The DARPA initiated Quiet Supersonic Platform (QSP) program is an excellent example problem requiring multidisciplinary design optimization (MDO) in which the noise level of the ground boom signature of a supersonic business jet should be significantly reduced while challenging aerodynamic performance requirements must be met at the same time. To address this kind of problem, an efficient and robust design methodology using approximation techniques such as response surface and Kriging methods, augmented by gradient information, has been developed and tested on simple analytic functions as well as on more realistic design test cases. An integrated boom prediction tool incorporating fully nonlinear CFD analyses has been developed to provide required sample data for the QSP problem. A multiobjective optimization to simultaneously minimize boom and drag at fixed lift has been performed using a genetic algorithm based on different kinds of approximation models to search for the Pareto design front. The results show that the proposed design procedure achieves its robustness and efficiency by using well-behaved low-fidelity approximations to more computationally expensive CFD analyses and by enhancing them with the gradient information available. In addition, various ways to integrate the information acquired from the approximation models into a genetic algorithm search method have been demonstrated to reduce its large computational costs and to make its use feasible for realistic high-dimensional design problems.