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

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.