Optimum beam design via stochastic programming

Eva Žampachová; Pavel Popela; Michal Mrázek

Kybernetika (2010)

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

Abstract

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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.

How to cite

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Žampachová, 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 -

References

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