# A Hybrid Grasshopper Optimization Algorithm Applied to the Open Vehicle Routing Problem
## 4 Computational Experiments
### Results with the Traveling Cost Minimization Objective Function
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Instance** & \(n\) & \(Q\) & \(BKS\) & **HGOALS** & **BRKGA** & **BBMO [37]** & **BLSA [38]** & **HBMO [44]** \\ \hline C1 & 50 & 160 & 412.96 & **412.96** & **412.96** & **412.96** & **412.96** & **412.96** & **412.96** \\ C2 & 75 & 140 & 564.06 & **564.06** & **564.06** & **564.06** & **564.06** & **564.06** \\ C3 & 100 & 200 & 639.26 & **639.26** & **639.26** & **639.26** & **639.26** & 640.08 \\ C4 & 150 & 200 & 733.13 & **733.13** & **733.13** & 735.18 & **733.13** & 738.49 \\ C5 & 199 & 200 & 869.00 & 875.49 & 871.21 & 872.15 & **869.00** & 878.25 \\ C6 & 50 & 160 & 412.96 & **412.96** & **412.96** & **412.96** & - & **412.96** \\ C7 & 75 & 140 & 567.59 & **567.59** & **567.59** & 568.95 & - & 568.49 \\ C8 & 100 & 200 & 644.63 & 646.75 & 646.75 & **644.63** & - & 647.26 \\ C9 & 150 & 200 & 743.51 & **742.35** & 743.51 & 757.24 & - & 761.28 \\ C10 & 199 & 200 & 873.89 & **873.69** & 873.89 & 879.38 & - & 903.10 \\ C11 & 120 & 200 & 676.40 & 678.70 & 680.23 & 678.54 & 678.54 & 680.15 \\ C12 & 100 & 200 & 534.24 & 536.20 & 536.20 & 535.28 & **534.24** & 536.37 \\ C13 & 120 & 200 & 862.74 & **841.92** & 862.74 & 897.10 & - & 922.28 \\ C14 & 100 & 200 & 554.67 & **554.67** & **554.67** & 592.16 & - & 600.66 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Comparison between the HGOALS and previous research for instances in group C (minimizing traveling cost). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Instance** & \(n\) & \(Q\) & \(BKS\) & **HGOALS** & **\%gap** & **BLSA [38]** & **BRKGA [43]** \\ \hline O1 & 200 & 900 & 5988.35 & 6003.08 & 0.25 & **5988.35** & 6003.08 \\ O2 & 240 & 550 & 4549.46 & 4621.41 & 1.58 & **4549.46** & 4609.25 \\ O3 & 280 & 900 & 7731.00 & 7734.70 & 0.05 & **7731.00** & 7735.16 \\ O4 & 320 & 700 & 7251.30 & 7269.20 & 0.25 & **7251.30** & 7280.98 \\ O5 & 360 & 900 & 9152.47 & **9132.88** & \(-\)0.22 & 9152.47 & 9178.13 \\ O6 & 400 & 900 & 9793.72 & 9833.41 & 0.41 & **9793.72** & 9847.00 \\ O7 & 440 & 900 & 10,344.37 & 10,463.80 & 1.16 & 10347.70 & 10,444.70 \\ O8 & 400 & 1000 & 12,412.26 & 12,457.10 & 0.36 & **12,412.26** & 12,449.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison between route decoder and previous research for instances in group O (minimizing traveling cost). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Instance** & \(\mathbf{n}\) & \(\mathbf{Q}\) & \(BKS\) & **HGOALS** & **\%gap** & **BLSA [38]** & **BRKGA [43]** \\ \hline O1 & 200 & 900 & 5988.35 & 6003.08 & 0.25 & **5988.35** & 6003.08 \\ O2 & 240 & 550 & 4549.46 & 4621.41 & 1.58 & **4549.46** & 4609.25 \\ O3 & 280 & 900 & 7731.00 & 7734.70 & 0.05 & **7731.00** & 7735.16 \\ O4 & 320 & 700 & 7251.30 & 7269.20 & 0.25 & **7251.30** & 7280.98 \\ O5 & 360 & 900 & 9152.47 & **9132.88** & \(-\)0.22 & 9152.47 & 9178.13 \\ O6 & 400 & 900 & 9793.72 & 9833.41 & 0.41 & **9793.72** & 9847.00 \\ O7 & 440 & 900 & 10,344.37 & 10,463.80 & 1.16 & 10347.70 & 10,444.70 \\ O8 & 400 & 1000 & 12,412.26 & 12,457.10 & 0.36 & **12,412.26** & 12,449.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Comparison between route decoder and previous research for instances in group O (minimizing traveling cost).