Abstract
We focus on the D-optimal design of screening experiments involving main-effects regression models, especially with large numbers of factors and observations. We propose a new selection strategy for the coordinate-exchange algorithm based on an orthogonality measure of the design. Computational experiments show that this strategy finds better designs within an execution time that is 30 % shorter than other strategies. We also provide strong evidence that the use of the prediction variance as a selection strategy does not provide any added value in comparison to simpler selection strategies. Additionally, we propose a new iterated local search algorithm for the construction of D-optimal experimental designs. This new algorithm outperforms the original coordinate-exchange algorithm.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Arnouts, H., Goos, P.: Update formulas for split–plot and block designs. Comput. Stat. Data Anal. 54(12), 3381–3391 (2010)
Atkinson, A.C., Donev, A.N.: The construction of exact D-optimum experimental designs with application to blocking response surface designs. Biometrika 76(3), 515 (1989)
Atkinson, A.C., Donev, A.N., Tobias, R.: Optimum Experimental Designs, with SAS, vol. 34. Oxford University Press, Oxford (2007)
Booth, K.H.V., Cox, D.R.: Some systematic supersaturated designs. Technometrics 4(4), 489–495 (1962)
Borkowski, J.J.: Using a genetic algorithm to generate small exact response surface designs. J. Probab. Stat. Sci. 1(1), 65–88 (2003)
Cawse, J.N.: The combinatorial challenge. In: Cawse, J.N. (ed.) Experimental Design for Combinatorial and High Throughput Materials Development, pp. 1–26. Wiley, Hoboken, NJ (2003)
Cook, R.D., Nachtsheim, C.J.: A comparison of algorithms for constructing exact D-optimal designs. Technometrics 22(3), 315–324 (1980)
Davis, L. (ed.): Handbook of Genetic Algorithms, vol. 115. Van Nostrand Reinhold, New York (1991)
Fedorov, V.V.: Theory of Optimal Experiments. Academic Press, New York (1972)
Glover, F.W.: Future paths for integer programming and links to artificial intelligence. Comput. Oper. Res. 13(5), 533–549 (1986)
Goos, P., Vandebroek, M.: D-optimal split–plot designs with given numbers and sizes of whole plots. Technometrics 45(3), 235–245 (2003)
Goos, P., Jones, B.: Optimal Design of Experiments: A Case Study Approach. Wiley, New York (2011)
Haines, L.M.: The application of the annealing algorithm to the construction of exact optimal designs for linear-regression models. Technometrics 29(4), 439–447 (1987)
Heredia-Langner, A., Carlyle, W.M., Montgomery, D.C., Borror, C.M., Runger, G.C.: Genetic algorithms for the construction of D-optimal designs. J. Qual. Technol. 35, 28–46 (2003)
Johnson, M.E., Nachtsheim, C.J.: Some guidelines for constructing exact D-optimal designs on convex design spaces. Technometrics 25(3), 271–277 (1983)
Jones, B.: Computer aided designs for practical experimentation. Ph.D. thesis, University of Antwerp, Faculty of Applied Economics (2008)
Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671 (1983)
Lejeune, M.A.: Heuristic optimization of experimental designs. Eur. J. Oper. Res. 147(3), 484–498 (2003)
Li, W.W., Wu, C.F.J.: Columnwise–pairwise algorithms with applications to the construction of supersaturated designs. Technometrics 39(2), 171–179 (1997)
Lourenco, H.R., Martin, O.C., Stützle, T.: Iterated local search. In: Glover, F., Kochenberger, G.A. (eds.) Handbook of Metaheuristics, pp. 320–353. Springer, Berlin (2003)
Mandal, B.N., Koukouvinos, C.: Optimal multi-level supersaturated designs through integer programming. Stat. Probab. Lett. 84, 183–191 (2014)
Meyer, R.K., Nachtsheim, C.J.: Simulated annealing in the construction of exact optimal design of experiments. Am. J. Math. Manag. Sci. 8, 329–359 (1988)
Meyer, R.K., Nachtsheim, C.J.: The coordinate-exchange algorithm for constructing exact optimal experimental designs. Technometrics 37(1), 60–69 (1995)
Michalewicz, Z., Fogel, D.B.: How to solve it: modern heuristics. Springer, New York (2004)
Mitchell, T.J.: Computer construction of “D-optimal” first-order designs. Technometrics 16(1), 211–220 (1974)
Mitchell, T.J.: An algorithm for the construction of “D-optimal” experimental designs. Technometrics 16(2), 203–210 (1974)
Montepiedra, G., Myers, D., Yeh, A.B.: Application of genetic algorithms to the construction of exact D-optimal designs. J. Appl. Stat. 25(6), 817–826 (1998)
Montgomery, D.C., Jennings, C.L.: An overview of industrial screening experiments. In: Dean, A., Lewis, S. (eds.) Screening: Methods for Experimentation in Industry, Drug Discovery, and Genetics, pp. 1–20. Springer, New York (2006)
Montgomery, D.C.: Design and Analysis of Experiments. Wiley, New York (2008)
Nguyen, N.K., Miller, A.J.: A review of some exchange algorithms for constructing discrete D-optimal designs. Comput. Stat. Data Anal. 14(4), 489–498 (1992)
Nguyen, N.K.: An algorithmic approach to constructing supersaturated designs. Technometrics 38(1), 69–73 (1996)
Plackett, R.L., Burman, J.P.: The design of optimum multifactorial experiments. Biometrika 33(4), 305–325 (1946)
Sörensen, K., Glover, F.: Metaheuristics. In: Gass, S., Fu, M. (eds.) Encyclopedia of Operations Research and Management Science, 3rd edn. Springer, London (2013)
Sung Jung, J., Jin Yum, B.: Construction of exact D-optimal designs by tabu search. Comput. Stat. Data Anal. 21(2), 181–191 (1996)
Talbi, E.G.: Metaheuristics: From Design to Implementation. Wiley, New York (2009)
Trinca, L.A., Gilmour, S.G.: An algorithm for arranging response surface designs in small blocks. Comput. Stat. Data Anal. 33(1), 25–43 (2000). Erratum 40(3), 475 (2002)
Welch, W.J.: Algorithmic complexity: three NP-hard problems in computational statistics. J. Stat. Comput. Simul. 15(1), 17–25 (1982)
Wu, C.F.J., Hamada, M.: Experiments: Planning, Analysis, and Parameter Design Optimization. Wiley, New York (2000)
Acknowledgments
We acknowledge the financial support of the Flemish Fund for Scientific Research (FWO).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Palhazi Cuervo, D., Goos, P. & Sörensen, K. Optimal design of large-scale screening experiments: a critical look at the coordinate-exchange algorithm. Stat Comput 26, 15–28 (2016). https://doi.org/10.1007/s11222-014-9467-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11222-014-9467-z