## 6 Conclusions  
In this study, we developed the MVMO-LSTM model by incorporating the advantages of the variational mode decomposition (VMD), long short-term memory (LSTM), and dung beetle optimization methods and multi-strategy improvement. In particular, the utilization of variational mode decomposition with the dung beetle algorithm incorporating multi-strategy optimization intelligently adjusts the parameters to mitigate signal noise effects. Furthermore, optimizing the long- and short-term memory with this algorithm significantly enhances the prediction accuracy by speeding up the convergence and steering clear of local optima. In addition, in this study, three assessment metrics are used to evaluate the predictions of the proposed model and other widely used models: the MAE, the RMSE, and the R\({}^{2}\). Ultimately, the integrated model underwent comparison with alternative predictive models and testing to validate the accuracy and consistency of its forecasts. In conclusion, the following summarizing points are established:  
1. The model proposed in this study achieves significant accuracy in power load forecasting. 2. The predictions of this hybrid model are more robust and efficient than a single model or a model with only one fusion algorithm. 3. A hybrid MODBO-VMD-MODBO-LSTM model is proposed, and previous studies need to reset the decomposition number when the center frequency domain is determined, and they seldom explore the penalty factor and decomposition layer values. This multi-strategy improved dung beetle algorithm not only optimizes the penalty factor and decomposition layer values of VMD but also optimizes the optimal number of hidden units, the optimal maximum training period and the optimal initial learning rate of LSTM. The combination of these two improvements can effectively help LSTM learn and adapt to the complexity and seasonal changes of power load data, thus improving the prediction accuracy and making the prediction results more reliable and practical. Therefore, more efforts are needed to further improve the performance of power load-forecasting models and expand their application scenarios. All of the authors contributed extensively to this work. Software, conceptualization, methodology and writing--original draft preparation, J.C.; Reviewing and software, writing--review and editing, L.L. ; Data curation and visualization, K.G. ; supervision, S.L. ; funding, D.H. All authors have read and agreed to the published version of the manuscript. This work was supported by the Natural Science Foundation of Fujian Province (Grant No. 2022N5020, 2022H6005). The experimental dataset in this paper is the Spanish Electricity Load Dataset, which is available from the authors upon request. Our profound appreciation goes out to the editors and reviewers whose meticulous effort and insightful comments helped make this publication stronger. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & \multicolumn{3}{c}{**Spring**} & \multicolumn{3}{c}{**Summer**} & \multicolumn{3}{c}{**Autumnumnumnumn{3}{c}}{**Winter**} \\ \cline{2-13}  & **RMSE** & **MAE** & **R\({}^{2}\)** & **RMSE** & **MAE** & **R\({}^{2}\)** & **RMSE** & **MAE** & **R\({}^{2}\)** & **RMSE** & **MAE** & **R\({}^{2}\)** \\ \hline MVMO-LSTM & **0.1502** & **0.1192** & **0.9932** & **0.1732** & **0.1289** & **0.9907** & **0.1013** & **0.0893** & **0.9955** & **0.2008** & **0.1488** & **0.9879** \\ \hline EMD-LSTM & 0.4724 & 0.3615 & 0.9311 & 0.5024 & 0.3915 & 0.9393 & 0.4354 & 0.3315 & 0.9406 & 0.5324 & 0.4447 & 0.9328 \\ \hline VMD-LSTM & 0.4230 & 0.3393 & 0.9532 & 0.4328 & 0.3422 & 0.9482 & 0.4302 & 0.3306 & 0.9582 & 0.4572 & 0.3871 & 0.9602 \\ \hline CEEMDAN-LSTM & 0.3827 & 0.2868 & 0.9752 & 0.4137 & 0.3163 & 0.9772 & 0.4073 & 0.3103 & 0.9843 & 0.4617 & 0.4016 & 0.9561 \\ \hline EEMD-LSTM & 0.4109 & 0.3190 & 0.9572 & 0.4435 & 0.3493 & 0.9637 & 0.4144 & 0.3190 & 0.9573 & 0.4704 & 0.4245 & 0.9477 \\ \hline \hline \end{tabular}
\end{table}