A Hybridized Self-Organizing Response Surface Methodology
Ramon J. Moral, George S. Dulikravich · 12th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference · 2008
Response surface methodologies receive much attention in the Multidisciplinary Optimization (MDO) community. They provide time-saving low fidelity models for complex objective function evaluations and can be used for objective function interpolation when the objective function is based on discrete experiments, or data points. In this work the Group Method for Data Handling (GMDH) technique developed by Ivakhnenko will be discussed, in particular the multi-layer self-organizing algorithm. In the multi-layer self-organizing concept, very simple polynomial basis functions are used to generate models describing highly non-linear multi-variable functions. In this work, multi-layer self-organizing algorithms with different order polynomial basis functions will be compared using Schittkowski’s suite of 296 non-linear optimization test cases. This exercise will determine if the accuracy of the multi-layer method can be increased by starting with an initially high order basis polynomial instead of relying on the method to create the interaction order between two variables on its own. The performance of the multi-layer self-organizing concept using Radial Basis Functions (RBF’s) on the Schittkowski’s test problems is also evaluated.