Seminario: Improving operating policies in stochastic optimization. An application to the medium-term hydrothermal scheduling problem [Jesús David Gómez] 03-02-23
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.