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SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning

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  • Vincent Guigues

Abstract

We consider interstage dependent stochastic linear programs where both the random right-hand side and the model of the underlying stochastic process have a special structure. Namely, for equality constraints (resp. inequality constraints) the right-hand side is an affine function (resp. a given function b t ) of the process value for the current time step t. As for m-th component of the process at time step t, it depends on previous values of the process through a function h tm . For this type of problem, to obtain an approximate policy under some assumptions for functions b t and h tm , we detail a stochastic dual dynamic programming algorithm. Our analysis includes some enhancements of this algorithm such as the definition of a state vector of minimal size, the computation of feasibility cuts without the assumption of relatively complete recourse, as well as efficient formulas for sharing optimality and feasibility cuts between nodes of the same stage. The algorithm is given for both a non-risk-averse and a risk-averse model. We finally provide preliminary results comparing the performances of the recourse functions corresponding to these two models for a real-life application. Copyright Springer Science+Business Media New York 2014

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  • Vincent Guigues, 2014. "SDDP for some interstage dependent risk-averse problems and application to hydro-thermal planning," Computational Optimization and Applications, Springer, vol. 57(1), pages 167-203, January.
    • Handle: RePEc:spr:coopap:v:57:y:2014:i:1:p:167-203
    DOI: 10.1007/s10589-013-9584-1
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    References listed on IDEAS

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    1. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Conditional Risk Mappings," Risk and Insurance 0404002, University Library of Munich, Germany, revised 08 Oct 2005.
    2. Andrzej Ruszczynski & Alexander Shapiro, 2004. "Optimization of Convex Risk Functions," Risk and Insurance 0404001, University Library of Munich, Germany, revised 08 Oct 2005.
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    9. Guigues, Vincent & Sagastizábal, Claudia, 2012. "The value of rolling-horizon policies for risk-averse hydro-thermal planning," European Journal of Operational Research, Elsevier, vol. 217(1), pages 129-140.
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    2. Escudero, Laureano F. & Garín, María Araceli & Merino, María & Pérez, Gloria, 2016. "On time stochastic dominance induced by mixed integer-linear recourse in multistage stochastic programs," European Journal of Operational Research, Elsevier, vol. 249(1), pages 164-176.
    3. Michelle Bandarra & Vincent Guigues, 2021. "Single cut and multicut stochastic dual dynamic programming with cut selection for multistage stochastic linear programs: convergence proof and numerical experiments," Computational Management Science, Springer, vol. 18(2), pages 125-148, June.
    4. W. Ackooij & X. Warin, 2020. "On conditional cuts for stochastic dual dynamic programming," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 8(2), pages 173-199, June.
    5. Aldasoro, Unai & Escudero, Laureano F. & Merino, María & Pérez, Gloria, 2017. "A parallel Branch-and-Fix Coordination based matheuristic algorithm for solving large sized multistage stochastic mixed 0–1 problems," European Journal of Operational Research, Elsevier, vol. 258(2), pages 590-606.
    6. Zhou, Shaorui & Zhang, Hui & Shi, Ning & Xu, Zhou & Wang, Fan, 2020. "A new convergent hybrid learning algorithm for two-stage stochastic programs," European Journal of Operational Research, Elsevier, vol. 283(1), pages 33-46.
    7. Lee, Jinkyu & Bae, Sanghyeon & Kim, Woo Chang & Lee, Yongjae, 2023. "Value function gradient learning for large-scale multistage stochastic programming problems," European Journal of Operational Research, Elsevier, vol. 308(1), pages 321-335.
    8. Guigues, Vincent, 2017. "Dual Dynamic Programing with cut selection: Convergence proof and numerical experiments," European Journal of Operational Research, Elsevier, vol. 258(1), pages 47-57.
    9. Pritchard, Geoffrey, 2015. "Stochastic inflow modeling for hydropower scheduling problems," European Journal of Operational Research, Elsevier, vol. 246(2), pages 496-504.
    10. Vitor L. de Matos & David P. Morton & Erlon C. Finardi, 2017. "Assessing policy quality in a multistage stochastic program for long-term hydrothermal scheduling," Annals of Operations Research, Springer, vol. 253(2), pages 713-731, June.
    11. Guigues, Vincent & Shapiro, Alexander & Cheng, Yi, 2023. "Duality and sensitivity analysis of multistage linear stochastic programs," European Journal of Operational Research, Elsevier, vol. 308(2), pages 752-767.
    12. Lorenzo Reus & Guillermo Alexander Sepúlveda-Hurtado, 2023. "Foreign exchange trading and management with the stochastic dual dynamic programming method," Financial Innovation, Springer;Southwestern University of Finance and Economics, vol. 9(1), pages 1-38, December.
    13. Lorenzo Reus & Rodolfo Prado, 2022. "Need to Meet Investment Goals? Track Synthetic Indexes with the SDDP Method," Computational Economics, Springer;Society for Computational Economics, vol. 60(1), pages 47-69, June.
    14. Guigues, Vincent & Juditsky, Anatoli & Nemirovski, Arkadi, 2021. "Constant Depth Decision Rules for multistage optimization under uncertainty," European Journal of Operational Research, Elsevier, vol. 295(1), pages 223-232.
    15. Weini Zhang & Hamed Rahimian & Güzin Bayraksan, 2016. "Decomposition Algorithms for Risk-Averse Multistage Stochastic Programs with Application to Water Allocation under Uncertainty," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 385-404, August.

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