This paper presents a simultaneous optimization study of two outputs performance of a previously proposed combined Brayton and inverse Brayton cycles. It has been carried out by varying the upper cycle pressure ratio, the expansion pressure of the bottom cycle and using variable, above atmospheric, bottom cycle inlet pressure. Multi-objective genetic algorithms are used for Pareto approach optimization of the cycle outputs. The two important conflicting thermodynamic objectives that have been considered in this work are net specific work (w(s)) and thermal efficiency (eta(th)). It is shown that some interesting, features among optimal objective functions and decision variables involved in the Baryton and inverse Brayton cycles can be discovered consequently.