Adaptive response surface method - A global optimization scheme for approximation-based design problems

Engineering Optimization

Volumn 33, Issue 6, 2001, Pages 707-733

  Wang, G Gary ^a   Dong, Zuomin ^b   Aitchison, Peter ^a  

^a UNIVERSITY OF MANITOBA   (Canada)

^b UNIVERSITY OF VICTORIA   (Canada)

Author keywords

Approximate optimization; Design automation; Global optimization; Response surface method

Indexed keywords

EID: 0012981186     PISSN: 0305215X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (62)

1. Alexandrov, N. M., Dennis, J. E., Lewis, R. M. and Torczon, V. (1998). A trust-region framework for managing the use of approximation models in optimization. Structural Optimization, 15, 16-23.
2. Balabanov, V. O., Giunta, A. A., Golovidov, O., Grossman, B., Mason, W. H., Watson, L. T. and Haftka, R. T. (1999). Reasonable design space approach to response surface approximation. Journal of Aircraft, 36(1), 308-315.
3. Bernado, M. C., Buck, R. and Liu, L. (1992). Integrated circuit design optimization using a sequential strategy. IEEE Transactions on Computer-Aided Design, 11(3), 361-372.
4. Bloebaum, C. L., Hong, W. and Peck, A. (1994). Improved move limit strategy for approximate optimization. Proceedings of the AIAA/USAF/NASA/ISSMO 5th Symposium on Multidisciplinary Analysis and Optimization, Panama City, Florida, Paper No. 94-4337, pp. 843-850.
5. Box, G. E. P. and Draper, N. R. (1969). Evolutionary Operation: A Statistical Method for Process Management. John Wiley & Sons, Inc., Toronto.
6. Box, G. E. P. and Hunter, J. S. (1957). Multifactor experimental designs for exploring response surfaces. Annals of Mathematical Statistics, 28, 195-241.
7. Chen, T. Y. (1993). Calculation of the move limits for the sequential linear programming method. International Journal for Numerical Methods in Engineering, 36(15), 2661-2679.
8. Chen, W. (1995). A Robust Concept Exploration Method for Configuring Complex System. Ph. D. Thesis, Georgia Institute of Technology.
9. 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. Journal of Mechanical Design, Transactions of the ASME, 118, 478-485.
10. Conn, A. R., Gould, N. I. M. and Toint, P. L. (1988). Global convergence of a class of trust region algorithms for optimization with simple bounds. SIAM Journal of Numeric Analysis, 25(2), 433-464.
11. Conn, A. R., Gould, N. I. M. and Toint, P. L. (1988). Testing a class of methods for solving minimization problems with simple bounds on the variables. Mathematics of Computation, 50(12), 399-430.
12. Conn, A. R., Gould, N. I. M. and Toint, P. L. (1991). A globally convergent augmented lagrangian algorithm for optimization with general constraints and simple bounds. SIAM Journal of Numerical Analysis, 28, 545-572.
13. Dennis, J. E. Jr. and Torczon, V. (1996). Approximation model management for optimization: work-in-progress. Paper No. AIAA-96-4099-CP, pp. 1044-1046.
14. Dixon, L. and Szegö, G. (Eds.) (1978). The Global Optimization Problem: An Introduction. Toward Global Optimization 2., North-Holland, New York, pp. 1-15.
15. Fadel, G. M., Riley, M. F. and Barthelemy, J. F. M. (1990). Two point exponential approximation method for structural optimization. Structural Optimization, 2, 117-124.
16. Grignon, P. and Fadel, G. M. (1994). Fuzzy move limit evaluation in structural optimization. Paper No. AIAA-94-4281.
17. Haftka, R., Scott, E. P. and Cruz, J. R. (1998). Optimization and experiments: a survey. Applied Mechanics Review, 51(7), 435-448.
18. Hock, W. and Schittkowski, K. (1981). Test Examples for Nonlinear Programming Codes. Lecture Notes in Economics and Mathematical Systems, Vol. 187, Springer-Verlag, Berlin, Heidelberg, New York.
19. Horst, R. and Tuy, H. (1990). Global Optimization: Deterministic Approaches. Springer-Verlag, Berlin.
20. Kaufman, M., Balabanov, V., Burgee, S. L., Giunta, A. A., Grossman, B., Haftka, R. T., Mason, W. H. and Watson, L. T. (1996). Variable-complexity response surface approximations for wing structural weight in HSCT design. Computational Mechanics, 18, 112-126.
