# Additional Taxi-Out Time Prediction for Flights at Busy Airports by Fusing Flow Control Information
## 3 Prediction of Additional Taxi-Out Time
### Prediction of ATT
#### 3.3.3 Model Construction  
Based on the dataset obtained in Section 3.3.2, we propose the NOA-XGBoost model for ATT prediction. First, we split the input dataset into training and testing sets with the ratio 4:1. Then, we initialize the parameters of XGBoost and NOA on the training set, using the RMSE as the fitness function. We apply the NOA algorithm to iteratively update the foraging and storage strategies, as well as the cache-search and recovery strategies, in order to find the optimal XGBoost hyper parameters. Then, we calculate the fitness value and check if the maximum number of iterations has been reached. If so, we proceed to train the NOA-XGBoost model and use it on the testing set to predict the ATT. Otherwise, we continue with the iterative updates. The process of the ATT prediction model based on NOA-XGBoost is as follows. The NOA algorithm consists of two phases: foraging and storage strategies, and cache-search and recovery strategies, with each phase including  
Figure 8: Construction process of the ATT dataset. global exploration and local exploitation. In the global exploration phase of the foraging and storage strategies, the position update formula is given by Equation (2). \[\overset{\rightarrow}{X}_{i}^{t+1}=\left\{ \begin{array}{ll}X_{i,j}^{t},&if\ \tau_{1}<\tau_{2}\\ \left\{\begin{array}{ll}X_{m,ij}^{t}+\gamma\cdot(X_{A,j}^{t}-X_{B,j}^{t})+ \mu\cdot(r^{2}\cdot U_{j}-L_{j}),&if\ t\leq T_{\max}/2.0\\ X_{C,j}^{t}+\mu\cdot(X_{A,j}^{t}-X_{B,j}^{t})+\mu\cdot(r_{1}<\delta)\cdot(r^{2} \cdot U_{j}-L_{j}),&otherwise\end{array}\right.,&otherwise\end{array} \right. \tag{2}\]  
Here, \(X_{i}^{t+1}\) represents the new position of the \(i\)-th nutracker in the current generation \(t\); \(X_{i,j}^{t}\) represents the \(j\)-th position of the \(i\)-th nutracker in the current generation; \(U_{j}\) and \(L_{j}\) are vectors that include the upper and lower bound of the \(j\)-th dimension in the optimization problem; \(\gamma\) is a random number generated based on the levy flight; \(X_{best,j}^{t}\) is the currently obtained optimal solution in the \(j\)-th dimension; A, B, and C are three different indicators randomly selected from the population to facilitate the exploration of high-quality food sources; \(\tau_{1},\tau_{2},\ r\) and \(r_{1}\) are random real numbers in the range of [0, 1]; \(X_{m,j}^{t}\) is the mean of all solutions in the \(j\)-th dimension in the current population at the \(t\) iteration; and \(\mu\) is generated based on the normal distribution (\(\tau_{4}\)), levy flight (\(\tau_{5}\)), and randomly between zero and one (\(\tau_{3}\)), as shown in Equation (3), where \(r_{2}\) and \(r_{3}\) are random real numbers in the range of [0, 1]. \[\mu= \begin{cases}\tau_{3},\,if\ r_{1}<r_{2}\\ \tau_{4},\,if\ r_{2}<r_{3}\\ \tau_{5},\,if\ r_{1}<r_{3}\end{cases}  \tag{3}\]  
In the local exploitation phase of the foraging and storage strategies, the position update formula is given by Equation (4). \[\overset{\rightarrow}{X}_{i}^{t+1(new)}=\left\{ \begin{array}{ll}\overset{ \rightarrow}{X}_{i}^{t}+\mu\cdot(X_{best}^{t}-\overset{\rightarrow}{X}_{i} ^{t})\cdot|\lambda|+r_{1}\cdot(\overset{\rightarrow}{X}_{A}^{t}-\overset{ \rightarrow}{X}_{B}^{t}),&if\ \tau_{1}<\tau_{2}\\ \overset{\rightarrow}{X}_{best}^{t}+\mu\cdot(\overset{\rightarrow}{X}_{A} -\overset{\rightarrow}{X}_{B}),&if\ \tau_{1}<\tau_{3}\\ \overset{\rightarrow}{X}_{best}^{t}\cdot l,&otherwise\end{array} \right. \tag{4}\]  
Here, \(\lambda\) is a number generated based on levy flight, \(\tau_{3}\) is a random number between 0 and 1, and \(l\) is a factor that linearly decreases from 1 to 0 in NOA exploitation behavior. In the global exploration phase of the cache-search and recovery strategies, the position update formulas are given by Equations (5)-(7). \[X_{i,j}^{t+1}=\left\{ \begin{array}{ll}X_{i,j}^{t},&if\ \tau_{3}<\tau_{4}\\ X_{i,j}^{t}+r_{1}\cdot(X_{best,j}^{t}-X_{i,j}^{t})+r_{2}\cdot(\overset{ \rightarrow}{R}_{i,1}^{t}-X_{C,j}^{t}),&otherwise\end{array} \right. \tag{5}\]  
\[X_{i}^{t+1}=\left\{