# Optimum beam design via stochastic programming

Eva Žampachová; Pavel Popela; Michal Mrázek

Kybernetika (2010)

- Volume: 46, Issue: 3, page 571-582
- ISSN: 0023-5954

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topŽampachová, Eva, Popela, Pavel, and Mrázek, Michal. "Optimum beam design via stochastic programming." Kybernetika 46.3 (2010): 571-582. <http://eudml.org/doc/196686>.

@article{Žampachová2010,

abstract = {The purpose of the paper is to discuss the applicability of stochastic programming models and methods to civil engineering design problems. In cooperation with experts in civil engineering, the problem concerning an optimal design of beam dimensions has been chosen. The corresponding mathematical model involves an ODE-type constraint, uncertain parameter related to the material characteristics and multiple criteria. As a~result, a~multi-criteria stochastic nonlinear optimization model is obtained. It has been shown that two-stage stochastic programming offers a~promising approach to solving similar problems. A~computational scheme for this type of problems is proposed, including discretization methods for random elements and ODE constraint. An approximation is derived to implement the mathematical model and solve it in GAMS. The solution quality is determined by an interval estimate of the optimality gap computed by a~Monte Carlo bounding technique. The parametric analysis of a~multi-criteria model results in efficient frontier computation. Furthermore, a~progressive hedging algorithm is implemented and tested for the selected problem in view of the future possibilities of parallel computing of large engineering problems. Finally, two discretization methods are compared by using GAMS and ANSYS.},

author = {Žampachová, Eva, Popela, Pavel, Mrázek, Michal},

journal = {Kybernetika},

keywords = {optimum engineering design; stochastic programming; multi-objective programming; Monte Carlo methods; progressive hedging algorithm; stochastic programming; optimum engineering design; multi-objective programming; Monte Carlo methods; progressive hedging algorithm},

language = {eng},

number = {3},

pages = {571-582},

publisher = {Institute of Information Theory and Automation AS CR},

title = {Optimum beam design via stochastic programming},

url = {http://eudml.org/doc/196686},

volume = {46},

year = {2010},

}

TY - JOUR

AU - Žampachová, Eva

AU - Popela, Pavel

AU - Mrázek, Michal

TI - Optimum beam design via stochastic programming

JO - Kybernetika

PY - 2010

PB - Institute of Information Theory and Automation AS CR

VL - 46

IS - 3

SP - 571

EP - 582

AB - The purpose of the paper is to discuss the applicability of stochastic programming models and methods to civil engineering design problems. In cooperation with experts in civil engineering, the problem concerning an optimal design of beam dimensions has been chosen. The corresponding mathematical model involves an ODE-type constraint, uncertain parameter related to the material characteristics and multiple criteria. As a~result, a~multi-criteria stochastic nonlinear optimization model is obtained. It has been shown that two-stage stochastic programming offers a~promising approach to solving similar problems. A~computational scheme for this type of problems is proposed, including discretization methods for random elements and ODE constraint. An approximation is derived to implement the mathematical model and solve it in GAMS. The solution quality is determined by an interval estimate of the optimality gap computed by a~Monte Carlo bounding technique. The parametric analysis of a~multi-criteria model results in efficient frontier computation. Furthermore, a~progressive hedging algorithm is implemented and tested for the selected problem in view of the future possibilities of parallel computing of large engineering problems. Finally, two discretization methods are compared by using GAMS and ANSYS.

LA - eng

KW - optimum engineering design; stochastic programming; multi-objective programming; Monte Carlo methods; progressive hedging algorithm; stochastic programming; optimum engineering design; multi-objective programming; Monte Carlo methods; progressive hedging algorithm

UR - http://eudml.org/doc/196686

ER -

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## Citations in EuDML Documents

top- Lubomír Klimeš, Pavel Popela, Tomáš Mauder, Josef Štětina, Pavel Charvát, Two-stage stochastic programming approach to a PDE-constrained steel production problem with the moving interface
- Martin Branda, Chance constrained problems: penalty reformulation and performance of sample approximation technique
- Jakub Kůdela, Pavel Popela, Chance constrained optimal beam design: Convex reformulation and probabilistic robust design

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