Skip to main content
SpringerLink
Log in
Book cover

COMPSTAT 2004 — Proceedings in Computational Statistics pp 37–48Cite as

Hybrid Algorithms for Construction of D-Efficient Designs

  • Conference paper

  • 673 Accesses

Abstract

We construct exact. D-efficient designs for linear regression models using a hybrid algorithm that consists of genetic and local search components. The genetic component is a genetic algorithm (GA) with a 100% mutation rate and ranking selection. The local search methods we use are based on the G-bit improvement and a combination of the Powel multidimensional and Brent line optimization techniques. Computational results show that the hybrid algorithm generates designs that are comparable in efficiency to those found using the modified Fedorov algorithm (MFA), but without being limited to using a given set of candidate points.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   129.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Altekar M., Scarlatti. A. N (1997). Resin vehicle characterization using statistically designed experiments. Chemometrics and Intelligent Laboratory Systems 36 207–211.

    Article  Google Scholar 

  2. Atkinson A.C., Donev A.N (1992). Optimum experimental designs. Oxford: Oxford University Press.

    MATH  Google Scholar 

  3. Ash H., Hedayat A (1978). An introduction to design optimality with an overview of the literature. Comm. Statist. Theory Methods. 7, 1259–1325.

    Article  Google Scholar 

  4. Box G.E.P. Draper N.R 1971. Factorial designs, the |F’F| criterion and some related matters. Techmetrics 13 731–742.

    Article  MATH  Google Scholar 

  5. Broudiscou A., Leardi R., Phan-Tan-Luu R (1996). Genetic algorithm as a tool for selection of D-optimal design. Chemometrics and Intelligent Laboratory Systems 35, 105–116.

    Article  Google Scholar 

  6. Cook R.D., Nachtsheim C.J. (1980). A comparison of algorithms for constructing exact D-optimum designs. Technometrics 22, 315–324.

    Article  MATH  Google Scholar 

  7. Dykstra O. 1971. The augmentation of experimental data to maximize |x’x|. Techmetrics 13 682–688.

    Google Scholar 

  8. Govaerts B., Sanchez R.P. (1992). Construction of exact D optimal designs for linear regression models using genetic algorithms. Belgian Journal of Operations Research, Statistics and Computer Science 1-2, 153–174.

    Google Scholar 

  9. Goldberg D.E. (1989). Genetic algorithms in search, optimization, and machine learning. Addison Wesley.

    Google Scholar 

  10. Heredia-Langner A., Carlyle. W.M., Montgomery D.C., Borror C.M., Runger G.C. (2003). Genetic algorithms for the construction of D-optimal designs. Journal of Quality Technology 35 28–46.

    Google Scholar 

  11. Johnson M.E., Nachtsheim C.J. (1983). Some guidelines for constructing exact D-optimal designs on convex design spaces. Technometrics 25, 271–277.

    MATH  MathSciNet  Google Scholar 

  12. Keifer J., Wolfowitz J. (1959). Optimum designs in regression problems. Ann. Math. Statist. 30, 271–294.

    Article  MathSciNet  Google Scholar 

  13. Lawler E.L. (1976). Combinatorial optimization: networks and matroids. New York: Holt, Reinhart and Winston.

    MATH  Google Scholar 

  14. Mitchell T.J. (1974). An algorithm for the construction of D-optimal experimental designs. Technometrics 20 211–220.

    Google Scholar 

  15. Montepiedra G., Myers D., Yeh A.B. (1998). Application of genetic algorithms to the construction of exact D-optimal designs. Journal of Applied Statistics 6, 817–826.

    Article  Google Scholar 

  16. Press W.H., Teukolsky S.A., Vetterling W.T., Flannery B.P. (1992). Numerical recipes in C, second edition: the art of scientific computing, Cambridge: Cambridge University Press.

    Google Scholar 

  17. Poland, J.A., Mitterer K., Knödler A., Zell (2001). Genetic algorithms can improve the construction of D-optimal experimental designs. In: Mastorakis N. (Ed.), Advances In Fuzzy Systems and Evolutionary Computation, WSES 2001, 227–231.

    Google Scholar 

  18. Silvey S.D (1980). Optimum design. London: Chapman & Hall.

    Book  Google Scholar 

  19. Syslo M.M., Deo N., Kowalik J.S (1983). Discrete optimization with pascal programs. Engelwood Cliffs, NJ: Prentice-Hall.

    MATH  Google Scholar 

  20. Wynn, H.P. (1970). The sequential generation of D-optimum experimental designs. Ann. Math. Statist. 41 1655–1664.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Clinical Information Management, AstraZeneca R&D Södertälje, S-151 85, Södertälje, Sweden

    Abdul Aziz Ali & Magnus Jansson

Authors
  1. Abdul Aziz Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Magnus Jansson
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Faculty of Mathematics and Physics Department of Statistics and Probability, Charles University, Sokolovská 83, 18675, Prague 8 - Karlin, Czech Republic

    Jaromir Antoch

Rights and permissions

Reprints and permissions

Copyright information

© 2004 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Ali, A.A., Jansson, M. (2004). Hybrid Algorithms for Construction of D-Efficient Designs. In: Antoch, J. (eds) COMPSTAT 2004 — Proceedings in Computational Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-2656-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-7908-2656-2_2

  • Publisher Name: Physica, Heidelberg

  • Print ISBN: 978-3-7908-1554-2

  • Online ISBN: 978-3-7908-2656-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation