# A Hierarchical Mission Planning Method for Simultaneous Arrival of Multi-UAV Coalition
## 5 Simulation Results
### Comparison of Three Task Allocation Algorithms  
The performance of the proposed task allocation algorithm was demonstrated in comparison with a PSO task allocation algorithm and a modified resource welfare-based [18] task allocation algorithm via Monte Carlo simulation. The system utility and mission computation time using different task allocation algorithms were compared.  
For a comparative study, the resource welfare-based task allocation algorithm was modified to adapt to the problem in this paper. For a target to be assigned, the UAVs consumed resources in a balanced way, the coalition with the highest resource welfare was selected to attack the target simultaneously. Algorithm 1 was also used in the modified resource welfare-based task allocation algorithm, the Line 9 and 11 of algorithm 1 were replaced by the resource welfare method.  
For the PSO-based task allocation algorithm, assuming there were \(N\) UAVs and \(M\) targets in the environment. The \(l^{th}\) particle at the \(k^{th}\) iteration in PSO task allocation algorithm is represented as:  
\[X_{l}^{k}=(x_{11}^{Jk},\ldots,x_{1M}^{Jk},x_{21}^{Jk},\ldots,x_{2M}^{Jk}, \ldots,x_{N1}^{Jk},x_{N2}^{Jk}\ldots,x_{NM}^{Jk}) \tag{32}\]  
where \(x_{ij}^{Jk}\in\{0,1,\ldots,M\}\) denotes that the UAV \(U_{i}\) will attack target \(x_{ij}^{Jk}\) in \(j^{th}\) sequence. The dimension of each particle is \(N\times M\). Each particle represents a solution to the task allocation problem. The fitness of each particle can be calculated using Equation (6). If the task allocation solution represented by a  
Figure 6: Comparison of the two path estimation methods. (**a**) Average mission completion time; (**b**) average system utility.  
particle violates the task allocation constraints in Equations (8)-(13), the fitness of this particle is set to \(-100\).  
To compare the performance of the three task allocation algorithms, a set of simulation with different number of targets were designed. The parameter setting of these simulations is the same with the Monte Carlo simulation shown in Section 5.1. The PH curve was used in the path estimation process for all these task allocation algorithms. All these simulations used the proposed path planning method. The comparison results of the average mission completion time and system utility are shown in Figure 7. It should be noted that, as the dimension of the PSO-based algorithm was too large, we only recorded the feasible solutions obtained within 24 h of the PSO-based task allocation algorithm.  
Figure 7a shows the comparison of the average mission completion time of these task allocation (TA) algorithms. Obviously, with the increase in the number of targets, the average mission completion time increased. When the number of targets was 10, the PSO-based task allocation algorithm could obtain the shortest mission completion time. However, the mission completion time using the PSO-based TA algorithm significantly increased with the number of targets. That was because when using the PSO-based TA algorithm, the dimension of particle was too high and increased with the number of targets, it was difficult for the PSO algorithm to obtain the optimal solution in a short time. From Figure 7a, the proposed TA algorithm performed better than the PSO-based and resource welfare-based TA algorithms.  
Figure 7b presents the average system utility obtained by these TA algorithms. When the number of targets was 10, the PSO-based TA algorithm could obtain a higher system utility than the other two TA algorithms. However, with the increasing number of targets, the proposed algorithm outperformed the PSO-based TA algorithm as well as the resource welfare-based TA algorithm. That was because the PSO-based TA algorithm could not obtain the optimal solution when the dimension of the particle was high. This also led to a slight decline in the system utility when the number of targets increased further (the number of targets was 30) using the PSO-based TA algorithm.