DOI QR코드

DOI QR Code

Hybrid Approach When Multiple Objectives Exist

  • Kim, Young-Il (Department of Information System, ChungAng University) ;
  • Lim, Yong-Bin (Department of Statistics, Ewha Women's University)
  • Published : 2007.12.31

Abstract

When multiple objectives exist, there are three approaches exist. These are maximin design, compound design, and constrained design. Still, each of three design criteria has its own strength and weakness. In this paper Hybrid approach is suggested when multiple design objectives exist, which is a combination of maximin and constrained design. Sometimes experimenter has several objectives, but he/she has only one or two primary objectives, others less important. A new approach should be useful under this condition. The genetic algorithm is used for few examples. It has been proven to be a very useful technique for this complex situation. Conclusion follows.

Keywords

References

  1. 강명욱, 김영일 (2002), Multiple constrained optimal experimental design. 한국통계학회논문집, 9, 619-627 https://doi.org/10.5351/CKSS.2002.9.3.619
  2. 강명욱, 김영일 (2006), Strategical issues in multiple-objective optimal expeerimental design. 한국통계학회논문집, 13, 1-10 https://doi.org/10.5351/CKSS.2006.13.1.001
  3. 염준근, 남기성 (2000), A study on D-optimal design using the genetic algorithm. 한국통계학회논문집, 7, 357-366
  4. Box, G. E. P. and Draper, N. R. (1975). A basis for the selection of a response surface design. Journal of the American Statistical Association, 54, 622-654 https://doi.org/10.2307/2282542
  5. Cook, R. D. and Fedorov, V. V. (1995). Constrained optimization of experimental design (with discussion). Statistics, 26, 129-178 https://doi.org/10.1080/02331889508802474
  6. Cook, R. D. and Wong, W. K. (1994). On the equivalence between constrained and compound optimal designs. Journal of the American Statistical Association, 89, 687-692 https://doi.org/10.2307/2290872
  7. Fedorov, V. V. (1972). Theory of Optimal Experiments. Translated and edited by W. J. Studden and E. M. Klimko, Academic Press, New York
  8. Kiefer, J. (1959). Optimum experimental design. Journal of the Royal Statistical Society, Ser. B, 21, 272-319
  9. Huang, Y. C. (1996). Multiple-objective optimal designs. Doctor of Public Health Dissertation, Department of Biostatistics, School of Public Health, UCLA
  10. Huang, Y. C. and Wong, W. K. (1998). Multiple-objective designs. Journal of Biopharmaceutical Statistics, 8, 635-643 https://doi.org/10.1080/10543409808835265
  11. Imhof, L. and Wong, W. K. (2000). A graphical method for finding maximin designs. Biometrics, 56, 113-117 https://doi.org/10.1111/j.0006-341X.2000.00113.x
  12. Lauter, E. (1974). Experimental planning in a class of models. Mathematishe Operationsforshung und Statistik, 5, 673-708
  13. Park, Y. J., Montgomery, D. C., Folwer, J. W. and Borror, C. M. (2005). Costconstrained G-efficient response surface designs for cuboidal regions. Quality and Reliability Engineering International, 22, 121-139 https://doi.org/10.1002/qre.690
  14. Pukelsheim, F. (1993). Optimal Design of Experiments. John Wiley & Sons, New York. Silvey, S. D. (1980). Optimal Design. Chapman & Hall/CRC
  15. Stigler, S. M. (1971). Optimal experimental design for polynomial regression. Journal of the American Statistical Association, 66, 311-318 https://doi.org/10.2307/2283928
  16. Studden, W. J. (1982). Some robust type D-optimal designs in polynomial regression. Journal of the American Statistical Association, 77, 916-921 https://doi.org/10.2307/2287327
  17. Wong, W. K. (1995). A graphical approach for constructing constrained D- and Loptimal designs using efficiency plot. Journal of Statistical Simulation and Computations, 53, 143-152 https://doi.org/10.1080/00949659508811702
  18. Wong, W. K. (1999). Recent advances in multiple-objective design strategies. Statistica Neerlandica, 53, 257-276 https://doi.org/10.1111/1467-9574.00111

Cited by

  1. Selection of extra support points for polynomial regression vol.25, pp.6, 2014, https://doi.org/10.7465/jkdi.2014.25.6.1491
  2. Some Examples of Constrained Optimal Experimental Design for Nonlinear Models vol.27, pp.7, 2014, https://doi.org/10.5351/KJAS.2014.27.7.1151
  3. Some Criteria for Optimal Experimental Design at Multiple Extrapolation Points vol.27, pp.5, 2014, https://doi.org/10.5351/KJAS.2014.27.5.693