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

@article{Carpentier2020MixedSA,
  title={Mixed Spatial and Temporal Decompositions for Large-Scale Multistage Stochastic Optimization Problems},
  author={P. Carpentier and J. Chancelier and M. Lara and F. Pacaud},
  journal={J. Optim. Theory Appl.},
  year={2020},
  volume={186},
  pages={985-1005}
}
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… Expand

Figures and Tables from this paper

Decentralized Multistage Optimization of Large-Scale Microgrids under Stochasticity
Microgrids are recognized as a relevant tool to absorb decentralized renewable energies in the energy mix. However, the sequential handling of multiple stochastic productions and demands, and ofExpand
Decomposition-Coordination Method for Finite Horizon Bandit Problems
Optimally solving a multi-armed bandit problem suffers the curse of dimensionality. Indeed, resorting to dynamic programming leads to an exponential growth of computing time, as the number of armsExpand

References

SHOWING 1-10 OF 32 REFERENCES
Decomposition of large-scale stochastic optimal control problems
TLDR
An Uzawa-based heuristic that is adapted to certain type of stochastic optimal control problems that can be divided into smallscale subsystems linked through a static almost sure coupling constraint at each time step is presented. Expand
Stochastic decomposition applied to large-scale hydro valleys management
TLDR
The algorithm introduced is based on Lagrangian relaxation, of which the application to decomposition is well-known in the deterministic framework, but its application to such closed-loop problems is not straightforward and an additional statistical approximation concerning the dual process is needed. Expand
Bundle Methods in Stochastic Optimal Power Management: A Disaggregated Approach Using Preconditioners
TLDR
A specialized variant of bundle methods suitable for large-scale problems with separable objective, applied to the resolution of a stochastic unit-commitment problem solved by Lagrangian relaxation, is presented. Expand
Progressive hedging innovations for a class of stochastic mixed-integer resource allocation problems
TLDR
The necessity and efficacy of the techniques is empirically assessed on a two-stage stochastic network flow problem with integer variables in both stages and algorithmic innovations in the context of a broad class of scenario-based resource allocation problem. Expand
On the Convergence of Decomposition Methods for Multistage Stochastic Convex Programs
We prove the almost-sure convergence of a class of sampling-based nested decomposition algorithms for multistage stochastic convex programs in which the stage costs are general convex functions ofExpand
Modeling time-dependent randomness in stochastic dual dynamic programming
TLDR
Two approaches to incorporate dependence into Stochastic Dual Dynamic Programming are compared based on a computational study using the long-term operational planning problem of the Brazilian interconnected power systems and it is found that for the considered problem the optimality bounds computed by the MC-SDDP method close faster than its TS-SD DP counterpart, and the MC -SDDP policy dominates the TS- SDDP policy. Expand
Dynamic Programming and Optimal Control
The leading and most up-to-date textbook on the far-ranging algorithmic methododogy of Dynamic Programming, which can be used for optimal control, Markovian decision problems, planning and sequentialExpand
Algorithmic innovations and software for the dual decomposition method applied to stochastic mixed-integer programs
TLDR
It is proven that the algorithm converges to an optimal solution of the Lagrangian dual problem in a finite number of iterations, and it is proved that convergence can be achieved even if the master problem is solved suboptimally. Expand
Scenarios and Policy Aggregation in Optimization Under Uncertainty
TLDR
This paper develops for the first time a rigorous algorithmic procedure for determining a robust decision policy in response to any weighting of the scenarios. Expand
Auxiliary problem principle and decomposition of optimization problems
The auxiliary problem principle allows one to find the solution of a problem (minimization problem, saddle-point problem, etc.) by solving a sequence of auxiliary problems. There is a wide range ofExpand
...
1
2
3
4
...