## 4 Computational Experiments
### Computational Results  
#### 4.2.1 Results on the 2L-VRP Benchmark Instances  
Moreover, four classes of 2L-VRP are tested and compared with existing methods, as shown in Tables 3-8. Tables 4-7 present the results obtained by our method under the 2|UO|L, 2|SO|L, 2|UR|L, 2|SR|L settings, respectively. Therein, \"Gap\" denotes the percentage gap between the Cost and BKS (best-known solution) (Gap(\(\%\)) = 100 \(\times\) (Cost-BKS)/BKS). Table 3 compares the best average cost of the classes (Classes 2-5) for each test instance (Instance 1-20) against the previous approaches, which shows our approach is capable of yielding comparable solutions under the 2|UO|L and 2|SO|L settings. Under the 2|UO|L setting, the overall performance of the proposed EATS-MOBFS method slightly outperforms those of GRASP \(\times\) ELS and EGTS \(+\) LBFH. In comparison to GRASP \(\times\) ELS and EGTS \(+\) LBFH, the proposed approach is able to produce better solutions for 6, 19 out of 20 instances, respectively. Under the 2|SO|L setting, our approach is superior to that of EGTS \(+\) LBFH and has gained comparable results compared with those obtained by PRMP and BR-LNS. Specifically, our approach can yield better solutions for 20 out of 20 instances compared with EGTS \(+\) LBFH. As shown in Table 4, the best results were obtained by our approach on some instances of Classes 2-5 under the 2|UO|L setting, which shows the proposed EATS-MOBFS method has reached the best-known solutions for 9, 8, 8 and 10 instances in Classes 2-5, respectively. In addition, the average percentage gaps between the solutions obtained by the proposed EATS-MOBFS method and the best-known solutions (BKS) are 0.72%, 1.01%, 0.91% and 0.88% for the instances in Classes 2-5, respectively. It infers that the proposed hybrid heuristic incorporating EATS and MOBFS is efficient for solving the 2L-VRP under the 2|UO|L setting. Moreover, Table 5 presents the best results obtained by our method on some instances of Classes 2-5 under the 2|UR|L setting, which shows the proposed EATS-MOBFS method has reached the best-known solutions for 8, 10, 7 and 10 testing instances in Classes 2-5, respectively. In addition, the average percentage gaps between the solutions obtained by our method and BKS are 0.56%, 0.50%, 0.54% and 0.54% for the instances in Classes 2-5, respectively. It infers that the proposed hybrid heuristic is efficient for solving the 2L-VRP under the 2|UR|L setting. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Inst. **} & \multicolumn{4}{c}{**UO**} & \multicolumn{4}{c}{**SO**} \\ \cline{2-10}  & **GRASP** & **EGTS+LBFH** & **LS** & **EATS-MOBFS** & **EGTS+LBFH** & **PRMP** & **BR-LNS** & **EATS-MOBFS** \\ \hline
1 & 282.68 & 295.46 & 281.23 & 281.84 & 303.40 & 287.09 & 291.43 & 288.61 \\
2 & 343.56 & 341.89 & 339.26 & 339.26 & 345.23 & 344.21 & 344. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Inst. **} & \multicolumn{3}{c}{**Class 2**} & \multicolumn{3}{c}{**Class 3**} & \multicolumn{3}{c}{**Class 4**} & \multicolumn{3}{c}{**Class 5**} \\ \cline{2-13}  & **BKS** & **Cost** & **Gap** & **BKS** & **Cost** & **Gap** & **BKS** & **Cost** & **Gap** & **BKS** & **Cost** & **Gap** \\ \hline
1 & 278.73 & 278.73 & **0.00** & 284.52 & 286.9  
Tables 6 and 7 present the best results obtained by our method on some instances of Classes 2-5 for 2L-VRP under the 2\(|\)SO\(|\)L and 2\(|\)SR\(|\)L settings, respectively. Table 5 shows that our EATS-MOBFS method can obtain high-quality solutions for all instances, where the average percentage gaps between the solutions obtained by our method and the BKS