Geodesic
Two-stage stochastic programming approach to a PDE-constrained steel production problem with the moving interface
Kybernetika, Tome 53 (2017) no. 6, pp. 1047-1070.

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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.
DOI : 10.14736/kyb-2017-6-1047
Classification : 49M27, 80A20, 80A22, 90C06, 90C15, 93C20
Keywords: stochastic programming; progressive hedging; parallel computing; steel production; heat transfer; phase change 
@article{10_14736_kyb_2017_6_1047,
     author = {Klime\v{s}, Lubom{\'\i}r and Popela, Pavel and Mauder, Tom\'a\v{s} and \v{S}t\v{e}tina, Josef and Charv\'at, Pavel},
     title = {Two-stage stochastic programming approach to a {PDE-constrained} steel production problem with the moving interface},
     journal = {Kybernetika},
     pages = {1047--1070},
     publisher = {mathdoc},
     volume = {53},
     number = {6},
     year = {2017},
     doi = {10.14736/kyb-2017-6-1047},
     mrnumber = {3758934},
     zbl = {06861640},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-6-1047/}
}
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AU  - Popela, Pavel
AU  - Mauder, Tomáš
AU  - Štětina, Josef
AU  - Charvát, Pavel
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%A Mauder, Tomáš
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%A Charvát, Pavel
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Klimeš, Lubomír; Popela, Pavel; Mauder, Tomáš; Štětina, Josef; Charvát, Pavel. Two-stage stochastic programming approach to a PDE-constrained steel production problem with the moving interface. Kybernetika, Tome 53 (2017) no. 6, pp. 1047-1070. doi : 10.14736/kyb-2017-6-1047. http://geodesic.mathdoc.fr/articles/10.14736/kyb-2017-6-1047/

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