Polynomial genetic programming for response surface modeling Part 1: a methodology

Yeun, Yun Seog; Yang, Young Soon; Ruy, Won-Sun; Kim, B.J.

doi:10.1007/s00158-004-0460-6

Cited by 10 publications

(10 citation statements)

References 18 publications

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“…RSM has its roots in statistical experiment design, and its goal is to obtain an approximate functional relationship between inputs and outputs of the objective function [43][44][45]. RSM carried out on the entire domain of interest results in what is called a metamodel [46].…”

Section: Response Surface Methodology (Rsm)mentioning

confidence: 99%

An improved dynamic structure-based neural networks determination approaches to simulation optimization problems

Zheng

Tan

Zhang

et al. 2010

Neural Comput & Applic

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Simulation optimization studies the problem of optimizing simulation-based objectives. This field has a strong history in engineering but often suffers from several difficulties including being time-consuming and NP-hardness. Simulation optimization is a new and hot topic in the field of system simulation and operational research. This paper presents a hybrid approach that combines Evolutionary Algorithms with neural networks (NNs) for solving simulation optimization problems. In this hybrid approach, we use NNs to replace the known simulation model for evaluating subsequent iterative solutions. Further, we apply the dynamic structure-based neural networks to learn and replace the known simulation model. The determination of dynamic structure-based neural networks is the kernel of this paper. The final experimental results demonstrated that the proposed approach can find optimal or close-to-optimal solutions and is superior to other recent algorithms in simulation optimization.

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Section: Response Surface Methodology (Rsm)mentioning

confidence: 99%

An improved dynamic structure-based neural networks determination approaches to simulation optimization problems

Zheng

Tan

Zhang

et al. 2010

Neural Comput & Applic

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“…This truss structure has been used as an example in many literatures on optimization, i.e., (19) and also RBDO. In this study, the volume minimization problem subject to only the stress reliability constraint is considered (20) . The member cross-sectional area and the allowable stresses are adopted as normally distributed random variables, and the mean values of the cross-sectional area are treated as design variables.…”

Section: Example 4: Ten-bar Truss Design Problemmentioning

confidence: 99%

“…x i and R are random variables with normal distribution as listed in Table 7. The target reliability index is set as β j = 2.0 for all members in order to compare with Yeun et als' results (20) .…”

Section: Example 4: Ten-bar Truss Design Problemmentioning

confidence: 99%

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Modified Single-Loop-Single-Vector Method for Efficient Reliability-Based Design Optimization

Kogiso

Yang

Kim

et al. 2012

JAMDSM

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Single-Loop-Single-Vector (SLSV) method is to resolve the excessive computational cost problem in the reliability-based design optimization (RBDO) by decoupling the nested iteration loops. The key idea of the method is that the reliability constraint is transformed to the equivalent deterministic constraint by approximating the most probable point (MPP) using the point obtained from the previous iteration. However, the SLSV method sometimes suffers from numerical instability or inaccuracy problem. Thus, in this paper, a new modified SLSV method is proposed to improve its convergence capability effectively by utilizing Inactive Design and Active MPP Design together with modified-HMV (Hybrid Mean Value) method. The effectiveness of the proposed method is verified through some numerical examples.

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“…widely used; see e.g., Cuyt and Lenin (2002), Cuyt et al (2006), Fassbender (1997), Forsberg and Nilsson (2005), Jansson et al (2003), and Yeun et al (2005). For books on approximation theory, we refer to Powell (1981) and Watson (1980).…”

mentioning

confidence: 99%

Discrete least-norm approximation by nonnegative (trigonometric) polynomials and rational functions

Siem

Klerk

Hertog

2007

Struct Multidisc Optim

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Polynomials, trigonometric polynomials, and rational functions are widely used for the discrete approximation of functions or simulation models. Often, it is known beforehand that the underlying unknown function has certain properties, e.g., nonnegative or increasing on a certain region. However, the approximation may not inherit these properties automatically. We present some methodology (using semidefinite programming and results from real algebraic geometry) for least-norm approximation by polynomials, trigonometric polynomials, and rational functions that preserve nonnegativity.

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Polynomial genetic programming for response surface modeling Part 1: a methodology

Cited by 10 publications

References 18 publications

An improved dynamic structure-based neural networks determination approaches to simulation optimization problems

An improved dynamic structure-based neural networks determination approaches to simulation optimization problems

Modified Single-Loop-Single-Vector Method for Efficient Reliability-Based Design Optimization

Discrete least-norm approximation by nonnegative (trigonometric) polynomials and rational functions

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