The Initialization Problem and Other Techniques for Robust Optimization

General optimization problems are hard to solve. Problems with expensive to evaluate goal functionals and constraints, large dimensional parameter spaces, non-convex (multi-modal), and ill-conditioned, are prevalent in many industrial applications and they are specially hard to solve in a robust, automated manner. Multi-modal, ill-conditioned problems require global optimization techniques and regularization. In high dimensional spaces the available techniques are problematic at their best and one must resort to surrogate functionals, divide and conquer techniques, and parallel computing in order to have a chance to solve the problem in a reasonable time. It is somewhat futile to expect that there is a magic bullet that will solve all problems automatically and without any a priori knowledge. On the other hand, tools can be developed to facilitate finding the best algorithm for a given problem, while allowing for the incorporation of all the known a priori knowledge and providing graphical and analysis support in a unified manner. In a separate project (A Toolbox for Optimal Design, NSF-SBIR Phase II) , we are developing such an environment for large-scale simulation guided by optimization, concentrating on Wave Propagation phenomena. In this project we will evaluate and implement techniques to make this optimization process more robust, concentrating on the problem of generating adequate initial values and some other additional techniques. With our consultant Prof. J. J. Alonso from the Aeronautics and Aerospace Department, Stanford University, we will consider the system vehicle design problem, where multiple disciplines interact within a complex analysis, thus enlarging the scope of our existing Toolbox.