# Deployment Optimization of Defense Stations in an Attack-Defense Aerial War Game
## 3 Simulation Results and Statistical Analysis
Figure 8b shows the optimal deployment plan of defense stations based on defense cost \(\zeta_{2}\). It is observed that five defense stations are placed near the major post, with three of them within 40 km of the latter. Since the weighting on major post is highlighted, more stations are placed around it than on \(\zeta_{1}\). In addition, three defense stations are placed near the south post, with one within 40 km of the latter, two defense stations are placed west to guard the north post, but none of them are within 40 km of the north post. Compared to the deployment plan on \(\zeta_{1}\), the defense stations are clustered into several swarms or pairs, and the protection on minor posts becomes weaker since fewer defense stations are placed near them, due to the reduced weighting on minor posts. Figure 8c shows the optimal deployment plan of defense stations based on defense cost \(\zeta_{3}\). It is observed that most defense stations are placed near the major post, with five defense stations within 40 km of the latter. Two defense stations are placed far west to the south post to guard it, and one more defense station is placed close to the south post for reinforcement. However, no defense station is placed near the north post, and the nearest defense station is 103 km away. More defense stations are placed near the major post than near the south post although they have the same weighting because more attackers aim for the major post, which is closer to the attack stations than the south post. Figure 8d shows the optimal deployment plan of defense stations based on defense cost \(\zeta_{4}\). It is observed that four defense stations are placed near the major post, with three defense stations within 40 km of the latter. Two defense stations are placed close to each other and west to the north post, and one more defense station is placed close to the  
Figure 8: Optimal deployment of defense stations against slant formation, based on (a) \(\zeta_{1}\); (b) \(\zeta_{2}\); (c) \(\zeta_{3}\); (d) \(\zeta_{4}\), square with cross: major post, square with slash: minor post, blue square: defense station. Figure 7: Convergence of defense cost against pincer formation, black: \(\zeta_{1}\), orange: \(\zeta_{2}\), green: \(\zeta_{3}\), purple: \(\zeta_{4}\). north post for reinforcement. Two defense stations are placed near the south post, with one within 40 km of the latter. In general, the defense stations are clustered near each protected post. Figure 9a shows the optimal deployment plan of defense stations against pincer attack formation, based on defense cost \(\zeta_{1}\). It is observed that four defense stations are placed near the major post, with three of them within 40 km, to the east, southeast and south, respectively, of the major post. There are two defense stations near the north and the south posts, respectively, and each minor post has one defense station within 40 km. Since the major post has the highest weighting and is targeted by many more attackers, more defense stations are placed around it. Figure 9b shows the optimal deployment plan of defense stations based on defense cost \(\zeta_{2}\). Compare to that on \(\zeta_{1}\), more defense stations are placed near the major post because its relative weighting is highlighted. There are six defense stations near the major post, and five of them are within 40 km of the latter. One defense station is placed within 40 km to the north post, one defense station is placed near the south post, but is farther than 40 km away, and two defense stations are placed between the major post and the north post to cover both. Figure 9c shows the optimal deployment plan of defense stations based on defense cost \(\zeta_{3}\). There are five defense stations within 40 km of the major post. The south post has one defense station within 40 km, but the north post has no defense station within 40 km. Although the weightings on major and minor posts are the same, more defense stations are placed around the major post because many more attackers target on it.