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Mixed Spatial and Temporal Decompositions for Large-Scale Multistage Stochastic Optimization Problems

Author

Listed:
  • Pierre Carpentier

    (UMA, ENSTA Paris, IP Paris)

  • Jean-Philippe Chancelier

    (CERMICS, Ecole des Ponts)

  • Michel Lara

    (CERMICS, Ecole des Ponts)

  • François Pacaud

    (CERMICS, Ecole des Ponts)

Abstract

We consider multistage stochastic optimization problems involving multiple units. Each unit is a (small) control system. Static constraints couple units at each stage. We present a mix of spatial and temporal decompositions to tackle such large scale problems. More precisely, we obtain theoretical bounds and policies by means of two methods, depending on whether the coupling constraints are handled by prices or by resources. We study both centralized and decentralized information structures. We report the results of numerical experiments on the management of urban microgrids. It appears that decomposition methods are much faster and give better results than the standard stochastic dual dynamic programming method, both in terms of bounds and of policy performance.

Suggested Citation

  • Pierre Carpentier & Jean-Philippe Chancelier & Michel Lara & François Pacaud, 2020. "Mixed Spatial and Temporal Decompositions for Large-Scale Multistage Stochastic Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 186(3), pages 985-1005, September.
    • Handle: RePEc:spr:joptap:v:186:y:2020:i:3:d:10.1007_s10957-020-01733-7
    DOI: 10.1007/s10957-020-01733-7
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    References listed on IDEAS

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    1. Jean-Paul Watson & David Woodruff, 2011. "Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems," Computational Management Science, Springer, vol. 8(4), pages 355-370, November.
    2. R. T. Rockafellar & Roger J.-B. Wets, 1991. "Scenarios and Policy Aggregation in Optimization Under Uncertainty," Mathematics of Operations Research, INFORMS, vol. 16(1), pages 119-147, February.
    3. Carpentier, P. & Chancelier, J.-Ph. & Leclère, V. & Pacaud, F., 2018. "Stochastic decomposition applied to large-scale hydro valleys management," European Journal of Operational Research, Elsevier, vol. 270(3), pages 1086-1098.
    4. Löhndorf, Nils & Shapiro, Alexander, 2019. "Modeling time-dependent randomness in stochastic dual dynamic programming," European Journal of Operational Research, Elsevier, vol. 273(2), pages 650-661.
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