Modeling strategies in multi-scale food-energy-water nexus system optimization

The modeling and optimization of multi-scale process systems is based on several interconnected process sub-systems. Due to the complexity of each individual sub-model, the resulting integrated process framework optimization formulations are computationally challenging to solve. While the richness of the multi-scale model employed is desired to maintain in order to obtain a solution with some degree of accuracy, simpler surrogate models are typically more attractive as a means to tame the underlying complexity, albeit often leading to an increase of the problem size. Here, the food-energy-water nexus (FEWN) is selected as a representative multi-scale process system, with focus on the reverse osmosis (RO) water supply sub-system. Based on a RO desalination model, two models are developed and compared in terms of accuracy, model complexity and size as well as computational efficiency, (i) a mixed-integer non-linear programming (MINLP) surrogate model, and (ii) a mixed-integer linear programming (MILP) surrogate model of reduced complexity but larger size. The results indicate that improved computational times can be obtained for a valid (lower bound) solution based on the MILP modeling strategy within the same level of accuracy, further underlying the importance of the selection of an appropriate surrogate model.