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

TL;DR

This paper introduces Penalty-Free SDDP, a novel method for multi-stage stochastic optimization that automatically manages infeasibilities without artificial penalties, improving robustness and interpretability in energy planning models.

Contribution

It proposes a new recursion with a Future Feasibility Function and feasibility cuts, removing the need for case-specific penalty calibration in SDDP.

Findings

Achieves equivalent feasibility to benchmark solutions

Eliminates miscalibrated artificial penalties

Demonstrates robustness in large-scale energy system case

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.