In this study, the optimal performance of a regenerative closed Brayton cycle is sought through power maximization. Optimization is performed on the output power as the objective function using genetic algorithm. In order to take into account the time and the size constraints in current problem, the dimensionless mass-flow parameter is used. The influence of the unavoidable exergy destruction due to finite time constraint is taken into account by developing the definition of heat exergy. Finally, the improved definitions are proposed for heat exergy, and the second law efficiency. Moreover, the new definitions will be compared with the conventional ones. For example, at a specified dimensionless mass-flow parameter, exergy overestimation in conventional definition, causes about 31% lower estimation of the second law efficiency. These results could be expected to be utilized in future solar thermal Brayton cycle assessment and optimization. (C) 2016 Elsevier Ltd. All rights reserved.