Colloquium on Fluid Dynamics Research - Selected Recent Results, University of Stuttgart, May 7, 2004
An alternative to this approach is given by direct numerical optimization (DNO). With DNO an automated, computer-based, search for an optimal solution with respect to a given scalar objective function is performed. The objective function may be the drag at a certain design point or a weighted mean for a complete design range. The optimization is accomplished by means of a more or less systematic variation of the design variables which parameterize the shape to be optimized. A multitude of different optimization algorithms, ranging from gradientbased methods to stochastic approaches with highly sophisticated schemes for the adaptation of the individual mutation step sizes, are available. In general, gradient-based methods converge fast for simple topologies of the objective function but will get trapped in a local optimum if multi-modal objective functions are considered. Evolutionary optimizers offer a greater chance to avoid this problem and can also cope with complex, noisy objective function topologies. As a drawback, they usually require much more iterations to converge, especially if a large number of design variables is considered.