0
TECHNICAL BRIEFS

Local Approximation of the Efficient Frontier in Robust Design

[+] Author and Article Information
Jinhuan Zhang

Caleb Technology Corporation, Former Graduate Assistant at the Department of Mechanical Engineering, Clemson University, Clemson, SC 29634-5124

Margaret M. Wiecek

Department of Mathematical Sciences, Clemson University, Clemson, SC 29634-10975

Wei Chen

Department of Mechanical Engineering, University of Illinois at Chicago, Chicago, IL 60607-7022

J. Mech. Des 122(2), 232-236 (Mar 01, 2000) (5 pages) doi:10.1115/1.533571 History: Received June 01, 1999; Revised March 01, 2000
Copyright © 2000 by ASME
Topics: Design , Approximation
Your Session has timed out. Please sign back in to continue.

References

Otto, K. N., and Antonsson, E. K., 1991, “Extensions to the Taguchi Method of Product Design,” Third International Conference on Design Theory and Methodology, Stauffer, L. A., ed., Miami, Florida, pp. 21–30.
Parkinson,  A., Sorensen,  C., and Pourhassan,  N., 1993, “A General Approach for Robust Optimal Design,” Trans. ASME, 115, pp. 74–80.
Sundareşan, S., Ishii, K., and Houser, D. R., 1993, “A Robust Optimization Procedure with Variations on Design Variables and Constraints,” Advances in Design Automation, ASME DE-Vol. 69-1, pp. 379–386.
Cagan, J., and Williams, B. C., 1993, “First-Order Necessary Conditions for Robust Optimality,” Advances in Design Automation, ASME DE-Vol. 65-1, pp. 539–549.
Chen,  W., Allen,  J. K., Mistree,  F., and Tsui,  K.-L., 1996, “A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors,” ASME J. Mech. Des., 118, pp. 478–485.
Su,  I., and Renaud,  J. E., 1997, “Automatic Differentiation in Robust Optimization,” AIAA J., 35, No. 6, p. 1072.
Iyer, H. V., and Krishnamurty, S., 1998, “A Preference-Based Robust Design Metric,” 1998 ASME Design Technical Conference, Paper No. DAC5625, Atlanta, GA.
Mulvey,  J., Vanderber,  R., and Zenios,  S., 1995, “Robust Optimization of Large-Scale Systems,” Oper. Res., 43, pp. 264–281.
Das, I., and Dennis, J. E., 1996, “Normal Boundary Intersection: A New Method for Generating Pareto Optimal Points in Nonlinear Multicriteria Optimization Problems,” from http://www.owlnet.rice.edu/∼indra/NBIhomepage.html.
Jahn,  J., and Merkel,  A., 1992, “Reference Point Approximation Method for the Solution of Bicriteria Optimization Problems,” J. Optim. Theory Appl., 74, pp. 87–103.
Cheng,  F. Y., and Li,  D., 1997, “Multi-objective Optimization Design with Pareto Genetic Algorithms,” J. Struct. Eng., 123, pp. 1252–1261.
Grignon, P., and Fadel, G. M., 1997, “Quality Criteria Measures for Multi-objective Solutions Obtained with a Genetic Algorithm,” CD Proceedings of the 38th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Kissimmee, FL, April 7–10, 1997.
Li, Y., Fadel, G. M., and Wiecek, M. M., 1998, “Approximating Pareto Curves Using the Hyper-Ellipse,” Proceedings of the 7th AIAA/USAF/NASA/ISSMO Multidisciplinary Analysis and Optimization Symposium, 3 , pp. 1990–2002.
Tappeta, R. V., and Renaud, J. E., 1998, “Interactive Multiobjective Optimization Procedure,” to appear in AIAA J.
Chen,  W., Wiecek,  M., and Zhang,  J., 1999, “Quality Utility: A Compromise Programming Approach to Robust Design,” ASME J. Mech. Des., 121, No. 2, pp. 179–187.
Tind,  J., and Wiecek,  M. M., 1999, “Augmented Lagrangian and Tchebycheff Approaches in Multiple Objective Programming,” J. Global Optim., 14-3, pp. 251–266.
Haimes, Y. Y., and Chankong, V., 1983, Multiobjective Decision Making: Theory and Methodology, North Holland, New York.

Figures

Grahic Jump Location
Determining parameter α
Grahic Jump Location
QUF approximation derived at (0.99969,6.80552), α=0.454607
Grahic Jump Location
QUF approximation derived at (1.1592,6.5619), α=0.71414
Grahic Jump Location
QUF approximation with α=±2.32568
Grahic Jump Location
Local approximation of the efficient frontier for two-bar design

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In