Ensemble of metamodels: extensions of the least squares approach to efficient global optimization

Ferreira, Wallace; Serpa, Alberto Luiz

doi:10.1007/s00158-017-1745-x

Cited by 14 publications

(15 citation statements)

References 21 publications

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“…We also explored this front in the context of LS ensembles and the results are promising. The developments and results in this branch of application for the proposed ensemble approach will be presented the continuation of the present research in Ferreira and Serpa (2015).…”

Section: Comparison Of Ensemble Methodsmentioning

confidence: 99%

“…As we mentioned in Section 1, by means of the variance estimate, (15), it is possible to derive an expected improvement function, which is the main ingredient for the application of efficient global optimization algorithms. This branch of the research will be covered in the companion work Ferreira and Serpa (2015).…”

Section: Basic Formulationmentioning

confidence: 99%

“…In the present one we will focus on the development of the LS ensemble of metamodels algorithm and the numerical experiments performed to verify the accuracy of the proposed method for prediction. The optimization objectives will be covered in a companion work, Ferreira and Serpa (2015), in which we will present the extensions and results of the proposed approach in the context of EGO algorithms and applications.…”

Section: Introductionmentioning

confidence: 99%

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Ensemble of metamodels: the augmented least squares approach

Ferreira¹,

Serpa

2015

Struct Multidisc Optim

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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.

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Section: Comparison Of Ensemble Methodsmentioning

confidence: 99%

Section: Basic Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ensemble of metamodels: the augmented least squares approach

Ferreira¹,

Serpa

2015

Struct Multidisc Optim

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“…Each of these metamodel techniques has its advantages and disadvantages. Recently, methods for generating hybrid models by combining these metamodels have been developed . We call such hybrid model an ensemble model or multiple surrogates.…”

Section: Introductionmentioning

confidence: 99%

“…To improve the accuracy of the optimal solution obtained from the metamodel, the following two approaches are commonly used. The first one is to build a hybrid model by combining two or more metamodels . The second one is to improve the reliability of the metamodel by reducing design space and adding new sample points iteratively .…”

Section: Introductionmentioning

confidence: 99%

An approximate optimization strategy using refined hybrid metamodel

Lee

Jeong

Lee

2019

Computational Intelligence

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An approximate model called metamodel or surrogate model is a mathematical model that numerically approximates response of a system during an engineering simulation process or test. The introduction of a metamodel makes it possible to express response defined in the design problem as a simple mathematical function of design variables. A metamodel can be built with response surface method (RSM), kriging, neural network, radial basis function, and so on. Each method has its advantages and disadvantages. A combined metamodel called hybrid model, ensemble model, or multiple surrogates has been developed to maximize each metamodel's strength. The hybrid model of this research includes RSM and kriging. Besides, a strategy to refine the hybrid metamodel is implemented by reducing design space. In this process, information related to Hessian is utilized for an unconstrained optimization problem, on the contrary feasibility for a constrained optimization problem. This research presents a new hybrid metamodel‐based optimization strategy called refined hybrid metamodel. Five mathematical test problems, two‐bar design, spring design, and propeller shaft design problems are solved with the suggested method, verifying its usefulness. Most of the optimal results with the proposed method are closer to exact solutions with smaller function evaluations than existing methods.

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A RBF-based constrained global optimization algorithm for problems with computationally expensive objective and constraints

Yin

Jie

et al. 2018

Struct Multidisc Optim

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Ensemble of metamodels: extensions of the least squares approach to efficient global optimization

Cited by 14 publications

References 21 publications

Ensemble of metamodels: the augmented least squares approach

Ensemble of metamodels: the augmented least squares approach

An approximate optimization strategy using refined hybrid metamodel

A RBF-based constrained global optimization algorithm for problems with computationally expensive objective and constraints

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