Hybrid metamodel-based design space management method for expensive problems

Gu, Jason; Li, Guangyao; Gan, Nianfei

doi:10.1080/0305215x.2016.1261126

Cited by 13 publications

(13 citation statements)

References 26 publications

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“…The RSM is a typical curve‐fitting method of building the metamodel and determining the coefficient of polynomial expression. Most of previous studies using RSM have introduced the second‐order polynomial . However, in this research, the third‐order polynomial is used as a basis and the second‐order polynomial could be used as an option.…”

Section: The Suggested Rhmm Algorithmmentioning

confidence: 99%

“…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%

“…Existing methods use a small number of initial sample points, which increases the number of cycle iterations and the number of function calculations. For example, Ran et al have set the initial number of sample points using ( n + 1)( n + 2)/2 + 1.…”

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%

“…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%

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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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Section: The Suggested Rhmm Algorithmmentioning

confidence: 99%

\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: Applied Examplesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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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Multi-surrogate-based global optimization using a score-based infill criterion

Dong

Sun

Song

et al. 2018

Struct Multidisc Optim

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Efficient strategies for constrained black-box optimization by intrinsically linear approximation (CBOILA)

Liu

Wang

et al. 2020

Engineering with Computers

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In this paper, a novel trust-region based surrogate-assisted optimization method, called CBOILA (Constrained Black-box Optimization by Intrinsically Linear Approximation), has been proposed to reduce the number of black-box function evaluations and enhance the efficient performance for solving complex optimization problems. This developed optimization approach utilizes an assembly of intrinsically linear approximations to seek the optimum with incorporation of three strategies: (1) extended-box selection strategy (EBS), ( 2) global intelligence selection strategy (GIS) and ( 3) balanced trust-region strategy. EBS aims at reducing the number of function evaluations in current iteration by selecting points close to the given trust region boundary. Whilst, GIS is designed to improve the exploration performance by adaptively choosing points outside the trust region. The balanced trust-region strategy works with four indicators, which will be triggered by the quality of the approximation, the movement direction of the search, the location of the sub-optimum, and the condition of the termination, respectively. By modifying the move limit of each dimension accordingly, CBOILA is capable of attaining a balanced search between exploitation and exploration for the optimal solutions. To demonstrate the potentials of the proposed optimization method, three widely used benchmark problems have been examined and the results have also been compared with solutions by other metamodel-based algorithms in published works. Results show that the proposed method can efficiently and robustly solve constrained black-box optimization problems within an acceptable computational time.

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Hybrid metamodel-based design space management method for expensive problems

Cited by 13 publications

References 26 publications

An approximate optimization strategy using refined hybrid metamodel

An approximate optimization strategy using refined hybrid metamodel

Multi-surrogate-based global optimization using a score-based infill criterion

Efficient strategies for constrained black-box optimization by intrinsically linear approximation (CBOILA)

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