Centered  $L_2$-discrepancy of random sampling  and Latin hypercube
design,   and construction of uniform designs

Fang, Kai‐Tai; Ma, Changxing; Winker, Peter

doi:10.1090/s0025-5718-00-01281-3

Cited by 159 publications

(87 citation statements)

References 19 publications

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“…First, we can build the relation between the computed discrepancy and the theoretical square discrepancy of LHS. In [16], the square discrepancy formula was represented as follows: …”

Section: Pairing Methods For 2-d Uniformitymentioning

confidence: 99%

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Enhanced-Precision LHSMC of Electrical Circuit Considering Low Discrepancy

Park¹,

Oh²,

Kim³

2015

JSTS:Journal of Semiconductor Technology and Science

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Abstract-The Monte-Carlo (MC) technique is very efficient solution for statistical problem. Various MC methods can easily be applied to statistical circuit performance analysis. Recently, as the number of process parameters and their impact, has increasingly affected circuit performance, a sufficient sample size is required in order to consider high dimensionality, profound nonlinearity, and stringent accuracy requirements. Also, it is important to identify the performance of circuit as soon as possible. In this paper, Fast MC method is proposed for efficient analysis of circuit performance. The proposed method analyzes performance using enhanced-precision Latin Hypercube Sampling Monte Carlo (LHSMC). To increase the accuracy of the analysis, we calculate the effective dimension for the low discrepancy value on critical parameters. This will guarantee a robust input vector for the critical parameters. Using a 90nm process parameter and OP-AMP, we verified the accuracy and reliability of the proposed method in comparison with the standard MC, LHS and Quasi Monte Carlo (QMC).Index Terms-Fast Monte Carlo, latin hypercube sampling, low discrepancy sequence, performance analysis, yield analysis

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“…First, we can build the relation between the computed discrepancy and the theoretical square discrepancy of LHS. In [16], the square discrepancy formula was represented as follows: …”

Section: Pairing Methods For 2-d Uniformitymentioning

confidence: 99%

“…Fig. 14 shows the calculated dimension using formula (16). The number of dimensions to apply to LDS increases, when the number of samples is not large enough.…”

Section: Pairing Methods For 2-d Uniformitymentioning

confidence: 99%

Enhanced-Precision LHSMC of Electrical Circuit Considering Low Discrepancy

Park¹,

Oh²,

Kim³

2015

JSTS:Journal of Semiconductor Technology and Science

View full text Add to dashboard Cite

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“…In the first step, the maximum degradation tolerable for the final design, d t and the step-size ∆ used to conduct nested searches are initialized. A population of designs is then generated randomly or using DOE methods such as the Latin hypercube sampling or minimum discrepancy sequences [24]. Each individual in the population is first evaluated to obtain its nominal fitness.…”

Section: Begin Ea (For Maximization Problem)mentioning

confidence: 99%

“…In particular, we consider the use of Design of Experiments (DOE) sampling approaches including Random Sampling (RS), Stratified Sampling (SS), and Latin Hypercube Sampling (LHS) [24][25][26] to generate m sampled design points as an approximation of the worst-case performance for a design in each of the k iterations (please refer to eq. (8)).…”

Section: Enhancing the Computational Efficiency Of Online Adaptive Immentioning

confidence: 99%

Inverse multi-objective robust evolutionary design

Lim

Ong

Jin

et al. 2006

Genet Program Evolvable Mach

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Abstract. In this paper, we present an Inverse Multi-Objective Robust Evolutionary (IMORE) design methodology that handles the presence of uncertainty without making assumptions about the uncertainty structure. We model the clustering of uncertain events in families of nested sets using a multi-level optimization search. To reduce the high computational costs of the proposed methodology we proposed schemes for 1) adapting the step-size in estimating the uncertainty, and 2) trimming down the number of calls to the objective function in the nested search. Both offline and online adaptation strategies are considered in conjunction with the IMORE design algorithm. Design of Experiments (DOE) approaches further reduce the number of objective function calls in the online adaptive IMORE algorithm. Empirical studies conducted on a series of test functions having diverse complexities show that the proposed algorithms converge to a pareto set of design solutions with non-dominated nominal and robustness performances efficiently.

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“…TA has been applied by Winker and Fang (1997a) to obtain lower bounds for the star-discrepancy, while Winker and Fang (1997b) use the approach to obtain low discrepancy U -type designs for the star-discrepancy. Fang et al (2000) extended the analysis to several modifications of the L 2 -discrepancy, while Fang et al (2002) and Fang et al (2003) consider the centered and wrap-around L 2 -discrepancy. Here, we use settings from Fang et al (2003) for the empirical demonstration of the formal framework.…”

Section: Introductionmentioning

confidence: 99%

The stochastics of threshold accepting: analysis of an application to the uniform design problem

Winker

Compstat 2006 - Proceedings in Computational Statistics

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Abstract Threshold Accepting (TA) is a powerful optimization heuristic from the class of stochastic local search algorithms. It has been applied successfully to different optimization problems in statistics and econometrics, including the uniform design problem. Using the latter application as example, the stochastic properties of a TA implementation are analyzed. We provide a formal framework for the analysis of optimization heuristics like TA, which can be used to estimate lower bounds and to derive convergence results. It is also helpful for tuning real applications. Based on this framework, empirical results are presented for the uniform design problem. In particular, for two problem instances, the rate of convergence of the algorithm is estimated to be of the order of a power of -0.3 to -0.7 of the number of iterations. Terms of use: Documents in

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Centered $L_2$-discrepancy of random sampling and Latin hypercube design, and construction of uniform designs

Cited by 159 publications

References 19 publications

Enhanced-Precision LHSMC of Electrical Circuit Considering Low Discrepancy

Enhanced-Precision LHSMC of Electrical Circuit Considering Low Discrepancy

Inverse multi-objective robust evolutionary design

The stochastics of threshold accepting: analysis of an application to the uniform design problem

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