Publication detail

Optimum Beam Design via Stochastic Programming

ŽAMPACHOVÁ, E. POPELA, P. MRÁZEK, M.

Original Title

Optimum Beam Design via Stochastic Programming

Type

journal article - other

Language

English

Original 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.

Keywords

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

Authors

ŽAMPACHOVÁ, E.; POPELA, P.; MRÁZEK, M.

RIV year

2010

Released

14. 6. 2010

Publisher

Institute of Information Theory and Automation

Location

Prague

ISBN

0023-5954

Periodical

Kybernetika

Year of study

46

Number

3

State

Czech Republic

Pages from

571

Pages to

582

Pages count

12

BibTex

@article{BUT49738,
  author="Eva {Mrázková} and Pavel {Popela} and Michal {Mrázek}",
  title="Optimum Beam Design via Stochastic Programming",
  journal="Kybernetika",
  year="2010",
  volume="46",
  number="3",
  pages="571--582",
  issn="0023-5954"
}