Investigation of the Robustness Index of the Objective Function in Robust Optimization

강건최적설계에서 목적함수의 강건성 지수에 대한 연구

  • Received : 2012.02.24
  • Accepted : 2013.01.28
  • Published : 2013.05.01


The concept of robust optimization is based on Taguchi's method. Especially, robustness indices of objective function pursue an insensitive and conservative design when there are variations on design variables and parameters. To accomplish the purpose, various robustness indices on the objective function have been developed. However, it can be caused limitations to develop the robustness index, because there is difference between the Taguchi's method and robust optimization. In this paper, an investigation is performed to identify the characteristics and the drawbacks of the previous studies. To achieve the purpose, evaluations are conducted by using the examples which have both a deterministic optimum and a robust optimum. Moreover, a new viewpoint as well as a robustness index using a supremum value of the objective function is proposed based on the investigation.


Robust Optimization;Robustness Index;Robustness of the Objective Function


Supported by : 한국연구재단


  1. Phadke, M. S., 1974, Quality Engineering Using Robust Design, Prentice-Hall, New Jersey.
  2. Arora J.S, 2012, Introduction to Optimum Design, Elsevier, Korea, pp. 17-56.
  3. Park, G. J., Lee, T. H., Lee, K. H. and Hwang, K. H, 2006, "Robust Design: An Overview," AIAA Journal, Vol. 44, No. 1, pp. 181-191.
  4. Sundaresan, S. Ishii, K. D. and Houser, R., 1993, "A Robust Optimization Procedure with Variations on Design Variables and Constraints," Engineering Optimization, Vol. 24, No. 2, pp. 101-117.
  5. Chen, W., Allen, J. K, Tsui, K. L., and Mistree, F., 1996, "A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors," ASME Journal of Mechanical Design, Vol. 118, No. 4.
  6. Park, G. J., 2006, 2007, Analytic Methods for Design Practice, Springer, London, pp. 393-435.
  7. Belegundu, A. D. and Zhang, S., 1992, "Robustness of Design Through Minimum Sensitivity," Journal of Mechanical Design, Vol. 114, No. 2, pp. 213-217.
  8. Han, J. S. and Kwak, B. M., 2004, "Robust Optimization Using a Gradient Index: MEMS Applications," Structural Multidisciplinary Optimization, Vol. 27, No. 6, pp. 439-478.
  9. Ramakrishnan, B. R. and Rao, S. S., 1996, "A General Loss Function Based Optimization Procedure for Robust Design," Engineering Optimization, Vol. 25, No. 4, pp. 255-276.
  10. Parkinson, D. B., 1997, "Robust Design by Variability Optimization," Quality and Reliability Engineering International, Vol. 13, No. 2, pp. 97-102.<97::AID-QRE80>3.0.CO;2-7
  11. Parkinson, D. B., 2000, "The Application of a Robust Design Method to Tolerancing," Journal of Mechanical Design, Vol. 122, No. 2, pp. 97-102.
  12. Su, J. and Renaud, J. E., 1997, "Automatic Differentiation in Robust Optimization," AIAA Journal, Vol. 35, No. 6, pp. 1072-1079.
  13. Doltsinis, I. and Kang, Z., 2004, "Robust Design of Structures Using Optimization Methods," Computer Methods in Applied Mechanics and Engineering, Vol. 193, No. 23-26, pp. 2221-2237.
  14. Lee, K. H. and Park, G. J., 2001, "Robust Optimization Considering Tolerance of Design Variables," Computers & Structures, Vol. 25, No. 2, pp. 99-116.
  15. Harzheim, L. and Warnecke, U., 2010, "Robustness Optimization of the Position of an Anti-roll Bar Link to Avoid the Toggling of a Rear Axle Stabilizer," Structural and Multidisciplinary Optimization, Vol. 42, No. 2, pp. 315-323.
  16. Jung, D. H. and Lee, B. C., 2002, "Development of a Simple and Efficient Method for Robust Optimization," International Journal for Numerical Methods in Engineering, Vol. 53, No. 9, pp. 2201-2215.
  17. PIAnO (Process Integration, Automation and Optimization) User's Manual, Version 3.4, FRAMAX Inc., 2006.
  18. Youn, B. D., Xi, Z. and Wang, P., 2008, "Eigenvector Dimension Reduction (EDR) Method for Sensitivity-Free Probability Analysis," Structural and Multidisciplinary Optimization, Vol. 37, No. 1, pp. 13-28.
  19. Youn, B. D. and Xi, Z., 2009, "Reliability-Based Robust Design Optimization Using the Eigenvector Dimension Reduction (EDR) Method," Structural and Multidisciplinary Optimization, Vol. 37, No. 5, pp. 475-492.
  20. Beyer, H. G. and Sendhoff, B., 2007, "Robust Optimization: A Comprehensive Survey," Computer Methods in Applied Mechanics and Engineering, Vol. 196, No. 33-34, pp. 3190-3218.
  21. Aharon, B. T, Laurent, E. G. and Arkadi, N., 2009, Robust Optimization, Princeton University Press, New Jersey.
  22. Parkinson, A., Sorensen, C., and Pourhassan, N., 1993, "A General Approach for Robust Optimal Design," ASME Journal of Mechanical Design, Vol. 115, No. 1, pp. 74-80.

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