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.

中文翻译：

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大规模多阶段随机优化问题的混合空间和时间分解

我们考虑涉及多个单元的多阶段随机优化问题。每个单元都是一个（小型）控制系统。静态约束在每个阶段耦合单元。我们提出了空间和时间分解的组合来解决如此大规模的问题。更准确地说，我们通过两种方法获得理论界限和政策，这取决于耦合约束是通过价格还是资源来处理。我们研究集中式和分散式信息结构。我们报告了城市微电网管理的数值实验结果。与标准随机对偶动态规划方法相比，分解方法在边界和策略性能方面似乎要快得多并给出更好的结果。