## 5 Computational Experiments
### Experimental Experiments and Comparative Analysis
#### 5.3.1 Comparison with the Gurobi Solver on Small-Scale Instances  
Based on node replication theory, the mathematical model exhibits an exponential increase in computational complexity with problem size when solved using Gurobi under a one-hour time constraint. To ensure fair heuristic performance evaluations with limited resources, we compare HACO and Gurobi on the small-scale instance set C15 under both unlimited and limited capacities of CI. The capacity constraints in HACO are programmatically adjustable, while in Gurobi, they are tightened or relaxed according to Equations (21)-(23). Tables 3 and 4 present the performance comparison, with bolded values highlighting the superior results in each case. From Tables 3 and 4, the following conclusions can be drawn:  
1. The HACO algorithm outperforms Gurobi in 6/10 and 9/10 instances under unlimited and limited capacities of CI, respectively, with solution quality improvements of 3.12% and 4.05%, demonstrating strong optimization capabilities. 2. Gurobi reaches its time limit on all small-scale instances, failing to obtain optimal solutions within 1 h. In contrast, HACO achieves solutions comparable to or better than Gurobi within 60 s, showing significant computational efficiency. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multicolumn{6}{c}{**Gurobi**} & \multicolumn{6}{c}{**HACO**} \\ \hline
**Instance** & **\#Veh** & **\#BS** & **TC** & **t (s)** & **\#Veh** & **\#BS** & **TC** & **t (s)** & **GAP2** \\ \hline C15\_1 & 5 & 0 & 1950.21 & \(>\)3600 & 5 & 0 & **1937.86** & 81.11 & 0.64\% \\ C15\_2 & 5 & 0 & 1922 & \(>\)3600 & 4 & 1 & **1690.96** & 48.31 & 13.66\% \\ C15\_3 & 5 & 0 & 1944.8 & \(>\)3600 & 4 & 1 & **1696.14** & 51.57 & 14.66\% \\ C15\_4 & 5 & 0 & 1955.78 & \(>\)3600 & 4 & 2 & **1786.65** & 54.49 & 9.47\% \\ C15\_5 & 4 & 0 & 1524.92 & \(>\)3600 & 4 & 0 & **1520.87** & 37.53 & 0.27\% \\ C15\_6 & 4 & 0 & 1513.49 & \(>\)3600 & 4 & 0 & **1510.22** & 109.59 & 0.22\% \\ C15\_7 & 4 & 0 & 1544.92 & \(>\)3600 & 4 & 0 & **1540.93** & 46.68 & 0.26\% \\ C15\_8 & 4 & 0 & **1493.01** & \(>\)3600 & 4 & 0 & **1516.35** & 58.51 & \(-\)1.54\% \\ C15\_9 & 4 & 0 & 1548.94 & \(>\)3600 & 4 & 0 & **1525.59** & 45.76 & 1.53\% \\ C15\_10 & 4 & 1 & 1662.88 & \(>\)3600 & 4 & 1 & **1640.44** & 45.12 & 1.37\% \\ Average & 4.4 & 0.1 & 1706.10 & \(>\)3600 & 4.1 & 0.5 & 1636.60 & 57.87 & 4.05\% \\ \hline \end{tabular} Note: GAP2 = 100% * (TC of Gurobi – TC of HACO)/TC of HACO.  
\end{table} 
Table 4: Comparison of results obtained with Gurobi under limited capacity of CI. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \multicolumn{6}{c}{**Gurobi**} & \multicolumn{6}{c}{**HACO**} \\ \hline
**Instance** & **\#Veh** & **\#BS** & **TC** & **t (s)** & **\#Veh** & **\#BS** & **TC** & **t (s)** & **GAP1** \\ \hline C15\_1 & 5 & 0 & 1948.21 & \(>\)3600 & 5 & 0 & **1937.86** & 49.40 & 0.53\% \\ C15\_2 & 5 & 0 & 1930.44 & \(>\)3600 & 4 & 1 & **1690.96** & 62.10 & 14.16\% \\ C15\_3 & 5 & 0 & 1931.93 & \(>\)3600 & 4 & 1 & **1692.10** & 32.57 & 14.17\% \\ C15\_4 & 5 & 0 & 1922.78 & \(>\)3600 & 4 & 2 & **1785.45** & 120.50 & 7.69\% \\ C15\_5 & 4 & 0 & **1519.39** & \(>\)3600 & 4 & 0 & 1520.87 & 35.16 & \(-\)0.10\% \\ C15\_6 & 4 & 0 & **1508.49** & \(>\)3600 & 4 & 0 & 1526.11 & 51.01 & \(-\)1.15\% \\ C15\_7 & 4 & 0 & 1553.33 & \(>\)3600 & 4 & 0 & **1541.01** & 65.64 & 0.80\% \\ C15\_8 & 4 & 0 & **1493.01** & \(>\)3600 & 4 & 0 & 1517.39 & 43.31 & \(-\)1.61\% \\ C15\_9 & 4 & 0 & 1526.88 & \(>\)3600 & 4 & 0 & **1525.59** & 54.04 & 0.08\% \\ C15\_10 & 4 & 1 & **1584.52** & \(>\)3600 & 4 & 1 & 1640.44 & 54.50 & \(-\)3.41\% \\ Average & 4.4 & 0.1 & 1691.90 & \(>\)3600 & 4.1 & 0.5 & 1637.78 & 56.82 & 3.12\% \\ \hline \end{tabular} Note: GAP1 = 100% * (TC of Gurobi – TC of HACO)/TC of HACO.  
\end{table} 
Table 3: Comparison of results obtained with Gurobi under unlimited capacity of CI. 3. The HACO algorithm effectively leverages the synergistic advantages of HERI by guiding vehicles to utilize both CI and BSI, achieving overall cost optimization.