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In the present study, a detailed thermodynamic model for an internal-reforming solid oxide fuel cell-gas turbine (SOFC-GT) hybrid system integrated with a Rankine (steam) cycle is developed, and exergetic, economic and environmental analyses have been carried out on the plant. Considering the exergetic efficiency and the total cost rate of the system as conflicting objectives, a multi-objective optimization of the system is conducted to determine the optimal design point of the plant. A set of optimal solutions (Pareto front) is achieved, each of which is a trade-off between the chosen objectives. Finally, TOPSIS (Technique for Order Preference by Similarity to an Ideal Solution) decision-making method is used to choose the final optimal design parameters. The results demonstrate that the final optimal design of the proposed plant leads to an exergetic efficiency of 65.11% and total cost rate of 0.13745 €/s. Furthermore, the optimization results reveal that the integration of the Rankine cycle with the SOFC-GT system has led to an 8.84% improvement in the total exergetic efficiency of the plant, producing additional 8439.2 MWh of electricity and avoiding ~ 5,900 metric tons of carbon dioxide emissions annually.