# Optimization Dubins Path of Multiple UAVs for Post-Earthquake Rapid-Assessment
## 3 HGSA Algorithm
### Mutation
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Instance**} & \multirow{2}{*}{\(N\)} & \multirow{2}{*}{\(K\)} & \multirow{2}{*}{\(T_{\text{max}}\)} & \multirow{2}{*}{\(\rho\)} & \multirow{2}{*}{\(N_{\theta}\)} & \multicolumn{2}{c}{**HGSA**} & \multirow{2}{*}{\(R_{BEST}\)} \\ \cline{5-8}  & & & & & & & \(R_{MAX}\) & & \(CPU_{AVG}\) \\ \hline \multirow{8}{*}{p1.2.h} & \multirow{8}{*}{32} & \multirow{8}{*}{2} & \multirow{8}{*}{20} & 3 & 105 & 4.52 & \multirow{8}{*}{\(CPI_{AVG}\)} \\  & & & & & 6 & 105 & 5.44 & \multirow{8}{*}{110} \\  & & & & & 8 & 110 & 6.51 & \multirow{8}{*}{110} \\  & & & & & 15 & 110 & 8.14 & \multirow{8}{*}{110} \\  & & & & & 24 & 110 & 10.62 & \multirow{8}{*}{15.80} \\  & & & & & 36 & 110 & 12.61 & \multirow{8}{*}{15.80} \\  & & & & & 60 & 110 & 15.80 & \\ \hline \multirow{8}{*}{p2.2.j} & \multirow{8}{*}{21} & \multirow{8}{*}{2} & \multirow{8}{*}{20} & 3 & 200 & 4.72 & \multirow{8}{*}{5.65} \\  & & & & & 6 & 230 & 5.65 & \multirow{8}{*}{260} \\  & & & & & 8 & 230 & 6.81 & \\  & & & & & 15 & 260 & 7.55 & \multirow{8}{*}{260} \\  & & & & & 24 & 260 & 10.76 & \multirow{8}{*}{11.35} \\  & & & & & 36 & 260 & 11.35 & \\  & & & & & 60 & 260 & 14.17 & \\ \hline \multirow{8}{*}{p3.2.f} & \multirow{8}{*}{33} & \multirow{8}{*}{2} & \multirow{8}{*}{20} & 3 & 250 & 6.19 & \multirow{8}{*}{8.06} \\  & & & & & 6 & 270 & 8.06 & \\  & & & & & 8 & 280 & 10.64 & \\  & & & & & 15 & 280 & 12.54 & 300 \\  & & & & & 24 & 300 & 13.92 & \\  & & & & & 36 & 300 & 14.66 & \\  & & & & & 60 & 300 & 16.42 & \\ \hline \multirow{8}{*}{p5.2.h} & \multirow{8}{*}{66} & \multirow{8}{*}{2} & \multirow{8}{*}{20} & 3 & 3 & 380 & 26.42 & \multirow{8}{*}{410} \\  & & & & & 6 & 385 & 29.70 & \\  & & & & & 8 & 410 & 30.49 & \\  & & & & & 15 & 410 & 32.11 & 410 \\  & & & & & 24 & 410 & 35.93 & \\  & & & & & 36 & 410 & 38.57 & \\  & & & & & 60 & 410 & 42.54 & \\ \hline \multirow{8}{*}{p6.2.f} & \multirow{8}{*}{64} & \multirow{8}{*}{2} & \multirow{8}{*}{20} & 3 & 3 & 510 & 37.19 & \multirow{8}{*}{546} \\  & & & & & 6 & 546 & 43.98 & \\ \cline{1-1}  & & & & & 8 & 588 & 52.75 & \multirow{8}{*}{588} \\ \cline{1-1}  & & & & & 15 & 588 & 58.84 & \\ \cline{1-1}  & & & & & 24 & 588 & 67.62 & \multirow{8}{*}{588} \\ \cline{1-1}  & & & & & 36 & 588 & 70.92 & \\ \cline{1-1}  & & & & & 60 & 588 & 75.03 & \\ \hline \multirow{8}{*}{p7.2.b} & \multirow{8}{*}{102} & \multirow{8}{*}{2} & \multirow{8}{*}{20} & 3 & 64 & 4.34 & \multirow{8}{*}{5.32} \\ \cline{1-1}  & & & & & 6 & 64 & 4.61 & \\ \cline{1-1}  & & & & & 8 & 64 & 5.32 & \\ \cline{1-1}  & & & & & 24 & 64 & 6.05 & \\ \cline{1-1}  & & & & & 36 & 64 & 7.08 & \\ \cline{1-1}  & & & & & 60 & 64 & 8.34 & \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Best results for the 42 benchmark instances

### Simulation Experiments

In this paper, we construct two types of datasets based on the TOP benchmark instances for simulation experiments. The first simulation scene is reconstructed on Set 6 of the TOP benchmark, which is called the even distribution dataset, denoted as \(E\). The second simulation scene, which is reconstructed on Set 2 of the TOP benchmark, is called the clustered distribution dataset, denoted as \(C\). The vertex positions and weights are shown in Figure 8.

For the above two scenarios, \(K\) heterogeneous UAVs visit potential targets after launching from different depots whose indices corresponds to the UAV indices, and finally return to their respective departure depots. The number, \(K\), of UAVs used increases from 2 to 4. The relevant parameter values of the UAVs used in the simulation experiment are shown in Table 5.

To demonstrate the influence of the number of UAVs and their depot position on the collected profit, we designed 22 simulation experiments. Each case is named according to the type of dataset, the number of UAVs, and the depot indices. For example, the _E2-12_ case indicates that the UAVs launch from \(D1\) and \(D2\) and perform a rapid assessment in the E-type dataset.