## 4 Results and Discussion
By reconstructing and decomposing the original data several times, ICEEMDAN effectively removed the noise in the data, allowing the model to focus more on the core trends of the data. To validate the impact of optimization algorithms, we compared four optimization algorithms, including BWO, Gray Wolf Optimization (GWO) [33], Dragonfly Algorithm (DA) [34], and Chameleon Swarm Algorithm (CSA) [35]. After the introduction of the optimization algorithms, the prediction accuracy was improved to different degrees. BWO-ICEEMDAN-iTransformer achieved an R\({}^{2}\) of 0.9873, with MAE reduced to 48.0014 and RMSE reduced to 66.2221, which significantly outperformed the other models. This indicates that BWO enhances the predictive ability of the model through global searches and optimization of parameters. Load data exhibits non-stationarity, leading to a complex solution space. By simulating the behaviors of beluga whales, BWO can effectively adjust the search direction and avoid getting trapped in local optima. Figure 8 illustrates the convergence analysis of four optimization algorithms with minimum envelope entropy as the fitness function. A comparison of the convergence curves highlights the superior performance of BWO, both in terms of convergence speed and final fitness value. It is worth noting that the effect of BWO is not limited to optimizing the parameters of ICEEMDAN, but also the performance of other data decomposition algorithms. The BWO-CEEMD-iTransformer and BWO-EEMD-iTransformer models also showed significant performance improvement. Although their metrics, such as R\({}^{2}\) and MAE, were not as improved as those of the BWO-ICEEMDAN-iTransformer model, they still showed considerable improvement compared to the original CEEMD and EEMD models. To highlight the superiority of the BWO-ICEEMDAN-iTransformer model, its prediction curves were compared with the rest of the models, as shown in Figures 9-11. The selected prediction curves represent the prediction results for an entire day. Figure 9 compares the proposed model with eight other individual models. The results show that the prediction curve of the proposed model was closest to the actual values with the best-fitting performance. Although the other individual models could predict the general trend of electricity load, they showed significant errors in specific values, especially during the day when the load is high. Figure 10 compares the proposed model with models using different decomposition algorithms. It can be seen that the proposed model performed better than the others. Compared to the individual iTransformer model, the ICEEMDAN-iTransformer,  
Figure 8: Convergence analysis of different optimization algorithms. Figure 11 compares the proposed model with models using different optimization algorithms. Compared to the individual models, all four hybrid models showed significant improvements in prediction accuracy both during the day and night, with BWO outperforming the other optimization algorithms. Figure 12 illustrates the errors of ablation models. The error of the individual iTransformer is larger, maintaining an error of about 200 MW for a period of time. The error of ICEEMDAN-iTransformer is significantly lower than that of iTransformer, but there is still a small period of time when the error reaches about 200 MW. The proposed BWO-ICEEMDAN-iTransformer model has the smallest error, and its error curve remains relatively smooth. Combined with Table 4, the proposed model improves 1.39% over ICEEMDAN-iTransformer and 3.09% over iTransformer. Based on the above experiments, the BWO-ICEEMDAN-iTransformer exhibited the most superior performance in electricity load forecasting. The predictive model, through combining ICEEMDAN and BWO, can more effectively handle complex electricity load data, providing more accurate and stable forecasting results in practical applications. Although model fusion introduces additional computational burden, the increase in training time remains within an acceptable range for practical applications.