## 5 Analytical Evaluation
### Sensitivity Analysis  
We present the sensitivity analysis here in order to test how much the simulation results could be affected by the variation of parameters, which reflects the sensitivity of the rescue plan to some parameters. The sensitivity is tested by varying the time limit for completing rescue operations in each buried site \(t_{need}\) from 10 min to 125 min with an interval of 5 min; the maximum turning angle \(s_{a}\) from \(\pi/6\) to \(2\pi\) with an interval of \(\pi/12\). For every case described here, the simulation was repeated 200 times.  
The time limit for completing rescue operations in each buried site \(t_{need}\) is used to estimate the number of teams required to complete a task \(n_{i}\), shown in Equation (4), the increase of \(t_{need}\) would lead to decrease of \(n_{i}\). As can be seen from Figure 9a, the rescue efficiency has shown a regular change with the time limit for completing rescue operations in each buried site \(t_{need}\). As \(t_{need}\) increases, the rescue efficiency improves significantly, but when \(t_{need}\) is larger than \(\hat{t}_{need}\ =\ 30\) min, the rescue efficiency lowers with the increase of \(t_{need}\). When \(t_{need}\) is less than \(\hat{t}_{need}\), the number of teams required to complete a task \(n_{i}\) would be huge, so a large number of rescue teams should be transferred here. As a result, all the rescue teams would spend a lot of time on the roads, and spare little time on independent search, which leads to high cost of cooperation and low rescue efficiency. When \(t_{need}\) is larger than \(\hat{t}_{need}\), the number of teams required to complete a task \(n_{i}\) would be small, which makes the cooperative  
Figure 8: Robustness analysis of cooperative rescue plan. (**a**) Effect of search radius on rescue efficiency; (**b**) Effect of cooperation scope on rescue efficiency.  
behavior hardly seen between rescue teams. Without enough cooperation, the rescue efficiency lowers significantly, and the result would worsen when \(t_{need}\) gets larger and larger. The relationship between \(t_{need}\) and rescue efficiency is fitted with a quadratic function, as can be seen from Figure 9a, and the R-squared statistic is 0.7552. The optimal value \(\hat{t}_{need}\) can be derived from the fitting function, and \(\hat{t}_{need}\) is 30 min in our given case. The above analysis shows that there exist a trade-off between cooperation and independent search; we always need to find the appropriate \(t_{need}\) to ensure the high rescue efficiency.  
The relationship between maximum turning angle \(s_{a}\) and rescue efficiency is depicted in Figure 9b. When \(s_{a}\) is less than \(\hat{s}_{a}\), the rescue efficiency is low and it improves with the increase of \(s_{a}\). Because \(s_{a}\) is small, the range of search angle would be limited. Thus, a new position is most likely generated at the same direction as in the previous step, and the search trajectory is like a straight line, which makes the search coverage incomplete. When \(s_{a}\) is larger than \(\hat{s}_{a}\), the rescue efficiency lowers with the increase of \(s_{a}\). The large value of \(s_{a}\) would lead to a wide range of search angle, and too wide a range would results in aimlessness. Rescue teams might spend a large amount of time searching the same area, resulting in low efficiency, and the results would worsen when \(s_{a}\) gets larger and larger. The relationship between \(s_{a}\) and rescue efficiency is also fitted with a quadratic function, and the R-squared statistic is 0.8537. The optimal value \(\hat{s}_{a}\) is approximately equal to \(2\pi/3\) in our given case. To summarize, there exists a trade-off between directional moves and search coverage, and we need to balance them and find the appropriate range of the turning angle.