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Constructing Optimal Designs for Order-of-Addition Experiments Using a Hybrid Algorithm

Author

Listed:
  • Dongying Wang

    (School of Statistics, Jilin University of Finance and Economics, Changchun 130117, China)

  • Sumin Wang

    (Center for Combinatorics, LPMC & KLMDASR, Nankai University, Tianjin 300071, China)

Abstract

For order-of-addition experiments, the response is affected by the addition order of the experimental materials. Consequently, the main interest focuses on creating a predictive model and an optimal design for optimizing the response. Van Nostrand proposed the pairwise-order (PWO) model for detecting PWO effects. Under the PWO model, the full PWO design is optimal under various criteria but is often unaffordable because of the large run size. In this paper, we consider the D -, A - and M . S . -optimal fractional PWO designs. We first present some results on information matrices. Then, a flexible and efficient algorithm is given for generating these optimal PWO designs. Numerical simulation shows that the generated design has an appealing efficiency in comparison with the full PWO design, though with only a small fraction of runs. Several comparisons with existing designs illustrate that the generated designs achieve better efficiencies, and the best PWO designs and some selected 100% efficient PWO designs generated by the new algorithm are reported.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:11:p:2538-:d:1161219
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    References listed on IDEAS

    as
    1. Yuna Zhao & Dennis K. J. Lin & Min-Qian Liu, 2021. "Designs for order-of-addition experiments," Journal of Applied Statistics, Taylor & Francis Journals, vol. 48(8), pages 1475-1495, June.
    2. 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.
    3. Zhao, Yuna & Lin, Dennis K.J. & Liu, Min-Qian, 2022. "Optimal designs for order-of-addition experiments," Computational Statistics & Data Analysis, Elsevier, vol. 165(C).
    4. Nguyen, Nam-Ky & Miller, Alan J., 1992. "A review of some exchange algorithms for constructing discrete D-optimal designs," Computational Statistics & Data Analysis, Elsevier, vol. 14(4), pages 489-498, November.
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