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

Dongying Wang and Sumin Wang ()
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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

Mathematics, 2023, vol. 11, issue 11, 1-20

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.

Keywords: pairwise-order model; D -optimal; A -optimal; M.S. -optimal; particle swarm optimization; Fedorov exchange algorithm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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