In this paper, thermodynamic and thermoeconomic analysis as well as genetic algorithm optimization of two combined cycles, a gas turbine-organic Rankine cycle (GT-ORC) and a gas turbine-Kalina cycle (GT-KAL) are carried out. The novelty of this study is that the cycles are adapted to an actual solid waste power plant to generate additional power from the exhaust gas. Thus, the power generation capacity of the actual power plant can be raised by using the combined cycle. Due to this reason, besides the thermodynamic analysis of the cycles, thermoeconomic analyses and optimizations are also very important in order to improve the actual system capacity. The net power output of GT-ORC and GT-KAL are found to be 1.51 MW and 1.59 MW, respectively. The results obtained are seen to be reasonable when compared to the net power output of the power plant (5.66 MW). Another originality of this study is that the thermoeconomic results are improved by utilizing a multi-objective optimization method namely non-dominated sorting genetic algorithm method (NSGA-II). Thus, the two objectives, total power output and the total cost rate, at the design stage of the cycles are optimized and enhanced. Due to the optimization results, it is found that the net power output of the GT-ORC and GT-KAL are increased by 11.34% and 0.99%, respectively, while the total cost rates are decreased by 18.59% and 1.31%, respectively. GTORC with the net power output of 1.70 MW is seen to be more efficient as compared to GT-KAL which produces a net power output of 1.61 MW. However, the total and the capital cost rates of GT-ORC are found to be higher than those of GT-KAL.