Exact I-Optimal Constrained Order-of-Addition Experiments
Description
In the chemical, pharmaceutical, and food industries, sometimes the order of adding a set of components has an impact on the final product. These are instances of the order-of-addition (OofA) problem, which aims to find the optimal sequence of the components. Extensive research on this topic has been conducted, but almost all designs are found by optimizing the D−optimality criterion. However, when prediction of the response is important, there is still a need for I−optimal designs, especially if there are constraints on components’ order or interactions among triplets of components. Several algorithms are used to find I−efficient designs under the popular pairwise ordering (PWO) model. Simulations show that the proposed algorithms find highly efficient subsets under the I−optimality criterion. Finally, two examples are shown to illustrate the effectiveness of the proposed designs at identifying optimal orders in scenarios with block constraints on the order of addition and interaction effects between pairwise orders of components.
Files
Exact_I_Optimal_Constrained_Order_of_Addition_Experiments_JSM_Proceeding.pdf
Files
(263.6 kB)
| Name | Size | Download all |
|---|---|---|
|
md5:746c28dc7e06733ef329b2488533d89d
|
263.6 kB | Preview Download |
Additional details
References
- Becerra, M. and P. Goos (2021). Bayesian i-optimal designs for choice experiments with mixtures. Chemometrics and Intelligent Laboratory Systems 217, 104395
- Chandrasekaran, S. M., S. Bhartiya, and P. P. Wangikar (2006). Substrate specificity of lipases in alkoxycarbonylation reaction: Qsar model development and experimental validation. Biotechnology and Bioengineering 94(3), 554–564.
- Chen, J., R. Mukerjee, and D. K. Lin (2020). Construction of optimal fractional order-of-addition designs via block designs. Statistics & Probability Letters 161, 108728.
- Goos, P., B. Jones, and U. Syafitri (2016). I-optimal design of mixture experiments. Journal of the American Statistical Association 111(514), 899–911.
- Goos, P. and U. Syafitri (2014). V-optimal mixture designs for the qth degree model. Chemometrics and Intelligent Laboratory Systems 136, 173–178.
- Joiner, B. L. and C. Campbell (1976). Designing experiments when run order is important. Technometrics 18(3), 249–259.
- Kirkpatrick, S., C. D. Gelatt Jr, and M. P. Vecchi (1983). Optimization by simulated annealing. science 220(4598), 671–680.
- Li, Y. and X. Deng (2021). An efficient algorithm for elastic i-optimal design of generalized linear models. Canadian Journal of Statistics 49(2), 438–470.
- Lin, D. K. and J. Peng (2019). Order-of-addition experiments: A review and some new thoughts. Quality Engineering 31(1), 49–59.
- Mahdavi, S., S. Rahnamayan, and A. Mahdavi (2019). Majority voting for discrete population-based optimization algorithms. Soft Computing 23, 1–18.
- Mee, R. W. (2020). Order-of-addition modeling. Statistica Sinica 30(3), 1543–1559
- Miller, J. M. and J. A. Krosnick (1998). The impact of candidate name order on election outcomes. Public Opinion Quarterly 62(3), 291.
- Sambo, F., M. Borrotti, and K. Mylona (2014). A coordinate-exchange two-phase local search algorithm for the d-and i-optimal designs of split-plot experiments. Computational Statistics & Data Analysis 71, 1193–1207.
- Schoen, E. D. and R. W. Mee (2023). Order-of-addition orthogonal arrays to study the effect of treatment ordering. The Annals of Statistics 51(4), 1877–1894
- Trojovsky, P. and M. Dehghani (2022). A new optimization algorithm based on mimicking the ` voting process for leader selection. PeerJ Computer Science 8, e976.
- Van Nostrand, R. C. (1995). Design of experiments where the order of addition is important. ASA proceedings of the Section on Physical and Engineering Sciences 155.
- Voelkel, J. G. (2019). The design of order-of-addition experiments. Journal of Quality Technology 51(3), 230–241. https://doi.org/10.1080/00224065.2019.1569958.
- Wang, Q. and Z. Li (2019). A modified solvay process with low-temperature calcination of NaHCO3 using monoethanolamine: Solubility determination and thermodynamic modeling. AIChE Journal 65.
- Wheeler, B. (2022). Algdesign: An r package for computing algorithmic experimental designs.
- Yang, J.-F., S. Fasheng, and X. Hongquan (2020). A component-position model, analysis and design for order-of-addition experiments. Technometrics 63, 212–224. https://doi.org/10. 1080/00401706.2020.1764394
- Zhao, Y., D. K. J. Lin, and M.-Q. Liu (2021). Designs for order-of-addition experiments. Journal of Applied Statistics 48, 1475–1495.