Graph-Theoretic Measures for Interpretable Multicriteria Decision Making in Emergency Department Layout Optimization

Overcrowding in emergency departments (ED) is a persistent problem exacerbated by population growth, emergence of pandemics, and increased morbidity and mortality rates. Thus, automated approaches for ED layout design have recently emerged as promising tools for boosting healthcare service quality. Still, ED design typically involves multiple conflicting objectives, where the interpretability of the associated solutions depends on the availability of intuitive metrics that can capture ED layout complexity. In this paper, we propose graph-theoretic measures to evaluate and rank ED layouts produced by a multi-objective metaheuristic optimization framework with the non-dominated sorting genetic algorithm (NSGA-II) and generalized differential evolution (GDE3). Indeed, Pareto-optimal ED layouts were sought to minimize patient flow cost while maximizing closeness between ED service areas. Then, the layouts were evaluated based on local graph measures (degree centrality, betweenness, clustering coefficient, closeness centrality, nodal strength, and eccentricity) as well as global ones (global efficiency, network characteristic path length and transitivity). Then, a multi-criteria decision-making technique was employed to rank the layouts based on either the objective functions, the graph measures, or combinations of both. The ranking results on a real-world scenario show that the top-ranking layouts are the ones with the best graph-theoretic values. This shows that the graph-theoretic measures can enhance solution interpretability and hence help medical planners in selecting the best layouts. In comparison with the input layout, optimal NSGA-II and GDE3 solutions reduce the patient flow cost by 18.32% and 11.42%, respectively. Also, the two solutions improve the closeness by 14.5% and 18.02%, respectively.