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The Scientific World Journal
Volume 2014, Article ID 163949, 15 pages
http://dx.doi.org/10.1155/2014/163949
Research Article

A Novel Latin Hypercube Algorithm via Translational Propagation

School of Marine Science and Technology, Northwestern Polytechnical University, Xi’an 710072, China

Received 14 May 2014; Revised 22 July 2014; Accepted 30 July 2014; Published 2 September 2014

Academic Editor: Ming-Huwi Horng

Copyright © 2014 Guang Pan et al. 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. L. Gu, “A comparison of polynomial based regression models in vehicle safety analysis,” in Proceedings of the ASME Design Engineering Technical Conference and Computers and Information in Engineering Conference (DAC' 01), pp. 509–514, September 2001. View at Scopus
  2. P. N. Koch, T. W. Simpson, J. K. Allen, and F. Mistree, “Statistical approximations for multidisciplinary design optimization: the problem of size,” Journal of Aircraft, vol. 36, no. 1, pp. 275–286, 1999. View at Publisher · View at Google Scholar · View at Scopus
  3. T. J. Mitchell, “An algorithm for the construction of “D-optimal” experimental designs,” Journal of Technometrics, vol. 16, no. 2, pp. 203–210, 1974. View at Google Scholar · View at MathSciNet · View at Scopus
  4. R. H. Myers and D. C. Montgomery, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley & Sons, 1995. View at MathSciNet
  5. W. Chen, A robust concept exploration method for configuring complex systems [Ph.D. thesis], Mechanical Engineering, Georgia Institute of Technology, Atlanta, Ga, USA, 1995.
  6. M. E. Johnson, L. M. Moore, and D. Ylvisaker, “Minimax and maximin distance designs,” Journal of Statistical Planning and Inference, vol. 26, no. 2, pp. 131–148, 1990. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  7. M. D. Morris and T. J. Mitchell, “Exploratory designs for computational experiments,” Journal of Statistical Planning and Inference, vol. 43, no. 3, pp. 381–402, 1995. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  8. T. W. Simpson, J. D. Peplinski, P. N. Koch, and J. K. Allen, “Metamodels for computer-based engineering design: survey and recommendations,” Engineering with Computers, vol. 17, no. 2, pp. 129–150, 2001. View at Publisher · View at Google Scholar · View at Scopus
  9. G. Rennen, B. Husslage, E. R. Van Dam, and D. Den Hertog, “Nested maximin Latin hypercube designs,” Structural and Multidisciplinary Optimization, vol. 41, no. 3, pp. 371–395, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  10. G. Rennen, E. R. van Dam, and D. Den Hertog, Space-Filling Latin Hypercube Designs for Computer Experiments, Tilburg University, 2006.
  11. J. R. Koehler and A. B. Owen, “Computer experiments,” in Handbook of Statistics, vol. 13, pp. 261–308, 1996. View at Google Scholar
  12. K. Q. Ye, W. Li, and A. Sudjianto, “Algorithmic construction of optimal symmetric Latin hypercube designs,” Journal of Statistical Planning and Inference, vol. 90, no. 1, pp. 149–159, 2000. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  13. R. Jin, W. Chen, and A. Sudjianto, “An efficient algorithm for constructing optimal design of computer experiments,” Journal of Statistical Planning and Inference, vol. 134, no. 1, pp. 268–287, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  14. . Bates S J, J. Sienz, and V. Toropov V, “Formulation of the optimal Latin hypercube design of experiments using a permutation genetic algorithm,” AIAA Journal, vol. 2011, pp. 1–7, 2004. View at Google Scholar
  15. M. Liefvendahl and R. Stocki, “A study on algorithms for optimization of Latin hypercubes,” Journal of Statistical Planning and Inference, vol. 136, no. 9, pp. 3231–3247, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  16. A. Grosso, A. R. M. J. U. Jamali, and M. Locatelli, “Finding maximin latin hypercube designs by Iterated Local Search heuristics,” European Journal of Operational Research, vol. 197, no. 2, pp. 541–547, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at Scopus
  17. A. Jourdan and J. Franco, “Optimal Latin hypercube designs for the Kullback-LEIbler criterion,” AStA. Advances in Statistical Analysis., vol. 94, no. 4, pp. 341–351, 2010. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  18. E. R. van Dam, B. Husslage, D. den Hertog et al., “Maximin Latin hypercube designs in two dimensions,” Journal of Operations Research, vol. 55, no. 1, pp. 158–169, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  19. F. A. C. Viana, G. Venter, and V. Balabanov, “An algorithm for fast optimal Latin hypercube design of experiments,” International Journal for Numerical Methods in Engineering, vol. 82, no. 2, pp. 135–156, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  20. H. Zhu, L. Liu, T. Long, and L. Peng, “A novel algorithm of maximin Latin hypercube design using successive local enumeration,” Engineering Optimization, vol. 44, no. 5, pp. 551–564, 2012. View at Publisher · View at Google Scholar · View at Scopus
  21. F. J. Hickernell, “A generalized discrepancy and quadrature error bound,” Mathematics of Computation, vol. 67, no. 221, pp. 299–322, 1998. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet · View at Scopus
  22. A. A. Mullur and A. Messac, “Extended radial basis functions: more flexible and effective metamodeling,” AIAA Journal, vol. 43, no. 6, pp. 1306–1315, 2005. View at Publisher · View at Google Scholar · View at Scopus
  23. G. S. Babu and S. Suresh, “Sequential projection-based metacognitive learning in a radial basis function network for classification problems,” IEEE Transactions on Neural Networks and Learning Systems, vol. 24, no. 2, pp. 194–206, 2013. View at Google Scholar
  24. W. Yao, X. Q. Chen, Y. Y. Huang, and M. van Tooren, “A surrogate-based optimization method with RBF neural network enhanced by linear interpolation and hybrid infill strategy,” Optimization Methods & Software, vol. 29, no. 2, pp. 406–429, 2014. View at Publisher · View at Google Scholar · View at MathSciNet
  25. N. Vuković and Z. Miljković, “A growing and pruning sequential learning algorithm of hyper basis function neural network for function approximation,” Neural Networks, vol. 46, pp. 210–226, 2013. View at Publisher · View at Google Scholar · View at Scopus
  26. R. Jin, X. Du, and W. Chen, “The use of metamodeling techniques for optimization under uncertainty,” Structural and Multidisciplinary Optimization, vol. 25, no. 2, pp. 99–116, 2003. View at Publisher · View at Google Scholar · View at Scopus
  27. A. A. Mullur and A. Messac, “Metamodeling using extended radial basis functions: a comparative approach,” Engineering with Computers, vol. 21, no. 3, pp. 203–217, 2006. View at Publisher · View at Google Scholar · View at Scopus
  28. L. D. S. Coelho, “Gaussian quantum-behaved particle swarm optimization approaches for constrained engineering design problems,” Expert Systems with Applications, vol. 37, no. 2, pp. 1676–1683, 2010. View at Publisher · View at Google Scholar · View at Scopus
  29. Y. J. Cao and Q. H. Wu, “Mechanical design optimization by mixed-variable evolutionary programming,” in Proceedings of the IEEE International Conference on Evolutionary Computation (ICEC '97), pp. 443–446, April 1997. View at Scopus
  30. X. Wei, Y. Wu, and L. Chen, “A global optimization algorithm based on incremental metamodel method,” China Mechanical Engineering, vol. 24, no. 5, pp. 623–627, 2013. View at Publisher · View at Google Scholar · View at Scopus