# Distributed Task Allocation for Multiple UAVs Based on Swarm Benefit Optimization
## 4 Experiment  
To validate the effectiveness of the proposed benefit variation (BV) method, this study selected the most representative CBBA and PI methods for comparison and conducted a series of experiments. The experiment adopted the settings from previous PI research [39; 41; 42], with an extension that incorporates the initial task value and the decay rate of task value over time, which were not considered in the original framework. The specific parameter settings are presented in Table 1.  
The experimental design is of universal applicability, utilizing a scenario of UAV swarm logistics delivery as the verification environment, which is set in a three-dimensional space with a horizontal range of 10 km \(\times\) 10 km and a height of 1 km. The communication radius (com-radius) of the UAVs is set at 15 km, forming a fully connected network topology in this scenario, which enables seamless information exchange between any pair of UAVs. The endurance of each UAV is 1 h, allowing for a maximum of five tasks to be executed within this scenario. The UAV swarm consists of two types of UAVs: one specialized in delivering fresh goods at a speed of 50 m/s, and the other responsible for delivering regular goods at a speed of 30 m/s. Both types of UAVs initially park at delivery points, which are \begin{table}
\begin{tabular}{c c c} \hline \hline
**Objects** & **Properties** & **Descriptions** \\ \hline \multirow{4}{*}{UAV} & location & randomly distributed in 10 km \(\times\) 10 km \(\times\) 0 km area \\ \cline{2-3}  & com-radius & 15 km (mesh topology) \\ \cline{2-3}  & endurance & 1 h (the maximum number of tasks \(L_{i}=5\)) \\ \cline{2-3}  & speed & delivering fresh goods: 50 m/s \\ \cline{2-3}  & & delivering regular goods: 30 m/s \\ \hline \multirow{4}{*}{Task} & location & randomly distributed in 10 km \(\times\) 10 km \(\times\) 1 km area \\ \cline{2-3}  & deadline & randomly distributed in the range of [0, 2000 s] \\ \cline{2-3}  & initial value & randomly distributed in the range of [100, 200] \\ \cline{2-3}  & decay rate & randomly distributed in the range of [0.9999, 1) \\ \cline{2-3}  & duration & delivering fresh goods: 350 s \\ \cline{2-3}  & & delivering regular goods: 300 s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The setting of simulation. randomly distributed within a 10 km \(\times\) 10 km ground area. The delivery duration for fresh goods is set at 350 s, while that for regular goods is 300 s. The latest executable time for both types of goods is randomly distributed within the time window of [0, 2000] seconds, and their initial value is randomly determined within the range of [100, 200]. Additionally, the rate \(\zeta_{j}\) at which the value of goods declines over time is randomly selected within the range of [0.9999, 1), simulating the dynamic change in goods value. The experiments are conducted under varying numbers of UAVs (\(N_{u}\)) and ratios of tasks to UAVs (\(p=N_{t}/N_{u}\)) to ensure comprehensive and robust results. The number of UAVs \(N_{u}\) is varied from 6 to 16 with a step size of 2, while the task-to-UAV ratio \(p\), was adjusted from 3 to 5 with a step size of 1. For each specific set of \(N_{p}\) and \(N_{u}\) values, 1000 Monte Carlo simulations are performed to ensure data stability and reliability. Figures 2-4 intuitively illustrates typical examples of task plans generated under three different methods, with a scenario of 6 UAVs and 18 tasks. In the figure, the center points of the circles represent the locations of the tasks, the sizes of the circles indicate the initial values of the tasks, and the colors of the circles indicate the types of the tasks. It can be observed that, in comparison to the task plans generated by the CBBA method (illustrated in Figure 2) and the PI method (illustrated in Figure 3), the task plan generated by the proposed BV method (depicted in Figure 4) exhibits real-time updates of task values, specifically targeting tasks with high values and rapid decay rates.