×

Trust region model management in multidisciplinary design optimization. (English) Zbl 0992.90042

Summary: A common engineering practice is the use of approximation models in place of expensive computer simulations to drive a multidisciplinary design process based on nonlinear programming techniques. The use of approximation strategies is designed to reduce the number of detailed, costly computer simulations required during optimization while maintaining the pertinent features of the design problem. This paper overviews the current state of the art in model management strategies for approximate optimization. Model management strategies coordinate the interaction between the optimization and the fidelity of the approximation models so as to ensure that the process converges to a solution of the original design problem. Approximations play an important role in multidisciplinary design optimization (MDO) by offering system behavior information at a relatively low cost. Most approximate MDO strategies are sequential, in which an optimization of an approximate problem subject to design variable move limits is iteratively repeated until convergence. The move limits or trust region are imposed to restrict the optimization to regions of the design space in which the approximations provide meaningful information. In order to insure convergence of the sequence of approximate optimizations to a Karash-Kuhn-Tucker solution, a trust region model management or move limit strategy is required. In this paper recent developments in approximate MDO strategies and issues of trust region model management in MDO are reviewed.

MSC:

90B50 Management decision making, including multiple objectives
90C59 Approximation methods and heuristics in mathematical programming

Software:

DFO
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] N. Alexandrov, On managing the use of surrogates in general nonlinear optimization and MDO, Proceedings of the Seventh AIAA/USAF/NASA/ISSMO Multidisciplinary Analysis & Optimization Symposium, Saint Louis, MO, 1998, Paper 98-4798, pp. 720-729.; N. Alexandrov, On managing the use of surrogates in general nonlinear optimization and MDO, Proceedings of the Seventh AIAA/USAF/NASA/ISSMO Multidisciplinary Analysis & Optimization Symposium, Saint Louis, MO, 1998, Paper 98-4798, pp. 720-729.
[2] N. Alexandrov, J.E. Dennis, A class of general trust-region multilevel algorithms for nonlinear constrained optimization, submitted for publication.; N. Alexandrov, J.E. Dennis, A class of general trust-region multilevel algorithms for nonlinear constrained optimization, submitted for publication.
[3] Alexandrov, N.; Dennis, J. E.; Lewis, R. M.; Torczon, V., A trust region framework for managing the use of approximation models in optimization, J. Structural Optim., 15, 16-23 (1998)
[4] Barthelemy, J. F.; Haftka, R. T., Approximation concepts for optimum structural design – a review, Structural Optim., 5, 129-144 (1993)
[5] C.L. Bloebaum, W. Hong, A. Peck, Improved moved limit strategy for approximate optimization, Proceedings of the Fifth AIAA/USAF/NASA/ISSMO Symposium, Panama City, FL, Paper 94-4337-CP, 1994, pp. 843-850.; C.L. Bloebaum, W. Hong, A. Peck, Improved moved limit strategy for approximate optimization, Proceedings of the Fifth AIAA/USAF/NASA/ISSMO Symposium, Panama City, FL, Paper 94-4337-CP, 1994, pp. 843-850.
[6] Booker, A. J.; Dennis, J. E.; Frank, P. D.; Serafini, D. B.; Torcson, V.; Trosset, M. W., A rigorous framework for optimization of expensive functions by surrogates, Struct. Optim., 17, 1-13 (1999)
[7] Box, G. E.; Draper, N. R., Empirical Model-Building and Response Surfaces (1987), Wiley: Wiley New York · Zbl 0614.62104
[8] Chen, T. Y., Calculation of the move limits for the sequential linear programming method, Internat. J. Numer. Methods Engrg., 36, 2661-2679 (1993) · Zbl 0800.73529
[9] Conn, A. R.; Gould, N. I.M.; Toint, Ph. L., A globally convergent augmented Lagrangian algorithm for optimization with general constraints and simple bounds, SIAM J. Numer. Anal., 28, 2, 545-572 (1991) · Zbl 0724.65067
[10] A.R. Conn, K. Scheinberg, Ph.L. Toint, On the convergence of derivative-free methods for unconstraint optimization, in: A. Iserles, A. Buhmann (Eds.), Approximation Theory and Optimization: Tributes to M.J.D. Powell, Cambridge University Press, Cambridge, 1997, pp. 83-108.; A.R. Conn, K. Scheinberg, Ph.L. Toint, On the convergence of derivative-free methods for unconstraint optimization, in: A. Iserles, A. Buhmann (Eds.), Approximation Theory and Optimization: Tributes to M.J.D. Powell, Cambridge University Press, Cambridge, 1997, pp. 83-108. · Zbl 1042.90617
