• Title, Summary, Keyword: Statistical optimization

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Simulation Optimization with Statistical Selection Method

  • Kim, Ju-Mi
    • Management Science and Financial Engineering
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    • v.13 no.1
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    • pp.1-24
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    • 2007
  • I propose new combined randomized methods for global optimization problems. These methods are based on the Nested Partitions(NP) method, a useful method for simulation optimization which guarantees global optimal solution but has several shortcomings. To overcome these shortcomings I hired various statistical selection methods and combined with NP method. I first explain the NP method and statistical selection method. And after that I present a detail description of proposed new combined methods and show the results of an application. As well as, I show how these combined methods can be considered in case of computing budget limit problem.

Statistical Optimization of Medium Components by Response Surface Methodology to Enhance Menaquinone-7 (Vitamin K2) Production by Bacillus subtilis

  • Wu, Wei-Jie;Ahn, Byung-Yong
    • Journal of Microbiology and Biotechnology
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    • v.28 no.6
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    • pp.902-908
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    • 2018
  • Optimization of the culture medium to maximize menaquinone-7 (MK-7) production by Bacillus subtilis strain KCTC 12392BP in static culture was carried out using statistical experimental methods, including one factor at a time, fractional factorial design, and response surface methodology (RSM). Maltose (carbon source), tryptone (nitrogen source), and glycerol (activator) were identified as the key medium components for MK-7 synthesis by the fractional factorial design, and were selected for statistical optimization by RSM. The statistical analysis indicated that, in the range that was studied, maltose, tryptone, and glycerol were all critical factors having profound effects on the production of MK-7, with their coefficients for linear and quadratic all significant at the p < 0.05 level. The established model was efficient and feasible, with a determination coefficient ($R^2$) of 0.9419. The predicted concentrations of maltose, tryptone, and glycerol in the optimal medium were determined as 36.78, 62.76, and 58.90 g/l, respectively. In this optimized medium, the maximum yield of MK-7 reached a remarkably high level of $71.95{\pm}1.00{\mu}g/ml$ after 9 days of static fermentation, which further verified the practicability of this optimized strategy.

Adjusting Practical Aims in Optimal Extended Double Sampling Plans

  • Ko, Seoung-gon
    • Communications for Statistical Applications and Methods
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    • v.6 no.1
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    • pp.143-150
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    • 1999
  • Ko(1998) proposed a procedure to enhance the efficiency of double sampling plans by allowing second-stage sample size and critical region to depend on first-stage evidence using constraint optimization approaches. In this study further developments of such plans by incorporating several practically possible researcher's aims into the optimization are considered. Comparisons are made with the optimal ordinary double sampling plan and also among them It is observed that it is to some extent possible to match the details of the optimization to certain qualitative methodological aims.

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Multiple-inputs Dual-outputs Process Characterization and Optimization of HDP-CVD SiO2 Deposition

  • Hong, Sang-Jeen;Hwang, Jong-Ha;Chun, Sang-Hyun;Han, Seung-Soo
    • JSTS:Journal of Semiconductor Technology and Science
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    • v.11 no.3
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    • pp.135-145
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    • 2011
  • Accurate process characterization and optimization are the first step for a successful advanced process control (APC), and they should be followed by continuous monitoring and control in order to run manufacturing processes most efficiently. In this paper, process characterization and recipe optimization methods with multiple outputs are presented in high density plasma-chemical vapor deposition (HDP-CVD) silicon dioxide deposition process. Five controllable process variables of Top $SiH_4$, Bottom $SiH_4$, $O_2$, Top RF Power, and Bottom RF Power, and two responses of interest, such as deposition rate and uniformity, are simultaneously considered employing both statistical response surface methodology (RSM) and neural networks (NNs) based genetic algorithm (GA). Statistically, two phases of experimental design was performed, and the established statistical models were optimized using performance index (PI). Artificial intelligently, NN process model with two outputs were established, and recipe synthesis was performed employing GA. Statistical RSM offers minimum numbers of experiment to build regression models and response surface models, but the analysis of the data need to satisfy underlying assumption and statistical data analysis capability. NN based-GA does not require any underlying assumption for data modeling; however, the selection of the input data for the model establishment is important for accurate model construction. Both statistical and artificial intelligent methods suggest competitive characterization and optimization results in HDP-CVD $SiO_2$ deposition process, and the NN based-GA method showed 26% uniformity improvement with 36% less $SiH_4$ gas usage yielding 20.8 ${\AA}/sec$ deposition rate.

A Robust Optimization Using the Statistics Based on Kriging Metamodel

  • Lee Kwon-Hee;Kang Dong-Heon
    • Journal of Mechanical Science and Technology
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    • v.20 no.8
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    • pp.1169-1182
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    • 2006
  • Robust design technology has been applied to versatile engineering problems to ensure consistency in product performance. Since 1980s, the concept of robust design has been introduced to numerical optimization field, which is called the robust optimization. The robustness in the robust optimization is determined by a measure of insensitiveness with respect to the variation of a response. However, there are significant difficulties associated with the calculation of variations represented as its mean and variance. To overcome the current limitation, this research presents an implementation of the approximate statistical moment method based on kriging metamodel. Two sampling methods are simultaneously utilized to obtain the sequential surrogate model of a response. The statistics such as mean and variance are obtained based on the reliable kriging model and the second-order statistical approximation method. Then, the simulated annealing algorithm of global optimization methods is adopted to find the global robust optimum. The mathematical problem and the two-bar design problem are investigated to show the validity of the proposed method.