21. Khuri, A. I. and Cornell, J. A. (1987). Response Surfaces: Design and Analyses, Marcel Dekker, Inc.
22. Kirkpatrick, S., Gelatt, C. D. and Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220, 671-680.
23. Koch, P. N., Simpson, T. W., Allen, J. K. and Mistree, F. (1999). Statistical approximations for multidisciplinary design optimization: the problem of size. Journal of Aircraft, 36(1), 275-286.
24. Korngold, J. C. and Gabriele, G. A. (1997). Multidisciplinary analysis and optimization of discrete problems using response surface methods. Journal of Mechanical Design, 119, 427-433.
25. Lewis, R. M. (1996). A trust region framework for managing approximation models in engineering optimization. Paper No. AIAA-96-4101-CP, pp. 1053-1055.
26. Li, X. (1996). Course Notes on Fuel Cells. Mechanical Engineering, University of Victoria, Canada.
27. McKay, M. D., Beckman, R. J. and Conover, W. J. (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics, 21(2), 239-245.
28. Montgomery, D. (1991). Design and Analysis of Experiments. John Wiley and Sons, New York.
29. Myers, R. H. (1971). Response Surface Methodology. Allyn and Bacon, Inc.
30. Otto, J. C., Landman, D. and Patera, A. T. (1996). A surrogate approach to the experimental optimization of multielement airfoils. Paper No. AIAA-96-4138-CP, pp. 1323-1333.
31. Pardalos, P. M. and Rosen, J. B. (1987). Constrained Global Optimization: Algorithms and Applications. Lecture Notes in Economics and Mathematical Systems, Vol. 268, Springer-Verlag, Berlin, Heidelberg, New York.
32. Pastula, M. (1997). Radiator Stack PEM Fuel Cell Architecture, System Modeling and Flow Field Design. Master Thesis, University of Victoria, Canada.
33. Pourazady, M. and Fu, Z. (1996). Integrated approach to structural shape optimization. Computers and Structures, 60(2), 279-289.
34. Renaud, J. E. and Gabriele, G. A. (1993). Improved coordination in non-hierarchical system optimization. AIAA Journal, 31, 2367-2373.
35. Renaud, J. E. and Gabriele, G. A. (1994). Approximation in non-hierarchical system optimization. AIAA Journal, 32, 198-205.
36. Rodríguez, J., Renaud, J. E. and Watson, L. T. (1998). Convergence of trust region augmented lagrangian methods using variable fidelity approximation data. Structural Optimization, 15, 141-156.
37. Ronne, J, and Podhorodeski, R. (1996). An integrated cost-performance model of a transportation solid polymer fuel cell system. Proceeding of the 2nd International Fuel Cell Conference, pp. 385-388.
38. Roux, W. J., Stander, N. and Haftka, R. T. (1996). Response surface approximations for structural optimization. Proceedings of the 6th AIAAI NASA/USAF Multidisciplinary Analysis and Optimization Symposium, Bellevue, Washington, Paper 96-4042, pp. 1053-1055.
39. Sacks, J., Schiller, S. B. and Welch, W. J. (1989). Designs for computer experiments. Technometrics, 31(1), 41-47.
40. Sacks, J., Welch, W. J., Mitchell, T. J. and Wynn, H. P. (1989). Design and analysis of computer experiments. Statistical Science, 4(4), 409-435.
41. Schittkowski, K. (1987). More Test Examples for Nonlinear Programming Codes. Lecture Notes in Economics and Mathematical Systems, Vol. 282, Springer-Verlag, Berlin, Heidelberg, New York.
42. Sell, J. W. and Lepeniotis, S. S. (1992). Thermoplastic polymer formulations: an approach through experimental design. Advances in Polymer Technology, 11(3) 193-202.
43. Sellar, R. S. and Batill, S. M. (1996). Concurrent subspace optimization using gradient-enhanced neural network approximation. Paper No. AIAA-96-4019-CP, pp. 319-330.
44. Sellar, R. S., Batill, S. M. and Renaud, J. E. (1994). Mixed discrete/continuous optimization of aircraft systems using neural networks. Proceedings of the 5th AIAA/USAF/NASA/ISSMO Symposium, Paper No. 94-4348, pp. 910-921.
