Approximated Unimodal Region Elimination Based Global Optimization Method for Engineering Design

Abstract

Computer analysis and simulation based design optimization requires more computationally efficient global optimization tools. In this work, a new global optimization algorithm based on design experiments, region elimination and response surface model, namely Approximated Unimodal Region Elimination Method (AUREM), is introduced. The approach divides the field of interest into several unimodal regions using design experiment data; identify and rank the regions that most likely contain the global minimum; form a response surface model with additional design experiment data over the most promising region; identify its minimum, remove this processed region, and move to the next most promising region. By avoiding redundant searches, the approach identifies the global optimum with reduced number of objective function evaluations and computation effort. The new algorithm was tested using a variety of benchmark global optimization problems and compared with several widely used global optimization algorithms. The experiments results present comparable search accuracy and superior computation efficiency, making the new algorithm an ideal tool for computer analysis and simulation black-box based global design optimization.

Trends, features, and tests of common and recently introduced global optimization methods

“…Recently, the authors introduced a new global optimization algorithm, based on design experiments, region elimination and response surface model, namely approximated unimodal region elimination (AUMRE) method (Younis et al 2009). The approach divides the field of interest into several unimodal regions using design experiment data: first we identify and rank the promising regions that most likely contain the global optima; then we form a response surface model using additional design experiment data over the most promising region; then we identify its optima, remove this processed region, and finally we recursively move to the next most promising region.…”

“…Named sequential Kriging optimization (SKO), the algorithm differs from the original EGO in implementing the Kriging meta-model and in formulating the expected improvement (EI) function. The authors of this article recently introduced a new deterministic, meta-model based global optimization search algorithm, namely approximated unimodal region elimination (AUMRE) (Younis et al 2009), based on design experiments, region elimination and response surface model.…”

Global Optimization Using Mixed Surrogates and Space Elimination in Computationally Intensive Engineering Designs

“…The sampling and detection process iterates until the global optimum is obtained. Another global optimization algorithm was introduced by the authors recently; the algorithm is based on design experiments, region elimination, and response surface model, namely the Approximated Unimodal Region Elimination (AUMRE) method [30]. The approach divides the field of interest into several unimodal regions using design experiment data; identifies and ranks the promising regions that most likely contain the global optima; forms a response surface model using additional design experiment data over the most promising region; identifies its optima, removes this processed region, and moves to the next most promising region.…”

Non-uniform mode-pursuing sampling method based on multivariate multimodal distribution model

“…The main goal of using the response surface model is to use it as an inexpensive approximation to the costly black-box function to identify promising search points. Kushner developed a response surface methods using the Bayes theorem [4]; Huang proposed an efficient global optimization (EGO) scheme, named sequential Kriging optimization (SKO), the algorithm differs from the original EGO in implementing the Kriging meta-model and in formulating the expected improvement function [5]; A new deterministic metamodel based global optimization search algorithm namely approximated unimodal region elimination (AUMRE) is introduced by Younis [6], based on design experiments, region elimination and response surface model; Recently, Liqun Wang proposed a new global optimization method for expensive black-box functions, assuming the design space cannot be confidently reduced [7]. The method is developed based on novel mode-pursuing sampling (MPS) method which systematically generates more sample points in the neighborhood of the function mode while statistically covers the entire space.…”