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Multi-objective optimization of a hypersonic airbreathing engine (scramjet technology) was carried out with the aim of maximizing thrust and minimizing drag while satisfying a series of design constraints, such as avoiding unstart (blockage of supersonic flow within the combustion chamber) by ensuring that the pressure ratio across the shock waves remains below the adverse pressure gradient given by the Korkegi limit, geometry correction to achieve shock on-lip condition, and temperature and pressure requirements at the inlet exit. Using the relations presented in the literature, pressure and viscous drag are estimated analytically. The analytical approach is verified against computational fluid dynamics data from Ansys Fluent to solve two-dimensional compressible Reynolds-averaged Navier–Stokes flow equations, with transition shear stress transport as the turbulence closure model. Comparing the total drag and the flow properties at the combustion chamber entrance shows the model's feasibility for the optimization approach. Three different approaches were conducted to formulate the multi-objective function to determine the one that can find the highest number of geometries satisfying the Korkegi limit with the highest net thrust. The best approach was the multi-objective function formulated with the uninstalled thrust, total pressure recovery, and pressure drag, concentrating the search in the region with greater uninstalled thrust and lower drag and nearly doubling the value of net thrust compared to the first formulation, which uses the uninstalled thrust, pressure drag, and viscous drag. [ABSTRACT FROM AUTHOR]