Kybernetika 53 no. 6, 1047-1070, 2017

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

Lubomír Klimeš, Pavel Popela, Tomáš Mauder, Josef Štětina and Pavel CharvátDOI: 10.14736/kyb-2017-6-1047


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.


stochastic programming, heat transfer, progressive hedging, parallel computing, steel production, phase change


90C15, 90C06, 80A20, 80A22, 49M27, 93C20


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