# Multi-UAV Mission Allocation under Constraint
## 4 Simulation Results
The main part of the loop  
(1) Randomly initialize the starting population P0. The non-dominated sorting of P0 is performed to initialize the rank value of each individual; (2) t = 0; (3) Select individuals from \(Pt\) through the binary tournament method, and perform crossover and mutation operations to generate a new generation population Qt; (4) Calculate the obj value of the new population; (5) By combining \(Pt\) and \(Qt\), a combined population \(Rt=Pt\cupQt\) is generated; (6) Non-dominated sorting of \(Rt\), and selecting N individuals by crowding out and elite retention strategies to form a new generation population \(Pt+1\); (7) Jump to step 3 and cycle until the end condition is met. The corresponding program flow chart is shown in Figure 7.  
In the case of population size 300 and 500 iterations, NSGA-II takes 32.8 s to obtain reconnaissance reward of 11.7845, and the total flight duration is 72.2369 h. GA takes 16.2 s to obtain reconnaissance  
Figure 7: Non-dominated sorting genetic algorithm with elite strategy (NSGA-II) basic process. reward of 10.8531 and the total flight duration is 78.6358 h. Figure 8 shows convergence trace of GA and NSGA-II and Table 2 shows a comparison of the results obtained by the three methods. It is easy to find that in the final simulation results, each UAV can obtain the reconnaissance reward as much as possible while satisfying various constraints, and the flight path is as short as possible. Table 3 shows the five sets of simulation data for the three methods. The results shown in Figures 3-5 are the optimal allocation results under all constraints, the total flight time is 72.5758 h, and the reconnaissance reward is 12.4338. From the data, we can see that the Lingo and NSGA-II methods are more stable than the GA algorithm, and the decision results obtained are more effective. Compared with the data of Lingo and NSGA-II, it can be seen that Lingo has obvious optimization in reconnaissance reward and optimization time, which is slightly higher than NSGA2-II algorithm in total flight time index. of 72.2369 km to obtain a reconnaissance reward of 11.7845, and GA used a total flight distance of 78.6538 km to obtain a reconnaissance reward of 10.8531. The results show that the new method is much better than the genetic algorithm in terms of speed and results. Compared with the NSGA-II, although the total flight time is slightly increased, the overall reconnaissance income obtained is much higher than that of the NSGA-II, and the simulation time is much less than the NSGA-II. From the aspects of waiting time and the total flight time of each UAV presented in the experimental results, the waiting time appears in those UAVs with less flight time, so that the total flight time of each UAV is relatively balanced. The superiority of the proposed method is achieved by modeling the reasonable constraints on resources and the quality of the overall task. Compared with the previous studies, the proposed model is closer to the actual needs of reconnaissance missions by taking into account the various attributes of different reconnaissance areas, thus, to allocate different reconnaissance time. At the same time, combining time window constraints with the balanced allocation of UAV resources makes the final allocation more balanced and more in line with actual operation needs. Based on reducing the dimensionality of high-dimensional variables, as well as combining with Lingo software, which can interoperate with MATLAB software through excel and txt flies, the proposed method reduces the simulation time. During the simulation, we set the settings that each reconnaissance mission area must reach, and the reconnaissance coverage area must be greater than 60%. However, it should be noted that the models and methods we use are generic. In the absence of this setting and insufficient resources, the final decision result will be assigned to the reconnaissance time of some areas 0 and will not go to the area for reconnaissance.