# A Forecast Model of the Number of Containers for Containers by Voyage
## 4 Example Analysis
### Prediction of Number of Allocated Containers for One Voyage Using Mixed Kernel SVM  
Weighted factors could be derived by multiplying the influencing factors by the corresponding weights:  
\[\overline{X}_{i}=w_{i}X_{i},\;\;i=1,2,\cdots,9 \tag{14}\]  
where \(\overline{X}_{i}\) is the weighted factor influencing the number of allocated containers for one voyage. When \(\overline{X}_{i}\) in the composition vector \(Q=\left[\overline{X}_{1},\overline{X}_{2},\cdots,\overline{X}_{9}\right]^{T}\) was considered the input variable and \(X_{0}\) was considered the corresponding output variable, a mixed kernel SVM for predicting the number of allocated containers for one voyage was constructed.  
All data were normalized to the interval \([0,1]\). The data presented in Table 1 served as training samples, whereas those presented in Table 4 served as test samples.  
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline
**No.** & \(X_{1}\) & \(X_{2}\) & \(X_{3}\) & \(X_{4}\) & \(X_{5}\) & \(X_{6}\) & \(X_{7}\) & \(X_{8}\) & \(X_{9}\) & \(X_{0}\) \\ \hline
1 & 4365 & 76 & 1596 & 24 & 13 & 18 & 43 & 5400 & 72 & 1250 \\
2 & 23,560 & 69 & 882 & 87 & 29 & 12 & 185 & 1900 & 83 & 900 \\
3 & 9841 & 81 & 2143 & 112 & 12 & 17 & 251 & 4580 & 70 & 750 \\
4 & 25,590 & 74 & 4265 & 159 & 50 & 14 & 211 & 3390 & 66 & 500 \\
5 & 18,763 & 62 & 1983 & 73 & 41 & 21 & 163 & 1080 & 74 & 310 \\ \hline \end{tabular}
\end{table}
Table 4: Test samples.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Factors** & **Relevance** & **Factors** & **Relevance** & **Factors** & **Relevance** \\ \hline \(X_{1}\) & 0.1669 & \(X_{4}\) & 0.1773 & \(X_{7}\) & 0.1770 \\ \(X_{2}\) & 0.6672 & \(X_{5}\) & 0.3998 & \(X_{8}\) & 0.8345 \\ \(X_{3}\) & 0.7084 & \(X_{6}\) & 0.6206 & \(X_{9}\) & 0.6232 \\ \hline \end{tabular}
\end{table}
Table 2: Correlation between each influencing factor and study object.  
\begin{table}
\begin{tabular}{c c c c c c} \hline
**Factors** & **Weight** & **Factors** & **Weight** & **Factors** & **Weight** \\ \hline \(X_{1}\) & 0.038 & \(X_{4}\) & 0.041 & \(X_{7}\) & 0.040 \\ \(X_{2}\) & 0.153 & \(X_{5}\) & 0.091 & \(X_{8}\) & 0.191 \\ \(X_{3}\) & 0.162 & \(X_{6}\) & 0.142 & \(X_{9}\) & 0.142 \\ \hline \end{tabular}
\end{table}
Table 3: Weight of each influencing factor.  
The GA control parameters were as follows: \(\varepsilon\), \(C\), \(q\), \(\sigma\), \(\rho\) were binary coded, with the optimal ranges being set to \(\varepsilon\in\left[10^{-10},10^{-1}\right]\), \(C\in\left[0,50\right]\), \(q\in\left[0,20\right]\), \(\sigma\in\left[0,500\right]\), and \(\rho\in\left[0,1\right]\), respectively. The series size was 50, maximum evolution algebra was 50 generations, crossover probability was 0.7, mutation probability was 0.01, and the judgment termination accuracy was \(10^{-4}\).  
This study applied MSE, mean absolute percentage error (\(e_{\text{MAPE}}\)), and correlation coefficients (\(R\)) to evaluate the predictive performance of the model. \(R\) was set to the interval \(\left[0,1\right]\). Lower MSE and \(e_{\text{{MRE}}}\) values and \(R\) values approaching 1 were considered to indicate higher model predictive performance.  
\[\text{MSE}=\frac{1}{l}\sum\limits_{i=1}^{l}(\overline{y}_{i}-y_{i})^{2}\]  
\[e_{\text{MAPE}}=\frac{1}{l}\sum\limits_{i=1}^{l}\left|\frac{\overline{y}_{i}-y _{i}}{y_{i}}\right|\cdot 100\%\]  
\[R=\sqrt{\frac{\left(l\sum\limits_{i=1}^{l}\frac{\overline{y}_{i}y_{i}-\sum \limits_{i=1}^{l}y_{i}\frac{l}{\sum\limits_{i=1}^{l}y_{i}}\right)^{2}}}{\left( l\sum\limits_{i=1}^{l}\overline{y}_{i}^{2}-\left(\sum\limits_{i=1}^{l} \overline{y}_{i}\right)^{2}\right)\left(l\sum\limits_{i=1}^{l}y_{i}^{2}-\left( \sum\limits_{i=1}^{l}y_{i}\right)^{2}\right)}} \tag{15}\]  
where \(l\) is the number of samples, \(y_{i}(i=1,2,\cdots l)\) is the real value of the \(i\)th sample, and \(\overline{y}_{i}(i=1,2,\cdots l)\) is the predicted value of the \(i\)th sample.