Graph modeling and optimization in process systems engineering

Graphs provide a natural language to mathematically represent a set of entities and their relationships and are used extensively across Process Systems Engineering (PSE). In particular, many PSE problems are composed of interconnected substructures, e.g., from molecules and flowsheets to supply chains and optimization models. In these settings, graph representations can expose underlying problem structures such as sparsity, modularity, connectivity, and separability. Moreover, graph algorithms and machine learning can be used to make predictions and support decisions in these applications. In this review, we survey graph modeling and optimization in PSE, including both methods and applications, with particular emphasis on the intersection with modern graph-based machine learning. We conclude by identifying cross-cutting themes and several open challenges and future directions.