Article
Version 2
Preserved in Portico This version is not peer-reviewed
Constructing Optimal Designs for Order-of-Addition Experiments Using a Hybrid Algorithm
Version 1
: Received: 28 April 2023 / Approved: 28 April 2023 / Online: 28 April 2023 (10:43:27 CEST)
Version 2 : Received: 30 May 2023 / Approved: 31 May 2023 / Online: 31 May 2023 (08:45:18 CEST)
Version 2 : Received: 30 May 2023 / Approved: 31 May 2023 / Online: 31 May 2023 (08:45:18 CEST)
A peer-reviewed article of this Preprint also exists.
Wang, D.; Wang, S. Constructing Optimal Designs for Order-of-Addition Experiments Using a Hybrid Algorithm. Mathematics 2023, 11, 2538. Wang, D.; Wang, S. Constructing Optimal Designs for Order-of-Addition Experiments Using a Hybrid Algorithm. Mathematics 2023, 11, 2538.
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 (1995) 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
Subject
Computer Science and Mathematics, Probability and Statistics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (1)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
Commenter: Sumin Wang
Commenter's Conflict of Interests: Author
2. We have made extensive revisions to the Introduction section.
3. we have made extensive corrections to the long sentences in our previous draft, such that the sentences in Line 121 on Page 4, in Line 162 on Page 5.
4. We have made extensive revisions to the Introduction section. The motivation has been addressed in the first paragraph, the summary of challenges of previous studies have been discussed in the second and third paragraphs, and the main contributions of our article have been mentioned in the fourth paragraph.