## 2 Problem Description and Modeling  
### Problem Description  
The 3L-CVRP problem can be described as follows: parcels are delivered by delivery vehicles to various customer points (i.e., destinations), all of which constitute a set. Daily orders are fixed and consist of a collection of parcels. The daily delivery plan is determined by the orders and includes multiple delivery routes, each with a unique packing scheme. Each route consists of a group of customer points, and the packing scheme for that route is composed of all the parcels from those customer points. The delivery vehicle departs from the distribution center and executes multiple delivery trips according to the delivery plan. For each trip, the vehicle loads parcels based on the packing scheme and visits the customer points in sequence. After completing a delivery trip (i.e., serving all the customer points assigned to that trip), the vehicle returns to the distribution center and proceeds to the next trip until all the parcels are delivered. Both the parcels and the vehicle compartment are defined as cuboids with three physical dimensions: length, width, and height. As shown in Figure 1, the delivery vehicle performs two delivery trips, serving two and three customer points, respectively. The parcel loading situation is represented by a red rectangle. Parcels of the same color belong to the same customer point, and parcels of different colors belong to different customer points.  
Based on this problem, the following assumptions are proposed:  
1. Single distribution center with multiple trips. There is only one distribution center and one delivery vehicle, and the delivery vehicle can perform multiple delivery trips;
2. Static network with fixed daily orders. The vehicle routing network is static, meaning daily order data are fixed and known in advance;
3. Regular cuboid shapes for parcels and vehicle compartment. Both the vehicle compartment and parcels are regular cuboids, and the dimensions of any single parcel do not exceed those of the vehicle compartment;
4. Orthogonal and non-overlapping packing. Parcels must be placed orthogonally in the compartment without overlapping;
5. Vehicle capacity constraint. The total volume of parcels loaded for each trip must not exceed the volume capacity of the vehicle compartment;
6. Known distances. The distances between arbitrary two customer points or the distribution center are known;
7. No backtracking. To minimize the total travel distance, each customer point is served only once per trip, avoiding \"backtracking\";
8. Constant speed. Energy consumption and travel costs are not considered, and vehicles travel at a constant speed without traffic delays;
9. No time window constraints. Customers can retrieve their parcels from temporary storage areas at customer points, eliminating the need for time window constraints;
10. No weight constraints. All the parcels only contain daily necessities, and there are no heavy items, so weight constraints are not considered;
11. The shortest path can enable customers to get parcels as soon as possible, which also increases customer satisfaction. The time for customers to take parcels is relatively concentrated, and the traffic situation is smooth during the delivery period, so other soft constraints are not considered.