# Short-Term Power Load Prediction of VMD-LSTM Based on ISSA Optimization
## 2 Fundamentals of the Model
### Testing the Performance of the ISSA Functions  
To intuitively demonstrate the overall performance of the Improved Sparrow Search Algorithm (ISSA), comparative experiments are conducted by comparing the ISSA with the Sparrow Search Algorithm (SSA), Seagull Optimization Algorithm (SOA), While Optimization Algorithm (WOA), Locust Optimization Algorithm (GOA), and Particle Swarm Optimization (PSO). In these experiments, the number of experimental populations is set as 30, and the iteration number is fixed at 500. The test function employed is defined in Equation (26) [32], with its relevant parameters listed in Table 2. Furthermore, the average fitness values of these algorithms (calculated as the mean of 30 independent iterations) are compared, as shown in Table 3.  
Figure 2: Flowchart for optimizing LSTM network parameters using ISSA.  
Table 3 reveals that the ISSA demonstrates the optimal capability in locating the optimal value, locating the optimal solution with fewer iterations across all five functions. This indicates that the ISSA exhibits a stronger global search capability and faster convergence speed, which can be attributed to the introduction of improved chaotic mapping into the SSA population. This enhancement boosts the randomness and ergodicity of the population, enabling the better handling of local optima during both local exploitation and global search processes. The SSA and SOA rank next in terms of performance, whereas the WOA, GOA, and PSO show relatively inferior results. Therefore, in Example 2 of this study, comparative experiments are carried out employing the ISSA, SSA, and SOA to further explore their performance discrepancies.  
Figures 3 and 4, respectively, depict the fitness curves of the unimodal function \(F_{2}\) and the multimodal function \(F_{4}\). When subjected to the same number of iterations, the ISSA demonstrates superiority by being the first to converge to the optimal fitness value.  
\[\left\{\begin{array}{l}F_{1}=\sum\limits_{i=1}^{n}x_{i}^{2}\\ F_{2}=\sum\limits_{i=1}^{n}|x_{i}|+\prod\limits_{i=1}^{n}|x_{i}|\\ F_{3}=\sum\limits_{i=1}^{n}\left[x_{i}^{2}-10\text{cos}(2\pi x_{i})+10\right] \\ F_{4}=\quad-20\text{exp}\left(-0.2\sqrt{\frac{1}{n}\sum\limits_{i=1}^{n}x_{i}^ {2}}\right)-\\ \qquad\qquad\text{exp}\left(\frac{1}{n}\sum\limits_{i=1}^{n}cos(2\pi x_{i}) \right)+20+e\\ F_{5}=4x_{1}^{2}-2.1x_{1}^{4}+\frac{1}{3}x_{1}^{6}+x_{1}x_{2}-4x_{2}^{2}+4x_{ 2}^{4}\end{array}\right. \tag{26}\]  
\begin{table}
\begin{tabular}{c c c c} \hline \hline  & **Function** & **Definition** & **Minimum Value** \\ \hline \multirow{2}{*}{Unimodal function} & \(F_{1}\) & \([-100,100]\) & \(0\) \\  & \(F_{2}\) & \([-10,10]\) & \(0\) \\ \hline \multirow{3}{*}{Multimodal function} & \(F_{3}\) & \([-5.12,5.12]\) & \(0\) \\  & \(F_{4}\) & \([-32,32]\) & \(0\) \\  & \(F_{5}\) & \([-5,5]\) & \(-1.0316\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: Test functions and their related parameters.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Function**} & \multicolumn{6}{c}{**Algorithms**} \\ \cline{2-7}  & **ISSA** & **SSA** & **SOA** & **WOA** & **GOA** & **PSO** \\ \hline \(F_{1}\) & \(0\) & \(3.44\times 10^{-57}\) & \(3.6\times 10^{-194}\) & \(6.01\times 10^{-20}\) & \(35.8871\) & \(0.1803\) \\ \(F_{2}\) & \(2.9\times 10^{-167}\) & \(3.12\times 10^{-18}\) & \(8\times 10^{-18}\) & \(6.18\times 10^{-14}\) & \(20.8136\) & \(1.5318\) \\ \(F_{3}\) & \(0\) & \(0\) & \(0\) & \(8.88\times 10^{-16}\) & \(97.5923\) & \(25.2767\) \\ \(F_{4}\) & \(4.44\times 10^{-16}\) & \(9.18\times 10^{-16}\) & \(4.44\times 10^{-16}\) & \(8.92\times 10^{-11}\) & \(5.4898\) & \(5.7464\) \\ \(F_{5}\) & \(-1.0316\) & \(-1.0314\) & \(-1.0316\) & \(-1.0318\) & \(-1.0318\) & \(-1.0319\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Data comparison of algorithms.