Feasibility and optimality cuts for the MultiStage benders decomposition approach: Application to the network constrained hydrothermal scheduling

Abstract

We consider the short term hydrothermal scheduling problem, modeled as a deterministic large-scale linear programming problem on a cost minimization basis. The problem is decomposed in time into several subproblems and solved by multi-stage Benders decomposition (MSBD). In this paper, we study two strategies to handle infeasible subproblems that may occur during the MSBD iterative process, even if the original problem is feasible. The first strategy consists in adding slack variables in all constraints, with large penalties in the objective function, and applying the conventional optimality cuts during the whole process. The second approach is to build the so-called “feasibility cuts” to be included in the subproblem of the previous stage whenever the subproblem of a certain stage becomes infeasible. Both strategies were applied to solve three kind of multi-stage problems: feasible problems, infeasible problems, and feasible problems that may present infeasible subproblems during its solving procedure. We make a comparative assessment of the performance and the final solution obtained by the two strategies, for a study case comprising the entire Brazilian power system.