Nonlinear chance-constrained problems with applications to hydro scheduling

Nonlinear Chance Constrained Problems: Optimality Conditions, Regularization and Solvers

We deal with chance constrained problems (CCP) with differentiable nonlinear random functions and discrete distribution. We allow nonconvex functions both in the constraints and in the objective. We reformulate the problem as a mixed-integer nonlinear program, and relax the integer variables into continuous ones. We approach the relaxed problem as a mathematical problem with complementarity con...

Solving chance-constrained combinatorial problems to optimality

The aim of this paper is to provide new efficient methods for solving general chance-constrained integer linear programs to optimality. Valid linear inequalities are given for these problems. They are proved to characterize properly the set of solutions. They are based on a specific scenario, whose definition impacts strongly on the quality of the linear relaxation built. A branch-and-cut algor...

Chance-Constrained Binary Packing Problems

We consider a class of packing problems with uncertain data, which we refer to as the chance-constrained binary packing problem. In this problem, a subset of items is selected that maximizes the total profit so that a generic packing constraint is satisfied with high probability. Interesting special cases of our problem include chance-constrained knapsack and set packing problems with random co...

Joint Chance Constrained Programming for Hydro Reservoir Management

In this paper, we deal with a hydraulic reservoir optimization problem with uncertainty on inflows in a joint chance constrained programming setting. In particular, we will consider inflows with a persistency effect, following a causal time series model, and examine the impact of the ”Gaussian” assumption for such inflows. We present an iterative algorithm for solving similarly structured joint...

Decomposition approaches for block-structured chance-constrained programs with application to hydro-thermal unit commitment