## 4 Results and Discussion
### Intra-Method Comparison  
Figure 9 presents the MAPEs and RMSEs of MLPs with different hidden sizes. It can be seen that 80% (16/20) of the container throughput time series can find lower MAPE and RMSE by increasing the hidden layer size of MLP, which are Antwerp, Busan, Dalian, Dubai, Guangzhou, Hong Kong, Kaohsiung, Kelang, Long Beach, Los Angeles, Ningbo, Rotterdam, Shanghai, Shenzhen, Tanjung, and Xiamen. In addition, many time series find the minimum error when the number of MLP layers is small, such as Antwerp, Kelang, Long Beach, Tanjung, etc. This observation indicates that increasing the size of the hidden layer is useful for finding models with higher forecasting accuracy when using MLP to build forecasting models. The number of MLP layers corresponding to the optimal result may not be too large. Figure 10 presents the MAPEs and RMSEs of GRUs with different hidden sizes. One obvious experimental result is that MAPE and RMSE values of all ports decrease with the increase of hidden layer size, which means that the GRU forecasting accuracy of all ports becomes more accurate with the increase of hidden layer size. However, the growth rate of forecasting accuracy decreases rapidly at a certain stage (hidden layer size \(\approx 100\)). This observation suggests that when using GRU to build the forecasting model, 100 can be selected as the initial hidden layer size considering the forecasting accuracy, computational complexity, and other factors, and then the hidden layer size can be modified to find the most appropriate hidden layer size. Figure 9: MAPE and RMSE of MLP with different hidden size. The MAPEs and RMSEs of LSTMs with different hidden sizes are presented in Figure 11. It can be seen that the values of MAPE and RMSE increase as the hidden layer size increases, which means that the LSTM forecasting accuracy of all ports becomes worse with the increase of hidden layer size. The possible reason for this situation is that LSTM model is good at analysing time series with a long time span and a large number of observations. For container throughput data, the LSTM model with a small time span and limited number of observations cannot accurately obtain the rules in container throughput, and it is easy to produce under-fitting results, which leads to lower accuracy with the increase of LSTM hidden layer size. This observation suggests that when LSTM is used for forecasting model construction, it is not necessary to select a large hidden layer size. Figure 11: Comparison between MAPE and RMSE of LSTM under different hidden layer size in the test set. Figure 10: Comparison between MAPE and RMSE of GRU under different hidden layer size in the test set. Figure 12 presents the MAPEs and RMSEs of CNNs with a different number of filters. It can be seen that around 90% of the CNN forecasting models can find the minimum MAPE and RMSE values under the increasing number of filters, which are Busan, Dalian, Dubai, Guangzhou, Hamburg, Hong Kong, Kaohsiung, Kelang, Los Angeles, Ningbo, Qingdao, Rotterdam, Shanghai, Shenzhen, Singapore, Tanjung, Tianjin, and Xiamen. There are also some unsynchronised changes in MAPE and RMSE, which are Guangzhou, Qingdao, Shenzhen, and Singapore. The unsynchronised change may be due to the change of extreme value in the forecasting results, because RMSE is more sensitive to the change of extreme value. Overall, this observation suggests that when CNN is used to build the container throughput forecasting model, it is necessary to increase the number of filters to search for the model that can produce the most accurate results. Figure 13 presents the MAPEs and RMSEs of Transformers with different number of layers. It can be seen from the figure that the forecasting accuracy of Transformer does not show the same rule as GRU, which is the forecasting error decreases with the increase of model size. However, we can find that by increasing the size of the Transformer, we can find the best model settings in the process of increasing the size.