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Contemporary Experimental Design, Multivariate Analysis and Data Mining pp 93–109Cite as

The Construction of Optimal Design for Order-of-Addition Experiment via Threshold Accepting

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Abstract

The objective of the order-of-addition (OofA) experiment is to find the optimal addition order by comparing all responses with different orders. Assuming that the OofA experiment involves \(m (\ge 2)\) components, there are m! different orders of adding sequence. When m is large, it is infeasible to compare all m! possible solutions (for example, \(10!\approx 3.6\) millions). Two potential construction methods are systematic combinatorial construction and computer algorithmic search. Computer search methods presented in the literature for constructing optimal fractional designs of OofA experiments appear rather simplistic. In this paper, based on the pairwise-order (PWO) model and the tapered PWO model, the threshold accepting algorithm is applied to construct the optimal design (D-efficiency for the present application) with subsets of size n among all possible size m!. In practical, the designs obtained by threshold accepting algorithm for \(4 \le m\le 30\) with \(n=m(m-1)/2+1, m(m-1)+1, 3m(m-1)/2+1\) respectively are provided for practical uses. This is apparently the most complete list of order-of-addition (OofA) designs via computer search for \(4 \le m\le 30\) in the literature. Their efficiencies are illustrated by a scheduling problem.

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Acknowledgements

All designs obtained can be found in website: www.jlug.de/optimaloofadesigns. This work was partially supported by the National Science Foundation via Grant DMS 18102925. The work of Jianbin Chen was supported by the National Natural Science Foundation of China (Grant Nos. 11771220). Professor Kai-Tai Fang has been a true leader in our society and has been a strong supporter of young fellows. His original work on uniform design had a significant impact on this work. It is our great privilege to contribute this work on computer experiments to this special issue in honor of his 80th birthday.

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Authors and Affiliations

  1. Justus-Liebig-University Giessen, Licher Str. 64, 35394, Giessen, Germany

    Peter Winker

  2. School of Statistics and Data Science & LPMC, Nankai University, Tianjin, 300071, China

    Jianbin Chen

  3. Department of Statistics, Purdue University, 250 N. University Street, West Lafayette, IN, 47907, USA

    Dennis K. J. Lin

Authors
  1. Peter Winker
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  2. Jianbin Chen
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  3. Dennis K. J. Lin
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Correspondence to Dennis K. J. Lin .

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Editors and Affiliations

  1. Department of Financial Engineering, Princeton University, Princeton, NJ, USA

    Jianqing Fan

  2. Department of Mathematics, The University of Manchester, Manchester, UK

    Jianxin Pan

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Winker, P., Chen, J., Lin, D.K.J. (2020). The Construction of Optimal Design for Order-of-Addition Experiment via Threshold Accepting. In: Fan, J., Pan, J. (eds) Contemporary Experimental Design, Multivariate Analysis and Data Mining. Springer, Cham. https://doi.org/10.1007/978-3-030-46161-4_6

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