45. Sellar, R. S., Stelmack, M. A., Batill, S. M. and Renaud, J. E. (1996). Multidisciplinary design and analysis of an integrated aeroelastic/propulsive system. Proceedings of the 37th AIAA/ASME/ASCE/AHS/ASC Structure, Structural Dynamics and Materials Conference, Salt Lake City, Utah, Paper No. 96-1383, pp. 583-594.
46. Shi, Q., Hagiwara, I. and Takashima, F. (1999). The most probable optimal design method for global optimization. Proceedings of the 1999 ASME Design Engineering Technical Conferences, DETC/DAC-8635, Las Vegas, Nevada, September 12-15.
47. Steinbugler, M. and Ogden, J. (1994). Design considerations for proton exchange membrane fuel cells in vehicles. Abstract in the Proceedings of the 1994 Fuel Cell Seminar, San Diego, California.
48. Swift, R. A. and Batill, S. M. (1991). Application of neural networks to preliminary structural design. Proceedings of the AIAA/ASME/ASCE/AHS/ASC 32nd Structures, Structural Dynamics and Materials Conference, Baltimore, Maryland, pp. 335-343.
49. Swift, R. A. and Batill, S. M. (1992). Simulated annealing utilizing neural networks for discrete variable optimization problems in structural design. Proceedings of the AIAA/ASME/ASCE/AHS/ASC 33rd Structures, Structural Dynamics and Materials Conference, Dallas, Texas, Paper No. 92-2311-CP.
50. Swift, R. A. and Batill, S. M. (1992). Damage tolerant structural design using neural networks. Paper No. AIAA Aerospace Design Conference and Exhibit, Irvine, California, Paper No. 92-1097-CP.
51. Swift, R. A. and Batill, S. M. (1993). Structural design space definition using neural networks and a reduced knowledge base. AIAA/AHS/ASEE Aerospace Design Conference, Irvine, California, Paper No. 93-1034-CP.
52. Taguchi, G., Yokoyama, Y. and Wu, Y. (1993). Taguchi Methods: Design of Experiments. American Supplier Institute, Allen Park, Michigan.
53. Thomas, H. L., Vanderplaats, G. N. and Shyy, Y. K. (1992). A study of move limit adjustment strategies in the approximation concepts approach to structural synthesis. Proceedings of the 4th AIAA/USAF/NASA/OAI Symposium on Multidisciplinary Analysis and Optimization, Cleveland, Ohio, pp. 507-512.
54. Torczon, V. and Trosset, M. W. (1998). Using approximations to accelerate industrial design optimization. Paper No. AIAA-98-4800, pp. 738-748.
55. Törn, A. and Zilinskas, A. (1987). Global Optimization, Lecture Notes in Computer Science (Ed. Goos, G. and Hartmanis, J.) Springer-Verlag, Berlin, Heidelberg, New York.
56. Venter, G., Haftka, R. T. and Starnes, J. H. (1996). Construction of response surfaces for design optimization applications. Proceedings of the 6th AIAA/ NASA/USAF Multidisciplinary Analysis and Optimization Symposium, Bellevue, Washington, Paper 96-4040, pp. 548-564.
57. Wang, G. (1999). A quantitative concurrent industrial design method using virtual prototyping-based global optimization and its application in transportation fuel cells. Ph. D. Dissertation, University of Victoria, Canada.
58. Wang, G. and Dong, Z. (1998). An extension to design of experiment for design optimization with implicit parameter models and virtual prototype. Proceedings of the IEEE International Conference on Systems, Man, and Cybernetics, La Jolla, California, October 11-14.
59. Wang, G. and Dong, Z. (1999). Virtual prototyping-based optimal design of multiple function panels for a new PEM fuel cell stack. Proceedings of the 1999 ASME Design Engineering Technology Conference, DETC99/DAC-8557, Las Vegas, Nevada, September 12-16.
60. Wujek, B. A. and Renaud, J. E. (1998). New adaptive move-limit management strategy for approximate optimization, Part 1. AIAA Journal, 36(10), 1911-1921.
61. Wujek, B. A. and Renaud, J. E. (1998). New adaptive move-limit management strategy for approximate optimization, Part 2. AIAA Journal, 36(10), 1922-1934.
62. Xue, D. and Dong, Z. (1997). Optimal fuel cell system design considering functional performance and production costs. Proceedings of the 1997 ASME Design Engineering Technical Conferences, DETC97/DAC-3971, Sacramento, California, September 14-17.