A cogeneration production system of power and freshwater was studied from the perspective of energy, exergy, economic, and environmental (4E). The main components of this system include a Brayton cycle (BC), dual-pressure heat recovery steam generator (HRSG), steam turbine (ST), and multi-effect evaporation with thermal vapor compression (MEE-TVC). The system was optimized with a multi-objective genetic algorithm using MATLAB software and by considering the performance of two objective functions: the total annual cost (TAC) to minimize and the thermal efficiency to maximize. The results showed that, with increasing gas turbine inlet temperature, thermal efficiency, exergy efficiency, and emission of pollutants improved, but the gain output ratio (GOR) decreased. GOR of desalination system, exergy efficiency of combined cycle power plant (CCPP), and emission of pollutants improved by increasing the compressor pressure ratio. In investigating the number of effects in desalination unit, by increasing this parameter the production of freshwater, GOR and exergy efficiency of MEE-TVC was increased. By adding a duct burner to the cogeneration system, the thermal efficiency, the exergy efficiency, and the net power output were reduced by 0.67, 3.9, and 5.91%, respectively. But the freshwater production, GOR, and TAC was improved about 7.97, 9.69, and 1.265%, respectively.