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TA algorithms for D-optimal OofA Mixture designs

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  • Rios, Nicholas
  • Winker, Peter
  • Lin, Dennis K.J.

Abstract

In a mixture experiment, m components are mixed to produce a response. The total amount of the mixture is a constant. This classical experiment has been studied for a long time, but little attention has been given to the addition order of the components. In an Order-of-Addition (OofA) Mixture experiment, the response depends on both the mixture proportions of components and their order of addition. The overall goal of the OofA Mixture experiment is to identify the addition order and mixture proportions that produce an optimal response. Methodology for constructing full OofA Mixture designs is discussed, but the size of these full designs increases rapidly as m increases. A Threshold Accepting (TA) algorithm is used to find a subset of n rows of the full OofA Mixture design that maximize the D-optimality criterion, reducing the number of required runs. Neighborhood structures are proposed for OofA simplex lattice and general mixture designs. The TA algorithm is compared with the well-known Fedorov algorithm, and recommendations for the use of this algorithm are provided.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:csdana:v:168:y:2022:i:c:s0167947321002450
    DOI: 10.1016/j.csda.2021.107411
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    References listed on IDEAS

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    1. Lyra, M. & Paha, J. & Paterlini, S. & Winker, P., 2010. "Optimization heuristics for determining internal rating grading scales," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2693-2706, November.
    2. 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.
    3. 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.
    4. García-Ródenas, Ricardo & García-García, José Carlos & López-Fidalgo, Jesús & Martín-Baos, José Ángel & Wong, Weng Kee, 2020. "A comparison of general-purpose optimization algorithms for finding optimal approximate experimental designs," Computational Statistics & Data Analysis, Elsevier, vol. 144(C).
    5. Chen, Jianbin & Mukerjee, Rahul & Lin, Dennis K.J., 2020. "Construction of optimal fractional Order-of-Addition designs via block designs," Statistics & Probability Letters, Elsevier, vol. 161(C).
    6. Peter Goos & Bradley Jones & Utami Syafitri, 2016. "I-Optimal Design of Mixture Experiments," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(514), pages 899-911, April.
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