Long-term reservoir management often uses bounds on the reservoir level, between which the operator can work. However, these bounds are not always kept up-to-date with the latest knowledge about the reservoir drainage area, and thus become obsolete. The main difficulty with bounds computation is to correctly take into account the high uncertainty about the inflows to the reservoir. In this article, we propose a methodology to derive minimum bounds while providing formal guarantees about the quality of the obtained solutions. The uncertainty is embedded using either stochastic or robust programming in a model-predictive-control framework. We compare the two paradigms to the existing solution for a case study and find that the obtained solutions vary substantially. By combining the stochastic and the robust approaches, we also assign a confidence level to the solutions obtained by stochastic programming. The proposed methodology is found to be both efficient and easy to implement. It relies on sound mathematical principles, ensuring that a global optimum is reached in all cases.
Distributionally Robust Optimisation in Congestion Control
被认为是实时提供的行驶时间信息对司机的行为的影响。Marecek等人的模型[arXiv：1406.7639，Int. J. Control 88（10），2015]被扩展以考虑驾驶员对每条路线提供的间隔的响应的不确定性。具体地，建议可以在与驾驶员的响应相关联的随机变量的所有分布上进行优化，其中前两个时刻是固定的，并且对于每条路线，在每条路线的行驶时间的一定数量的先前实现中的最小值和最大值内的子间隔上进行优化。
Decision Making under the Exponential Family: Distributionally Robust Optimisation with Bayesian Ambiguity Sets
Department of Statistics, University of Warwick, Coventry, UK（威斯敏斯特大学统计学系）；Department of Computer Science, University of Warwick, Coventry, UK（威斯敏斯特大学计算机科学系）；Department of Statistics, University College London, UK（伦敦大学学院统计学系）；The Alan Turing Institute, London, UK（艾伦·图灵研究所）
