# A Hybrid Grasshopper Optimization Algorithm Applied to the Open Vehicle Routing Problem
## 4 Computational Experiments
### Results with the Traveling Cost Minimization Objective Function
For the benchmark problems including route length constraints, the HGOALS performs better than the rest of the algorithms obtaining new best solutions for instances C9, C10 and C13 and reaching the best-known solutions for instances C6, C7 and C14. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Instance** & \(n\) & \(Q\) & \(BKS\) & \(Avg\) & \(Best\) & \(CPU\) & \%\(gap\) \\ \hline C1 & 50 & 160 & 412.96 & 412.96 & **412.96** & 3.12 & 0.00 \\ C2 & 75 & 140 & 564.06 & 564.06 & **564.06** & 4.97 & 0.00 \\ C3 & 100 & 200 & 639.26 & 644.36 & **639.26** & 21.84 & 0.00 \\ C4 & 150 & 200 & 733.13 & 733.84 & 733.84 & 54.50 & 0.10 \\ C5 & 199 & 200 & 869.00 & 876.33 & 875.49 & 147.48 & 0.75 \\ C6 & 50 & 160 & 412.96 & 412.96 & **412.96** & 2.94 & 0.00 \\ C7 & 75 & 140 & 567.59 & 567.59 & **567.59** & 4.91 & 0.00 \\ C8 & 100 & 200 & 644.63 & 646.35 & 644.63 & 20.88 & 0.00 \\ C9 & 150 & 200 & 743.51 & 743.22 & **742.35** & 71.62 & \(-0.16\) \\ C10 & 199 & 200 & 873.89 & 875.83 & **873.69** & 140.66 & \(-0.02\) \\ C11 & 120 & 200 & 676.40 & 679.80 & 678.70 & 85.84 & 0.34 \\ C12 & 100 & 200 & 534.24 & 536.20 & 536.20 & 10.22 & 0.37 \\ C13 & 120 & 200 & 862.74 & 849.64 & **841.92** & 122.42 & \(-2.41\) \\ C14 & 100 & 200 & 554.67 & 554.67 & **554.67** & 11.79 & 0.00 \\ \hline \multicolumn{2}{c}{\(Avg\)} & & & & & 50.23 & \(-0.07\) \\ \hline O1 & 200 & 900 & 5988.35 & 6003.08 & 6003.08 & 277.41 & 0.25 \\ O2 & 240 & 550 & 4549.46 & 4557.38 & 4550.21 & 603.40 & 0.02 \\ O3 & 280 & 900 & 7731.00 & 7735.43 & **7731.00** & 1000.00 & 0.00 \\ O4 & 320 & 700 & 7251.30 & 7254.18 & 7253.20 & 1000.00 & 0.03 \\ O5 & 360 & 900 & 9152.47 & 9163.25 & **9132.88** & 1000.00 & \(-0.21\) \\ O6 & 400 & 900 & 9793.72 & 9803.41 & **9793.72** & 1000.00 & 0.00 \\ O7 & 440 & 900 & 10,344.37 & 10,349.57 & 10,347.70 & 1000.00 & 0.03 \\ O8 & 400 & 1000 & 12,412.26 & 12,426.58 & 12,415.36 & 1000.00 & 0.02 \\ \hline \multicolumn{2}{c}{\(Avg\)} & & & & & 860.10 & 0.02 \\ \hline K01 & 240 & 550 & 4629.21 & 4637.86 & **4622.58** & 901.95 & \(-0.14\) \\ K02 & 320 & 700 & 7285.98 & 7304.73 & 7296.15 & 957.26 & 0.14 \\ K03 & 400 & 900 & 9837.78 & 9848.97 & **9831.07** & 817.50 & \(-0.07\) \\ K04 & 480 & 1000 & 12,431.50 & 12,449.32 & **122**,**422.20** & 806.17 & \(-0.07\) \\ K05 & 200 & 900 & 6004.74 & 6006.72 & **6004.74** & 275.42 & 0.00 \\ K06 & 280 & 900 & 7731.21 & 7735.93 & 7735.16 & 807.58 & 0.05 \\ K07 & 360 & 900 & 9188.11 & 9183.54 & **9162.29** & 1000.00 & \(-0.28\) \\ K08 & 440 & 900 & 10,488.50 & 10,486.70 & **10**,**457.60** & 873.22 & \(-0.29\) \\ \hline \multicolumn{2}{c}{\(Avg\)} & & & & 804.89 & \(-0.08\) \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Results obtained by the HGOALS for all the test instances (minimizing traveling cost). The comparison of the results with previous research for instances of group O is made in Table 8. In this set of instances, the BLSA performs the best obtaining the best-known solutions for six of the eight instances, followed by the HGOALS obtaining the best-known solution for one of the eight instances. For the benchmark problems in group K, the comparison with results obtained in previous research is made in Table 9. The results show that the HGOALS outperforms the other two metaheuristics by obtaining five new best solutions for the eight instances in the group.