## 3 Hybrid Algorithm--RSO-IGA
The primary focus of this study is to improve the delivery efficiency of H University's distribution center and ensure that campus students and staff receive their parcels as quickly as possible. Therefore, the priority of minimizing route length is higher than maximizing the three-dimensional packing loading rate. The weights \(\lambda_{1}\) and \(\lambda_{2}\) are set to 0.7 and 0.3, respectively. The comprehensive evaluation index correction parameter \(\gamma\) is set to 1. The maximum number of cycles is set to 10. As shown in Figure 11, under the data context of the H University case, the improved genetic algorithm generally stabilizes within 1000 generations. The distance metric in the convergence curve (see Figures 11 and 12) is defined as the total routing distance corresponding to the best-found solution per iteration. Therefore, the maximum number of iterations for solving the case is set to 1000. The crossover probability (\(P_{c}\)) and mutation probability (\(P_{m}\)) are set to 0.9 and 0.1, respectively. Using the \"Gaode API\" function from Gaode Maps' WebAPI, the latitude and longitude of customer points requiring delivery on a certain day at H University is obtained, as detailed in the Appendix A. For route visualization, the \"Driving Route Planning\" module of Gaode Maps' \"Route Planning API\" was utilized to acquire the shortest road distances and route nodes between two points. Figure 11: RSO-IGA algorithm iteration curve diagram. ### Solution Comparison

As shown in Figure 12, the objective function value converges after 627 iterations. The optimal solution involves a total of four delivery trips: first trip: [0, 31, 15, 24, 11, 10, 0], second trip: [0, 13, 34, 1, 5, 0], third trip: [0, 21, 3, 2, 29, 26, 25, 17, 32, 12, 8, 14, 4, 7, 0], and fourth trip: [0, 33, 6, 16, 18, 19, 9, 27, 30, 28, 23, 22, 20, 0]. The average loading rate is 75.65%, and the total route length is 7501 m. The route diagram of the optimal solution computed by RSO-IGA is shown in Figure 13, where each color represents a delivery trip, totaling four trips. The packing plans for each route are illustrated in Figure 14. The red lines outline the cargo space of the vehicle, and the different colors of the boxes inside each vehicle represent different customer points, meaning that parcels for each customer are assigned the same color. Figure 14: (**a–d**) are the first, second, third, and fourth path packing schemes of the optimal solution of RSO-IGA algorithm, respectively. Figure 12: Iteration curve diagram. Figure 13: The path scheme of the optimal solution of RSO-IGA algorithm. Table 5 presents the delivery plan for H University on a certain day which involves a total of four delivery trips. The plan achieves an average loading rate of 75.65% and a total route length of 10,347 m.

Based on certain day order data from H University, this paper applies the artificial bee colony algorithm and the GA-TS algorithm for optimization. The results obtained from the ABC algorithm are shown in Figure 15, while those from the GA-TS algorithm are shown in Figure 16. Both algorithms yield solutions with five delivery routes, illustrated in Figures 15f and 16f. The three-dimensional packing plans for each route are depicted in Figures 15a-e and 16a-e.

A comparison of the proposed RSO-IGA, the original delivery plan, and the two algorithms (ABC algorithm and GA-TS algorithm) is presented in Table 6. In practical logistics scenarios, customers consistently prioritize rapid parcel retrieval, making the reduction of total distribution distance a critical determinant for enhancing delivery efficiency. The three-dimensional bin packing problem, as a spatial constraint, directly influences delivery sequencing and routing distance. As shown in Table 6, both the H university delivery plan and the RSO-IGA-optimized scheme required four trips, while the ABC algorithm and GA-TS algorithm strategies necessitated five trips.