Hybrid AI models for multi-depot vehicle routing with split deliveries and multiple trips

Last-mile logistics operations in urban environments are becoming increasingly complex due to fragmented customer demands, multiple depots, vehicle capacity constraints, and the need for split deliveries across multiple trips. Classical optimization approaches often fail to address these challenges, as they typically rely on static heuristics or do not integrate real-time data and adaptive learning. Addressing the computational complexity of Multi-Depot Vehicle Routing Problems (MDVRPs) with last-mile split deliveries and multiple trips requires algorithmic innovation and system-level efficiency. To tackle this challenge, we propose a hybrid Artificial Intelligence (AI)-based framework that integrates list-based scheduling heuristics-As Soon As Possible (ASAP), As Late As Possible (ALAP), and List Scheduling-with Transformer networks, Deep Reinforcement Learning (DRL), NeuroEvolution of Augmented Topologies (NEAT), and Model-Agnostic Meta-Learning (MAML). Among the models evaluated, the List Scheduling + Transformer (LST-Former) configuration achieved the best performance regarding route accuracy, resource utilization, and robustness under varying demand conditions. While DRLbased models demonstrated strong adaptability to dynamic logistics, they incurred higher computational costs. This trade-off was mitigated by designing the proposed architecture with High-Level Synthesis (HLS) compatibility, enabling future deployment on low-latency, energy-efficient hardware platforms. The framework was validated using a real-world case involving a distribution company based in Istanbul, T & uuml;rkiye. The scenario captures realistic daily last-mile operations with dynamic orders, multi-depot routing, and high-volume palletized deliveries. In addition to real-world data, five widely used Cordeau MDVRP benchmark instances (p01, p07, p11, p17, p22) were used to assess generalizability and solution competitiveness against best-known solutions (BKS). Experimental validation was conducted through K-Fold cross-validation and a suite of performance metrics, including MSE, MAE, RMSE, DTW, PAP10, POFP, and Coverage Score. Furthermore, comparative analyses with classical algorithms-List Scheduling (LS), Nearest Neighbor (NN), Genetic Algorithm (GA), and Ant Colony Optimization (ACO)-showed that while traditional heuristics offered simplicity or stability, the proposed LST-Former consistently achieved lower route costs and more balanced travel times across datasets. This explicit integration of split delivery, multi-depot coordination, and hardware-aware optimization distinguishes the proposed study from prior VRP research and underscores its practical relevance for urban last-mile logistics. The results confirm the effectiveness of combining learning-based optimization with hardware-aware design to support scalable, real-time routing in logistics. This integrated approach enhances solution quality under complex constraints and facilitates deployment feasibility in embedded systems for next-generation logistics platforms.