# Mdpj _sciences_
## 4 Experiments and Results
### Simulation Experiments  
The above experiments show the statistical results of agent training, and the following experiments show the simulation results of agent training. Figure 5 shows the air combat simulation results of the final agent against the first, eighth, 16 th, 24 th and 32 nd agents starting from the equal initial situation. The initial position of the final agent is (0, 0, 10,000), the initial yaw angle is 0\({}^{\circ}\), and the initial pitch angle is 0\({}^{\circ}\). The initial positions of other agents are (70,000, 70,000, and 10,000), the initial yaw angle is 180\({}^{\circ}\), and the initial pitch angle is 0\({}^{\circ}\). Figure 5a,c,e,g,i are three-dimensional trajectories of the final agent against the first, eighth, 16 th, 24 th and 32 nd agents, respectively. Figure 5b,d,f,h,j are top views corresponding to the three-dimensional trajectories. In Figure 5, the solid line represents the trajectory of the aircraft, the dotted line represents the trajectory of the corresponding missile, and the two dots represent the initial positions of both sides of air combat.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **GAE** & **DSR** & **FRE-U** & **FRE-S** & **FRE** \\ \hline maximum wins & 32 & 14 & 32 & 28 & 55 \\ average wins & 9.20 & 3.75 & 12.45 & 10.68 & 26.22 \\ average loses & 7.96 & 4.37 & 8.96 & 9.03 & 18.08 \\ average draws & 90.84 & 99.88 & 86.59 & 88.29 & 63.70 \\ average time of each decision-making & 0.001 s & 0.001 s & 0.001 s & 0.001 s & 0.001 s \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistical results of evaluations.  
Figure 5: Comparison of Training Results of Different Iterations. (**a**) The 3D trajectory of the first agent. (**b**) Top view of the trajectory of the first agent. (**c**) The 3D trajectory of the eighth agent. (**d**) Top view of the trajectory of the eighth agent. (**e**) The 3D trajectory of the 16 th agent. (**f**) Top view of the trajectory of 16 th agent. (**g**) The 3D trajectory of the 24 th agent. (**h**) Top view of the trajectory of the 24 th agent. (**i**) The 3D trajectory of the 32 nd agent. (**j**) Top view of the trajectory of the 32 nd agent.  
As can be seen from Figure 5a,b, because the first agent has not been trained, it maneuvers randomly, and it can be considered that the first agent cannot make effective maneuver decision-making. It can be seen from Figure 5a that the flight altitude of the first agent gradually rises with random maneuvers, and the final agent also gradually rises in order to defeat it. From the top view of the flight trajectory of the final agent, it can be seen that the final agent flies in the direction of the first agent and launches a missile, and the first agent is hit by the missile of the final agent at last, which indicates that the agent acquired how to attack its target after training of the proposed method.  
As can be seen from Figure 5c,d, after launching its missile, the eighth agent soon loses its target, so it flies away from the final agent to avoid the missile of the final agent. At this time, the final agent does not lose its target by means of its maneuver decision-making. Finally, the eighth agent is hit by the missile of the final agent, and the simulation ends. According to the above analysis, the eighth agent does not acquire effective attack policies, but it acquires some evasive policies to get rid of missile tracking, although these policies are not effective enough.