Effective generation of the Pareto frontier using the normal constraint method

40th AIAA Aerospace Sciences Meeting and Exhibit

Volumn , Issue , 2002, Pages

  Ismail Yahaya, Amir ^a   Messac, Achille ^a  

^a RENSSELAER POLYTECHNIC INSTITUTE   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

AEROSPACE ENGINEERING;

ANALYTICAL EXPRESSIONS; DESIGN OBJECTIVES; ENGINEERING DESIGN; ENGINEERING DESIGN OPTIMIZATION; ENGINEERING OPTIMIZATION; EPSILON-CONSTRAINT METHOD; NORMAL BOUNDARY INTERSECTIONS; NORMAL CONSTRAINT METHODS;

DECISION MAKING;

EID: 85087605824     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.2514/6.2002-178     Document Type: Conference Paper

References (17)

1. Steuer, R. Multiple Criteria Optimization: Theory, Computation, and Application, John Wiley & Sons, New York, 1986, Chapter 3.
2. Belegundu, A., and Chandrupatla, T., Optimization Concepts and Applications in Engineering, Prentice Hall, New Jersey, 1999, pp. 373-382.
3. Grandhi, R. V., and Bharatram, G., "Multiobjective Optimization of Large-Scale Structures, " AIAA Journal, Vol. 31, No. 7, July 1993, pp. 1329-1337.
4. Messac, A., and Sundaraj, G. J., "Physical Programming's Ability to Generate a Well-Distributed Sets of Pareto Points, " 41st AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conference, Paper No. AIAA 2000-1666, Atlanta, Georgia, April 3-6, 2000.
5. Das, I., and Dennis, J., "A Closer Look at Drawbacks of Minimizing Weighted Sums of Objective for Pareto Set Generation in Multicriteria Optimization Problems, " Structural Optimization, Vol. 14, 1997, pp. 63-69.
6. Chen, W., Wiecek, M. M., and Zhang, J., "Quality Utility-A Compromise Programming Approach to Robust Design, " Journal of Mechanical Design, Vol. 121, June 1999, pp. 179-187.
7. Messac, A., and Ismail-Yahaya, A., "Required Relationship between Objective Function and Pareto Frontier Orders: Practical Implications, " AIAA Journal, Vol. 39, No. 11, Nov. 2001, pp. 2168-2174.
8. Soismaa, M., "A Note on Efficient Solutions for the Linear Bilevel Programming Problem, " European Journal of Operational Research, Vol. 112, pp. 2427-431, 1999.
9. Cheng, F. Y., Li, D., "Multiobjective Optimization Design with Pareto Genetic Algorithm, " Journal of Structural Engineering, Sept. 1997, pp 1252-1261.
10. Tappeta, R. V., Renaud, J. E., Messac, A., and Sundararaj, G. J., "Interactive Physical Programming: Tradeoff Analysis and Decision Making in Multidisciplinary Optimization, " AIAA Journal, Vol. 38, No. 5, May 2000, pp. 917-926.
11. Fadel, G., and Li, Y., "Approximating the Pareto Curve to Help Solve Bi-objective Design Problems, " (IN PRESS).
12. Das, L, and Dennis, J., "Normal-Boundary Intersection: A New Method for Generating Pareto Optimal Points in Multicriteria Optimization Problems, " SIAM Journal on Optimization, Vol. 8, No. 3, August 1998, pp. 631-657.
13. Das, L, "On Characterizing the vKnee' of the Pareto Curve based on Normal-Boundary Intersection, " Structural Optimization, Vol. 18, No. 2/3, Oct. 1999, pp. 107-115.
14. Das, I., "An Improved Technique for Choosing Parameters for Pareto Surface Generation Using Normal-B oundary Intersection, " WCSMO-3 Proceedings, Buffalo, NY, March 1999.
15. Lim, Y., and Joulia, X., "Efficient Implementation of the Normal Boundary Intersection (NBI) Method on Multiobjective Optimization Problems, " Industrial & Engineering Chemistry Research, Vol. 40, No. 2, 2001, pp. 648-655.
16. Messac, A., "Physical Programming: Effective Optimization for Computational Design, " AIAA Journal, Vol. 34, No. 1, Jan. 1996, pp. 149-158.
17. Das. I, Nonlinear Multicriteria Optimization and Robust Optimality, Ph.D. Thesis. Dept. of Computational and Applied Mathematics, Rice University, Houston, TX, 1997.