Multi-objective optimization results using genetic algorithm are reported for a cogeneration system based on indirect integration of solid oxide fuel cell and gas turbine. In this case, solid oxide fuel cell and gas turbine operate with different working fluids and at different pressures and only heat is transferred between these two systems. A heat recovery unit is placed to provide hot water from solid oxide fuel cell-gas turbine exiting stream. Multi-objective optimization is applied to determine the optimal design condition in which exergy efficiency is maximum and sum of the unit costs of products is minimum. The result demonstrates that final optimal design has an exergy efficiency of 55.11% and sum of the unit costs of products of 170.5 $/GJ, which is a trade-off between thermodynamic and exergoeconomic single-objective optimization cases. It is also revealed that heat recovery unit, combustion chamber and afterburner have the most contribution to the system's exergy destruction. Furthermore, 44.3% of input exergy is destructed in the system components. The overall system exergoeconomic factor is 47.31%. Therefore, it is expected that an increase in the components' capital costs may improve the exergoeconomic performance of the system. Moreover, it is shown that fuel cell current density and gas turbine inlet air flow rate have the highest effect on the trade-off between the defined objective functions. (C) 2016 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.