One of the promising methods to increase exergoeconomic performance and decrease effects of environmental adverse of energy systems is integration of energy systems. Gas turbine power plant is one of the favorable power generation systems because of its acceleration in start-up and low investment cost. However, the thermal efficiency of gas turbine cycle is low because of the significant heat loss due to high-temperature effluent gas exhausted from the stack. Therefore, if this huge heat loss is recovered by another heat engine coupled with gas turbine cycle the total efficiency will increase, considerably. Stirling engine owing to its high efficiency is one of the promising candidates which can be used as a part of the combined system. Hence, an optimization analysis on standalone gas turbine cycle, as well as combined cycle of gas turbine and Stirling engine are considered in this paper to find out the optimal operational point, thermodynamically and economically. Both single-objective and multi-objective genetic algorithm is performed to optimize the overall plant parameters, subjecting three optimization scenarios of maximizing exegetic efficiency, minimizing levelized cost of electricity and exergoeconomic optimization. A comprehensive comparison of gas turbine and Stirling engine combined cycle and standalone gas turbine cycle was performed for these optimization scenarios. Results show a significant improvement in power output and reduction of levelized cost of electricity in combined cycle of gas turbine and Stirling engine. In the optimal point of this hybrid system, levelized cost of electricity reduces by 10.3% and exergetic efficiency improves by 16.1% compared with the optimal point of standalone gas turbine cycle.