zbMATH — the first resource for mathematics

A coordinate-exchange two-phase local search algorithm for the D- and I-optimal designs of split-plot experiments. (English) Zbl 06975457
Summary: Many industrial experiments involve one or more restrictions on the randomization. In such cases, the split-plot design structure, in which the experimental runs are performed in groups, is a commonly used cost-efficient approach that reduces the number of independent settings of the hard-to-change factors. Several criteria can be adopted for optimizing split-plot experimental designs: the most frequently used are D-optimality and I-optimality. A multi-objective approach to the optimal design of split-plot experiments, the coordinate-exchange two-phase local search (CE-TPLS), is proposed. The CE-TPLS algorithm is able to approximate the set of experimental designs which concurrently minimize the D-criterion and the I-criterion. It allows for a flexible choice of the number of hard-to-change factors, the number of easy-to-change factors, the number of whole plots and the total sample size. When tested on four case studies from the literature, the proposed algorithm returns meaningful sets of experimental designs, covering the whole spectrum between the two objectives. On most of the analyzed cases, the CE-TPLS algorithm returns better results than those reported in the original papers and outperforms the state-of-the-art algorithm in terms of computational time, while retaining a comparable performance in terms of the quality of the optima for each single objective.

62 Statistics
Full Text: DOI
[1] Dubois-Lacoste, J.; López-Ibáñez, M.; Stützle, T., A hybrid TP + PLS algorithm for bi-objective flow-shop scheduling problems, Computers & Operations Research, 38, 8, 1219-1236, (2011) · Zbl 1208.90059
[2] Dubois-Lacoste, J.; López-Ibáñez, M.; Stützle, T., Improving the anytime behavior of two-phase local search, Annals of Mathematics and Artificial Intelligence, 61, 2, 125-154, (2011) · Zbl 1234.68362
[3] Fleischer, M., The measure of Pareto optima applications to multi-objective metaheuristics, (Proceedings of the 2nd International Conference on Evolutionary Multi-Criterion Optimization, Lecture Notes in Computer Science, vol. 2632, (2003)), 519-533 · Zbl 1036.90530
[4] Gilmour, S.G., Pardo, J.M., Trinca, L.A., Niranjan, K., Mottram, D.S., 2000. A split-plot response surface design for improving aroma retention in freeze dried coffee. In: Proceedings of the 6th. European conference on Food-Industry Statist. pp. 18.0-18.9.
[5] Goos, P., The optimal design of blocked and split-plot experiments, (2002), Springer New York · Zbl 1008.62068
[6] Goos, P., Optimal versus orthogonal and equivalent-estimation design of blocked and split-plot experiments, Statistica Neerlandica, 60, 361-378, (2006) · Zbl 1108.62073
[7] Goos, P.; Donev, A., The \(d\)-optimal design of blocked experiments with mixture components, Journal of Quality Technology, 38, 319-332, (2006)
[8] Goos, P.; Jones, B., Optimal design of experiments: A case study approach, (2011), Wiley
[9] Goos, P. P.; Langhans, I.; Vandebroek, M., Practical inference from industrial split-plot design, Journal of Quality Technology, 38, 162-179, (2006)
[10] Goos, P.; Vandebroek, M., Optimal split-plot designs, Journal of Quality Technology, 33, 436-450, (2001) · Zbl 1079.62532
[11] Goos, P.; Vandebroek, M., D-optimal split-plot designs with given numbers and sizes of whole plots, Technometrics, 45, 235-245, (2003)
[12] Goos, P.; Vandebroek, M., Outperforming completely randomized designs, Journal of Quality Technology, 36, 12-26, (2004)
[13] Hardin, R. H.; Sloane, N. J.A., Computer-generated minimal (and larger) response-surface designs: (II). the cube. tech. rep., (1991)
[14] Hoos, H. H.; Stützle, T., (Stochastic Local Search: Foundations & Applications, The Morgan Kaufmann Series in Artificial Intelligence, (2004), Morgan Kaufmann) · Zbl 1126.68032
[15] Jones, B.; Goos, P., A candidate-set-free algorithm for generating D-optimal split-plot designs, Journal of the Royal Statistical Society Series C-Applied Statistics, 56, 347-364, (2007)
[16] Jones, B.; Goos, P., I-optimal versus D-optimal split-plot response surface designs, Journal of Quality Technology, 44, 85-101, (2012)
[17] Jones, B.; Nachtsheim, C. J., Split-plot designs: what, why, and how, Journal of Quality Technology, 41, 340-361, (2009)
[18] Khuri, A. I.; Cornell, J. A., Response surfaces, (1996), Dekker New York · Zbl 0953.62073
[19] Knowles, J.; Watson, R.; Corne, D., Reducing local optima in single-objective problems by multi-objectivization, (Evolutionary Multi-Criterion Optimization, (2001), Springer), 269-283
[20] Langhans, I.; Goos, P. P.; Vandebroek, M., Identifying effects under a split-plot design structure, Journal of Chemomentrics, 19, 5-15, (2005)
[21] Letsinger, J. D.; Myers, R. H.; Lentner, M., Response surface methods for bi-randomization structures, Journal of Quality Technology, 28, 381-397, (1996)
[22] Lu, L.; Anderson-Cook, C. M.; Robinson, T. J., Optimization of design experiments based on multiple criteria utilizing a Pareto frontier, Technometrics, 53, 4, 353-365, (2011)
[23] Lust, T.; Teghem, J., Two-phase Pareto local search for the biobjective traveling salesman problem, Journal of Heuristics, 16, 3, 475-510, (2010) · Zbl 1189.90145
[24] Macharia, H.; Goos, P., D-optimal and D-efficient equivalent-estimation second-order split-plot designs, Journal of Quality Technology, 42, 358-372, (2010)
[25] Myers, R. H.; Montgomery, D. C., Response surface methodology: process and product optimization using designed experiments, (2002), Wiley New York · Zbl 1161.62393
[26] Paquete, L.; Stützle, T., Stochastic local search algorithms for multiobjective combinatorial optimization: a review, (Gonzalez, T. F., Handbook of Approximation Algorithms and Metaheuristics, Computer and Information Science Series, (2007), Chapman & Hall/CRC Boca Raton, FL), 29.1-29.15
[27] Sartono, B.; Goos, P.; Schoen, E. D., Classification of three-level strength-3 arrays, Journal of Statistical Planning and Inference, 142, 794-809, (2012) · Zbl 1232.62112
[28] Schoen, E. D.; Jones, B.; Goos, P., A split-plot experiment with factor-dependent whole-plot sizes, Journal of Quality Technology, 43, 66-79, (2011)
[29] Smucker, B. J.; del Castillo, E.; Rosenberger, J. L., Model-robust designs for split-plot experiments, Computational Statistics & Data Analysis, 56, 12, 4111-4121, (2012) · Zbl 1255.62222
[30] Sun, D. X.; Jeff Wu, C. F.; Chen, Y., Optimal blocking schems for \(2^n\) and \(2^{n - p}\) designs, Technometrics, 39, 298-307, (1997) · Zbl 0891.62055
[31] Trinca, L. A.; Gilmour, S. G., Multi-stratum response surface designs, Technometrics, 43, 25-33, (2001) · Zbl 1072.62623
[32] Zitzler, E.; Thiele, L.; Laumanns, M.; Fonseca, C. M.; da Fonseca, V. G., Performance assessment of multiobjective optimizers: an analysis and review, IEEE Transactions on Evolutionary Computation, 7, 117-132, (2003)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.