Two hybrid optimization methods used for preliminary aerodynamic design are introduced. The first is a gradient method based on Rosen's projection method and the method of feasible directions. The second technique is a genetic algorithm that uses elements of the Nelder-Mead simplex method to aid in search direction determination, as well as gradient methods to handle constrained problems. These methods are applied to three-dimensional shape optimization of ogive-shaped, star-shaped, spiked projectiles and lifting bodies in a hypersonic flow. Flowfield analyses are performed using Newtonian flow theory and, in one case, verified using a parabolized Navier-Stokes flow analysis algorithm. Three-dimensional geometrical rendering is achieved using a variety of techniques including beta splines from the computer graphics industry. In a comparison to the gradient-based method, the hybrid genetic algorithm is shown to be able to achieve impressive convergence on highly constrained problems while avoiding local minima.
