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Solving joint chance constrained problems using regularization and Benders' decomposition

Submission Status:in press
  • In this paper we investigate stochastic programs with joint chance constraints. We consider discrete scenario set and reformulate the problem by adding auxiliary variables. Since the resulting problem has a difficult feasible set, we regularize it. To decrease the dependence on the scenario number, we propose a numerical method by iteratively solving a master problem while adding Benders cuts. We find the solution of the slave problem (generating the Benders cuts) in a closed form and propose a heuristic method to decrease the number of cuts. We perform a numerical study by increasing the number of scenarios and compare our solution with a solution obtained by solving the same problem with continuous distribution.

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Metadaten
Author:Lukas Adam, Martin Branda, Holger Heitsch, René Henrion
DOI:https://doi.org/10.1007/s10479-018-3091-9
Parent Title (English):Annals of Operations Research
Document Type:Article
Language:English
Date of Publication (online):2020/10/06
Release Date:2020/10/06
Tag:Benders cuts; chance constrained programming; gas networks; optimality conditions; regularization
Volume:292
First Page:683
Last Page:709
Institutes:Weierstraß-Institut für Angewandte Analysis und Stochastik
Subprojects:B04
Licence (German):License LogoCreative Commons - CC BY-NC-ND - Namensnennung - Nicht kommerziell - Keine Bearbeitungen 4.0 International