WIAS Preprint No. 2471, (2018)

Solving joint chance constrained problems using regularization and Benders' decomposition


Authors

  • Adam, Lukáš
    ORCID: 0000-0001-8748-4308
  • Branda, Martin
  • Heitsch, Holger
    ORCID: 0000-0002-2692-4602
  • Henrion, René
    ORCID: 0000-0001-5572-7213

2010 Mathematics Subject Classification

  • 90B15 90C15 90C26 49M05

Keywords

  • Chance constrained programming, optimality conditions, regularization, Benders cuts, gas networks

DOI

10.20347/WIAS.PREPRINT.2471

Abstract

In this paper we investigate stochastic programms 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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