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Penalty-Free SDDP: Feasibility Cuts for Robust Multi-Stage Stochastic Optimization in Energy Planning

Guilherme Freitas, Luiz Carlos da Costa Junior, Tiago Andrade, Alexandre Street

TL;DR

This paper introduces Penalty-Free SDDP, a general extension of stochastic dual dynamic programming that eliminates artificial penalties for infeasibilities by incorporating a Future Feasibility Function and a dual-stage recursion. Feasibility information is handled via a union of feasibility cuts, separating constraint satisfaction from economic optimization while preserving SDDP's decomposition and convergence properties. The approach is validated on a large-scale hydrothermal energy planning problem, demonstrating equivalent feasibility to a benchmark problem and improved interpretability by clearly identifying infeasible conditions without penalty calibration. The results suggest robust applicability to complex multi-stage energy planning and provide a foundation for extending to fully stochastic settings.

Abstract

Multi-stage decision problems under uncertainty can be efficiently solved with the Stochastic Dual Dynamic Programming (SDDP) algorithm. However, traditional implementations require all stage problems to be feasible. Feasibility is usually enforced by adding slack variables and penalizing them in the objective function, a process that depends on case-specific calibration and often distorts the economic interpretation of results. This paper proposes the Penalty-Free SDDP, an extension that introduces a Future Feasibility Function alongside the traditional Future Cost Function. The new recursion handles infeasibilities automatically, distinguishing between temporary and truly infeasible cases, and propagates feasibility information across stages through dedicated feasibility cuts. The approach was validated in a large-scale deterministic case inspired by the Brazilian hydrothermal system, achieving equivalent feasibility to the benchmark solution while eliminating miscalibrated artificial penalties. Results confirm its robustness and practicality as a foundation for future stochastic, multi-stage applications.

Penalty-Free SDDP: Feasibility Cuts for Robust Multi-Stage Stochastic Optimization in Energy Planning

TL;DR

This paper introduces Penalty-Free SDDP, a general extension of stochastic dual dynamic programming that eliminates artificial penalties for infeasibilities by incorporating a Future Feasibility Function and a dual-stage recursion. Feasibility information is handled via a union of feasibility cuts, separating constraint satisfaction from economic optimization while preserving SDDP's decomposition and convergence properties. The approach is validated on a large-scale hydrothermal energy planning problem, demonstrating equivalent feasibility to a benchmark problem and improved interpretability by clearly identifying infeasible conditions without penalty calibration. The results suggest robust applicability to complex multi-stage energy planning and provide a foundation for extending to fully stochastic settings.

Abstract

Multi-stage decision problems under uncertainty can be efficiently solved with the Stochastic Dual Dynamic Programming (SDDP) algorithm. However, traditional implementations require all stage problems to be feasible. Feasibility is usually enforced by adding slack variables and penalizing them in the objective function, a process that depends on case-specific calibration and often distorts the economic interpretation of results. This paper proposes the Penalty-Free SDDP, an extension that introduces a Future Feasibility Function alongside the traditional Future Cost Function. The new recursion handles infeasibilities automatically, distinguishing between temporary and truly infeasible cases, and propagates feasibility information across stages through dedicated feasibility cuts. The approach was validated in a large-scale deterministic case inspired by the Brazilian hydrothermal system, achieving equivalent feasibility to the benchmark solution while eliminating miscalibrated artificial penalties. Results confirm its robustness and practicality as a foundation for future stochastic, multi-stage applications.

Paper Structure

This paper contains 12 sections, 3 equations, 1 figure, 1 table, 1 algorithm.

Table of Contents

  1. Introduction
  2. Background and Related Work
  3. Penalty-Free SDDP Framework
  4. Classical SDDP with penalized slacks
  5. Penalty-Free SDDP formulation
  6. Algorithmic implementation
  7. Forward pass
  8. Backward pass
  9. Convergence criteria
  10. Algorithm summary
  11. Case Study: Application to Energy Planning
  12. Conclusions and Future Work

Figures (1)

  • Figure 1: Total minimum outflow violations.