Statistics and Computing

, Volume 26, Issue 1–2, pp 15–28 | Cite as

Optimal design of large-scale screening experiments: a critical look at the coordinate-exchange algorithm

  • Daniel Palhazi Cuervo
  • Peter Goos
  • Kenneth Sörensen


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.


Optimal design of experiments D-optimality criterion  Coordinate-exchange algorithm Metaheuristic Iterated local search 



We acknowledge the financial support of the Flemish Fund for Scientific Research (FWO).


  1. Arnouts, H., Goos, P.: Update formulas for split–plot and block designs. Comput. Stat. Data Anal. 54(12), 3381–3391 (2010)zbMATHMathSciNetCrossRefGoogle Scholar
  2. 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)zbMATHMathSciNetCrossRefGoogle Scholar
  3. Atkinson, A.C., Donev, A.N., Tobias, R.: Optimum Experimental Designs, with SAS, vol. 34. Oxford University Press, Oxford (2007)zbMATHGoogle Scholar
  4. Booth, K.H.V., Cox, D.R.: Some systematic supersaturated designs. Technometrics 4(4), 489–495 (1962)zbMATHMathSciNetCrossRefGoogle Scholar
  5. Borkowski, J.J.: Using a genetic algorithm to generate small exact response surface designs. J. Probab. Stat. Sci. 1(1), 65–88 (2003)MathSciNetGoogle Scholar
  6. 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)Google Scholar
  7. Cook, R.D., Nachtsheim, C.J.: A comparison of algorithms for constructing exact D-optimal designs. Technometrics 22(3), 315–324 (1980)zbMATHCrossRefGoogle Scholar
  8. Davis, L. (ed.): Handbook of Genetic Algorithms, vol. 115. Van Nostrand Reinhold, New York (1991)Google Scholar
  9. Fedorov, V.V.: Theory of Optimal Experiments. Academic Press, New York (1972)Google Scholar
  10. Glover, F.W.: Future paths for integer programming and links to artificial intelligence. Comput. Oper. Res. 13(5), 533–549 (1986)zbMATHMathSciNetCrossRefGoogle Scholar
  11. Goos, P., Vandebroek, M.: D-optimal split–plot designs with given numbers and sizes of whole plots. Technometrics 45(3), 235–245 (2003)MathSciNetCrossRefGoogle Scholar
  12. Goos, P., Jones, B.: Optimal Design of Experiments: A Case Study Approach. Wiley, New York (2011)CrossRefGoogle Scholar
  13. 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)zbMATHGoogle Scholar
  14. 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)Google Scholar
  15. Johnson, M.E., Nachtsheim, C.J.: Some guidelines for constructing exact D-optimal designs on convex design spaces. Technometrics 25(3), 271–277 (1983)Google Scholar
  16. Jones, B.: Computer aided designs for practical experimentation. Ph.D. thesis, University of Antwerp, Faculty of Applied Economics (2008) Google Scholar
  17. Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671 (1983)zbMATHMathSciNetCrossRefGoogle Scholar
  18. Lejeune, M.A.: Heuristic optimization of experimental designs. Eur. J. Oper. Res. 147(3), 484–498 (2003)zbMATHMathSciNetCrossRefGoogle Scholar
  19. Li, W.W., Wu, C.F.J.: Columnwise–pairwise algorithms with applications to the construction of supersaturated designs. Technometrics 39(2), 171–179 (1997)zbMATHMathSciNetCrossRefGoogle Scholar
  20. 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)Google Scholar
  21. Mandal, B.N., Koukouvinos, C.: Optimal multi-level supersaturated designs through integer programming. Stat. Probab. Lett. 84, 183–191 (2014)zbMATHMathSciNetCrossRefGoogle Scholar
  22. 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)zbMATHMathSciNetGoogle Scholar
  23. Meyer, R.K., Nachtsheim, C.J.: The coordinate-exchange algorithm for constructing exact optimal experimental designs. Technometrics 37(1), 60–69 (1995)zbMATHMathSciNetCrossRefGoogle Scholar
  24. Michalewicz, Z., Fogel, D.B.: How to solve it: modern heuristics. Springer, New York (2004)zbMATHCrossRefGoogle Scholar
  25. Mitchell, T.J.: Computer construction of “D-optimal” first-order designs. Technometrics 16(1), 211–220 (1974)Google Scholar
  26. Mitchell, T.J.: An algorithm for the construction of “D-optimal” experimental designs. Technometrics 16(2), 203–210 (1974)Google Scholar
  27. 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)zbMATHCrossRefGoogle Scholar
  28. 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)CrossRefGoogle Scholar
  29. Montgomery, D.C.: Design and Analysis of Experiments. Wiley, New York (2008)Google Scholar
  30. 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)zbMATHMathSciNetCrossRefGoogle Scholar
  31. Nguyen, N.K.: An algorithmic approach to constructing supersaturated designs. Technometrics 38(1), 69–73 (1996)zbMATHCrossRefGoogle Scholar
  32. Plackett, R.L., Burman, J.P.: The design of optimum multifactorial experiments. Biometrika 33(4), 305–325 (1946)zbMATHMathSciNetCrossRefGoogle Scholar
  33. Sörensen, K., Glover, F.: Metaheuristics. In: Gass, S., Fu, M. (eds.) Encyclopedia of Operations Research and Management Science, 3rd edn. Springer, London (2013)Google Scholar
  34. Sung Jung, J., Jin Yum, B.: Construction of exact D-optimal designs by tabu search. Comput. Stat. Data Anal. 21(2), 181–191 (1996)zbMATHCrossRefGoogle Scholar
  35. Talbi, E.G.: Metaheuristics: From Design to Implementation. Wiley, New York (2009)CrossRefGoogle Scholar
  36. 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)Google Scholar
  37. Welch, W.J.: Algorithmic complexity: three NP-hard problems in computational statistics. J. Stat. Comput. Simul. 15(1), 17–25 (1982)zbMATHMathSciNetCrossRefGoogle Scholar
  38. Wu, C.F.J., Hamada, M.: Experiments: Planning, Analysis, and Parameter Design Optimization. Wiley, New York (2000)Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • Daniel Palhazi Cuervo
    • 1
  • Peter Goos
    • 1
    • 2
  • Kenneth Sörensen
    • 1
  1. 1.Faculty of Applied EconomicsUniversity of AntwerpAntwerpBelgium
  2. 2.Faculty of Bioscience EngineeringUniversity of LeuvenLeuvenBelgium

Personalised recommendations