This research presents the multi-disciplinary modeling and multi-objective optimization of a low-bypass heavy turbofan engine equipped with a mixer and afterburner. The engine was parametrically analyzed at the design point using exergy analysis to assess the efficiency of its various components. The afterburner was identified as the most inefficient component, responsible for 52.5% of the engine's total exergy destruction, primarily due to high-temperature chemical reactions. The combustion chamber followed as the second-highest source of exergy destruction. The emissions of nitrogen oxides (NOx) from the engine at the design point amounted to 7.88 grams per kilogram of fuel. For optimization, the NSGA-II algorithm was employed, running a population of 10,000 over approximately 500 generations. The optimization considered four objective functions and ten decision variables. The results showed significant improvements: specific fuel consumption reduced by 15.99%, NOx emissions by 59.11%, specific thrust increased by 3.44%, and total exergy destruction decreased by 23.66%.