A Computational Fluid Dynamics (CFD) and response surface based multi-objective design optimization were performed for a Rocket Based Combined Cycle (RBCC) engine and the global Pareto optimal front is presented. A two-dimensional rocket ejector system was studied over a matrix of engine design variables. Bypass ratio, ejector compression ratio, and ejector mixer thrust efficiency were used to analyse RBCC internal flow path physics. The CFD simulations of the engine were carried out with CHEM, a general purpose, multidimensional, multi-species, viscous chemistry solver built upon a rule-based specification system. The Mentor ’s Shear Stress Transport (SST) model for turbulence was used. The  combustion physics were solved for finite volume conditions with a Hydrogen-Air, seven species and thirty two reactions (H2air_7s32r) model. The standard least square method is used to generate response surfaces. Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) tied with a local search strategy (e-constraint) were used to determine the Pareto optimal solution set. The global Pareto optimal front is then obtained from the Pareto optimal solution set and is presented.