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An outer approximations approach to reliability-based optimal design of structures. (English) Zbl 0908.90141
Summary: We present a new formulation of the problem of minimizing the initial cost of a structure subject to a minimum reliability requirement, expressed in terms of the so-called design points of the first-order reliability theory, i.e., points on limit-state surfaces that are nearest to the origin in a transformed standard normal space, as well as other deterministic constraints. Our formulation makes it possible to use outer approximations algorithms for the solution of such optimal design problems, eliminating some of the major objections associated with treating them as bilevel optimization problems. A numerical example is presented that illustrates the reliability and efficiency of the algorithm.

90B25 Reliability, availability, maintenance, inspection in operations research
90C90 Applications of mathematical programming
Full Text: DOI
[1] Thoft-Christensen, P., 151 References in Reliability-Based Structural Optimization, Proceedings of the IFIP WG 7.5 Working Conference on Reliability and Optimization of Structural Systems, Munich, Germany, 1991.
[2] Hohenbichler, M., and Rackwitz, R., Non-Normal Dependent Vectors in Structural Safety, ASCE Journal of Engineering Mechanics, Vol. 107, pp. 1227–1238, 1981.
[3] Liu, P. L., and Der Kiureghian, A., Multivariate Distribution Models with Prescribed Marginals and Covariances, Probabilistic Engineering Mechanics, Vol. 1, pp. 105–112, 1986. · doi:10.1016/0266-8920(86)90033-0
[4] Hohenbichler, M., and Rackwitz, R., First-Order Concepts in System Reliability, Journal of Structural Safety, Vol. 1, pp. 177–188, 1983. · doi:10.1016/0167-4730(82)90024-8
[5] Bertsekas, D. P., Nonlinear Programming, Athena Scientific, Belmont, Massachusetts, 1995.
[6] Vincente, L. N., and Calamai, P. H., A Bibliography Review, Report, University of Waterloo, Waterloo, Ontario, Canada, 1995 [bilevel-review.bib and bilevel-review.tex, obtainable via email from phcalamai@dial.uwaterloo.ca.].
[7] Mayne, D. Q., and Polak, E., Outer Approximations Algorithm for Nondifferentiable Optimization Problems, Journal of Optimization Theory and Applications, Vol. 42, pp. 19–30, 1984. · Zbl 0505.90068 · doi:10.1007/BF00934131
[8] Polak, E., On the Mathematical Foundations of Nondifferentiable Optimization in Engineering Design, SIAM Review, Vol. 29, pp. 21–89, 1987. · doi:10.1137/1029002
[9] Gonzaga, C., Polak, E., and Trahan, R., An Improved Algorithm for Optimization Problems with Functional Inequality Constraints, IEEE Transactions on Automatic Control, Vol. 25, pp. 49–54, 1979. · Zbl 0433.65033 · doi:10.1109/TAC.1980.1102227
[10] Gill, P. E., Murray, W., Saunders, M. A., and Wright, M. H., User’s Guide for NPSOL: A Fortran Package for Nonlinear Programming, Technical Report 86–2, Department of Operations Research, Stanford University, 1986.
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