4E analysis is used on a Brayton–Rankine combined cycle power plant (CCPP) with a dual pressure heat recovery steam generation (HRSG) system. A multi-objective genetic-based evolutionary optimization has been used to estimate the most optimal exergy efficiency status, exergy cost reduction, carbon emission reduction, and NOx emission reduction. For the validation of the data, the simulation results are compared with the plant’s data. This study investigates the effect of every decisive parameter on the objective performance parameters of the CCPP. The primary estimated results are the emission rates, efficiencies, and the exergoeconomic cost of the system. At the optimum operational state, the exergy efficiency may increase by 10%, while the total emissions may decrease by 14.6%. The conventional technical measures’ effectiveness to improve the combined cycle power plant’s energy performance is applied to the simulated case study. Results have shown that the main source of the exergy destruction in this system is the HRSG and the combustion chamber, and also the overall performance of the plant shows great sensitivity to the ambient air temperature. This fact has shown that climate change and global warming are effective in thermal power plants’ performance. Therefore, the effect of the climate change on the ambient air temperature impact on the power plant and the 4E performance of the simulated combined cycle power plant is also studied. The results show that, due to the global warming effect, the exergy efficiency of the CCPP unit is decreased by over 0.2% in the last two decades, which can be generalized to all thermal electricity generation units throughout the world based on the mean global temperature rise in the last decades.