(530e) Food-Energy-Water Nexus: A Multi-Level Optimization Approach

The food-energy-water nexus strives to address concerns faced by the supply of food, energy, and water amid rising population growth and industrialization. The interdependence and interconnectedness of its constituent resource supply systems intrinsically adds a layer of complexity to the nexus system [1]. In response to navigating this challenge, the nexus leverages holistic approaches that consider all three resources and their systems simultaneously when establishing decisions pertaining to their design and operation. Conventionally, these decisions are made by a single decision-maker with complete access to information related to each of the components that form the nexus. However, in a more realistic milieu, decisions are often made by various decision-makers in a decentralized fashion at several levels of hierarchy [2]. In other words, a more accurate representation of the nexus would incorporate three levels of decision-making, one for each of the resource supply systems of the food-energy-water nexus, as opposed to the sole presence of a central nexus authority.

From a process systems perspective, tri-level programming can be employed to facilitate decision-making across three levels of hierarchy within the food-energy-water nexus. The formulation for tri-level programming consists of three optimization problems, referred to as the first-, second-, and third-level problems, nested within one another [3]. At its essence, each of these problems corresponds to a distinct level of decision-making. As such, the food, energy, and water supply systems within the nexus are respectively modeled at the three levels under consideration. The sequence or designation of these supply systems reflects the order of priority their decision or they themselves hold in the overall system. Multiple configurations can be analyzed in this manner to determine the hierarchical decision sequences for achieving sustainable objectives in these nexus systems. While valuable insights of this nature can be derived from tri-level optimization frameworks, their computational and mathematical complexities must be addressed. Towards this effort, the tri-level framework presented in this work combines relaxation techniques to tackle modeling complexities [4] and multi-parametric programming to handle the tri-level nature of the problem [5]. Accordingly, variables of the upper-level problems are set as parameters in the lower-level problems and solved using multi-parametric algorithms. The solution to these problems yields explicit functions of the lower-level variables in terms of upper-level parameters. The upper-level problems are subsequently modified by incorporating these obtained functions and then solved to derive the optimal solutions for the overall nexus system.

References
[1] C´esar Ram´ırez-M´arquez and Jos´e M Ponce-Ortega. Process systems engineering tools for the water–energy–food nexus: Challenges and opportunities. Current Opinion in Chemical Engineering, 42:100980, 2023.
[2] Elizabeth J Abraham, Marcello Di Martino, Dustin Kenefake, Dhabia M Al-Mohannadi, and Efstratios N Pistikopoulos. A multi-parametric optimization approach for bi-level decision-making strategies in energy-water nexus supply systems. In Computer Aided Chemical Engineering, volume 53, pages 2395–2400. Elsevier, 2024.
[3] Athanasios Migdalas, Panos M Pardalos, and Peter V¨arbrand. Multilevel optimization: algorithms and applications, volume 20. Springer Science & Business Media, 2013.
[4] Marcello Di Martino, Patrick Linke, and Efstratios N Pistikopoulos. Overcoming modeling and computational complexity challenges in food-energy-water nexus optimization. Computers & Chemical Engineering, page 108902, 2024.
[5] Styliani Avraamidou and Efstratios Pistikopoulos. Multi-level Mixed-Integer Optimization: Parametric Programming Approach. Walter de Gruyter GmbH & Co KG, 2022.