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Solving joint chance constrained problems using regularization and Benders’ decomposition

Author

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  • Lukáš Adam

    (Southern University of Science and Technology
    The Czech Academy of Sciences, Institute of Information Theory and Automation)

  • Martin Branda

    (The Czech Academy of Sciences, Institute of Information Theory and Automation
    Charles University)

  • Holger Heitsch

    (Weierstrass Institute for Applied Analysis and Stochastics)

  • René Henrion

    (Weierstrass Institute for Applied Analysis and Stochastics)

Abstract

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.

Suggested Citation

  • Lukáš Adam & Martin Branda & Holger Heitsch & René Henrion, 2020. "Solving joint chance constrained problems using regularization and Benders’ decomposition," Annals of Operations Research, Springer, vol. 292(2), pages 683-709, September.
    • Handle: RePEc:spr:annopr:v:292:y:2020:i:2:d:10.1007_s10479-018-3091-9
    DOI: 10.1007/s10479-018-3091-9
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    References listed on IDEAS

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    2. Holger Berthold & Holger Heitsch & René Henrion & Jan Schwientek, 2022. "On the algorithmic solution of optimization problems subject to probabilistic/robust (probust) constraints," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 96(1), pages 1-37, August.

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