Solving the robustness puzzle: The joint impact of optimization approach, robustness metrics, and scenarios on water resources management under deep uncertainty

The concept of robustness has been widely used in water resources management to identify solutions that perform satisfactorily across a range of plausible future conditions to increase confidence in decision-making in a deeply uncertain future. However, the selection of an appropriate metric to quantify robustness remains challenging due to the existence of multiple choices reflecting different risk preferences. In addition, different scenarios can be used to represent plausible future conditions, which adds another layer of complexity to solution identification. While previous studies have explored the impact of different robustness metrics and scenarios on the robustness of the solutions obtained, these two aspects have usually been investigated in isolation. In addition, the majority of past studies utilize post-optimization robustness analysis, where solutions are optimized under each future scenario before the robustness of these solutions is quantified across all scenarios. In contrast, how these impacts may vary when the robustness of potential solutions is explicitly optimized, is unknown. Therefore, in this study, the joint impact of the choice of robustness metric, scenarios, and optimization approach on system robustness and performance is investigated. Results from two real-world case studies show that the optimization approach can have a significant impact on system robustness and performance when scenarios represent a wide range of plausible future conditions, but this impact also depends on which robustness metrics are used. The results of this study provide insight into identifying robust solutions using different robustness metrics through different optimization approaches, leading to the fit-for-purpose selection of both robustness metric and optimization approach.