Hybrid Metaheuristics for Equity-Oriented P-Center Facility Location in Health Surveillance Networks: Evidence from Andalusia

Abstract

The COVID-19 pandemic exposed critical fragilities in health systems, particularly regarding the equitable distribution of resources and the logistical capacity of early warning systems. This study addresses the optimization of the Sentinel Surveillance Network in Andalusia, Spain, proposing a shift from traditional efficiency-based models to an equity-oriented approach. The facility location problem is formulated using a Capacitated Vertex-Restricted P-center model, which aims to minimize the maximum access time for the most remote population, thereby preventing the creation of “healthcare deserts” common in P-median approaches that minimize average distance or total travel cost. To solve this NP-hard combinatorial problem, a hybrid metaheuristic, named the ACME-GA (Acceleration by Clustering and Memetic Exploitation) refined with Simulated Annealing, is introduced. Using real-Andalusia demographic data and road travel times across 406 municipalities and 133 candidate hospitals, the proposed method is compared against standard evolutionary schemes. The results demonstrate that ACME-GA consistently yields superior solution quality and stability. Furthermore, the analysis confirms that the P-center approach significantly enhances territorial equity compared to density-focused models, ensuring that even sparsely populated rural areas maintain robust access to epidemiological surveillance. This work provides a resilient methodological framework for public health planning in post-pandemic scenarios.