## 5 Case Study and Algorithm Validation
### Effects of Individual Dimensions
By using the proposed BSO, the global best can be found only within 30 iterations, as well as the shortest path lengths. Even with the lowest individual dimension of 15, the proposed BSO method is still 28.10%, 61.79%, 58.95%, and 42.72% better than PSO, GA, FA, and BAS in the UAV path length, respectively. The overall cost of the generated paths by the five algorithms is provided in Figure 16. From all the curves, we can see that our proposed BSO method works well under all the individual dimension settings with the minimum path cost. Also, the optimal waypoints can be found as soon as possible once it starts running. Particularly when the individual dimension is set as 20, only 30 iterations are needed to locate the global best solutions. It is smooth enough that there are no big fluctuations in the cost curves in all the circumstances. Figure 14: Effects of individual dimensions on turning angles. From Figure 16, we can see that PSO works as stably as the proposed BSO method. However, the path cost it generates is more than that of the proposed method, which is much better than the other three with the lower cost and the quicker convergence. Standard BAS would go through a lot of ups and downs in the first few iterations to find the correct optimization fields. However, when the dimensions of the beetle get higher, such as 25 and 30, the ups and downs would be fewer and fewer. Even though the final cost is a little more than that of PSO, 11.52% and 28.51%, respectively, with the dimensions of 25 and 30. GA and FA are the worst of all. For FA, it falls into the local optimum so easily that the cost of the UAV path will not change after the iteration starts. However, there is so much randomness during the optimization of GA. In this way, ups and downs would exist in the whole optimization process. GA cannot find optimum solutions, which is not suitable to solve continuity problems like this. When the individual dimension is set as 30, the proposed BSO method is 31.00%, 75.86%, 77.87%, and 46.31% better than PSO, GA, FA, and standard BAS in the normalized path cost. The generated UAV paths are provided in Figure 17. From this figure, it can be seen that all the listed five algorithms could generate the paths for the UAVs, but with quite different smoothness and fluctuations. It is desirable to keep the paths as smooth as possible so that the UAVs can easily follow them. In this way, it is obvious that the path provided by the proposed BSO method is the smoothest under all the conditions with the fewest turns on the paths. Especially when the individual dimension is 20, the given path is nearly a straight line that connects the starting point \(S\) and destination point \(D\) directly. Figure 15: Effects of individual dimensions on path length. As Figure 17 shows, we can see that the higher individual dimensions would generate very negative effects, which correspondingly bring more turns. PSO could find an optimal flying path for the UAVs under all the settings. But there are more turns on the path compared with the proposed BSO method. Especially when the dimension is 30, the path of PSO is the most fluctuant compared with others. All the UAVs have to turn all the time to achieve a lower path cost. Standard BAS is in the middle position, which is better than GA and FA but worse than the proposed BSO method and PSO. The corresponding amplitudes of the variations are much better than GA and FA. Obviously, FA is the worst, which jumps all the time from the beginning to the end, trying to make the path cost the global optimum. Combined with the previous results, this is caused by the local optimum problem. No more better waypoints can be provided. GA presents similar characteristics to FA, but the amplitude of the fluctuation is a little smaller because GA is always trying to locate an optimum solution, even though it fails in the end. Oppositely, the quality of GA's solution is higher than that of FA's. In this way, the path given by GA is much smoother than FA.