In recent years, CO2 released by fossil fuel power plants, through the process of capture and storage, has been tried to be separated from other combustion products and directed to the underground to prevent it from entering the environment. While various methods exist for this purpose, they are typically expensive and consume a significant amount of power. In this research, a proposed solution to study and optimize the capture and storage process involves a combined cycle power plant with two gas turbines and four steam turbines, equipped with a carbon dioxide capture and storage system using the chemical looping combustion (CLC) method. The storage of released CO2 is facilitated by four compressors operating in four stages. To begin, the developed model is validated in terms of energy, exergy, and economic factors. Subsequently, the system is optimized using an NSGA genetic algorithm, with two objective functions: exergy efficiency and total cost rate. Sensitivity analysis is conducted to define the decision variables. The results demonstrate that the optimization process has led to a 4.37 % increase in the system’s power output, from 379.75 MW to 396.37 MW. Moreover, the optimization has improved both the exergy and energy efficiency values, with these parameters rising from 51.97 % and 54.23 % to 54.24 % and 56.61 %, respectively. Furthermore, the total cost rate has slightly decreased from 46,267 to 46,020 $/hr as a result of system optimization.