Solving joint chance constrained problems using regularization and Benders’ decomposition

We consider stochastic programs with joint chance constraints with discrete random distribution. We reformulate the problem by adding auxiliary variables. Since the resulting problem has a non-regular feasible set, we regularize it by increasing the feasible set. We solve the regularized problem by...

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Bibliographic Details
Published in:Annals of operations research 2020-09, Vol.292 (2), p.683-709
Main Authors: Adam, Lukáš, Branda, Martin, Heitsch, Holger, Henrion, René
Format: Article
Language:English
Subjects:
Benders decomposition
Business and Management
Combinatorics
Decomposition method
Learning models (Stochastic processes)
Operations research
Operations Research/Decision Theory
Regularization
S.I.: Stochastic Optimization:Theory&Applications in Memory of M.Bertocchi
Stochastic models
Theory of Computation
Variables
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Summary:We consider stochastic programs with joint chance constraints with discrete random distribution. We reformulate the problem by adding auxiliary variables. Since the resulting problem has a non-regular feasible set, we regularize it by increasing the feasible set. We solve the regularized problem by iteratively solving a master problem while adding Benders’ cuts from a slave problem. Since the number of variables of the slave problem equals to the number of scenarios, we express its solution in a closed form. We show convergence properties of the solutions. On a gas network design problem, 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 the continuous distribution.
ISSN:0254-5330
1572-9338
DOI:10.1007/s10479-018-3091-9