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Stochastic Programming pp 109–122Cite as

Multipoint Approximation Method for Structural Optimization Problems with Noisy Function Values

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 423))

Abstract

The multipoint approximation method is considered as a general iterative technique, which uses in each iteration simplified approximations of the original stochastic objective/constraint functions. They are obtained by the multiple regression analysis methods which can use information being more or less inaccurate. The technique allows to use in each iteration the information gained in several previous design points which are considered as a current design of numerical experiments (multipoint approximations). It allows to consider instead of the initial stochastic optimization problem a sequence of simpler mathematical programming problems and to reduce the total number of time-consuming structural analyses. The obtained approximations are assumed to be valid within a current subregion of the space of design variables, defined by move limits.

Several particular forms of approximations are considered including explicit expressions (linear, intrinsically linear, general nonlinear) and simplified implicit expressions. The proposed approach provides flexibility in choosing design variables and objective/constraint functions and allows the designer to use his/her experience and judgement in directing the optimization process.

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Author information

Authors and Affiliations

  1. Department of Civil Engineering, University of Bradford, Bradford, West Yorkshire, BD7 1DP, UK

    Vassili V. Toropov

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  1. Vassili V. Toropov
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Editor information

Editors and Affiliations

  1. Fk. LRT, Universität der Bundeswehr Müchen, D-85577, Neubiberg/München, Germany

    Kurt Marti

  2. Institut für Operations Research, Universität Zürich, Moussonstr. 15, CH-8044, Zürich, Switzerland

    Peter Kall

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© 1995 Springer-Verlag Berlin Heidelberg

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Toropov, V.V. (1995). Multipoint Approximation Method for Structural Optimization Problems with Noisy Function Values. In: Marti, K., Kall, P. (eds) Stochastic Programming. Lecture Notes in Economics and Mathematical Systems, vol 423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-88272-2_7

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  • DOI: https://doi.org/10.1007/978-3-642-88272-2_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-58996-9

  • Online ISBN: 978-3-642-88272-2

  • eBook Packages: Springer Book Archive

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