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TECHNICAL PAPERS

Adaptive Response Surface Method Using Inherited Latin Hypercube Design Points

[+] Author and Article Information
G. Gary Wang

Dept. of Mech. and Indus. Engineering, University of Manitoba, Winnipeg, MB, Canada R3T 5V6

J. Mech. Des 125(2), 210-220 (Jun 11, 2003) (11 pages) doi:10.1115/1.1561044 History: Received August 01, 2001; Revised July 01, 2002; Online June 11, 2003
Copyright © 2003 by ASME
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References

Haftka,  R., Scott,  E. P., and Cruz,  J. R., 1998, “Optimization and Experiments: A Survey,” Appl. Mech. Rev., 51(7), pp. 435–448.
Myers, R. H., and Montgomery, D. C., 1995, Response Surface Methodology: Process and Product Optimization Using Designed Experiments, John Wiley and Sons, Inc., Toronto.
Chen, W., 1995, “A Robust Concept Exploration Method for Configuring Complex System,” Ph.D. Thesis, Georgia Institute of Technology.
Mitchell,  T. J., 1974, “An Algorithm for the Construction of “D-Optimal” Experimental Designs,” Technometrics, 16(2), pp. 203–210.
Bernado,  M. C., Buck,  R., and Liu,  L., 1992, “Integrated Circuit Design Optimization Using a Sequential Strategy,” IEEE Trans. Comput.-Aided Des., 11(3), pp. 361–372.
Sell,  J. W., and Lepeniotis,  S. S., 1992, “Thermoplastic Polymer Formulations: An Approach through Experimental Design,” Adv. Polym. Technol., 11(3), pp. 193–202.
Giunta,  A. A., Balabanov,  V., Haim,  D., Grossman,  B., Mason,  W. H., Watson,  L. T., and Haftka,  R. T., 1997, “Multidisciplinary Optimization of a Supersonic Transport Using Design of Experiments theory and Response Surface Modeling,” Aeronaut. J., 101(1008), pp. 347–356.
Unal, R., Lepsch, R. A., Engelund, W., and Stanley, D. O., 1996, “Approximation Model Building and Multidisciplinary Optimization Using Response Surface Methods,” AIAA-96-4044-CP, pp. 592–598.
Unal, R., Lepsch, R. A., and McMillin, M. L., 1998, “Response Surface Model Building and Multidisciplinary Optimization Using D-Optimal Designs,” AIAA-98-4759, pp. 405–411.
Sacks,  J., Welch,  W. J., Mitchell,  T. J., and Wynn,  H. P., 1989a, “Design and Analysis of Computer Experiments,” Stat. Sci., 4(4), pp. 409–435.
Simpson, T. W., Mauery, T. M., Korte, J. J., and Mistree, F., 1998, “Comparison of Response Surface and Kriging Models for Multidisciplinary Design Optimization,” Proceedings of the 7th AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis & Optimization, St. Louis, MO, September 2–4, AIAA, 1 (381–391) AIAA-98-4755.
Taguchi, G., Yokoyama, Y., and Wu, Y., 1993, Taguchi Methods: Design of Experiments, American Supplier Institute, Allen Park, Michigan.
Owen,  A., 1992, “Orthogonal Arrays for Computer Experiments, Integration, and Visualization,” Statistica Sinica, 2, pp. 439–452.
McKay,  M. D., Bechman,  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), May, pp. 239–245.
Iman,  R. L., and Conover,  W. J., 1980, “Small Sensitivity Analysis Techniques for Computer Models with an Application to Risk Assessment,” Commun. Stat: Theory Meth., A9(17), pp. 1749–1842.
Tang,  B., 1993, “Orthogonal Array-based Latin Hypercubes,” J. Am. Stat. Assoc., 88(424), Theory and Methods, pp. 1392–1397.
Park,  J. S., 1994, “Optimal Latin-hypercube Designs for Computer Experiments,” J. Stat. Plan. Infer., 39, pp. 95–111.
Ye,  K. Q., Li,  William, and Sudianto,  A., 2000, “Algorithmic Construction of Optimal Symmetric Latin Hypercube Designs,” J. Stat. Plan. Infer., 90, pp. 145–159.
Sacks,  J., Schiller,  S. B., and Welch,  W. J., 1989, “Designs for Computer Experiments,” Technometrics, 31(1), pp. 41–47.
Varaarajan,  S., Chen,  W., and Pelka,  C. J., 2000, “Robust concept Exploration of Propulsion Systems with Enhanced Model Approximation Capabilities,” Eng. Optimiz., 32(3), pp. 309–334.
Giunta, A. A., and Watson, L. T., 1998, “A Comparison of Approximation Modeling Techniques: Polynomial Versus Interpolating Models,” AIAA-98-4758, American Institute of Aeronautics and Astronautics, Inc., pp. 392–401.
Koch,  P. N., Simpson,  T. W., Allen,  J. K., and Mistree,  F., 1999, “Statistical Approximations for Multidisciplinary Design Optimization: The Problem of Size,” J. Aircr., 36(1), pp. 275–286.
