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Optimized U-type Designs on Flexible Regions


  • Dennis K.J. Lin
  • Chris Sharpe
  • Peter Winker


The concept of a flexible region describes an infinite variety of symmetrical shapes to enclose a particular region of interest within a space. In experimental design, the properties of a function on the region of interest is analyzed based on a set of design points. The choice of design points can be made based on some discrepancy criterion. This paper investigates the generation of design points on a flexible region. It uses a recently proposed new measure of discrepancy for this purpose, the Central Composite Discrepancy. The optimization heuristic Threshold Accepting is used to generate low discrepancy Utype designs. The proposed algorithm is capable to construct optimal U-type designs under various flexible experimental regions in two or more dimensions. The illustrative results for the two dimensional case indicate that using an optimization heuristic in combination with an appropriate discrepancy measure, it is possible to produce high quality experimental designs on flexible regions.

Suggested Citation

  • Dennis K.J. Lin & Chris Sharpe & Peter Winker, 2009. "Optimized U-type Designs on Flexible Regions," Working Papers 013, COMISEF.
  • Handle: RePEc:com:wpaper:013

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    References listed on IDEAS

    1. Winker, Peter & Gilli, Manfred, 2004. "Applications of optimization heuristics to estimation and modelling problems," Computational Statistics & Data Analysis, Elsevier, vol. 47(2), pages 211-223, September.
    2. Winker, Peter & Fang, Kai-Tai, 1995. "Application of threshold accepting to the evaluation of the discrepancy of a set of points," Discussion Papers, Series II 248, University of Konstanz, Collaborative Research Centre (SFB) 178 "Internationalization of the Economy".
    3. Winker, Peter, 2005. "The Stochastics of Threshold Accepting: Analysis of an Application to the Uniform Design Problem," Discussion Papers 2005,003E, University of Erfurt, Faculty of Economics, Law and Social Sciences.
    4. Chuang, S.C. & Hung, Y.C., 2010. "Uniform design over general input domains with applications to target region estimation in computer experiments," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 219-232, January.
    5. Huang, Mong-Na Lo & Lee, Chuan-Pin & Chen, Ray-Bing & Klein, Thomas, 2010. "Exact D-optimal designs for a second-order response surface model on a circle with qualitative factors," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 516-530, February.
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    Cited by:

    1. Chen, Ray-Bing & Hsu, Yen-Wen & Hung, Ying & Wang, Weichung, 2014. "Discrete particle swarm optimization for constructing uniform design on irregular regions," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 282-297.
    2. Marianna Lyra, 2010. "Heuristic Strategies in Finance – An Overview," Working Papers 045, COMISEF.

    More about this item


    Central composite discrepancy; Experimental design; Flexible regions; Threshold accepting; U-type design;

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