## 5 Analysis of Experimental Results  
### Analysis of Prediction Results of Missing Soil Heavy-Metal Values  
Using soil from a certain area in North China as the experimental object, the experimental data included soil heavy-metal content, soil pH, and sampling latitude and longitude. The data dimensions differed. Before the experiment, it was necessary to normalize the data characteristics to eliminate the influences between data with different dimensions and improve the speed of the model calculation. In this experiment, the data sample size was not large, and the input and output layer dimensions were small; thus, the neural network model used a three-layer network structure to reduce the amount of mathematical calculation while ensuring accuracy. In a neural network, we attempt to ensure that the dimension of the input vector matches the number of neurons in the input layer, and the dimension of the output vector matches the number of neurons in the output layer. In the missing value prediction experiment, the number of neurons in the input layer was set to five and the number of neurons in the output layer was set to three. The data were divided into training and test sets in a ratio of 7:3. Table 1 shows a comparison of the measured values of Hg, Cd, and Pb with the predicted results based on the SA-FOA-BP neural network model and the traditional BP neural network algorithm. Due to the particularity of soil heavy-metal data, the specific values are inconvenient for public display. The 40 predicted datasets were divided into four groups, each with 10 data points, and the average values were tabulated. The predicted results of the SA-FOA-BP neural network model and the measured results were compared; the relative error range for Hg was 6.78-23.16%, and the average error was 16.35%. Compared with the traditional BP neural network prediction, the average error value was reduced by 11.251%. The relative error range for Cd was 7.33-22.86%, and the average error value was 16.37%. Compared with the traditional BP neural network prediction, the average error value was reduced by 10.21%. The relative error range of Pb was 1.71-26.20%, and the average error value was 14.69%. Compared with the traditional BP neural network prediction, the average prediction, the average error value was reduced by 11.699%. Overall, the error between the value predicted by the SA-FOA-BP neural network model and the measured value ranged from 1.71 to 26.20%; the average error was 15.8033%, within the error range reported in similar research (0.93-26.67%), indicating that prediction using the SA-FOA-BP neural network model is reasonable. Figures 5-7 show comparison charts of the measured values of the three heavy metals and the values predicted by the different models. To validate the effectiveness of the SA-FOA algorithm, this section used the SA-FOA algorithm and the FOA algorithm to solve a univariate quadratic equation for its minimum value in MATLAB. The parameter settings were as follows: In the FOA algorithm, the maximum number of iterations was set to maxgen = 200, and the population size was size = 50. In the SA-FOA algorithm, the maximum number of iterations was also set to maxgen = 200, the population size was size = 50, and the non-uniform mutation factor \(\lambda\) was set to 2. The univariate quadratic equation to be solved is represented as Equation (18):  
\[\mathrm{f(x)}=-5+\mathrm{x}^{2} \tag{18}\]