[11] A.R. Conn, K. Scheinberg, Ph.L. Toint, A derivative-free optimization algorithm in practice, Proceedings of the Seventh AIAA/USAF/NASA/ISSMO Multidisciplinary Analysis & Optimization Symposium, Saint Louis, MO, 1998, Paper 98-4718, pp. 129-139.; A.R. Conn, K. Scheinberg, Ph.L. Toint, A derivative-free optimization algorithm in practice, Proceedings of the Seventh AIAA/USAF/NASA/ISSMO Multidisciplinary Analysis & Optimization Symposium, Saint Louis, MO, 1998, Paper 98-4718, pp. 129-139.
[12] Currin, C.; Mitchell, T.; Morris, M.; Ylvisaker, D., Bayesian prediction of deterministic functions, with applications to the design and analysis of experiments, J. Amer. Statist. Assoc., 86, 416, 953-963 (1991)
[13] Dennis, J. E.; Schnabel, R. B., Numerical Methods for Unconstrained Optimization and Nonlinear Equations (1983), Prentice-Hall: Prentice-Hall Engelwood Cliffs, NJ · Zbl 0579.65058
[14] Fadel, G. M.; Riley, M. F.; Barthelemy, J. F.M., Two point exponential approximation method for structural optimizations, Struct. Optim., 2, 117-124 (1990)
[15] R.M. Lewis, V. Torczon, A globally convergent augmented Lagrangian pattern search algorithm for optimization with general constraints and simple bounds, Technical Report 98-31, ICASE, NASA Langley Research Center, Hampton, VA 23681-2199, 1998.; R.M. Lewis, V. Torczon, A globally convergent augmented Lagrangian pattern search algorithm for optimization with general constraints and simple bounds, Technical Report 98-31, ICASE, NASA Langley Research Center, Hampton, VA 23681-2199, 1998.
[16] Lewis, R. M.; Torczon, V., Pattern search algorithms for bound constrained minimization, SIAM J. Optim., 9, 1082-1099 (1999) · Zbl 1031.90047
[17] Owen, A. B., Orthogonal arrays for computer experiments, integration and visualization, Statist. Sinica, 2, 439-452 (1992) · Zbl 0822.62064
[18] S. Padula, N. Alexandrov, L. Green, MDO test suite at NASA Langley Research Center, Proceedings of the Sixth AIAA/NASA/ISSMO Symposium on Multidisciplinary Analysis & Optimization, Bellevue, WA, 1996, Paper 96-4028.; S. Padula, N. Alexandrov, L. Green, MDO test suite at NASA Langley Research Center, Proceedings of the Sixth AIAA/NASA/ISSMO Symposium on Multidisciplinary Analysis & Optimization, Bellevue, WA, 1996, Paper 96-4028.
[19] Rasmussen, J., Nonlinear programming by cumulative approximation refinement, Struct. Optim., 15, 1-7 (1998)
[20] Rodrı́guez, J. F.; Renaud, J. E.; Watson, L. T., Convergence of trust region augmented Lagrangian methods using variable fidelity approximation data, Struct. Optim., 15, 141-156 (1998)
[21] Sacks, J.; Welch, W. J.; Mitchell, T. J.; Wynn, H. P., Design and analysis of computer experiments, Statist. Sci., 4, 409-435 (1989) · Zbl 0955.62619
[22] J. Sobieszczanski-Sobieski, R.T. Haftka, Multidisciplinary aerospace optimization: survey of recent developments, Struct. Optim. 14 (1997) 1-23, Paper No. AIAA 96-0711.; J. Sobieszczanski-Sobieski, R.T. Haftka, Multidisciplinary aerospace optimization: survey of recent developments, Struct. Optim. 14 (1997) 1-23, Paper No. AIAA 96-0711.
[23] H.L. Thomas, G.N. Vanderplaats, Y.K. Shyy, A study of move limit adjustment strategies in the approximation concepts approach to structural synthesis, Proceedings of the Fourth AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis & Optimization, Cleveland, OH, 1992, pp. 507-512.; H.L. Thomas, G.N. Vanderplaats, Y.K. Shyy, A study of move limit adjustment strategies in the approximation concepts approach to structural synthesis, Proceedings of the Fourth AIAA/USAF/NASA/ISSMO Symposium on Multidisciplinary Analysis & Optimization, Cleveland, OH, 1992, pp. 507-512.
[24] Torczon, V., On the convergence of pattern search algorithms, SIAM J. Optim., 7, 1-25 (1997) · Zbl 0884.65053
[25] Wujek, B. A.; Renaud, J. E., A new adaptive move limit management strategy for approximate optimization, Part 1, AIAA J., 36, 10, 1911-1921 (1998)
[26] Wujek, B. A.; Renaud, J. E.; Batill, S. M., A concurrent engineering approach for multidisciplinary design in a distributed computing environment, (Alexandrov, N.; Hussaini, M. Y., Multidisciplinary Design Optimization: State-of-the-Art. Multidisciplinary Design Optimization: State-of-the-Art, Proceedings in Applied Mathematics, Vol. 80 (1997), SIAM: SIAM Philadelphia), 189-208
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.