Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2014, Article ID 746914, 6 pages
http://dx.doi.org/10.1155/2014/746914
Research Article

A Simulated Annealing Algorithm for D-Optimal Design for 2-Way and 3-Way Polynomial Regression with Correlated Observations

1Business School, Shandong University of Political Science and Law, 63 East Jiefang Road, Jinan, Shandong 250014, China
2Department of Mathematics and Statistics, Utah State University, Logan, UT 84341, USA

Received 10 November 2013; Revised 1 March 2014; Accepted 1 March 2014; Published 26 March 2014

Academic Editor: Li Weili

Copyright © 2014 Chang Li and Daniel C. Coster. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. Z. Zhu, D. C. Coster, and L. B. Beasley, “Properties of a covariance matrix with an application to D-optimal design,” Electronic Journal of Linear Algebra, vol. 10, pp. 65–76, 2003. View at Google Scholar · View at MathSciNet
  2. H. Dette, J. Kunert, and A. Pepelyshev, “Exact optimal designs for weighted least squares analysis with correlated errors,” Statistica Sinica, vol. 18, no. 1, pp. 135–154, 2008. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  3. W. G. Muller, Collecting Spatial Data: Optimum Design of Experiments for Random Fields, Springer, 2001.
  4. L. M. Haines, “The application of the annealing algorithm to the construction of exact optimal designs for linear-regression models,” Technometrics, vol. 29, no. 4, pp. 439–447, 1987. View at Google Scholar · View at Scopus
  5. M. A. Lejeune, “Heuristic optimization of experimental designs,” European Journal of Operational Research, vol. 147, no. 3, pp. 484–498, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. B. Dimitris and N. Omid, Robust Optimization with Simulated Annealing, Springer Science+Business Media, LLC, 2009.
  7. S. Abdullah, L. Golafshan, and M. Z. A. Nazri, “Re-heat simulated annealing algorithm for rough set attribute reduction,” International Journal of Physical Sciences, vol. 6, no. 8, pp. 2083–2089, 2011. View at Google Scholar · View at Scopus
  8. Z. Zhu, Application of simulated annealing to d-optimal design for polynomial regression with correlated observations [Ph.D. thesis], Department of Mathematics and Statistics, Utah State University, 2004.
  9. C.-S. Cheng, “Optimal regression designs under random block-effects models,” Statistica Sinica, vol. 5, no. 2, pp. 485–497, 1995. View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. J. E. Boon, “Generating exact d optimal design for polynomial models,” in Proceedings of the Spring Simulation Multiconference (SpringSim '07), 2007.
  11. F. Pukelsheim, Optimal Design of Experiments, vol. 50, SIAM, Philadelphia, Pa, USA, 2006. View at Publisher · View at Google Scholar · View at MathSciNet
  12. Z. Zhu, Optimal experimental designs with correlated observations [Ph.D. thesis], Department of Mathematics and Statistics , Utah State University, 2004.
  13. J. Cadima, F. L. Calheiros, and I. P. Preto, “The eigenstructure of block-structured correlation matrices and its implications for principal component analysis,” Journal of Applied Statistics, vol. 37, no. 3-4, pp. 577–589, 2010. View at Publisher · View at Google Scholar · View at MathSciNet
  14. J. E. Atkins and C.-S. Cheng, “Optimal regression designs in the presence of random block effects,” Journal of Statistical Planning and Inference, vol. 77, no. 2, pp. 321–335, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet