## 4 The Scheduling Algorithm Based on GA
### Carrier Aircraft Landing Recovery Dispatch  
The essence of carrier aircraft landing scheduling optimization problem is to improve the landing speed of carrier aircraft under the premise of ensuring the safety of carrier aircraft landing. Its model can be described as \(I=\{1,2,\ldots,n\}\) aircraft group to be guaranteed, under the premise of meeting various constraints, landing sequentially in order to minimize the objective function of the landing sequence. In Equation (32), \(T^{i}_{m}\) represents the landing completion time of carrier aircraft \(i\) in the \(m\)-th scheduling, and \begin{table}
\begin{tabular}{c c c} \hline
**Symbolic Variable** & **Signified** & **Remark** \\ \hline \(i\in Mc=\{1,2,\ldots,m\}\) & Ejector & \(M_{c}\) is the set of catapult \\ \hline \(j\in N=\{1,2,\ldots,n\}\) & Operating aircraft number & \(N\) is airplane set \\ \hline \(k\in A_{j}\) & Process number & \(A_{j}\) is / process set for aircraft \\ \hline \(M_{k}\in M_{c}\) & Ejector set of process \(k\) & — \\ \hline \(S^{k}_{i,j}(t)\) & Aircraft operation start time & \\ \hline \(\mathcal{C}^{k}_{i,j}(t)\) & End time of aircraft operation & Aircraft / of ejection position \(i\) in process \(k\) \\ \hline \(D^{k}_{i,j}(t)\) & Aircraft operation departure time & \\ \hline \(P^{k}_{i,j}\) & Processing time & The operating time of aircraft / on catapult \(i\) of process \(k\) \\ \hline \(a^{k,i}_{j_{m},j_{m}}\) & \(a^{k,i}_{j_{m},j_{m}}=\left\{\begin{array}{l}1\\ 0\end{array}\right.\) & \(1\) indicates that \(j_{m}\) precedes \(j_{n}\) on catapult \(i\) in operation \(k\); otherwise, it is \(0\) \\ \hline \(b^{k}_{i,j}\) & \(b^{k}_{i,j}=\left\{\begin{array}{l}1\\ 0\end{array}\right.\) & \(1\) indicates that aircraft / operates on catapult \(i\) in operation \(k\); otherwise, it is \(0\) \\ \hline \end{tabular}
\end{table} 
Table 2: Symbolic variable table. \(\max(T_{m}^{i})\) represents the latest landing time among all carrier aircraft landing times, that is, the optimization objective is to minimize the maximum landing completion time. The corresponding constraints are as follows:  
\[Min(max(T_{m}^{i})) \tag{32}\]  
(1) The wake interval time \(\Delta TS_{ij}\) at the landing point is constrained by Equation (33) to avoid flight accidents caused by the exhaust gas discharged by the engine of the forward aircraft being inhaled by the engine of the subsequent carrier aircraft. Where \(\forall i,l\in I,m=0,1,\dots,N\), represents the landing completion time of carrier aircraft \(j\) in the \(m\)-th scheduling, \(T_{i}^{m}\) represents the landing completion time of carrier aircraft \(i\) in the \(m\)-th scheduling, and \(\Delta TS_{ij}\) represents the wake interval time between carrier aircraft \(i\) and \(j\) in the landing. \[T_{j}^{m}\geq\Delta TS_{ij}+T_{i}^{m} \tag{33}\]  
(2) The time constraint of deck clearance is expressed as Equation (34). During this period, the carrier aircraft that successfully landed on the ship slowed down to a stop, and the deck staff removed the blocking cable from the tail of the carrier aircraft, and then checked the landing runway. \[T_{j}^{m}\geq\Delta Tc+T_{i}^{m} \tag{34}\]  
(3) For the carrier aircraft with a return flight, its return flight landing may conflict with the subsequent carrier aircraft landing. In this case, it is necessary to let the returning carrier aircraft adjust its landing time after the return flight to solve the conflict; otherwise, the subsequent carrier aircraft cannot land. \(\left(T_{i}^{m}\right)_{landing}\) represents the landing time of carrier aircraft \(i\) that is currently making a return flight, and \(\Delta Tc\) represents the minimum adjustment time required for carrier aircraft \(i\) to make a return flight. \[T_{j}^{m}\geq\Delta Tc+\left(T_{i}^{m}\right)_{landing} \tag{35}\]  
(4) The landing sequence of carrier aircraft should follow a certain logical sequence. In each scheduling process, it must be ensured that the landing sequence of carrier aircraft conforms to the actual situation. The order constraint should be set as Equation (36).