Many decision-making problems require considering the uncertainty of
different parameters to implement robust operational and strategical solutions.
Optimization under uncertainty provides different ways to face this kind of
problem. In this background, we propose the nodal sampling algorithm in the
Stochastic Dynamic Dual Programming (SDDP) framework based on sampling the
elements that belong to Voronoi's region of every node of the scenario tree.
Additionally, we suggest two new stopping criteria: extending the classical
criteria to other scenario tree nodes, and verifying a minimum number of
Benders cuts in every node. We used a stylized version of the Spanish
hydrothermal system as the case study. The experiment showed that our proposals
could build policies that result in more robust reservoir management under
uncertainty than the traditional SDDP, preserving the algorithm's performance.
The nodal sampling method allows us to minimize the effect of discretizing the
stochastic variables into scenario trees, since it evaluates more scenarios
inside every node of the scenario tree.
This work is part of the research work that is being carried out on
multi-horizon models for medium-term hydrothermal programming by Jesús David
Gómez Pérez.