Space-Filling Latin Hypercube Designs for Computer Experiments

Husslage, B.G.M.; Rennen, G.; Dam, Edwin van; Hertog, Dick den

doi:10.2139/ssrn.895464

Cited by 16 publications

(16 citation statements)

References 38 publications

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“…The original formulation of the AE criterion [1] (see also [4,5,6,7]) considers the analogy between the sampling plan and a system of charged particles with repulsive forces. The potential energy of the system is the sum of energies 2 1/ ij L accumulated by each pair of points i and j.…”

Section: Audze-eglajs and Phi Criteriamentioning

confidence: 99%

On the Influence of the Interaction Laws of a Dynamical Particle System for Sample Optimization

Masek¹,

Vořechovský²

2017

Transactions of the VŠB – Technical University of Ostrava, Civil Engineering Series.

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The presented paper investigates the effect of the formulation of the energy potential of a dynamical particle system used for the optimization of statistical point sampling. The dynamical particle system, originally developed as a physical analogy to the Audze-Eglajs (AE) optimization criterion and its periodical modification (PAE), effectively demonstrated that the originally proposed energy potential performs well only in poorly applicable scenarios featuring low-dimensional design domains filled with a rather high number of design points. A remedy is presented which involves a refined formulation of the energy potential, as well as its derivation. The reasoning behind this approach is also dealt with in detail.

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Section: Audze-eglajs and Phi Criteriamentioning

confidence: 99%

On the Influence of the Interaction Laws of a Dynamical Particle System for Sample Optimization

Masek¹,

Vořechovský²

2017

Transactions of the VŠB – Technical University of Ostrava, Civil Engineering Series.

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“…In this paper a maximin sampling scheme is applied, a distancebased space-filling scheme that maximises the minimal distance between Latin Hypercube sampling points [27].…”

Section: Sampling Schemementioning

confidence: 99%

“…They would like to thank Bart Husslage and Gijs Rennen from the Tilburg University as well for sharing their MATLAB code for calculation of maximin sampling schemes [27].…”

Section: Acknowledgementsmentioning

confidence: 99%

Probabilistic design and analysis of building performances: Methodology and application example

Gelder

Janssen

Roels

2014

Energy and Buildings

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Both building performance analysis and multi-criteria performance optimisation often use deterministic simulations. Since many influencing parameters are generally inherently uncertain, this may lead to unreliable predictions of design impact. Therefore, this paper proposes a probabilistic analysis and design method to incorporate these uncertainties. The embedded Monte Carlo based uncertainty and sensitivity analyses investigate the output distributions. To greatly reduce computational efforts, meta-models can be incorporated, replacing the original model. Additionally, multi-layered sampling schemes are used to subject all design options to the same uncertainties and to check the validity of optimisation results for potential scenarios. Since reliability is a key aspect in this methodology, the paper also focuses on output convergence and method reliability.To optimise both average performances and spread, effectiveness ε and robustness R P are introduced as output uncertainty indicators, inspired by robust design. Here, effectiveness is defined as the ability of the design option to optimise the performance, while robustness is defined as the ability to stabilise this performance for the entire range of input uncertainties.The successive methodology steps are explained using a simplified application example.

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“…One possible heuristic is the ESE-algorithm of Jin et al (2005). In Husslage et al (2008), this algorithm obtains good results for approximate maximin LHDs. Although this algorithm was originally designed for non-nested designs, with some changes it is also applicable to nested designs.…”

Section: Higher Dimensional Nested Designs 41 Enhanced Stochastic Evmentioning

confidence: 99%

“…Jin et al (2005) introduce the enhanced stochastic evolutionary (ESE) algorithm for finding various space-filling designs, among which approximate maximin LHDs. In Husslage et al (2008), the ESE-algorithm is also used to construct approximate maximin LHDs for up to 10 dimensions and up to 300 design points. Furthermore, they also construct approximate maximin LHDs by optimizing the maximin criterion over all LHDs having a certain periodic structure.…”

Section: Introductionmentioning

confidence: 99%

Nested Maximin Latin Hypercube Designs

et al. 2009

Self Cite

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In the field of design of computer experiments (DoCE), Latin hypercube designs are frequently used for the approximation and optimization of black-boxes. In certain situations, we need a special type of designs consisting of two separate designs, one being a subset of the other. These nested designs can be used to deal with training and test sets, models with different levels of accuracy, linking parameters, and sequential evaluations. In this paper, we construct nested maximin Latin hypercube designs for up to ten dimensions. We show that different types of grids should be considered when constructing nested designs and discuss how to determine which grid to use for a specific application. To determine nested maximin designs for dimensions higher than two, four different variants of the ESE-algorithm of Jin et al. (2005) are introduced and compared. In the appendix, maximin distances for different numbers of points are provided; the corresponding nested maximin designs can be found on the website http://www.spacefillingdesigns.nl.

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Space-Filling Latin Hypercube Designs for Computer Experiments

Cited by 16 publications

References 38 publications

On the Influence of the Interaction Laws of a Dynamical Particle System for Sample Optimization

On the Influence of the Interaction Laws of a Dynamical Particle System for Sample Optimization

Probabilistic design and analysis of building performances: Methodology and application example

Nested Maximin Latin Hypercube Designs

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