Rising labor costs and increasing logistical demands pose significant challenges to modern delivery systems. Automated Electric Vehicles (AEVs) could reduce reliance on delivery personnel and increase route flexibility, but their adoption is limited due to varying customer acceptance and integration complexities. Shared Distribution Locations (SDLs) offer an alternative to door-to-door (D2D) delivery by providing a wider delivery window and serving multiple community customers, thereby improving last-mile logistics through reduced delivery time, lower costs, and higher customer satisfaction.This paper introduces the Multi-Trip Time-Dependent Hybrid Vehicle Routing Problem (MTTD-MVRP), a challenging variant of the Vehicle Routing Problem (VRP) that combines Autonomous Electric Vehicles (AEVs) with conventional vehicles. The problem's complexity arises from factors such as time-dependent travel speeds, strict time windows, battery limitations, and driver labor constraints, while integrating both SDLs and D2D deliveries. To solve the MTTD-MVRP efficiently, we develop a tailored meta-heuristic based on Adaptive Large Neighborhood Search (ALNS) augmented with column generation (CG). This approach intensively explores the solution space using problem-specific operators and adaptively refines solutions, balancing high-quality outcomes with computational effort. Extensive experiments show that the proposed method delivers near-optimal solutions for large-scale instances within practical time limits.From a managerial perspective, our findings highlight the importance of integrating autonomous and human-driven vehicles in last-mile logistics. Decision-makers can leverage SDLs to reduce operational costs and carbon footprints while still accommodating customers who require or prefer D2D services.

Deep learning approaches have shown promising results in solving routing problems. However, there is still a substantial gap in solution quality between machine learning and operations research algorithms. Recently, another line of research has been introduced that fuses the strengths of machine learning and operational research algorithms. In particular, search perturbation operators have been used to improve the solution. Nevertheless, using the perturbation may not guarantee a quality solution. This paper presents "Learning to Guide Local Search" (L2GLS), a learning-based approach for routing problems that uses a penalty term and reinforcement learning to adaptively adjust search efforts. L2GLS combines local search (LS) operators' strengths with penalty terms to escape local optimals. Routing problems have many practical applications, often presetting larger instances that are still challenging for many existing algorithms introduced in the learning to optimise field. We show that L2GLS achieves the new state-of-the-art results on larger TSP and CVRP over other machine learning methods.