Detection and Correction of Poorly Converged Optimizations by Iteratively Reweighted Least Squares

The use of Iteratively Reweighted Least Squares (IRLS) for detecting design points where structural optimizations give poor designs is demonstrated. Since most optimization error is one sided with poor results producing an overweight objective value, a nonsymmetrical version of IRLS (NIRLS) that takes into account the asymmetry in optimization errors is also developed. Optimization studies with various sets of convergence criteria on wing bending material weight of a high speed civil transport are used to demonstrate these techniques. First, inspection of poor designs by a visualization technique that plots objective function and constraint boundaries on planes including the suspected points, indicated that poor results were due to incomplete convergence of the optimization procedure rather than due to local minima. Results obtained with several hundred design points indicated that IRLS techniques can find most of the points with large optimization errors, but that NIRLS techniques are much more reliable in this task. Finally, the paper shows that the choice of convergence settings and parameters can have large effects on optimization errors. In particular, tighter * Graduate Research Assistant, Department of Aerospace and Ocean Engineering, Student Member AIAA. † Graduate Research Assistant, Department of Aerospace Engineering, Mechanics and Engineering Science, University of Florida, Gainesville, FL, Student Member AIAA. ‡ Professor, Department of Aerospace and Ocean Engineering, Associate Fellow AIAA. § Distinguished Professor, Department of Aerospace Engineering, Mechanics and Engineering Science, University of Florida, Gainesville, FL, Fellow AIAA. ¶ Professor, Departments of Computer Science and Mathematics. ** Professor and Department Head, Department of Aerospace and Ocean Engineering, Associate Fellow AIAA. Copyright  2000 by Hongman Kim. Published by the American Institute of Aeronautics and Astronautics, Inc. with permission. criteria for some parameters may actually increase optimization error.