# Drone Arc Routing Problems and Metaheuristic Solution Approach
## 5 Computational Results
### Computational Results for CARP

Table 3: Number of iterations in simulated annealing algorithm. Table 3 summarizes the results of 20 differently sized test problems taken from the seven sets. The first column of Table 3 contains the names of the test problems. The names of the largest sized test problems in the set are denoted with an asterisk (kshs-6*, gdb-23*, bmcv-f24*, val-104*, egl-s4c*, and eglL-g2e*). The number of required edges and the total number of edges in the relevant test problems are presented in the second column. The third column of the table shows the number of vehicles that serve the required edges. In the fourth column, the obtained objective function values for the test problems are presented. The next column contains the optimal or the best known objective function values. Deviation values (gap) are given in the fifth column. The last column shows the computation times reported in seconds. The values of the optimal or best known results presented in the fifth column of Table 3 are based on findings from the literature. [PERSON] et al. [40] used a genetic algorithm for solving the CARP. In the structure of this algorithm, a random key was used for solution representation. The result of the kshs-6* problem presented in Table 3 was obtained in the study. [PERSON] et al. [41] proposed two divide-and-conquer algorithms called RCO-RDG-MAENS and RCO-SAHiD to solve a large-sized CARP. In this study, the unified hybrid genetic search (UHGS) algorithm proposed by [PERSON] [42] was used to compare the algorithms, and the best known solution for the Hefei-4 problem, as presented in Table 3, was obtained by the UHGS algorithm. [PERSON] et al. [43] proposed the hybrid metaheuristic approach (HMA) for effectively solving the CARP. In the structure of the algorithm, inversion, single insertion, double insertion, swap, two-opt, and merge-split operators were used as local refinement methods. The results of all other test problems presented in Table 3 (gdb-5, gdb-21, gdb-23*, val-5c, val-5d, bmcv-d1, bmcv-f24*, val-10c, val-10d*, egl-edc, bmcv-c18, bmcv-d18, egl-s4a, egl-s4b, egl-s4c*, eglL-g2a, and eglL-g2e*) were obtained in the study. Since the number of vehicles to be used in the test problems is fixed, the same number of vehicles as presented in the third column of Table 3 was used in the aforementioned studies. The test problems kshs-6 and gdb-23, which are the largest-sized problems in the kshs and gdb sets, were able to be solved optimally using the proposed algorithm. On the other hand, the optimal solutions could be obtained for the val-5c problem with 65 required edges and for the val-10c problem with 97 required edges. The optimal solution to the bmcv-d18 problem, which includes 121 required edges and a total of 133 edges, was achieved in 1345 s. This is the largest-sized problem for which the optimal solution could be obtained with the proposed algorithm. From these results, it is clear that the proposed algorithm is capable of reaching optimal solutions even for large-sized problems. On the other hand, high-quality solutions were obtained for large-sized test problems in the egl set. For the egl-s4a and egl-s4b problems with 190 required edges, the solution with a deviation of about 1% from the best known result was reached in about 2300 s. The egl-s4c test problem, the largest-sized problem in the egl set, was solved with a 3.5% deviation from the best known result. For the egl-g2a and egl-g2e problems in the Egl set with 375 required edges, high-quality solutions could be obtained in about 2 h with a deviation of about 3% from the best known result. Comparing the proposed algorithm with the genetic algorithm proposed by [PERSON] et al. [40] for the kshs test problem, it is evident that both algorithms achieved the optimal solution. On the other hand, for the problems in the gdb, val, bmcv, egl, and eglL sets presented in Table 3, the proposed algorithm was compared with the HMA algorithm proposed by [PERSON] et al. [43].