Multi-Objective Evolutionary Algorithms for Scheduling in Intensive Care Unit Bed Allocation

Intensive care unit (ICU) bed allocation is a high-stakes scheduling problem involving conflicting objectives and constraints. We evaluate multi-objective evolutionary algorithms (MOEAs) using a new benchmark derived from real Brazilian healthcare data, managing up to 1,171 decision variables. Specifically, we analyze here the performance of Non-dominated Sorting Genetic Algorithm II (NSGA-II) and Generalized Differential Evolution 3 (GDE3). Comparative analysis reveals that NSGA-II significantly outperforms GDE3, achieving feasibility 60% faster (generation 18 vs. 45) and maintaining a higher hypervolume (0.85 vs. 0.42). We also identify a consistent empirical lower bound of 6,936 bed-hours, emerging from the interaction between finite planning horizons and heavy-tailed length-of-stay distributions. Our contributions include: (1) a large-scale, real-world benchmark for constrained MOEAs, (2) a performance comparison under varying capacities, and (3) methodological insights for evolutionary scheduling in healthcare systems. This research provides a scalable framework for optimizing critical resource distribution in high-pressure clinical environments.