On the computation of solution spaces in high dimensions

被引：19

作者：

Graff, Lavinia ^{[1
]}

Harbrecht, Helmut ^{[2
]}

Zimmermann, Markus ^{[1
]}

机构：

[1] BMW Grp Res & Innovat Ctr, Knorrstr 147, D-80937 Munich, Germany

[2] Univ Basel, Dept Math & Comp Sci, Spiegelgasse 1, CH-4051 Basel, Switzerland

来源：

STRUCTURAL AND MULTIDISCIPLINARY OPTIMIZATION | 2016年 / 54卷 / 04期

关键词：

Robust design; Uncertainty; Solution space; High-dimensional systems; Nonlinear systems; ROBUST DESIGN; OPTIMIZATION;

D O I：

10.1007/s00158-016-1454-x

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

A stochastic algorithm that computes box-shaped solution spaces for nonlinear, high-dimensional and noisy problems with uncertain input parameters has been proposed in Zimmermann and von Hoessle (Int J Numer Methods Eng 94(3):290-307, 2013). This paper studies in detail the quality of the results and the efficiency of the algorithm. Appropriate benchmark problems are specified and compared with exact solutions that were derived analytically. The speed of convergence decreases as the number of dimensions increases. Relevant mechanisms are identified that explain how the number of dimensions affects the performance. The optimal number of sample points per iteration is determined in dependence of the preference for fast convergence or a large volume.

引用

页码：811 / 829

页数：19

共 35 条

[1] Reliability-based analysis and design optimization of electrostatically actuated MEMS [J].

Allen, M ;

Raulli, M ;

Maute, K ;

Frangopol, DM .

COMPUTERS & STRUCTURES, 2004, 82 (13-14) :1007-1020

[2]

[Anonymous], 2000, An Introduction to Mathematical Modeling

[3]

[Anonymous], 1961, Adaptive Control Processes: a Guided Tour, DOI DOI 10.1515/9781400874668

[4]

[Anonymous], MULTIDISCIPLINARY DE

[5] Designing robust structures - A nonlinear simulation based approach [J].

Beer, Michael ;

Liebscher, Martin .

COMPUTERS & STRUCTURES, 2008, 86 (10) :1102-1122

[6] Robust optimization - A comprehensive survey [J].

Beyer, Hans-Georg ;

Sendhoff, Bernhard .

COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING, 2007, 196 (33-34) :3190-3218

[7]

Fender J, 2013, STRUCT MULTIDISCIP O

[8] A Bayesian approach to reliability-based optimization with incomplete information [J].

Gunawan, Subroto ;

Papalambros, Panos Y. .

JOURNAL OF MECHANICAL DESIGN, 2006, 128 (04) :909-918

[9]

Hacking Ian, 1975, The Emergence of Probability. A Philosophical Study of Early Ideas about Probability, Induction, and Statistical Inference

[10] Finding robust solutions for product design problems [J].

Hendrix, EMT ;

Mecking, CJ ;

Hendriks, THB .

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH, 1996, 92 (01) :28-36

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