Solving joint chance constrained problems using regularization and Benders’ decomposition

0501589 - ÚTIA 2021 RIV US eng J - Journal Article
Adam, Lukáš - Branda, Martin - Heitsch, H. - Henrion, R.
Solving joint chance constrained problems using regularization and Benders’ decomposition.
Annals of Operations Research. Roč. 292, č. 2 (2020), s. 683-709. ISSN 0254-5330. E-ISSN 1572-9338
R&D Projects: GA ČR(CZ) GA18-04145S
Grant - others:GA ČR(CZ) GA18-05631S
Institutional support: RVO:67985556
Keywords : Stochastic programming * Chance constrained programming * Optimality conditions * Regularization * Benders' decomposition * Gas networks
OECD category: Pure mathematics
Impact factor: 4.854, year: 2020
Method of publishing: Limited access
http://library.utia.cas.cz/separaty/2019/MTR/adam-0501589.pdf https://link.springer.com/article/10.1007/s10479-018-3091-9

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.
Permanent Link: http://hdl.handle.net/11104/0294165