Programação dinâmica dual inteira estocástica: análise conceitual, avanço metodológico e aplicação ao problema de planejamento energético

Abstract

Medium-term hydrothermal operation planning requires decision-making under uncertainty while accounting for operational, electrical, environmental, and regulatory constraints. In realworld applications, many of these constraints are conditional in nature, requiring the introduction of integer variables into optimization models. However, the presence of integer variables significantly increases the complexity of multistage stochastic optimization problems and poses major challenges to the application of classical decomposition methods. This thesis investigates the impacts of representing conditional constraints in hydrothermal planning problems and proposes new strategies for their efficient solution. First, a theoretical analysis of the dual structure of the subproblems arising in the Stochastic Dual Dynamic Integer Programming (SDDiP) framework is conducted, identifying properties that are relevant to the construction of cost-to-go function approximations. Based on these findings, a new family of Lagrangian cuts, termed Tighter Lagrangian Cuts, is proposed, together with a hybrid decomposition strategy that combines features of both Benders cuts and Lagrangian cuts. The proposed methodologies are evaluated through case studies representative of the Brazilian power system operation planning problem. The results show that Tighter Lagrangian Cuts provide more accurate approximations of the cost-to-go function and accelerate the convergence of the iterative solution process. Furthermore, the hybrid strategy proved capable of combining computational scalability with an enhanced ability to represent the nonconvexities associated with integer variables. Overall, the proposed techniques expand the applicability of decomposition methods to multistage stochastic problems with conditional constraints and contribute to advancing the state of the art in the field.