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The mixture design threshold accepting algorithm for generating \(\varvec{D}\)-optimal designs of the mixture models

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Abstract

This paper proposes a target specialized meta-heuristic optimization algorithm, called Mixture Design Threshold Accepting (MDTA) algorithm, which applies the idea of the Threshold Accepting to generate the corresponding approximate D-optimal designs for a wide range of mixture models, with or without constraints imposed on the components. The MDTA algorithm is tested by many of common mixture models, among which some even have no solutions of the D-optimal design available in the literature. Other tests include 5 models with specific upper bound constraints. These results prove that the MDTA algorithm is very efficient in finding D-optimal designs for mixture models. In some scenarios it even outperforms the state-of-art algorithms, such as the ProjPSO algorithm and the REX algorithm. The source codes of the MDTA algorithm are freely available by writing to the first author.

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Acknowledgements

We would like to thank the referees and the journal editorial team for providing valuable advice that improved the quality of the original manuscript. This work is supported by National Nature Sciences Foundation of China (12071096) and Guangzhou University graduate innovative ability training funding program (2018GDJC-D20).

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  1. School of Economics and Statistics, Guangzhou University, No. 230, West Waihuan Road, Higher Education Mega Center, Panyu District, Guangzhou City, Guangdong Province, People’s Republic of China

    Haoyu Wang & Chongqi Zhang

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  1. Haoyu Wang
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  2. Chongqi Zhang
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Correspondence to Chongqi Zhang.

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Wang, H., Zhang, C. The mixture design threshold accepting algorithm for generating \(\varvec{D}\)-optimal designs of the mixture models. Metrika 85, 345–371 (2022). https://doi.org/10.1007/s00184-021-00832-3

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