model is developed in Engineering Equation Solver (EES) program. Then, the system's simulated data from the EES has been sent to MATLAB to promote the best operating condition based on the optimization criteria. An energetic, exergetic, economic, and environmental analysis has been performed and a Non-dominated Sorting Genetic Algorithm (NSGA-II) is used to achieve the goal. The two-objective optimization is performed to maximize the exergetic efficiency of the proposed system while minimizing the system's total cost of production. This cost is a weighted distribution of the Levelized Cost of Electricity (LCOE) and Levelized Cost of freshwater (LCOW). The results showed that the exergetic and energetic efficiencies of the system can reach 73.5% and 69.06% at the optimum point. The total electricity production of the system is 99 MW. The production cost is 11.71 Cents/kWh, of which 1.04 Cents/kWh is emission-related and environmental taxes. The freshwater production rate is 42.44 kg/s which costs 4.38 USD/m³.