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

Haoyu Wang () and Chongqi Zhang ()
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Haoyu Wang: Guangzhou University
Chongqi Zhang: Guangzhou University

Metrika: International Journal for Theoretical and Applied Statistics, 2022, vol. 85, issue 3, No 4, 345-371

Abstract: 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.

Keywords: Mixture experiment; Optimal design; Mixture model; Meta-heuristic algorithm (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s00184-021-00832-3

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