## 4 Results and Discussion  
To validate the predictive ability of the proposed model, we compared the performance of 17 forecasting algorithms on real datasets. The parameters of the intelligent optimization algorithms and the deep learning models are shown in Table 3. The experimental data used in this paper was obtained from the EMC [25]. It contains 2019-2020 data on electricity load, price, and weather recorded at 30-min intervals. The data is divided into three parts: training, validation, and test datasets, in a 3:1:1 ratio. Figure 7 shows the trends of four variables over 30 days, comprising a total of 1440 records in the test dataset. The variation in load follows a certain pattern. During a given week, daytime load levels on working days are generally higher than on weekends due to increased industrial and commercial electricity consumption. The trends of electricity prices, temperature, and relative humidity also show a certain degree of correlation with the load. The input sequence length set for the experiment was 96, and the output sequence length was 48. The experiments were conducted on a computer with a 2.5 GHz Intel CPU (Intel Corporation, Santa Clara, CA, USA), 32 GB of RAM (Samsung Electronics, Seoul, Republic of Korea), using Python 3.8 as the programming language. As shown in Table 4, among the seven individual models, iTransformer was the best method among all the models, with an R\({}^{2}\) of 0.9577, MAE of 83.2604, and RMSE of 120.8423. iTransformer encoded the different variables into independent tokens, transforming the \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Population size & 30 \\ Maximum number of iterations & 30 \\ Nstd & [0.15, 0.6] \\ NR & [10, 600] \\ Batch\_size & 72 \\ Epochs & 10 \\ Patience & 3 \\ Learning rate & 0.0001 \\ linear layer & 512 \\ FFN layer & 2048 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Parameter settings. Figure 6: The process of the proposed BWO–ICEEMDAN–iTransformer model. roles of the attention mechanism and the feedforward network, which enabled the model to better capture the temporal relationships within the data and the relationships between variables. To assess the effectiveness of the data decomposition technique, we compared three decomposition algorithms. It has been shown through past experiments that predictive ability is improved after the introduction of data decomposition algorithms. The three data decomposition algorithms, ICEEMDAN, CEEMD, and EEMD, improved the predictive ability of the model to different degrees. For the three performance metrics--R\({}^{2}\), MAE, and RMSE--ICEEMDAN improved by 1.68%, 14.49%, and 21.37%; CEEMD improved by 1.58%, \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Method** & **R\({}^{2}\)** & **MAE** & **RMSE** \\ \hline iTransformer & 0.9577 & 83.2604 & 120.8423 \\ FEDformer [26] & 0.9316 & 114.4395 & 153.7248 \\ Pyraformer [27] & 0.8888 & 135.9388 & 195.9085 \\ Autoformer [28] & 0.8138 & 193.9856 & 253.5933 \\ FreTS [29] & 0.9029 & 126.8714 & 183.1028 \\ LightTS [30] & 0.8796 & 149.3750 & 203.8944 \\ PatchTST [31] & 0.9162 & 118.5022 & 170.0605 \\ Koopa [32] & 0.8654 & 158.0816 & 215.6215 \\ ICEEMD–iTransformer & 0.9738 & 71.1998 & 95.0231 \\ CEEMD–iTransformer & 0.9728 & 72.0094 & 96.9611 \\ EEMD-iTransformer & 0.9686 & 80.4151 & 104.0551 \\ CSA–ICEEMDAN–iTransformer & 0.9867 & 49.1543 & 67.7606 \\ DA–ICEEMADN–iTransformer & 0.9858 & 50.0338 & 69.9737 \\ GWO–ICEEMADN–iTransformer & 0.9869 & 48.8129 & 67.3607 \\ BWO–CEEMD–iTransformer & 0.9767 & 67.1662 & 89.6762 \\ BWO–EEMD-iTransformer & 0.9689 & 78.1639 & 103.5629 \\ BWO–ICEEMADN–iTransformer & **0.9873** & **48.0014** & **66.2221** \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Prediction results of different models. Figure 7: Visualization of a subset of the test dataset. 13.51%, and 19.76%; and EEMD improved by 1.14%, 3.42%, and 13.89%, respectively. The degree of improvement of ICEEMDAN for the model was higher than that of CEEMD and EEMD.