Journal of Statistical Theory and Practice

, Volume 5, Issue 2, pp 357–367 | Cite as

An Algorithmic Construction of E(s2)-optimal Supersaturated Designs

  • C. KoukouvinosEmail author
  • K. Mylona
  • D. E. Simos


A general method based on an effective algorithm for construction of E(s2)-optimal, two-level supersaturated designs with the equal occurrence property, from supplementary difference sets is introduced. Supersaturated designs constructed in this way are E(s2)-optimal. Comparisons are made with previous works and it is shown that the proposed method gives promising results for the construction of supersaturated designs with good properties.

AMS Subject Classification

Primary: 62K10 62K15 Secondary: 05B20 


Cyclotomy E(s2)-optimality Supersaturated designs Supplementary difference sets Tabu-search 


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  1. Blum, C., Roli, A., 2003. Metaheuristics in combinatorial optimization: Overview and conceptual comparison. ACM Computing Surveys, 35, 268–308.CrossRefGoogle Scholar
  2. Booth, K.H.V., Cox, D.R., 1962. Some systematic supersaturated designs. Technometrics, 4, 489–495.MathSciNetCrossRefGoogle Scholar
  3. Box, G.E.P., Meyer, R.D., 1986. An analysis for unreplicated fractional factorials. Technometrics, 28, 11–18.MathSciNetCrossRefGoogle Scholar
  4. Bulutoglu, D.A., 2007. Cyclicly constructed E(s 2))-optimal supersaturated designs. J. Statist. Plann. Inference, 137), 2413–2428.MathSciNetCrossRefGoogle Scholar
  5. Bulutoglu, D.A., Cheng, C.S., 2004. Construction of E(s 2))-optimal supersaturated designs. Annals of Statistics, 32, 1662–1678.MathSciNetCrossRefGoogle Scholar
  6. Bulutoglu, D.A., Ryan, K.J., 2008. E(s 2))-optimal supersaturated designs with good minimax properties when N is odd. J. Statist. Plann. Inference, 138, 1754–1762.MathSciNetCrossRefGoogle Scholar
  7. Butler, N., Mead, R., Eskridge, K.M., Gilmour, S.G., 2001. A general method of constructing E(s 2)-optimal supersaturated designs. J. R. Statist. Soc. B, 63, 621–632.MathSciNetCrossRefGoogle Scholar
  8. Cheng, C.S., 1997. E(s 2))-optimal supersaturated designs. Statist. Sinica, 7, 929–939.MathSciNetzbMATHGoogle Scholar
  9. Cheng, C.S., Tang, B., 2001. Upper bounds on the number of columns in supersaturated designs. Biometrika, 88, 1169–1174.MathSciNetCrossRefGoogle Scholar
  10. Eskridge, K.M., Gilmour, S.G., Mead, R., Butler, N.A., Travnicek, D.A., 2004. Large supersaturated designs. J. Stat. Computat. Simulation, 74, 525–542.MathSciNetCrossRefGoogle Scholar
  11. Georgiou, S.D., 2008. On the construction E(s 2))-optimal supersaturated designs. Metrika, 68, 189–198.MathSciNetCrossRefGoogle Scholar
  12. Geramita, A.V., Seberry, J., 1979. Orthogonal Designs: Quadratic Forms and Hadamard Matrices. Marcel Dekker, New York - Basel.zbMATHGoogle Scholar
  13. Gilmour, S.G., 2006. Factor Screening via Supersaturated Designs. In Screening Methods for Experimentation in Industry, Drug Discovery, and Genetics, Dean, A. and Lewis, S. (Editors). Springer-Verlag, New York, pp. 169–190.Google Scholar
  14. Glover, F., 1977. Heuristics for integer programming using surrogate constraints. Dec. Sci., 8, 156–166.CrossRefGoogle Scholar
  15. Glover, F., 1986. Future paths for integer programming and links to artificial intelligence. Comput. Oper. Res., 13, 533–549.MathSciNetCrossRefGoogle Scholar
  16. Glover, F., Laguna, M., 1997. Tabu Search. Kluwer Academic Publishers.CrossRefGoogle Scholar
  17. Gysin, M., Seberry, J., 1998. On new families of supplementary difference sets over rings with short orbits. J. Combin. Math. Combin. Comput., 28, 161–186.MathSciNetzbMATHGoogle Scholar
  18. Holcomb, D.R., Montgomery, D.C., Carlyle, W.M., 2007. The use of supersaturated experiments in turbine engine development. Quality Engineering, 19, 17–27.CrossRefGoogle Scholar
  19. Koukouvinos, C., Mantas, P., Mylona, K., 2008. A general construction of E(s 2))-optimal large supersaturated designs, Metrika, 68, 99–110.MathSciNetCrossRefGoogle Scholar
