# Analysis of Weighted Factors Influencing Submarine Cable Laying Depth Using Random Forest Method
## 2 Materials and Methods
### Method  
#### 2.3.1 Improved Seagull Optimization Algorithm (ISOA)  
The seagull optimization algorithm (SOA) is a heuristic optimization algorithm proposed by [PERSON] et al. in 2019 [23]. It is a population-based intelligent optimization algorithm inspired by the foraging behavior of seagulls. This algorithm exhibits strong capabilities in solving problems that are nonlinear, non-convex, high-dimensional, and have multiple locally optimal solutions. The basic principle of the SOA is to simulate the process of a flock of seagulls searching for food. In the algorithm, individual seagulls are randomly distributed in the search space and update their positions based on specific rules to find the optimal solution. The main steps of the algorithm are as follows:  
Step 1. Initialization: Generate a random flock of seagulls, where each seagull represents a solution. Set algorithm parameters such as the number of iterations and the size of the seagull population. Step 2. Fitness evaluation: Calculate the fitness value for each seagull individual, which is the objective function value of the optimization problem. In this case, it can be the number of layers and the number of neurons in a neural network. Step 3. Position update: Update the position of each seagull individual based on the current best individual's position and fitness value in the seagull flock, as well as the boundary conditions of the search space. This process involves two main behaviors: Starving Search and Satisfied Search. 1. Starving Search: When a seagull is in a hungry state, it becomes more aggressive in searching for food. In the algorithm, this means that the individual will move toward the direction of the current best individual. \[S_{i}(t+1)=S_{i}(t)+rand(0,1)\times(S_{m}(t)-S_{i}(t)) \tag{3}\]  
Figure 1: Correlation heatmap. 2. Satisfied Search: When a seagull is satisfied, it searches in the nearby area at a slower pace. At this stage, the individual will conduct a random search near their current position to find better solutions. \[S_{i}(t+1)=S_{i}(t)+rand(0,1)\times(S_{r}(t)-S_{i}(t))\] (4) where \(S_{i}(t+1)\) represents the updated position, \(S_{i}(t)\) represents the current position, \(S_{m}(t)\) represents the current optimal individual position, and \(S_{r}(t)\) represents the current nearby random individual. Step 4. Convergence check: If the predetermined number of iterations or other convergence criteria are met, stop the algorithm. Otherwise, return to step 2 and continue iterating. The main advantage of the SOA is its strong global search capability, allowing it to find globally optimal solutions or approximate solutions in most optimization problems. However, the distribution of the initial population can significantly impact the algorithm's performance. Traditional methods of randomly selecting initial population positions can lead to uneven population distribution, resulting in problems such as getting stuck in local optima [24]. To address these issues, the following enhancements are introduced: 1. Logistic Chaotic Mapping: Instead of using a random number generator for initializing the population, Logistic Chaotic Mapping is employed. Logistic Chaotic Mapping has better distribution characteristics, which helps generate high-quality initial solutions and improves the algorithm's search efficiency and convergence speed. The formula for Logistic Chaotic Mapping is as follows: \[x^{*}=r\times x\times(1-x)\] (5) Here, \(x^{*}\) is the new mapped value, \(x\) is the current mapped value, and \(r\) is a constant usually set to 4. Distance Factor in Position Update: In addition to the Starving Search and Satisfied Search in position updating, a distance factor is introduced to control the rate at which the search range decreases with the number of iterations.