High technology energy systems have generated a lot of interest due to their significant contribution to efficient and environmentally friendly energy production. Among them there are hybrid cycles which usually have higher energy efficiencies and can provide different forms of energy at the same time. The present research poses a question concerning thermodynamic performance of a molten carbonate fuel cell (MCFC)-Braysson heat engine, conducting a multi-objective optimization study, to give a general description of this hybrid cycle. For this purpose, energy efficiency, power density and exergy destruction rate density are considered as the objective functions in conjunction with ecological function density. First, a parametric evaluation is conducted in order to study the effect of the decision variables on the targets separately. These variables include current density of the fuel cell, turbine inlet temperature, effectiveness of the hot side of the heat exchanger which recovers the waste heat of the fuel cell to run the Braysson cycle, and ratio of heat capacity to heat conductance of the cold side of the heat exchanger which rejects the extra low-temperature heat of the Braysson cycle to the environment. Afterwards, due to the great conflict between the objective functions, three case scenarios of triple multi-objective optimization are defined, considering different combinations of the objective functions; and a Pareto front is obtained for each. Multi-objective evolutionary algorithm joined with non-dominated sorting genetic algorithm approach is employed to this aim. In order to ascertain final solutions between Pareto fronts, three fast and robust decision making methods are employed including LINMAP, TOPSIS and Fuzzy. Finally, the relationship between the objective functions is studied. Examining the outcomes of each decision making method in each case scenario raises some interesting points in addition to the fact that any potential improvement in one objective function is always confined to a certain amount of sacrifice in the other ones. The present research clearly demonstrates to what extent these compromises have to be made in each case scenario, based on the results of each decision making method. Furthermore, a sensitivity analysis of the final optimal solutions is carried out to critically examine these parameters in the design process of the MCFC-Braysson hybrid cycle. (C) 2017 Elsevier Ltd. All rights reserved.