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Discrete particle swarm optimization for constructing uniform design on irregular regions

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  • Chen, Ray-Bing
  • Hsu, Yen-Wen
  • Hung, Ying
  • Wang, Weichung

Abstract

Central composite discrepancy (CCD) has been proposed to measure the uniformity of a design over irregular experimental region. However, how CCD-based optimal uniform designs can be efficiently computed remains a challenge. Focusing on this issues, we proposed a particle swarm optimization-based algorithm to efficiently find optimal uniform designs with respect to the CCD criterion. Parallel computation techniques based on state-of-the-art graphic processing unit (GPU) are employed to accelerate the computations. Several two- to five-dimensional benchmark problems are used to illustrate the advantages of the proposed algorithms. By solving a real application in data center thermal management, we further demonstrate that the proposed algorithm can be extended to incorporate desirable space-filling properties, such as the non-collapsing property.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:72:y:2014:i:c:p:282-297
    DOI: 10.1016/j.csda.2013.10.015
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    References listed on IDEAS

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    1. Rennen, G. & Husslage, B.G.M. & van Dam, E.R. & den Hertog, D., 2009. "Nested Maximin Latin Hypercube Designs," Discussion Paper 2009-06, Tilburg University, Center for Economic Research.
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    4. Hung, Ying, 2011. "Adaptive Probability-Based Latin Hypercube Designs," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 213-219.
    5. 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.
    6. Paterlini, Sandra & Krink, Thiemo, 2006. "Differential evolution and particle swarm optimisation in partitional clustering," Computational Statistics & Data Analysis, Elsevier, vol. 50(5), pages 1220-1247, March.
    7. Ying Hung & Yasuo Amemiya & Chien-Fu Jeff Wu, 2010. "Probability-based Latin hypercube designs for slid-rectangular regions," Biometrika, Biometrika Trust, vol. 97(4), pages 961-968.
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    Cited by:

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    2. Dongying Wang & Sumin Wang, 2023. "Constructing Optimal Designs for Order-of-Addition Experiments Using a Hybrid Algorithm," Mathematics, MDPI, vol. 11(11), pages 1-20, May.
    3. Xiao, Qian & Xu, Hongquan, 2021. "A mapping-based universal Kriging model for order-of-addition experiments in drug combination studies," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).

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