Solving joint chance constrained problems using regularization and Benders’ decomposition

Adam，Lukáš1,2; Branda，Martin2,3; Heitsch，Holger4; Henrion，René4

2020-09-01

10.1007/s10479-018-3091-9

ANNALS OF OPERATIONS RESEARCH   影响因子和分区

0254-5330

1572-9338

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.

Benders’ decomposition Chance constrained programming Gas networks Optimality conditions Regularization Stochastic programming

SCI

英语

第一 ; 通讯

Operations Research & Management Science

Operations Research & Management Science

WOS:000563054500006

SPRINGER

ENGINEERING

2-s2.0-85056150669

Scopus

1.Department of Computer Science and Engineering,Southern University of Science and Technology,Shenzhen,1088 Xueyuan Ave,518055,China
2.The Czech Academy of Sciences,Institute of Information Theory and Automation,Prague 8,Pod Vodárenskou vězí 4,182 08,Czech Republic
3.Department of Probability and Mathematical Statistics,Faculty of Mathematics and Physics,Charles University,Prague,Sokolovská 83,186 75,Czech Republic
4.Weierstrass Institute for Applied Analysis and Stochastics,Berlin,Mohrenstraße 39,10117,Germany

Adam，Lukáš,Branda，Martin,Heitsch，Holger,等. Solving joint chance constrained problems using regularization and Benders’ decomposition[J]. ANNALS OF OPERATIONS RESEARCH,2020,292(2):683-709.

Adam，Lukáš,Branda，Martin,Heitsch，Holger,&Henrion，René.(2020).Solving joint chance constrained problems using regularization and Benders’ decomposition.ANNALS OF OPERATIONS RESEARCH,292(2),683-709.

Adam，Lukáš,et al."Solving joint chance constrained problems using regularization and Benders’ decomposition".ANNALS OF OPERATIONS RESEARCH 292.2(2020):683-709.