# Optimization Dubins Path of Multiple UAVs for Post-Earthquake Rapid-Assessment
## 3 HGSA Algorithm
### Mutation
We modeled this problem as a MURARP model and HGSA is used to obtain the routing scheme for rapid assessment. Table 6 records the results for the 22 simulation instances, which was run 10 times under the same experimental conditions. The maximum profit of the 10 runs are listed in the \(R_{MAX}\) column, the average profit of the 10 runs are listed in the \(R_{AVG}\) column, the minimum profit of the 10 runs are listed in the \(R_{MIN}\) column, and the average computational time of the 10 runs in seconds are listed in the \(CPU_{AVG}\) column. Figure 8: Schematic diagram of simulation experiment scenes. (**a**) the even distribution dataset, denoted as E; (**b**) the clustered distribution dataset, denoted as C. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Parameters** & **UAV1** & **UAV2** & **UAV3** & **UAV4** \\ \hline Speed (m/min) & 1 & 1 & 1.5 & 1.5 \\ Turning radius (m) & 0.1 & 0.1 & 0.3 & 0.3 \\ Endurance (min) & 10 & 15 & 10 & 15 \\ Sensor error (\%) & 0.1 & 0.1 & 0.2 & 0.2 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Relevant parameter values of the UAVsTable 6 shows that with additional UAVs, the collected profit increases continuously. Moreover, the profits collected by the same number of UAVs launched from different depots may also be different, which indicates that the selection of the launching depot has a certain impact on the quality of mission completion. The results inspired us to improve the completion quality of the task by optimizing the location of the depot that launches the UAV in the case of limited UAV resources. Table 6 also shows that the stability of the HGSA algorithm is strong. The average gap between \(R_{MAX}\) and \(R_{AVG}\) is only 5.28% and between \(R_{MAX}\) and \(R_{MIN}\) is only 11.11%. From the experimental results shown in Table 6, it can also be seen that the average value of the \(R_{MAX}\) column is only 5.28% different from the average value of the \(R_{AVG}\), and the average value of the \(R_{MAX}\) column is only 11.11% different from the average value of the \(R_{MIN}\) column. This demonstrates that the stability of the HGSA algorithm is strong. ### Case Study

To illustrate how our method can be applied in a post-earthquake scenario, a case study based on the actual data of the 2017 Jiuzhaigou earthquake in China is conducted. An earthquake with a magnitude of 7.0 struck in Jiuzhaigou County, China at 21:19:46 on 8 August 2017. The epicenter was located at 33.20\({}^{\circ}\) N, 103.82\({}^{\circ}\) E, and the focal depth was 20 km. Soon after, the rescue organization used a UAV to quickly survey the buildings in the disaster area. Data analysis and field surveys based on UAVs were subsequently conducted for the disaster area to assess the geological hazards generated by the earthquake [41]. National Earthquake Response Support Service (NERSS) participated in the post-earthquake survey and rescue operations of the Jiuzhaigou earthquake. Experts of NERSS determined several potential targets, such as schools, hospitals, and other important buildings, that needed UAVs to assess quickly and to capture images and videos. Then, combined with the distance from the epicenter and the population size of these buildings, the possible damage degree of these potential targets was estimated in the form of weights. Then, four rescue teams were sent to carry out rapid assessment of the disaster area from different directions by UAVs. This paper makes a case study from the actual situation of relief operation. Thus, 50 potential targets and the UAV depots are selected for case studies, as shown in Figure 9.