Jin, R., Chen, W., and Simpson, T., 2000, “Comparative Studies of Metamodeling Techniques under Multiple Modeling Criteria,” 8th AIAA/NASA/USAF/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Long Beach, CA, September 6–8.
Lin, Y., Krishnapur, K., Allen, J. K., and Mistree, F., 2000, “Robust Concept Exploration in Engineering Design: Metamodeling Techniques and Goal Formulations,” Proceedings of the 2000 ASME Design Engineering Technical Conferences, DETC2000/DAC-14283, September 10–14, Baltimore, Maryland.
Simpson,  T. W., Peplinski,  J. D., Koch,  P. N., and Allen,  J. K., 2001, “Metamodels for Computer-based Engineering Design: Survey and Recommendations,” Eng. Comput., 17, pp. 129–150.
Dennis, J. E., and Torczon, V., 1996, “Managing Approximation Models in Optimization,” Alexandrov, N. and Hussaini, M. Y., eds., Multidisciplinary Design Optimization: State of the Art, Society for Industrial and Applied Mathematics, Philadelphia.
Box, G. E. P., and Draper, N. R., 1969, Evolutionary Operation: A Statistical Method for Process Management, John Wiley & Sons, Inc., New York.
Giunta, A. A., Balbanov, V., Kaufmann, M., Burgee, S., Grossman, B., Haftka, R. T., Mason, W. H., and Watson, L. T., 1996, “Variable Complexity Response Surface Design of an HSCT Configuration,” Multidisciplinary Design Optimization: State of the Art, Alexandrov, N., and Hussaini, M. Y., eds., Society for Industrial and Applied Mathematics, Philadelphia.
Wujek,  B. A., and Renaud,  J. E., 1998a, “New Adaptive Move-Limit Management Strategy for Approximate Optimization, Part 1,” AIAA J., 36(10), pp. 1911–1921.
Wujek,  B. A., and Renaud,  J. E., 1998b, “New Adaptive Move-Limit Management Strategy for Approximate Optimization, Part 2,” AIAA J., 36(10), pp. 1922–1934.
Renaud,  J. E., and Gabriele,  G. A., 1993, “Improved Coordination in Non-hierarchical System Optimization,” AIAA J., 31, pp. 2367–2373.
Renaud,  J. E., and Gabriele,  G. A., 1994, “Approximation in Non-hierarchical System Optimization,” AIAA J., 32, pp. 198–205.
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 J. Mech. Des., 118, pp. 478–485.
Korngold,  J. C., and Gabriele,  G. A., 1997, “Multidisciplinary Analysis and Optimization of Discrete Problems Using Response Surface Methods,” ASME J. Mech. Des., 9, pp. 427–433.
Wang,  G. G., Dong,  Z., and Aitchison,  P., 2001, “Adaptive Response Surface Method—A Global Optimization Scheme for Computation-intensive Design Problems,” Journal of Engineering Optimization, 33(6), pp. 707–734.
Kirkpatrick,  S., Gelatt,  C. D., and Vecchi,  M. P., 1983, “Optimization by Simulated Annealing,” Science, 220, pp. 671–680.
Dixon, L., and Szegö, G., 1978, “The Global Optimization Problem: An Introduction,” Toward Global Optimization 2, L. Dixon and G. Szegö, eds, North-Holland, New York, pp. 1–15.
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.
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.
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.
Törn, A., and Zilinskas, A., 1987, Global Optimization, Lecture Notes in Computer Science, Vol. 350, Springer, Berlin, Heidelberg, New York.
Jones,  D. R., Perttuen,  C. D., and Stuckman,  B. E., 1993, “Lipschitzian Optimization Without the Lipschitz Constant,” J. Optim. Theory Appl., 79(1), pp. 157–181.
Gold, S., and Krishnamurty, S., 1997, “Trade-offs in Robust Engineering Design,” Proceedings of the 1997 ASME Design Engineering Technical Conferences, DETC97/DAC3757, September 14–17, Saramento, California.

Figures

Grahic Jump Location
The flowchart of the improved ARSM
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Inherited design points and underrepresented variable intervals in the new space
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A new Latin Hypercube sample set of three points
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Mapping new LHD points to the design space
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Two inherited points falling in the same variable interval
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Mapping when the number of underrepresented intervals for each variable is different
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Samples generated by two inheritance methods at the 8th iteration for Goldstein and Price function

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