A hybridized self-organizing response surface methodology Conference

Moral, RJ, Dulikravich, GS. (2008). A hybridized self-organizing response surface methodology .

cited authors

  • Moral, RJ; Dulikravich, GS

authors

abstract

  • 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. Finally, a hybridized multi-layer self-organizing algorithm is presented. In this method, the algorithm can choose the basis functions that locally capture the interaction between the variables in the most accurate fashion. Two hybridized methods will be presented. In the first method, the hybridized algorithm will be able to choose from linear, quadratic, cubic and quartic basis polynomials, as needed. In the second hybridized algorithm, the same basis polynomial options from the first hybrid method are given to the algorithm plus the capability to choose a simple RBF as a basis function to describe interactions among the variables. These methods will be compared to the single basis function response surface models using the same test problems. Furthermore, in kriging, an underlying regression can be performed in order to capture simple trends in the model's data before the actual kriging is performed. In the spirit of this technique, the polynomial only hybrid multi-layer self-organizing algorithm will be used to capture complicated trends in the function to be fitted. Then, an RBF model will be used to fit the data to residual errors from the hybridized multi-layer self-organizing method. This approach will be tested using the same set of test problems. Finally, a comparison of all multi-layer self-organizing algorithms will be presented. Copyright © 2008 by Marcelo J. Colaco and George S. Dulikravich.

publication date

  • December 1, 2008

International Standard Book Number (ISBN) 13