## 2 Improved Adaptive VMD Algorithm
### IFOA-VMD Decomposition
#### 2.2.3 Improved FOA Algorithm  
In order to avoid the FOA falling into local optimization and improve the convergence speed and convergence precision of the algorithm, this paper keeps the process of learning the lessons learned from the worst individuals while retaining the FOA algorithm to the optimal individual learning process, that is, increasing the \"reverse cognition\" part. The improvement strategy is to adjust Equations (11) and (12) to Equations (13) and (14), respectively. At the same time, the degree of learning from the optimal and worst individuals can also be adjusted by the linearly decreasing dynamic coefficient \(\omega\). At the beginning of the iteration, \(\omega\) is larger, mainly to learn from the optimal individual and improve the convergence speed of the algorithm; after continuous iteration, \(\omega\) gradually decreases, at which time the learning to the worst individual is enhanced, and the learning to the optimal individual is weakened so that the algorithm has the ability to jump out of the local extremum. At the same time, in the case that \(\omega\) does not decrement to 0, the individual Drosophila can always learn from the optimal individual, thus improving the convergence speed and convergence precision of the algorithm. The flow chart for optimizing the VMD parameters using IFOA is shown in Figure 2.  
\[\left\{\begin{array}{c}[\text{bestSmell bestIndex}]\ =\ \min(\text{Smell})\\ [\text{worstSmell worstIndex}]\ =\ \max(\text{Smell})\end{array}\right. \tag{13}\]  
\[\left\{\begin{array}{c}\text{Smellbest}=\text{bestSmell},\text{Smellworst Smell}\\ \text{X(best)}=\text{X(bestIndex)},\text{Y(best)}=\text{Y(bestIndex)}\\ \text{X(worst)}=\text{X(worstIndex)},\text{Y(worst)}=\text{Y(worstIndex)}\\ \text{X\_axis}=\ \omega\text{X(bestIndex)}(1\omega)\text{X(worstIndex)},\text{Y\_axis}= \ \omega\text{Y(bestIndex)}(1\omega)\text{Y(worstIndex)}\end{array}\right. \tag{14}\]  
In order to verify that the IFOA algorithm can reduce the local optimization probability and improve the convergence accuracy, the Wine dataset in the UCI database is used to compare the performance of IFOA and FOA. The feature dimension is 13, categories is 3, and the training sample and test sample are respectively 89. The data set is input into the SVM for classification and identification. Figure 3 is the optimization iteration curve of the cross-validation classification accuracy of the Wine data set, where Sizepop is 10 and Maxgen is 20. As can be seen from Figure 2, the FOA curve is relatively monotonous, and it is difficult to jump out of the local optimum. After classification calculation, the classification accuracy of IFOA is 97.75%, the algorithm calculation time is 14.25 s, the classification accuracy of FOA is 92.69%, the calculation time of the algorithm is 12.98 s, and the classification accuracy of IFOA is increased by 5.06%, indicating that IFOA has higher convergence precision. Since IFOA has increased the information on the worst individual information and location update of the population, the calculation time is slightly longer than FOA, but the difference between the two is not large.