Two-stage stochastic programming approach to a PDE-constrained steel production problem with the moving interface

Lubomír Klimeš; Pavel Popela; Tomáš Mauder; Josef Štětina; Pavel Charvát

Kybernetika (2017)

  • Volume: 53, Issue: 6, page 1047-1070
  • ISSN: 0023-5954

Abstract

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The paper is concerned with a parallel implementation of the progressive hedging algorithm (PHA) which is applicable for the solution of stochastic optimization problems. We utilized the Message Passing Interface (MPI) and the General Algebraic Modelling System (GAMS) to concurrently solve the scenario-related subproblems in parallel manner. The standalone application combining the PHA, MPI, and GAMS was programmed in C++. The created software was successfully applied to a steel production problem which is considered by means of the two-stage stochastic PDE-constrained program with a random failure. The numerical heat transfer model for the steel production was derived with the use of the control volume method and the phase changes were taken into account with the use of the effective heat capacity. Numerical experiments demonstrate that parallel computing facility has enabled a significant reduction of computational time. The quality of the stochastic solution was evaluated and discussed. The developed system seems computationally effective and sufficiently robust which makes it applicable in other applications as well.

How to cite

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Klimeš, Lubomír, et al. "Two-stage stochastic programming approach to a PDE-constrained steel production problem with the moving interface." Kybernetika 53.6 (2017): 1047-1070. <http://eudml.org/doc/294729>.

@article{Klimeš2017,
abstract = {The paper is concerned with a parallel implementation of the progressive hedging algorithm (PHA) which is applicable for the solution of stochastic optimization problems. We utilized the Message Passing Interface (MPI) and the General Algebraic Modelling System (GAMS) to concurrently solve the scenario-related subproblems in parallel manner. The standalone application combining the PHA, MPI, and GAMS was programmed in C++. The created software was successfully applied to a steel production problem which is considered by means of the two-stage stochastic PDE-constrained program with a random failure. The numerical heat transfer model for the steel production was derived with the use of the control volume method and the phase changes were taken into account with the use of the effective heat capacity. Numerical experiments demonstrate that parallel computing facility has enabled a significant reduction of computational time. The quality of the stochastic solution was evaluated and discussed. The developed system seems computationally effective and sufficiently robust which makes it applicable in other applications as well.},
author = {Klimeš, Lubomír, Popela, Pavel, Mauder, Tomáš, Štětina, Josef, Charvát, Pavel},
journal = {Kybernetika},
keywords = {stochastic programming; progressive hedging; parallel computing; steel production; heat transfer; phase change},
language = {eng},
number = {6},
pages = {1047-1070},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Two-stage stochastic programming approach to a PDE-constrained steel production problem with the moving interface},
url = {http://eudml.org/doc/294729},
volume = {53},
year = {2017},
}

TY - JOUR
AU - Klimeš, Lubomír
AU - Popela, Pavel
AU - Mauder, Tomáš
AU - Štětina, Josef
AU - Charvát, Pavel
TI - Two-stage stochastic programming approach to a PDE-constrained steel production problem with the moving interface
JO - Kybernetika
PY - 2017
PB - Institute of Information Theory and Automation AS CR
VL - 53
IS - 6
SP - 1047
EP - 1070
AB - The paper is concerned with a parallel implementation of the progressive hedging algorithm (PHA) which is applicable for the solution of stochastic optimization problems. We utilized the Message Passing Interface (MPI) and the General Algebraic Modelling System (GAMS) to concurrently solve the scenario-related subproblems in parallel manner. The standalone application combining the PHA, MPI, and GAMS was programmed in C++. The created software was successfully applied to a steel production problem which is considered by means of the two-stage stochastic PDE-constrained program with a random failure. The numerical heat transfer model for the steel production was derived with the use of the control volume method and the phase changes were taken into account with the use of the effective heat capacity. Numerical experiments demonstrate that parallel computing facility has enabled a significant reduction of computational time. The quality of the stochastic solution was evaluated and discussed. The developed system seems computationally effective and sufficiently robust which makes it applicable in other applications as well.
LA - eng
KW - stochastic programming; progressive hedging; parallel computing; steel production; heat transfer; phase change
UR - http://eudml.org/doc/294729
ER -

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