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Optimized U-type designs on flexible regions

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  • Lin, D.K.J.
  • Sharpe, C.
  • Winker, P.

Abstract

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 are analyzed based on a set of design points. The choice of design points can be made based on some discrepancy criterion. The generation of design points on a flexible region is investigated. A recently proposed discrepancy measure, the central composite discrepancy, is used for this purpose. The optimization heuristic Threshold Accepting is applied to generate low-discrepancy U-type designs. The proposed algorithm is capable of constructing optimal U-type designs under various flexible experimental regions in two or more dimensions. The illustrative results for the two-dimensional case indicate that by using an optimization heuristic in combination with an appropriate discrepancy measure produces high-quality experimental designs on flexible regions.

Suggested Citation

  • Lin, D.K.J. & Sharpe, C. & Winker, P., 2010. "Optimized U-type designs on flexible regions," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1505-1515, June.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:6:p:1505-1515
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    References listed on IDEAS

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    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.
    6. Gilli, Manfred & Winker, Peter, 2007. "2nd Special Issue on Applications of Optimization Heuristics to Estimation and Modelling Problems," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 2-3, September.
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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. Rios, Nicholas & Winker, Peter & Lin, Dennis K.J., 2022. "TA algorithms for D-optimal OofA Mixture designs," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    3. Marianna Lyra, 2010. "Heuristic Strategies in Finance – An Overview," Working Papers 045, COMISEF.

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