Research on route optimization for bus–drone collaborative delivery under time-dependent road networks

With the increasing demand for time-sensitive urban distribution services, traditional ground-based last-mile delivery faces challenges such as traffic congestion, rising costs, and unstable timeliness. This study investigates the bus–drone collaborative delivery route optimization problem under time-dependent road network conditions and mixed-cargo demand. Different from most truck–drone delivery studies, fixed-route buses are introduced as mobile transfer platforms for drones, and the coordination between bus stop sequences and drone launch/recovery decisions is considered. A cost-minimization model is developed by incorporating time-dependent bus travel times, drone payload and endurance constraints, customer time windows, and different delivery time requirements of ordinary and fresh products.An improved adaptive large neighborhood search algorithm (IALNS) is proposed, which integrates greedy initialization, multiple destruction and repair operators, adaptive operator weight updating, improved genetic operations, and a simulated annealing acceptance criterion. Computational results show that IALNS reduces delivery costs by 2.69–6.22% compared with ALNS and by 2.79–7.76% compared with GA. The average convergence curve over 10 independent runs indicates that the algorithm converges stably after about 200 iterations. Ablation experiments show that removing key improvement strategies increases the average delivery cost by 2.89–8.82%. Sensitivity analyses further indicate that increasing the proportion of fresh cold-chain customers raises total cost, while improving drone payload capacity helps reduce total cost. This study provides a reference for integrating public transit resources into urban last-mile delivery systems.