## 5 Case Study and Algorithm Validation
### Effects of Individual Dimensions  
In this subsection, the effects of the different individual dimensions in a swarm are explored and presented, which are set as 15, 20, 25, and 30. The swarm size and the number of iterations are set as 20 and 100, respectively. Figure 13 illustrates how the path risk can be affected by the individual dimensions. There is no doubt that the proposed BSO method could generate a path with the lowest risk, no matter what the individual dimensions are. Also, the rate and efficiency of convergence are the best of the five. The global optimum waypoints are found within 50 iterations. PSO can provide a sub-optimum solution compared with the proposed BSO method, which produces a higher path risk on the ground. The convergence rate and efficiency of PSO are both worse than those of the proposed BSO method. There are more fluctuations on the ground risk curves given by standard BAS, especially in the first few iterations. But it will be improved as the higher individual dimensions are set. The ground risk of a UAV path produced by standard BAS is higher than that produced by PSO. But when the individual  
Figure 12: Effects of swarm sizes on generated path. dimension is 15, the path risk of standard BAS is a little lower than that of PSO in the 100 th iteration. GA and FA are the worst of all under all the conditions. It is difficult for GA to locate the optimum solutions. FA falls into the local optimum and cannot get out in the whole optimization process. Based on the data in Figure 13, the path risk of the proposed BSO method is 39.72%, 64.90%, 61.58%, and 39.04% lower than that of PSO, GA, FA, and standard BAS with the individual dimensions of 15, which proves the proposed BSO method is quite suitable for the limited individual dimensions. It is obvious that when the dimensions are set as 15, 25, and 30, the turning angles of the proposed BSO method are the best. However, PSO is a little better than BSO under the condition of the individual dimension of 20 after the 72 nd iteration. Combined with the results provided in Figure 9, the turning angles are used to offset the path risk to guarantee the safety of the people on the ground, which is satisfied with the optimization objectives. PSO is worse than the proposed BSO method but better than the other three, with much fewer turning angles. The individual dimension generates a great number of effects on standard BAS. The high dimensions would make it more efficient and converge quickly. From the figure, we can see that both GA and FA fail to find the global best waypoints. GA fluctuates acutely from the beginning to the end, with a lot of turnings on the generated path. FA falls into the local optimum in the first iteration. The biggest improvements of the proposed BSO method are 39.72%, 69.40%, 72.04%, and 50.20% better compared with PSO, GA, FA, and standard BAS with an individual dimension of 30. Figure 13: Effects of individual dimensions on path risk. Figure 14 shows the sum of the turning angles on the generated UAV paths with the different individual dimension settings. The path lengths of the five different algorithms are provided in Figure 15. GA and FA are the worst of all. GA fluctuates frequently to try to find the best solutions all the time. But it cannot even get closer to the best positions in the search space. In this way, the global best cannot be found but with a lot of fluctuations in the search process. FA falls into the local optimum at the beginning and would not change at all. The path lengths of the two are the longest In the last Iteration. Standard BAS, PSO, and the proposed BSO method present the same downward trends. However, standard BAS will jump a lot in the first few iterations because only one beetle exists to locate the optimum solutions, which makes it inefficient and impossible. PSO can calculate the positions of the best waypoints with higher efficiency and quicker convergence. But it is worse than the proposed BSO method.