Global Design Space Exploration for Multidisciplinary Design Optimization

• Develop kernel regression techniques, neural networks, and DACE models for fitting the low-fidelity analyses using millions of numerical experiments for training. The large numbers of experiments will be selected by niched genetic algorithms. The very large number of training pairs will ensure accuracy in the relatively high dimensional space. However, it will entail challenges of performing the optimization process associated with training the network. In addition, the use of the network for completing the low-fidelity optimization using Lipschitz and interval methods will be explored. A significant portion of this task is to assess the effectiveness of kernel regression, DACE, and neural networks in high dimensions, and how well these nonlinear approximation techniques scale with dimension.



• Develop polynomial, multidimensional spline, or other linear regression models based on a study of the nonlinear approximation obtained in the first task, and use them for improved response surface approximations to the high-fidelity models in small regions. This task could be performed in parallel with the first task by starting the effort for lower dimensional spaces, where Task 1 is easy to perform because only thousands of training pairs are involved.



• The two tasks will also interact and help with the development of a MDO problem solving environment, currently underway in several existing software and research projects within the Computer Science departments at Virginia Tech and the University of Florida.

• L. T. Watson and C. A. Baker, ``A fully-distributed parallel global search algorithm'', {\sl Engrg. Comput.}, 18 (2001) 155--169.



• S. E. Cox, R. T. Haftka, C. A. Baker, B. Grossman, W. H. Mason, and L. T. Watson, ``Global multidisciplinary optimization of a high speed civil transport'', {\sl J. Global Optim.}, 21 (2001) 415--433.