# Multi-UAV Mission Allocation under Constraint
## 1 Introduction  
Unmanned aerial vehicle (UAV) mission allocation means to allocate and aggregate the available UAV resources depending on the mission requirements and the resource status [1, 2]. Obviously, some missions are more pivotal than others in the reconnaissance process for military operation, therefore, priorities are usually assigned to the locations [3, 4]. The mathematical modeling and optimizing for multi-UAV mission allocation is a key issue in the study of UAV issues [5, 6, 7, 8]. [PERSON] et al. described a mathematical model with tightly coupled missions and rigid relative timing constraints and achieved good simulation results of the model with a tabu search algorithm [9]. [PERSON] et al. proposed a mathematical model with time window constraints and used a multi-objective genetic algorithm (CR-MOGA) to solve this problem [10, 11]. [PERSON] and [PERSON] presented an improved tree search algorithm for the UAV mission planning problem and completed the overall simulation experiment [12]. [PERSON] et al. considered this problem with sequential resource allocation and proposed an information gain in the mathematical model [13]. [PERSON] et al. proposedan improved genetic algorithm for the UAV mission planning problem with limited resources, and the simulation results were analyzed and verified [14]. [PERSON] et al. presented a maximum coverage stochastic orienteering problem with time windows (MCS-OPTW) planning approach for mission planning and showed the simulation data [15]. [PERSON] et al. proposed a new reconnaissance mission planning model and used a genetic algorithm with the UAVs' task sequence to solve the model [16]. The existing reconnaissance mission models used the shortest path as the objective function and only considered a single task sequence assignment without considering the reconnaissance time allocation of the UAV. In reality, the allocation of reconnaissance time is often the decisive factor in determining the success of the reconnaissance mission and the core indicator that the commander is concerned about. The new model proposed in this paper considers the reconnaissance reward maximization as the objective function. By considering the allocation of each UAV's reconnaissance time resource, the reconnaissance time allocation and task sequence allocation are considered simultaneously. The UAV mission planning problem is the extended multiple Dubins traveling salesmen problem (MDTSP), which is a typical NP-hard combinatorial optimization problem. Some studies translated related models into a mixed integer linear programming (MILP) and achieved good results [17; 18; 19]. The time window was first applied to the vehicle routing problem (VRP) problem model. [PERSON] and [PERSON] systematically introduced the VRP with time window and presented an exact optimization algorithm for the orienteering problem with time windows [20]. Then [PERSON] et al. [21] and [PERSON] et al. [22] improved the VRP problem with time windows and completed simulation verification. The existing time window problem model only required the time window problem condition without considering the equilibrium problem. In the actual result, it is clear that certain UAVs perform more tasks, while the other UAVs perform fewer tasks. When a UAV flies back to the base, another UAV may only perform half of the total mission. In this paper, by considering the time window factor, each UAV's resource is reasonably and evenly distributed. Thus, the time window model is more in line with actual military requirements. Lingo software was developed by Professor [PERSON] in 1980s, and it can independently solve problems, such as linear programming problems, nonlinear programming problems, and mixed integer programming problems [23]. Many existing studies have proven the advantages and effectiveness of Lingo software in solving these problem models in different fields.