Routing problems, central to logistics and transportation, involve appointing vehicles to fulfill various delivery tasks or commuting requests from customers randomly located within a region. While existing learn-to-construct methods can instantly plan high-quality vehicle routes to simultaneously serve a group of customers’ requests, the routes’ quality (e.g., transporting costs) is highly affected by the group size (i.e., number of requests simultaneously considered), thereby necessitating repetitive training on specific group size to adapt the model to different problem scales. Our proposed mix-scale learning framework effectively overcome this issue, using only once-off training to enable the learn-to-construct method to plan high-quality vehicle routes for any number of customer requests, equipping the model with favorable generalization ability on diverse problem scales in real-world logistics applications without requiring repetitive adaptation, pioneering in exploring the scale...

When utilizing end-to-end learn-to-construct methods to solve routing problems for multiagent systems, the model is usually trained individually for different problem scales (i.e., the number of customers to be concurrently served within a map) to make the model adaptive to the corresponding scale, ensuring good solution quality. Otherwise, the model trained for one specific scale can lead to poor performance when applied to another different scale, and this situation can get worse when the scale discrepancy increases. Such a separate training strategy is inefficient and time-intensive. In this article, we propose a mix-scale learning framework that requires only a single training session, enabling the model to effectively plan high-quality routes for various problem scales. Based on the capacitated vehicle routing problem (CVRP), the test results reveal that: for problem scales which are no matter seen or unseen during training, our once-trained model can produce solution routes with ...