Data availability: Data will be made available on request. Acknowledgment: The work is done as part of the collaboration between Pandit Deendayal Energy University and the Heat Pipe and Thermal Management Research Group at Brunel University London, UK. The multi-objective optimization study of the combined Brayton and inverse Brayton cycle is carried out with the aim to maximize specific work output and minimize thermal efficiency using an evolutionary heat transfer search optimization algorithm. The design variation considers the top cycle pressure ratio and bottom cycle expansion pressure. From the results of the multi-objective optimization, multiple optimal solutions for the objective functions are presented using a Pareto optimal curve. Further, five optimal points (A) – (E) from the Pareto curve are selected, and a sensitivity analysis on the objective functions is performed. The conflicting nature between the objective functions is observed, and with any attempt to increase the thermal efficiency, the system’s specific work output decreases and vice versa. The proposed system can produce a maximum specific work output of 497 kJ/kg with a thermal efficiency of 44 %. For the system to be operated at a maximum thermal efficiency of 50 %, it can produce specific work output of 464 kJ/kg. Additionally, the effects of the inlet air temperature, the turbine inlet gas temperature, the exhaust gas temperature from the heat exchanger, turbine efficiency, and compressor efficiency on the specific work output and thermal efficiency are studied and presented. The findings of the study should help users to select the operating parameters based on the need as multiple solutions are presented for the system. Finally, the distribution of the design variables during the optimization is identified and presented.