# Research on Driving Style Recognition of Autonomous Vehicles Based on ACO-BP
## 3 Methodology
### Introduction to the ACO-BP Model
#### 3.1.3 Utilizing the Ant Colony Algorithm for BP Neural Network Optimization  
The basic idea of the optimization is to extract the elements of the weight matrix and threshold vector to form the path coordinates of the ant population. These elements collectively form the path coordinates of the ant population, constituting the fundamental concept underlying this approach. Because the shorter the path for ants to reach the food source, the higher the pheromone content on the path, the ants' fitness value is determined by considering the mean square error. The shortest path determined by the final ant population is used as the optimal initial weights and threshold parameters, which are then assigned to the BP neural network, trained, and tested. To validate the rationality of the ACO-BP model, a comparison was conducted between its results and those obtained from the BP neural network. Figure 2 depicts the optimization process.  
ACO-BP algorithm-specific steps:  
Step 1: Read the data, initialize the structure of the BP neural network and the parameters of the ant colony optimization algorithm, and set the parameter set \(I_{pi}\).  
Step 2: Place each ant on the initial starting point, where the number of ants is denoted as m and the number of paths chosen by ants is denoted as \(n\). The ant \(k\) can randomly choose its element \(j\) according to the following probability:  
\[P(\tau_{j}^{k}(I_{pi}))=\frac{\tau_{j}(I_{pi})}{\sum\limits_{j=1}^{n}\tau_{j}( I_{pi})} \tag{11}\]  
Figure 2: Flowchart of the ACO-BP algorithm.  
Step 3: Train the model, record the optimal solution, and update the pheromone \(\tau\) in the set \(I_{Pi}\). The pheromones on the paths from the initial position to the destination for each ant need to be adjusted according to the following equations:  
\[\tau_{j}(I_{Pi})(t+h)=\rho\tau_{j}(I_{Pi})(t)+\Delta\tau_{j}(I_{Pi}) \tag{12}\]  
\[\Delta\tau_{j}(I_{Pi})=\sum_{k=1}^{m}\Delta\tau_{j}^{k}(I_{Pi}) \tag{13}\]  
In Equations (12) and (13), \(\Delta\tau_{j}^{k}(I_{Pi})\) represents the amount of pheromone that ant \(k\) deposits on element \(j\) in one iteration, as shown in the equation:  
\[\Delta\tau_{j}^{k}(I_{Pi})=\left\{\begin{array}{l}Q/e_{k}\_the\ i-th\ ant\ selects\ element\ P_{j}(I_{Pi})\\ 0,\mathit{other}\end{array}\right. \tag{14}\]  
In Equation (14), \(Q\) is the fixed value of the pheromone, and \(e_{k}\) is the output error of the neural network corresponding to ant \(k\).  
Step 4: Repeat steps 2 and 3 until the maximum number of iterations is reached, then proceed to step 5.  
Step 5: Extract the coordinates of the best ant position after optimization and assign them to the BP neural network to obtain the optimal initial weight matrix and threshold vector.  
Step 6: Train and test the optimized BP neural model and compare the recognition performance of the BP neural network before and after optimization.  
Although ant colony optimization (ACO) sometimes falls into local optima, making it difficult to find the globally optimal configuration of neural networks, in ACO-BP, the ACO algorithm updates ant positions in each iteration based on certain rules (such as pheromone concentration and heuristic information) to explore new potential solutions. Additionally, ACO employs pheromone evaporation mechanisms and state transition rules to prevent premature convergence to local optima. In this process, the ACO algorithm not only retains the current best solution found (global optimum) but also stores the best solution found by each ant (local optimum). These local optima are reconsidered in subsequent iterations, thereby enhancing the algorithm's ability to escape local optima. Moreover, when ACO is used for training BP neural networks, after each iteration, the gradient descent method can assist the ACO algorithm in achieving local optimization.