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Owing to the energy demands and global warming issue, employing more effective power cycles has become a responsibility. This paper presents a thermodynamical study of an irreversible Brayton cycle with the aim of optimizing the performance of the Brayton cycle. Moreover, four different schemes in the process of multi-objective optimization were suggested, and the outcomes of each scheme are assessed separately. The power output, the concepts of entropy generation, the energy, the exergy output, and the exergy efficiencies for the irreversible Brayton cycle are considered in the analysis. In the first scheme, in order to maximize the exergy output, the ecological function and the ecological coefficient of performance, a multi-objective optimization algorithm (MOEA) is used. In the second scheme, three objective functions including the exergetic performance criteria, the ecological coefficient of performance, and the ecological function are maximized at the same time by employing MOEA. In the third scenario, in order to maximize the exergy output, the exergetic performance criteria and the ecological coefficient of performance, a MOEA is performed. In the last scheme, three objective functions containing the exergetic performance criteria, the ecological coefficient of performance, and the exergy-based ecological function are maximized at the same time by employing multi-objective optimization algorithms. All the strategies are implemented via multi-objective evolutionary algorithms based on the NSGAII method. Finally, to govern the final outcome in each scheme, three well-known decision makers were employed.