The gas turbine cycle either as an individual power production cycle or as a part of yet another cycle, is one of the most common industrials till now which, has been ever evaluated and analyzed. In the present research, this cycle has been modeled individually along with a pre-heater and a compressor at two stages with the objective to maximize the exergic efficiency and in the meantime decreasing the costs and environmental pollution. In addition, the isentropic turbine efficiency, the isentropic compressor efficiency, the ratio of the total pressure of the cycle, and the percentage of extra air has been defined as the design variables. Two objective functions are evaluated to be optimized by the genetic algorithm using the Pareto fitness approach as the determining comparison function. Finally, the exergo-economic coefficient of the related components and the amount of their exergy destruction and cost, at the optimum point, has been compared.