# Load Forecasting Based on LVMD-DBFCM Load Curve Clustering and the CNN-IVIA-BLSTM Model
## 2 Influenza Virus Immunity Optimization Algorithm
### Algorithm Testing  
To test the actual optimization effect of the proposed IVIA, it was evaluated in this paper on 23 sets of standard test functions. The optimization results were compared with those of turbulent flow of water-based optimization (TFWO), golden eagle optimization (GEO), the parasitism-predation algorithm (PPA), the rat swarm optimizer (RSO), gray - wolf optimization (GWO), particle swarm optimization (PSO), and the whale optimization algorithm (WOA).  
Table 1 shows the expression of the test function, the dimension of the optimization problem, and the overall search range, and the last column shows the minimum value of the test function expectation, which is the theoretical optimum. The IVIA population size \(n\) is 30, the maximum number of iterations \(N_{\max}\) is 1000, the maximum safe contact distance \(L\) is \(0.5 ub\), and the population immunity rate \(R\) is 80% during the test period. The number of dimensions of the test function and the parameters, such as search intervals \(lb\) and \(ub\), are set according to Table 1. The overall and iteration numbers of the other optimization functions are the same as those of the IVIA.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Standard** & **Dimension** & **Search Space** & **Minimum** \\ \hline \(F_{1}(x)=\sum\limits_{i=1}^{n}x_{i}^{2}\) & 30 & \([-100,\,100]\) & 0 \\ \hline \(F_{2}(x)=\sum\limits_{i=1}^{n}|x_{i}|+\prod\limits_{i=1}^{n  
The viability of the proposed IVIA is tested using 23 well-known benchmark functions with different sizes and complexity. Figure 5 shows the three-dimensional graphs of the standard test functions and their corresponding test results. The convergence of the IVIA is very good for both single-peaked and multipeaked functions.  
From the test results in Table 2, the accuracy of the IVIA for function finding is much higher than that of several other optimization algorithms, and the theoretical optimal value can be found for some functions. IVIA has fewer iterations, a shorter running time, and faster convergence compared to the other seven algorithms.  
For comparative evaluation, the proposed IVIA is compared against seven well-established comparative methods using the same benchmark functions. IVIA optimizes best in F1, F2, F3, F4, F5, F6, F7, F8, converges fastest in F11, F12, F13, F14, F15, F17, and it has the same effect as other algorithms in F18, F19, F20, F21, F22, F23. The comparative results show the effectiveness of IVIA.  
In summary, the IVIA is based on the characteristics of fast convergence, better robustness, and good optimization search. In this paper, the IVIA is selected to optimize the relevant parameters, such as the number of neurons in the hidden layer, the number of training times, the learning rate, and the regularization coefficients in the BLSTM network.  
Figure 5: _Cont._  
Figure 5: Standard test function optimization result.  
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\begin{table}
\begin{tabular}{l l l l l l l l l l} \hline F & & **IVIA** & **TFWO** & **GEO** & **PPA** & **RSO** & **GWO** & **PSO** & **WOA** \\ \hline F12 & average & **6.942 \(\times\)10\({}^{-6}\)** & 1.656 \(\times\) 10\({}^{-3