## 3 Experimental Study
### Prediction Results  
We compared seven prediction models, such as MLR, LASSO, SVR, RF, XGBoost, LSTM, and MLP with the proposed method on 25 mail center datasets to predict postal parcel volume during special periods. We selected the special periods for the training dataset from Korean Thanksgiving Day 2016 to the target peak period. For example, holidays that started from the Korean Thanksgiving Day 2016 to the Lunar New Year 2018 were used to train the model that predicts the 2018 Korean Thanksgiving Day. Figure 6 shows a visualization of the train-test split. Foremost, we compared several MLP models that were trained on the differently prepared training datasets to demonstrate how the proposed method can enhance the performance of compared MLP models. Table 2 shows the prediction performance of compared MLP models for each mail center, and the best results are emphasized. The prediction results show that the proposed external and internal MLP model-based weighted ensemble method outperforms other MLP models on 13 of 25 mail center datasets. From Table 2, the EF-MLP model performed better than the baseline MLP model using the initial dataset on most of the mail center datasets, and its average MAPE was less than the baseline MLP model by 4.98%. Moreover, the MAPE of the IF-MLP model was decreased by enriching the training dataset using synthetic data generated from the VAE model, and its average MAPE dropped to 10.77% compared with the MAPE of the baseline MLP model of 14.43%. Moreover, the average MAE, RMSE, SMAPE, and MAPE of the proposed model ensembling EF-MLP and IF-MLP models with the weight were less than the baseline MLP model by 25,917.1, 35,215.1, 4.87%, and 4.98%, respectively. Finally, the proposed method was superior to the baseline MLP model in giving the minimum errors. For each mail center, we selected the different weights for EF-MLP and IF-MLP based on the training performance of the proposed method. Table 3 shows the performance comparison between the proposed method and the individual predictive methods. For 25 mail center datasets, ten centers have a higher coefficient of variation than the average, and the names of these mail centers are bolded in Table 3. The performance of our proposed method tends to be better for mail centers with large fluctuations. Among mail centers with a high coefficient of variation, the bolded highlight indicates that the proposed method is excellent. As shown from the MAPE, SMAPE, RMSE, and MAE results of Table 3, the proposed weighted ensemble method gave better performance than other individual compared models for most mail centers. The proposed method achieved better accuracy in MAPE and SMAPE than the MLR-based, LASSO-based, SVR-based, XGBoost-based, RF-based, and LSTM-based methods. It dropped MAPE and SMAPE values from MLR, LASSO, SVR, XGBoost, RF and LSTM-based  
Figure 6: Train-test split; LNY: Lunar New Year, KTD: Korean Thanksgiving Day. methods by 3.9%, 3.9%, 4.5%, 4.2%, 4.3%, 3.2% and 4.1%, 3.8%, 4.2%, 3.7%, 4.2%, 3.4%, respectively. For the MAE and RMSE results, the proposed ensemble method outperformed the compared methods by giving 83,012.5 of MAE and 147,883.2 of RMSE on average. Its MAE value is less than the compared methods by 20,158.7, 17,994.5, 21,858.7, 18,269.8, 18,887.3, 15,087.2, and RMSE is lower by 29,240.3, 26,028.4, 29,411.1, 31,937.6, 17,351.2, 20,666.6, and 42,155.1, respectively. \begin{table}
\begin{tabular}{l c c c c c c c} \hline \hline  & \multicolumn{2}{c}{**MLP (Baseline)**} & \multicolumn{2}{c}{**EF-MLP**} & \multicolumn{2}{c}{**IF-MLP**} & \multicolumn{2}{c}{**Proposed**} \\ \cline{2-9}
**Mail Centers** & **MAPE** & **MAE** & **MAPE** & **MAE** & **MAPE** & **MAPE** & **MAE** \\  & **SMAPE** & **RMSE** & **SMAPE** & **RMSE** & **SMAPE** & **RMSE** & **SMAPE** & **RMSE** \\ \hline \multirow{2}{*}{Mail Center \#1} & 8.245 & 166,430.0 & 9.237 & 201,634.5 & 5.923 & 128,320.7 & 6.076 & 131,779.3 \\  & 8.679 & 187,  
Figure 7 represents the average performance of the compared methods on the 25 mail center datasets.