An efficient ensemble of radial basis functions method based on quadratic programming

Shi, Renhe; Liu, Li; Li, Teng; Liu, Jian

doi:10.1080/0305215x.2015.1100470

Cited by 28 publications

(13 citation statements)

References 19 publications

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“…Additionally, some studies are specifically focused on the EoS of just one type of metamodel. For instance, Shi et al (2016) introduce a combination of radial basis functions (RBFs) to determine the weights by solving a quadratic programming (QP) subproblem. The results show that an ensemble of multiple RBFs can remarkably enhance the modeling efficacy compared to single RBF models.…”

Section: Frame Of Referencementioning

confidence: 99%

Ensemble of surrogates and cross-validation for rapid and accurate predictions using small data sets

Alizadeh

Jia

Nellippallil

et al. 2019

AIEDAM

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In engineering design, surrogate models are often used instead of costly computer simulations. Typically, a single surrogate model is selected based on the previous experience. We observe, based on an analysis of the published literature, that fitting an ensemble of surrogates (EoS) based on cross-validation errors is more accurate but requires more computational time. In this paper, we propose a method to build an EoS that is both accurate and less computationally expensive. In the proposed method, the EoS is a weighted average surrogate of response surface models, kriging, and radial basis functions based on overall cross-validation error. We demonstrate that created EoS is accurate than individual surrogates even when fewer data points are used, so computationally efficient with relatively insensitive predictions. We demonstrate the use of an EoS using hot rod rolling as an example. Finally, we include a rule-based template which can be used for other problems with similar requirements, for example, the computational time, required accuracy, and the size of the data.

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Section: Frame Of Referencementioning

confidence: 99%

Ensemble of surrogates and cross-validation for rapid and accurate predictions using small data sets

Alizadeh

Jia

Nellippallil

et al. 2019

AIEDAM

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“…The results show that an ensemble of multiple metamodels seems to be able to avoid a misleading optimum by using a single metamodel. Jiang et al (2015) also applied the ensemble model combined with the analytical target cascading strategy in the multidisciplinary design optimization of a super-heavy vertical lathe, and similar ensemble methods can be found in Acar (2010), Zhou et al (2011) and Shi et al (2016). Gu et al (2012) proposed a hybrid and adaptive metamodel (HAM)-based global optimizing method, which can automatically select appropriate metamodels during the search process to improve search efficiency.…”

Section: Multiple Metamodels 71mentioning

confidence: 99%

A hybrid global optimization method based on multiple metamodels

Cai

Qiu

Gao

et al. 2018

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Purpose This paper aims to propose hybrid global optimization based on multiple metamodels for improving the efficiency of global optimization. Design/methodology/approach The method has fully utilized the information provided by different metamodels in the optimization process. It not only imparts the expected improvement criterion of kriging into other metamodels but also intelligently selects appropriate metamodeling techniques to guide the search direction, thus making the search process very efficient. Besides, the corresponding local search strategies are also put forward to further improve the optimizing efficiency. Findings To validate the method, it is tested by several numerical benchmark problems and applied in two engineering design optimization problems. Moreover, an overall comparison between the proposed method and several other typical global optimization methods has been made. Results show that the global optimization efficiency of the proposed method is higher than that of the other methods for most situations. Originality/value The proposed method sufficiently utilizes multiple metamodels in the optimizing process. Thus, good optimizing results are obtained, showing great applicability in engineering design optimization problems which involve costly simulations.

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“…Lee and Choi (2014) proposed a new pointwise affine combination of metamodels by using a nearest points cross-validation approach. Shi et al (2016) proposed efficient affine combinations of radial basis function networks. Most recently, Song et al (2018) suggested an advanced and robust affine combination of metamodels by using extended adaptive hybrid functions.…”

Section: Introductionmentioning

confidence: 99%

Comparison of optimal linear, affine and convex combinations of metamodels

Strömberg

2020

Engineering Optimization

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In this article, five different formulations for establishing optimal ensembles of metamodels are presented and compared. The comparison is done by minimizing different norms of the residual vector of the leave-oneout cross-validation errors for linear, affine and convex combinations of 10 metamodels. The norms are taken to be the taxicab, the Euclidean and the infinity norm, respectively. The ensemble of metamodels consists of quadratic regression, Kriging with linear or quadratic bias, radial basis function networks with a-priori linear or quadratic bias, radial basis function networks with a-posteriori linear or quadratic bias, polynomial chaos expansion, support vector regression and least squares support vector regression. Eight benchmark functions are studied as 'black-boxes' using Halton and Hammersley samplings. The optimal ensembles are established for either one of the samplings and then the corresponding root mean square errors are established using the other sampling and vice versa. In total, 80 different test cases (5 formulations, 8 benchmarks and 2 samplings) are studied and presented. In addition, an established design optimization problem is solved using affine and convex combinations. It is concluded that minimization of the taxicab or Euclidean norm of the residual vector of the leave-one-out cross-validation errors for convex combinations of metamodels produces the best ensemble of metamodels.

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An efficient ensemble of radial basis functions method based on quadratic programming

Cited by 28 publications

References 19 publications

Ensemble of surrogates and cross-validation for rapid and accurate predictions using small data sets

Ensemble of surrogates and cross-validation for rapid and accurate predictions using small data sets

A hybrid global optimization method based on multiple metamodels

Comparison of optimal linear, affine and convex combinations of metamodels

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