Two-layer evolutionary optimization problem for home healthcare pathways and scheduling under multi-center resource sharing.

To address inter-center workload imbalance and low resource utilization in multi-center home healthcare systems, this study proposes a bilevel optimization approach for routing and scheduling that enables cross-center resource sharing. First, we formulate a weighted single-objective model that jointly accounts for travel time, service costs, penalties for time-window violations, and workload-imbalance penalties, thereby providing a unified representation of multi-criteria trade-offs while incorporating skill-matching and labor-compliance constraints. Second, we develop a bilevel evolutionary framework, termed the Bilevel Evolutionary Planning Framework for Multi-Center Routing and Scheduling with Resource Sharing (BEPSF). At the upper level, a genetic algorithm (GA) determines client-to-center assignments and performs global workload regulation. At the lower level, a hybrid GAPSO strategy is employed to solve the within-center routing and scheduling of multi-skilled staff, integrating a time-window-driven feasibility repair mechanism with an elitist preservation strategy to enhance solution accuracy and robustness. Computational experiments on 18 standardized benchmark instances demonstrate that BEPSF significantly outperforms the GA-GA and DE-DE baselines in both solution quality and stability, achieving average improvements of approximately 31% and 63%, respectively, and attaining 0% deviation from the reference optimum on small-scale instances. Sensitivity and scenario analyses further reveal that maximum working hours, time-window tolerance, and break intervals substantially affect the cost composition. After enabling cross-center resource sharing, the total system cost is generally reduced by 20-50%, with a maximum reduction of 66%.