In this article, the effect of inlet air temperature on turbofan engine’s performance and optimization of turbofan engine’s performance in take-off conditions with an inlet air cooling system is investigated. The objective functions are parameters that represent the performance of the turbofan engine, are as follows thrust force, Specific fuel consumption (SOx), thermal efficiency, nitrogen oxides emission index coefficient (SOx), and turbine inlet temperature. Overall compressor pressure ratio, fan pressure ratio, and bypass ratio are considered design variables. With inlet air temperature drop, thrust, TSFC, thermal efficiency, inlet air mass flow rate, fuel mass flow rate increase, and the SOx decreases. Values of the performance parameters of the turbofan engine vary based on the optimization with four objective functions and hydrogen fuel to choose the optimal modes, by defining the weight coefficient and using the TOPSIS algorithm that has been selected for two environmental and economic approaches. For both engines with both approaches and using the decision-making method, the highest score and low score for optimization state belong to the SNOx objective function and TSFC objective function, respectively. The thrust force of CFM56 3B2 and GENX 1B70 engines based on optimization with the SNOx has increased by about 19.1% and 12.6%compared to the design.