A hybrid global optimization method based on multiple metamodels

Cai, Xiwen; Qiu, Haobo; Gao, Liang; Li, Xiaoke; Shao, Xinyu

doi:10.1108/ec-05-2016-0158

Cited by 5 publications

(9 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Selected problems include unconstrained optimization problems that minimize Branin function (BF), six‐hump camel‐back function (SCF), Himmelblau function (HBF), Goldstein‐Price function (GPF), and Hartmann 6‐dimensional function (HF) of test problems widely used for investigating performance of global optimization algorithms. Each function is as follows: (a)BF

\begin{matrix} true \\ f (boldx) = a {((), x_{2} - b x_{1}^{2} + c x_{1} - r)}^{2} + s (1 - t) \cos (x_{1}) + s \\ - 5 \leq x_{1} \leq 10, - 5 \leq x_{2} \leq 10, a = 1, b = \frac{5.1}{4 π^{2}}, c = \frac{5}{π}, r = 6, s = 10, t = \frac{1}{8 π} \end{matrix}

(b)SCF

\begin{matrix} true \\ f (boldx) = (4 - 2.1 x_{1}^{2} + \frac{x_{1}^{4}}{3}) x_{1}^{2} + x_{1} x_{2} + (- 4 + 4 x_{2}^{2}) x_{2}^{2} \\ - 2 \leq x_{1} \leq 2, - 2 \leq x_{2} \leq 2 \end{matrix}

(c)HBF

\begin{matrix} true \\ f (boldx) = {((), x_{1}^{2} + x_{2} - 11)}^{2} + ((), x_{1} + x_{...}) \end{matrix}

…”

Section: Applied Examplesmentioning

confidence: 99%

“…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%

“…An adaptive metamodel‐based global optimization (AMGO) algorithm suggested by Jie et al built a hybrid model using kriging and augmented RBF, solved suboptimization problem, and added a sample point to generate a new hybrid model. Cai et al and Ferreira and Serpa utilized the efficient global optimization (EGO) algorithm in building metamodels.…”

Section: Introductionmentioning

confidence: 99%

“…For a constrained optimization problem, the minimum point at the sample points is determined by considering feasibility. To verify the effectiveness of the proposed refined hybrid metamodel (RHMM) algorithm, the method is applied to five test problems, two‐bar design problem, spring design problem, and propeller shaft design problem.…”

Section: Introductionmentioning

confidence: 99%

“…Recently, methods for generating hybrid models by combining these metamodels have been developed. [10][11][12][13][14][15][16][17][18][19][20][21] We call such hybrid model an ensemble model or multiple surrogates. The performance of metamodel-based optimization algorithm depends on the reliability of the metamodel.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

An approximate optimization strategy using refined hybrid metamodel

Lee

Jeong

Lee

2019

Computational Intelligence

View full text Add to dashboard Cite

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.

show abstract

\begin{matrix} true \\ f (boldx) = a {((), x_{2} - b x_{1}^{2} + c x_{1} - r)}^{2} + s (1 - t) \cos (x_{1}) + s \\ - 5 \leq x_{1} \leq 10, - 5 \leq x_{2} \leq 10, a = 1, b = \frac{5.1}{4 π^{2}}, c = \frac{5}{π}, r = 6, s = 10, t = \frac{1}{8 π} \end{matrix}

(b)SCF

\begin{matrix} true \\ f (boldx) = (4 - 2.1 x_{1}^{2} + \frac{x_{1}^{4}}{3}) x_{1}^{2} + x_{1} x_{2} + (- 4 + 4 x_{2}^{2}) x_{2}^{2} \\ - 2 \leq x_{1} \leq 2, - 2 \leq x_{2} \leq 2 \end{matrix}

(c)HBF

\begin{matrix} true \\ f (boldx) = {((), x_{1}^{2} + x_{2} - 11)}^{2} + ((), x_{1} + x_{...}) \end{matrix}

…”

Section: Applied Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

An approximate optimization strategy using refined hybrid metamodel

Lee

Jeong

Lee

2019

Computational Intelligence

View full text Add to dashboard Cite

show abstract

Processing parameter optimization of fiber laser beam welding using an ensemble of metamodels and MOABC

Zhang

Lian

et al. 2022

Front. Mech. Eng.

View full text Add to dashboard Cite

Multi-Armed Bandit Regularized Expected Improvement for Efficient Global Optimization of Expensive Computer Experiments With Low Noise

et al. 2021

View full text Add to dashboard Cite

Computer experiments are widely used to mimic expensive physical processes as black-box functions. A typical challenge of expensive computer experiments is to find the set of inputs that produce the desired response. Here, we propose a multi-armed bandit regularized expected improvement (BREI) method to adaptively adjust the balance between exploration and exploitation for efficient global optimization of long-running computer experiments with low noise. To integrate the information of additional exploration and exploitation into the optimization process, we propose to add a stochastic regularization term to the objective function of the expected improvement. We also develop a multi-armed bandit strategy based on Thompson sampling for adaptive optimization of the tuning parameter of the regularization term based on the preexisting and newly tested points. We discuss the intuitive relation between the proposed BREI and the mode of stochastic improvement, integrated experimental design, and the upper confidence bound Gaussian process. Using a case study on optimization of the collision avoidance algorithm in mobile robot motion planning as well as extensive simulation studies, we validate the proposed algorithm against some of the existing methods in the literature under different levels of noise.

show abstract

A hybrid global optimization method based on multiple metamodels

Cited by 5 publications

References 41 publications

An approximate optimization strategy using refined hybrid metamodel

An approximate optimization strategy using refined hybrid metamodel

Processing parameter optimization of fiber laser beam welding using an ensemble of metamodels and MOABC

Multi-Armed Bandit Regularized Expected Improvement for Efficient Global Optimization of Expensive Computer Experiments With Low Noise

Contact Info

Product

Resources

About