Research on One-to-Many Pickup and Delivery Vehicle Routing Optimization Method Considering Three-Dimensional Loading

Simultaneous optimization of vehicle routing and cargo loading is essential for reducing operational costs and improving the environmental performance of logistics systems. To overcome the limitations of traditional sequential approaches to the one-to-many pickup and delivery vehicle routing problem with three-dimensional loading constraints (3L-PDVRP), this paper proposes a deeply coupled hybrid genetic algorithm (HGA). The algorithm adopts a grouping-based genetic encoding strategy to accommodate variable fleet sizes and incorporates a tree-search-based loading module. A dynamic three-dimensional loading feasibility verification mechanism is embedded directly into the evolutionary search so that routing decisions are continuously guided by fragility, stacking stability, support constraints, and other loading constraints. In addition, an adaptive hybrid insertion strategy is employed to balance global exploration and local exploitation during route construction and repair. Extensive computational experiments on extended benchmark instances derived from standard datasets show that the proposed method consistently outperforms a large neighborhood search (LNS)-based baseline from the literature, reducing the average total travel distance by 10.60% and increasing the average vehicle loading rate by 2.76%. These results indicate that the proposed HGA provides an effective approach to the synergistic optimization of routing and loading in one-to-many distribution settings, offering practical value for lowering transportation costs and supporting more sustainable logistics operations. This methodology provides decision support for logistics enterprises, reducing travel distances while ensuring three-dimensional loading feasibility, thereby enabling greener and safer transportation operations.