The Efficient Sensitivity Analysis on Statistical Moments and Probability Constraints in Robust Optimal Design (강건 최적설계에서 통계적 모멘트와 확률 제한조건에 대한 효율적인 민감도 해석)

  • Huh, Jae-Sung;Kwak, Byung-Man
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.32 no.1
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    • pp.29-34
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    • 2008
  • The efforts of reflecting the system's uncertainties in design step have been made and robust optimization or reliability-based design optimization are examples of the most famous methodologies. In their formulation, the mean and standard deviation of a performance function and constraints expressed by probability conditions are involved. Therefore, it is essential to effectively and accurately calculate them and, in addition, the sensitivity results are required to obtain when the nonlinear programming is utilized during optimization process. We aim to obtain the new and efficient sensitivity formulation, which is based on integral form, on statistical moments such as the mean and standard deviation, and probability constraints. It does not require the additional functional calculation when statistical moments and failure or satisfaction probabilities are already obtained at a design point. Moreover, some numerical examples have been calculated and compared with the exact solution or the results of Monte Carlo Simulation method. The results seem to be very satisfactory.

Systemic Statistical Optimization of Astaxanthin Inducing Methods in Haematococcus pluvialis cells -Statistical Optimization of Astaxanthin Production in Haematococcus

  • Kim, Sun-Hyoung;Jeong, Sung Eun;Hong, Seong-Joo;Lee, Choul-Gyun
    • Journal of Marine Bioscience and Biotechnology
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    • v.6 no.1
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    • pp.31-40
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    • 2014
  • The production of astaxanthin in the microalga Haematococcus pluvialis has been investigated using a sequential methodology based on the application of two types of statistical designs. The employed preliminary experiment was a fractional factorial design $2^6$ in which the factors studied were: excessive irradiance and nitrate starvation, phosphate deficiency, acetate supplementation, salt stress, and elevated temperature. The experimental results indicate that the amount of astaxanthin accumulation in the cells can be enhanced by excessive irradiance and nitrate starvation whereas the other factors tested did not yield any enhancement. In the subsequent experiment, a central composite design was applied with four variables, light intensity, nitrate, phosphate, and acetate, at five levels each. The optimal conditions for the highest astaxanthin production were found to be $1040{\mu}E/(m^2{\cdot}s)$ light intensity, 0.04 g/L nitrate, 0.31 g/L phosphate, 0.05 g/L acetate concentration.

Robust Structural Optimization Using Gauss-type Quadrature Formula (가우스구적법을 이용한 구조물의 강건최적설계)

  • Lee, Sang-Hoon;Seo, Ki-Seog;Chen, Shikui;Chen, Wei
    • Transactions of the Korean Society of Mechanical Engineers A
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    • v.33 no.8
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    • pp.745-752
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    • 2009
  • In robust design, the mean and variance of design performance are frequently used to measure the design performance and its robustness under uncertainties. In this paper, we present the Gauss-type quadrature formula as a rigorous method for mean and variance estimation involving arbitrary input distributions and further extend its use to robust design optimization. One dimensional Gauss-type quadrature formula are constructed from the input probability distributions and utilized in the construction of multidimensional quadrature formula such as the tensor product quadrature (TPQ) formula and the univariate dimension reduction (UDR) method. To improve the efficiency of using it for robust design optimization, a semi-analytic design sensitivity analysis with respect to the statistical moments is proposed. The proposed approach is applied to a simple bench mark problems and robust topology optimization of structures considering various types of uncertainty.

A Design Study of Aerodynamic Noise Reduction In Centrifugal Compressor Part II . Low-noise Optimization Design (원심압축기의 공력소음 저감에 관한 설계연구 Part II : 저소음 최적설계)

  • 선효성;이수갑
    • Transactions of the Korean Society for Noise and Vibration Engineering
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    • v.14 no.10
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    • pp.939-944
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    • 2004
  • The numerical methods including the performance analysis and the noise prediction of the centrifugal compressor impeller are coupled with the optimization design skill, which consists of response surface method, statistical approach, and genetic algorithm. The flow-field Inside of a centrifugal compressor is obtained numerically by solving Wavier-Stokes equations. and then the propagating noise is estimated from the distributed surface pressure by using Ffowcs Williams-Hawkings formulation. The quadratic response surface model with D-optimal 3-level factorial experimental design points is constructed to optimize the impeller geometry for the advanced centrifugal compressor. The statistical analysis shows that the quadratic model exhibits a reasonable fitting quality resulting in the impeller blade design with high performance and low far-field noise level. The influences of selected design variables, objective functions, and constraints on the impeller performance and the impeller noise are also examined as a result of the optimization process.