Flexible decision variables in multi-objective reservoir operation

This study explores optimal control in the case when certain input uncertainties cannot be well quantified. In these scenarios, the decision-maker prefers to have the most flexibility, which is defined to be the largest range of options for decision variables, and still achieve the objectives of the operation while satisfying all constraints. Each decision variable is generalized to be a range of potential actions. These ranges are modelled with random variables, thus uncertainty quantification techniques are employed to compute expected values of objectives and probabilities of chance constraints. The proposed framework determines optimal probability densities for the decision variables by treating the amount of flexibility as an additional objective. There is a clear trade-off between the amount of flexibility that can be allowed and the resulting expected values of the other objectives. A dimension reduction technique is employed to ensure a reasonable dimension for the search space.