A multi-parametric approach for bi-level optimization within the energy–water nexus

The energy–water nexus (EWN) holistically integrates energy and water supply systems to meet their respective demands in an efficient and sustainable manner. Modeling and optimization strategies are of paramount importance in determining the optimal design and operation of these interconnected systems. Decision-making facilitated through these strategies in the EWN are conditional on the assumption that all sub-systems and their respective authorities work together with perfect coordination for the benefit of the overall system. However, the independent decision-making processes of these interdependent systems naturally introduces hierarchies through their joint functionality under the EWN. To enable decision-making at multiple levels of hierarchy, this work proposes a bi-level optimization framework based on multi-parametric programming to determine the optimal design and operation of a nexus with two levels of decision-makers. Two scenarios are investigated as part of a case study to illustrate the nuances of multi-level decision-making. The role of decision sequences in determining system outcomes is emphasized through this study as it varies significantly based on the order and prioritization of decision-makers. It further highlights the scope of bi-level optimization in contrast with single-level optimization for centralized and decentralized system configurations. Through this analysis, the proposed framework emphasizes the importance of hierarchical decision-making for deriving practical and effective solutions for the design and operation of interconnected energy and water supply systems in the EWN.