A Machine Learning and Distribu- tionally Robust Optimization Framework for strategic energy planning under uncertainty

This paper investigates how the choice of stochastic approaches and distribution assumptions impacts strategic investment decisions in energy planning problems. We formulate a two-stage stochastic programming model assuming different distributions for the input parameters and show that there is significant discrepancy among the associated stochastic solutions and other robust solutions published in the literature. To remedy this sensitivity issue, we propose a combined machine learning and distributionally robust optimization (DRO) approach which produces more robust and stable strategic investment decisions with respect to uncertainty assumptions. DRO is applied to deal with ambiguous probability distributions and Machine Learning is used to restrict the DRO model to a subset of important uncertain parameters ensuring computational tractability. Finally, we perform an out-of-sample simulation process to evaluate solutions performances. The Swiss energy system is used as a case study all along the paper to validate the approach.