Ensemble of metamodels with optimized weight factors

115

The determination of complex underlying relationships between system parameters from simulated and/or recorded data requires advanced interpolating functions, also known as surrogates. The development of surrogates for such complex relationships often requires the modeling of high dimensional and non-smooth functions using limited information. To this end, the hybrid surrogate modeling paradigm, where different surrogate models are combined, offers an effective solution. In this paper, we develop a new high fidelity surrogate modeling technique that we call the Adaptive Hybrid Functions (AHF). The AHF formulates a reliable Crowding Distance-Based Trust Region (CD-TR), and adaptively combines the favorable characteristics of different surrogate models. The weight of each contributing surrogate model is determined based on the local measure of accuracy for that surrogate model in the pertinent trust region. Such an approach is intended to exploit the advantages of each component surrogate. This approach seeks to simultaneously capture the global trend of the function as well as the local deviations. In this paper, the AHF combines four component surrogate models: (i) the Quadratic Response Surface Model (QRSM), (ii) the Radial Basis Functions (RBF), (iii) the Extended Radial Basis Functions (E-RBF), and (iv) the Kriging model. The AHF is applied to standard test problems and to a complex engineering design problem. Subsequent evaluations of the Root Mean Squared Error (RMSE) and the Maximum Absolute Error (MAE) illustrate the promising potential of this hybrid surrogate modeling approach.

Section: Surrogate Modeling Reviewmentioning

confidence: 99%

Section: Surrogate Modeling Reviewmentioning

confidence: 99%

An adaptive hybrid surrogate model

Zhang

Chowdhury

Messac

2012

115

“…The use of multiple metamodels has recently been studied, for example, by Viana and Haftka (2008), Viana et al (2009) and Acar and Rais-Rohani (2009) where coefficients b l in (5) were treated as weights that reflect the accuracy of the individual surrogates on a set of validation points. Thus, more accurate assembly components ϕ l have larger values of the multipliers and vice versa provided that…”

Section: Approximation Buildingmentioning

confidence: 99%

“…Such an approach was recently studied, for example, by Viana and Haftka (2008) and Acar and Rais-Rohani (2009) where metamodel assembly was based on a weighted sum formulation. In the present work metamodel assembly is built using a linear regression.…”

mentioning

confidence: 99%

Mid-range metamodel assembly building based on linear regression for large scale optimization problems

Polynkin

Торопов

2011

In this work an approach to building a high accuracy approximation valid in a larger range of design variables is investigated. The approach is based on an assembly of multiple surrogates into a single surrogate using linear regression. The coefficients of the model assembly are not weights of the individual models but tuning parameters determined by the least squares method. The approach was utilized in the Multipoint Approximation Method (MAM) method within the mid-range approximation framework.The developed technique has been tested on several benchmark problems with up to 1000 design variables and constraints. The obtained results show a high degree of accuracy of the built approximations and the efficiency of the technique when applied to large-scale optimization problems.

“…See, for instance Zerpa et al (2005), Goel et al (2007), Sanchez et al (2008), Viana et al (2009), Acar and Rais-Rohani (2009), Acar (2010) and Viana (2011). In most of these studies, it is suggested that ensemble of metamodels, or weighted averaged surrogate (WAS) models are able to provide better accuracy than individual metamodels working alone, and can improve the overall robustness of the metamodel based optimization process.…”

Section: Introductionmentioning

confidence: 99%

Ensemble of metamodels: the augmented least squares approach

Ferreira¹,

Serpa

2015

In this work we present an approach to create ensemble of metamodels (or weighted averaged surrogates) based on least squares (LS) approximation. The LS approach is appealing since it is possible to estimate the ensemble weights without using any explicit error metrics as in most of the existent ensemble methods. As an additional feature, the LS based ensemble of metamodels has a prediction variance function that enables the extension to the efficient global optimization. The proposed LS approach is a variation of the standard LS regression by augmenting the matrices in such a way that minimizes the effects of multicollinearity inherent to calculation of the ensemble weights. We tested and compared the augmented LS approach with different LS variants and also with existent ensemble methods, by means of analytical and real-world functions from two to forty-four variables. The augmented least squares approach performed with good accuracy and stability for prediction purposes, in the same level of other ensemble methods and has computational cost comparable to the faster ones.