Summary:
In decision-making under uncertainty, a robust representation of uncertainty is vital for optimal operational and strategic solutions. We extend existing methods by utilizing Fourier decomposition to create multivariate synthetic time series, capturing stochastic seasonal patterns while preserving correlations. These synthetic time series are transformed into a recombining scenario tree via K-means clustering. To enhance the resulting policy in the Stochastic Dual Dynamic Programming (SDDP) framework, we propose an additional sampling within scenario-tree nodes to consider a better representation of the cost-to-go function. A convergence proof for this sampling technique is provided. Moreover, two new stopping criteria are introduced for better solution accuracy and robustness. The first criterion extends traditional stopping rules to all scenario-tree nodes. The second criterion enforces a minimum count of Benders cuts per node, promoting accurate and robust solutions. Our approach is evaluated on the Spanish hydrothermal system, incorporating synthetic time series with seasonal-trend uncertainty in optimization and simulation. Policies from traditional SDDP and our technique were tested over a thousand realizations, demonstrating that our proposals yield reservoir operation policies closer to the thresholds set by the operator compared to traditional SDDP. Computational efficiency is maintained. The proposed sampling mitigates the impact of discretizing stochastic variables into scenario trees by evaluating more scenarios per node. Our framework offers robust policies under uncertainty through stochastic seasonal patterns by Fourier analysis, novel SDDP sampling, and additional stopping criteria.
Spanish layman's summary:
Este trabajo usa descomposición de Fourier para crear series temporales sintéticas multivariadas, capturando patrones estacionales estocásticos y preservando correlaciones. Referente al SDDP, mejoramos la política proponiendo muestreos adicionales dentro de los nodos del árbol de escenarios e introduciendo dos nuevos criterios de parada
English layman's summary:
This work employs Fourier decomposition to create multivariate synthetic time series, capturing stochastic seasonal patterns and preserving correlations. In the SDDP framework, we improve the policy by proposing additional sampling within scenario-tree nodes and introducing two new stopping criteria
Keywords: Time series; Fourier analysis; Optimization methods; Stochastic programming; SDDP; Sampling methods
JCR Impact Factor and WoS quartile: 11,200 - Q1 (2022)
DOI reference:
https://doi.org/10.1016/j.apenergy.2024.122688
Published on paper: April 2024.
Published on-line: January 2024.
Citation:
J.D. Gómez, J.M. Latorre, A. Ramos, A. Perea, P. Sanz González, F. Hernández, Improving operating policies in stochastic optimization: an application to the medium-term hydrothermal scheduling problem. Applied Energy. Vol. 359, pp. 122688-1 - 122688-18, April 2024. [Online: January 2024]
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