# Deployment Optimization of Defense Stations in an Attack-Defense Aerial War Game
## 4 Inspection of Some Interesting Outlier Cases  
Given an attack formation and a type of defense cost function, the PSO algorithm is applied to acquire an optimal deployment plan of defense stations, which is used to play multiple games for statistical analysis. The imperfect kill probability of interceptors brings in uncertainty, and sometimes delivers unexpected results in terms of asset loss. In this section, four interesting outlier cases are inspected to learn more details about the game operations. Case 1: On \(\zeta_{4}\) against Slant Formation, Low Score on South Post, and More Defense Stations Lost  
In this case, an optimal deployment plan based on \(\zeta_{4}\) inflicts an unexpected low score on the south post but loses more defense stations than expected. By inspecting the game scenario, we find two defense stations near the south post attracting to themselves some attackers originally aiming for the south post, with each being pursued by more than two interceptors. Figure 12 shows some sequential footages in part of the deployment area to demonstrate the progress. The focus will be on the attackers originally assigned to the south post and the interceptors that pursue those attackers. In the beginning, five attackers are assigned to strike the south post. One of the attackers is marked by two interceptors at an early stage and detours to strike the nearest defense station. Figure 12a shows that at \(t=860\) s, attackers A1, A2, A3, and A4 fly to the south post and are marked by interceptors B1, B2, B3, and B4, respectively. As A2, A3, and A4 manage to evade head-on hit, B2, B3, and B4 turn to tailgate A2, A3, and A4, respectively. Figure 11: CDF of (**a**) impact score on major post; (**b**) impact score on south post; (**c**) impact score on north post; (**d**) number of lost defense stations; (**e**) number of launched interceptors; (**f**) number of lost attackers, against pincer attack formation, black: \(\zeta_{1}\), orange: \(\zeta_{2}\)-green: \(\zeta_{3}\), purple: \(\zeta_{4}\). Figure 12: Scenario in case 1 on \(\zeta_{4}\), against slant formation, (**a**) \(t=860\) s; (**b**) \(t=880\) s; (**c**) \(t=900\) s; (**d**) \(t=920\) s; (**e**) \(t=940\) s; (**f**) \(t=980\) s; (**g**) \(t=1000\) s; (**h**) \(t=1020\) s; (**i**) \(t=1080\) s (**j**) \(t=1240\) s; (**e**): attacker, \(\bullet\): interceptor, square with cross: major post, square with slash: minor post, —: planned attacker path, —: anticipated attacker path, —: anticipated interceptor path, \(\times\): anticipated intercept point. Figure 12b shows that, at \(t=880\) s, the nearest defense station S1 fires an interceptor B5 for A4 when the latter flies within 50 km of S1 and is marked by only one interceptor. Meanwhile, [PERSON] finds itself marked by [PERSON] and begins to turn its moving direction. Figure 12c shows that at, \(t=900\) s, [PERSON] finds itself marked by B5 and begins to turn its moving direction. Meanwhile, [PERSON] loses the intercept point to [PERSON] and turns to tailgate the latter. Figure 12d shows that, at \(t=920\) s, [PERSON] resumes its target after shaking off its chaser. Shortly after, interceptors B4 and B5 regain their intercept points, respectively, with [PERSON]. Figure 12e shows that, at \(t=940\) s, [PERSON] finds itself marked by two interceptors and changes its course to attack defense station S2, then [PERSON] and B5 turn to tailgate [PERSON]. The scenario looks as if S2 attracts the assault of [PERSON]. Figure 12f shows that, at \(t=980\) s, [PERSON] makes turn to evade [PERSON], then the latter changes its course to tailgate the former. Meanwhile, [PERSON] hits S2 successfully, hence [PERSON] and B5 are released to intercept the nearest attacker [PERSON]. Figure 12g shows that, at \(t=1000\) s, [PERSON] burns out of fuel, [PERSON] is hit by B5, hence [PERSON] and B6 are released to intercept the nearest attacker [PERSON]. Figure 12h shows that, at \(t=1020\) s, [PERSON] finds itself marked by more than one interceptor and detours to attack S1, as if S1 attracts the assault of [PERSON].