Title
Nonlinear chance-constrained problems with applications to hydro scheduling
Abstract
We present a Branch-and-Cut algorithm for a class of nonlinear chance-constrained mathematical optimization problems with a finite number of scenarios. Unsatisfied scenarios can enter a recovery mode. This class corresponds to problems that can be reformulated as deterministic convex mixed-integer nonlinear programming problems with indicator variables and continuous scenario variables, but the size of the reformulation is large and quickly becomes impractical as the number of scenarios grows. The Branch-and-Cut algorithm is based on an implicit Benders decomposition scheme, where we generate cutting planes as outer approximation cuts from the projection of the feasible region on suitable subspaces. The size of the master problem in our scheme is much smaller than the deterministic reformulation of the chance-constrained problem. We apply the Branch-and-Cut algorithm to the mid-term hydro scheduling problem, for which we propose a chance-constrained formulation. A computational study using data from ten hydroplants in Greece shows that the proposed methodology solves instances faster than applying a general-purpose solver for convex mixed-integer nonlinear programming problems to the deterministic reformulation, and scales much better with the number of scenarios.
Year
DOI
Venue
2022
10.1007/s10107-019-01447-3
MATHEMATICAL PROGRAMMING
Keywords
DocType
Volume
Chance-constraints, Outer approximation, Benders decomposition, Branch-and-Cut, Hydro scheduling
Journal
191
Issue
ISSN
Citations 
1
0025-5610
0
PageRank 
References 
Authors
0.34
0
4
Name
Order
Citations
PageRank
Andrea Lodi12198152.51
Enrico Malaguti231221.69
Giacomo Nannicini326331.72
Dimitri Thomopulos400.34