  20. Koukouvinos, C., Mylona, K., 2009. A general construction of E(s 2))-optimal supersaturated designs via supplementary difference sets. Metrika, 70, 257–265.MathSciNetCrossRefGoogle Scholar
  21. Koukouvinos, C., Mylona, K., Simos, D.E., 2007. Exploring k-circulant supersaturated designs via genetic algorithms. Comput. Statist. Data Anal., 51, 2958–2968.MathSciNetCrossRefGoogle Scholar
  22. Koukouvinos, C., Mylona, K., Simos, D.E., 2008. E(s 2))-Optimal and minimax-optimal cyclic supersaturated designs via multi-objective simulated annealing. J. Statist. Plann. Inference, 138, 639–1646.MathSciNetCrossRefGoogle Scholar
  23. Koukouvinos, C., Mylona, K., Simos, D.E., 2009. A Hybrid SAGA Algorithm for the construction of E(s 2))-optimal cyclic supersaturated designs. J. Statist. Plann. Inference, 139, 478–485.MathSciNetCrossRefGoogle Scholar
  24. Li, W.W., Wu, C.F.J., 1997. Columnwise-pairwise algorithms with applications to the construction of supersaturated designs. Technometrics, 39, 171–179.MathSciNetCrossRefGoogle Scholar
  25. Lin, D.K.J., 1993. A new class of supersaturated designs. Technometrics, 35, 28–31.CrossRefGoogle Scholar
  26. Lin, D.K.J., 1995. Generating systematic supersaturated designs. Technometrics, 37, 213–225.CrossRefGoogle Scholar
  27. Liu, Y.F., Dean, A., 2004. k-circulant supersaturated designs. Technometrics, 46, 32–43.MathSciNetCrossRefGoogle Scholar
  28. Liu, M., Zhang, R., 2000. Construction of E(s 2)) optimal supersaturated designs using cyclic BIBDs. J. Statist. Plann. Inference, 91, 139–150.MathSciNetCrossRefGoogle Scholar
  29. Lu, X., Meng, Y., 2000. A new method in the construction of two-level supersaturated designs. J. Statist. Plann. Inference, 86, 229–238.MathSciNetCrossRefGoogle Scholar
  30. Nguyen, N.K., 1996. An algorithmic approach to constructing supersaturated designs. Technometrics, 38, 69–73.CrossRefGoogle Scholar
  31. Nguyen, N.K., Cheng, C.S., 2008. New E(s 2))-optimal supersaturated designs constructed from incomplete block designs. Technometrics, 50, 26–31.MathSciNetCrossRefGoogle Scholar
  32. Plackett, R.L., Burman, J.P., 1946. The design of optimum multifactorial experiments. Biometrika, 33, 303–325.MathSciNetzbMATHGoogle Scholar
  33. Ryan, K.J., Bulutoglu, D.A., 2007. E(s 2))-optimal supersaturated designs with good minimax properties. J. Statist. Plann. Inference, 137, 2250–2262.MathSciNetCrossRefGoogle Scholar
  34. Satterthwaite, F.E., 1959. Random balance experimentation (with discussions). Technometrics, 1, 111–137.MathSciNetCrossRefGoogle Scholar
  35. Seberry Wallis, J., 1973. Some remarks on supplementary difference sets. Colloquia Marhematica Societatis Janos Bolyai, Hungary, 10, 1503–1526.MathSciNetGoogle Scholar
  36. Tang, B., Wu, C.F.J., 1997. A method for constructing supersaturated designs and its Es 2-optimality. Canadian J. Statist., 25, 191–201.MathSciNetCrossRefGoogle Scholar
  37. Walker II, R.A., Colbourn, C.J., 2009. Tabu search for covering arrays using permutation vectors. J. Statist. Plann. Inference, 139, 69–80.MathSciNetCrossRefGoogle Scholar
  38. Wallis, W.D., Street, A.P., Seberry Wallis, J., 1972. Combinatorics: Room squares, sum-free sets, Hadamard matrices. Lecture Notes in Mathematics, Vol. 292, Springer-Verlag, Berlin, Heidelberg, New York.Google Scholar
  39. Wu, C.F.J., 1993. Construction of supersaturated designs through partially aliased interactions. Biometrika, 80, 661–669.MathSciNetCrossRefGoogle Scholar
  40. Yamada, S., Lin, D.K.J., 1997. Supersaturated designs including an orthogonal base. Canadian J. Statist., 25, 203–213.MathSciNetCrossRefGoogle Scholar

Copyright information

© Grace Scientific Publishing 2011

Authors and Affiliations

  1. 1.Department of MathematicsNational Technical University of AthensZografouGreece
  2. 2.Faculty of Applied EconomicsUniversiteit AntwerpenAntwerpenBelgium

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