Hybrid surrogate-based optimization using space reduction (HSOSR) for expensive black-box functions

Dong, Huachao; Song, Baowei; Wang, Peng; Dong, Zuomin

doi:10.1016/j.asoc.2017.12.046

Cited by 46 publications

(17 citation statements)

References 36 publications

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“…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%

“…Ran et al have built a hybrid model using quadratic RSM, kriging, and RBF in an algorithm called hybrid metamodel‐based two‐level global optimization (HMTGO) and tried to find an optimal solution using space reduction method . In the hybrid surrogate‐based optimization using space reduction (HSOSR) algorithm proposed by Dong et al, a hybrid model consisting of kriging and RBF was generated and the space reduction method using two subspaces alternately was used to find the optimal solution . In the hybrid metamodel‐based design space management (HMDSM) developed by Gu et al, a hybrid model was generated using quadratic RSM, kriging, and RBF and the optimal solution was searched by dividing design range into important and not important regions.…”

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%

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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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\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

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A multi-fidelity RBF surrogate-based optimization framework for computationally expensive multi-modal problems with application to capacity planning of manufacturing systems

Shen

Shoemaker

2020

Struct Multidisc Optim

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This paper presents a multi-fidelity RBF (radial basis function) surrogate-based optimization framework (MRSO) for computationally expensive multi-modal optimization problems when multi-fidelity (high-fidelity (HF) and low-fidelity (LF)) models are available. The HF model is expensive and accurate while the LF model is cheaper to compute but less accurate. To exploit the correlation between the LF and HF models and improve algorithm efficiency, in MRSO, we first apply the DYCORS (dynamic coordinate search algorithm using response surface) algorithm to search on the LF model and then employ a potential area detection procedure to identify the promising points from the LF model. The promising points serve as the initial start points when we further search for the optimal solution based on the HF model. The performance of MRSO is compared with 6 other surrogate-based optimization methods (4 are using a single-fidelity surrogate and the rest 2 are using multi-fidelity surrogates). The comparisons are conducted on a multi-fidelity optimization test suite containing 10 problems with 10 and 30 dimensions. Besides the benchmark functions, we also apply the proposed algorithm to a practical and computationally expensive capacity planning problem in manufacturing systems which involves discrete event simulations. The experimental results demonstrate that MRSO outperforms all the compared methods.

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A generalized hierarchical co-Kriging model for multi-fidelity data fusion

Zhou

Guo

et al. 2020

Struct Multidisc Optim

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Hybrid surrogate-based optimization using space reduction (HSOSR) for expensive black-box functions

Cited by 46 publications

References 36 publications

An approximate optimization strategy using refined hybrid metamodel

An approximate optimization strategy using refined hybrid metamodel

A multi-fidelity RBF surrogate-based optimization framework for computationally expensive multi-modal problems with application to capacity planning of manufacturing systems

A generalized hierarchical co-Kriging model for multi-fidelity data fusion

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