Centered L 2 -discrepancy of random sampling and Latin hypercube design, and construction of uniform designs
TL;DR: In this paper properties and construction of designs under a centered version of the L2-discrepancy are analyzed and optimization is performed using the threshold accepting heuristic which produces low discrepancy designs compared to theoretic expectation and variance.
read more
Abstract: In this paper properties and construction of designs under a centered version of the L2-discrepancy are analyzed. The theoretic expectation and variance of this discrepancy are derived for random designs and Latin hypercube designs. The expectation and variance of Latin hypercube designs are significantly lower than that of random designs. While in dimension one the unique uniform design is also a set of equidistant points, low-discrepancy designs in higher dimension have to be generated by explicit optimization. Optimization is performed using the threshold accepting heuristic which produces low discrepancy designs compared to theoretic expectation and variance.
read more
Chat with Paper
AI Agents for this Paper
Find similar papers on Google Scholar, PubMed and Arxiv
Write a critical review of this paper
Analyze citations of this paper to find unaddressed research gaps
Citations
Memetic algorithm using multiple surrogates for complex engineering design optimization
Zongzhao. Zhou
- 01 Jan 2008
TL;DR: A novel hierarchical surrogate-assisted memetic algorithm (HSAMA) combining both global and local surrogate models for accelerating the optimization process is proposed and described and results show that the HSAMA algorithm is capable of achieving good designs efficiently under a limited computational budget.
The Contribution to Experimental Designs by Kai-Tai Fang
Min-Qian Liu,Dennis K.J. Lin,Yong-Dao Zhou +2 more
- 01 Jan 2020
TL;DR: This paper focuses on the contribution of Kai-Tai Fang to experimental designs such as uniform designs, orthogonal designs, supersaturated designs and computer experiments.
Development, Optimization, and Design for Robustiness of a Novel FMVSS 201U Energy Absorber
David M Fox
- 03 Jun 2005
TL;DR: In this paper, the design space for FMVSS 201 U impact performance of a steel mechanical energy absorber assembly was investigated by means of LS-DYNA 970 explicit finite element simulation methods in conjunction with statistical analytical procedures.
Modification of the Maximin and ϕp (Phi) Criteria to Achieve Statistically Uniform Distribution of Sampling Points
Miroslav Vořechovský,Jan Eliáš +1 more
TL;DR: Using a periodic metric to guarantee the statistical uniformity of the family of distance-based designs is proposed, which forces univariate projections to be uniform and improves accuracy in Monte Carlo integration of some functions.
References
A comparison of three methods for selecting values of input variables in the analysis of output from a computer code
TL;DR: In this paper, two sampling plans are examined as alternatives to simple random sampling in Monte Carlo studies and they are shown to be improvements over simple sampling with respect to variance for a class of estimators which includes the sample mean and the empirical distribution function.
10.3K
•Book
Random number generation and quasi-Monte Carlo methods
Harald Niederreiter
- 01 Jan 1992
TL;DR: This chapter discusses Monte Carlo methods and Quasi-Monte Carlo methods for optimization, which are used for numerical integration, and their applications in random numbers and pseudorandom numbers.
4K
Monte Carlo and quasi-Monte Carlo methods
TL;DR: In this paper, the authors presented an introduction to Monte Carlo methods for integration problems, including convergence theory, sampling methods and variance reduction techniques, and showed Monte Carlo to be very robust but also slow.
1.9K
Orthogonal Array-Based Latin Hypercubes
TL;DR: It is proved that when used for integration, the sampling scheme with OA-based Latin hypercubes offers a substantial improvement over Latin hypercube sampling.
872
A generalized discrepancy and quadrature error bound
TL;DR: An error bound for multidimensional quadrature is derived that includes the Koksma-Hlawka inequality as a special case and includes as special cases the L p -star discrepancy and P α that arises in the study of lattice rules.
775