# A Task Allocation Strategy of the UAV Swarm Based on Multi-Discrete Wolf Pack Algorithm
## 2 Task Assignment Model
### UAV and Task Modeling  
This article models the above actual combat scenarios, which can be expressed as a four-tuple \(<U,T,M,C>\), where \(U\) is the set of UAVs, T is the set of targets in the combat area, and M is the set of tasks on the target. C is the set of constraints in the problem model. Based on the literature [32], this paper further considers the problem of the cooperative task allocation of UAVs in actual combat area scenarios, further considers multiple constraints and optimization objectives, and constructs a cooperative multi-task assignment model for UAVs in combat scenarios. Table 1 shows the attributes of three objects in the model.  
The definition of the UAV system has \(N_{u}\) reconnaissance UAVs. In this paper, for any UAV \(u_{i}(i\in\ [1,N_{u}])\), given its constant flight speed \(v_{i}\), maximum navigation distance \(d_{i}^{max}\) and maximum flight time \(\tau_{i}^{max}\).  
Due to the dynamic update of information in the battlefield environment, the intelligence information of each target point may be updated after reconnaissance. Therefore, each target point \(T_{j}\ (j\in\ [1,N_{l}])\) involved in this article contains at least one reconnaissance mission. Among them, define \(N_{l}\) as the number of targets. \(l_{j}\) is the reconnaissance time required to complete the intelligence collection work at the target point \(T_{j}\).  
On the premise of ensuring the validity of the model, in order to simplify the model and reduce the difficulty of solving the model, this article puts forward the following reasonable assumptions about the model:  
1. The number and approximate location coordinates of all targets are known to the command center of UAV base;  
\begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{2}{c}{**Attributes**} \\ \hline \hline  & The total number of UAVs: \(N_{u}\) \\ UAV \(U\) & Initial position (the base) \(P_{i}=(x_{i},y_{i})\ (i=0)\) \\ (For any UAV \(u_{i}\)) & Flying speed: \(v_{i}\) \\  & The maximum travel distance of UAV: \(d_{i}^{max}\) \\  & The maximum travel time of UAV: \(\tau_{i}^{max}\) \\ \hline \hline Target \(T\) & The number of targets: \(N_{l}\) \\ (For any target \(T_{j}\)) & Position coordinates: \(P_{j}=\left(x_{j},y_{j}\right)\) \\  & Reconnaissance time required for completion of missions: \(l_{j}\) \\ \hline \hline \end{tabular}
\end{table}
Table 1: Object attributes and symbol interpretation.  
2. The UAV flies at a constant speed, and the flying heights of the UAVs are not consistent in order to prevent collisions between the UAVs;
3. The same task can be completed by multiple UAVs, and it is assumed that the UAVs working in coordination reach the target point at the same time, and there is no waiting time for each other.  
Based on the above symbolic interpretation and model assumptions, the scheme of cooperative multi-task allocation for UAVs can be expressed as a vector, as shown in Table 2. The vector has three rows, the first row represents the target sequence, the second row represents the task sequence on the target (mainly multiple intelligence searches, taking two searches as an example), and the third row represents the result of task assignment.  
In Table 2, \(M_{K}\) represents the \(K\)th mission of target \(T_{j}\) and it is assigned to \(u_{i}\), so the third row \(X_{i}^{j}\ (i\in\ [1,N_{u}])\) is 1. For other \(i^{\prime}(i^{\prime}\
eq i,\ i^{\prime}\in\ [1,N_{u}]),\ X_{i^{\prime}}^{j}\) is 0, which means that \(T_{j}\) is not assigned to \(u_{i^{\prime}}\).