# Analysis of Weighted Factors Influencing Submarine Cable Laying Depth Using Random Forest Method
## 3 Results and Discussion
### Model Performance Comparison  
The improved seagull optimization algorithm is used to optimize the structural parameters of the BP neural network. In the optimization process, the chosen fitness function used to evaluate the population's fitness is mean squared error (MSE). Hence, the fitness function's value reflects the population's quality inversely. A lower fitness function value indicates higher fitness for the population and a greater probability of the population being retained. The calculation formula for MSE is shown in the following equation. \[MSE=\sum_{i=1}^{n}(y_{i}-y_{i}^{*})^{2}/n \tag{19}\]  
where \(y_{i}\) represents the actual values and \(y_{i}^{*}\) is the predicted values. The improved seagull optimization algorithm determines the upper and lower bounds for the number of layers (\(l\)) and the number of neurons (\(n\)) as [1; 5] and [1; 64], respectively. The population size (\(N\)) is set to 50, and the maximum number of iterations (\(M\)) is set to 100. For the BP neural network, the activation function used in each hidden layer is the Rectified Linear Unit (ReLU) function. Since it is a regression model, the output layer consists of one neuron, and a linear activation function is used to map the final values. During the parameter updating process, the mean squared error (MSE) function is used as the loss function. L2 regularization with a hyperparameter of 0.01 is introduced to reduce the risk of overfitting. The fitness value of the optimization process, represented by the change in fitness value over iterations, can be observed in Figure 4.  
Based on Figure 4, it can be observed that the fitness value of the algorithm decreases as the number of iterations increases. This indicates that the ISOA can achieve a smaller mean squared error in a relatively small number of iterations, and it is less likely to get stuck in local optima. The optimal number of hidden layers and neurons obtained through the ISOA is 5 and 41, respectively. Based on these parameters, the BP neural network structure is established as follows:  
1. Input layer: Number of neurons determined by the input data. 2. Hidden layers: five layers with 41 neurons in each layer, using the ReLU activation function. 3. Output layer: one neuron with a linear activation function. This optimized structure obtained through the ISOA can help improve the performance of the BP neural network in terms of accuracy and prediction capability. The input layer structure is related to the data features, with 11 input features, and thus the input layer consists of 11 neurons. The hidden layers consist of six layers. The parameters of the first layer are determined by the number of neurons in the input layer and the number of neurons in the current layer, resulting in a total of 492 parameters. The remaining five layers each have 41 neurons, resulting in 1722 parameters per layer. The output layer consists of one neuron, which requires 41 parameters plus a bias term, resulting in a total of 42 parameters. The entire network has a total of 9144 parameters. The improved network model is trained on the training set data, with the burial depth as the target label. Then, the model is used to predict the burial depth on the test set, obtaining predicted values. The performance of the model is compared with the SVR, DT, and GBDT algorithms using the evaluation metrics mentioned earlier, and the results are shown in Table 2.  
Generally, the coefficient of determination R\({}^{2}\) for an effective model is in the range of [0, 1]. A higher R\({}^{2}\) value indicates a better regression performance, while a value closer to 0 indicates a poorer fit. According to Table 2, the BP regression model optimized by the seagull optimization algorithm has the highest R\({}^{2}\) value, and all regression models have smaller MAE and MSE values compared to the default parameter random forest regression model. The comparison of the predictive performance of each model is shown in Figure 5.