## 2 The Driving Decision-Making Process of Autonomous Vehicle
### The Optimized Support Vector Machine Regression Model
#### 2.2.2 Parameter Optimization  
Particle swarm optimization (PSO) algorithm is a new evolutionary and iterative optimization algorithm developed in recent years. PSO algorithm is also started from the random solution and the quality of its solution is evaluated by the fitness. It finds the global optimum following the optimal particles in the solution space [23]. PSO algorithm has a fast convergence rate, and can avoid falling into the local optimum [24; 25]. So, in this paper, we adopt PSO algorithm to optimize the undetermined parameters of the SVR model and the weighted hybrid kernel function. In the PSO algorithm, particles dynamically adjust their positions in the \(n\)-dimensional space through their individual and peer flight experience. In \(n\)-dimensional space, the number of particles is \(l\), and the position of particle \(i\) can be represented as \(x_{i}=[x_{i1},\ x_{i2},\ \ldots,\ x_{in}]\), and its flying speed is \(v_{i}=[v_{i1},\ v_{i2},\ \ldots,\ v_{in}]\). The best position visited by the particle \(i\) so far can be noted as the particle best, i.e., \(\mathit{Pbest}_{i}=[\mathit{Pbest}_{i1},\ \mathit{Pbest}_{i2},\ \ldots,\ \mathit{Pbest}_{in}]\), and the best position found by all the particles so far can be noted as the global best, i.e., \(\mathit{Gbest}=[\mathit{Gbest}_{i1},\ \mathit{Gbest}_{i2},\ \ldots,\ \mathit{Gbest}_{in}]\). At every moment \(t\), the particle will adjust its speed and position by:  
\[v_{id}^{t+1}=\mu v_{id}^{t}+c_{1}rand(0,\ 1)(\mathit{Pbest}_{id}-x_{id}^{t})+c _{2}rand(0,\ 1)(\mathit{Gbest}_{id}-x_{id}^{t}) \tag{9}\]  
\[\left\{ \begin{array}{c}v_{id}=v_{\max},\ v_{id}>v_{\max}\\ v_{id}=-v_{\max},\ v_{id}<-v_{\max}\end{array} \right. \tag{10}\]  
\[x_{id}^{t+1}=x_{id}^{t}+v_{id}^{t+1} \tag{11}\]  
where \(i=1,\ 2,\ \ldots,\ l,\ d=1,\ 2,\ \ldots,\ n,v_{\max}\) is the limited maximum flying speed, and \(rand(0,\ 1)\) is the uniform random number on the interval \([0,\ 1]\), it can increase the searching randomness of particles based on the \(\mathit{Pbest}\) and the \(\mathit{Gbest}\). Then, the PSO-SVR parameter optimization architecture is established in Figure 4. We set the updated step factor as \(\mu=1\) and the positive acceleration coefficients of particle as \(c_{1}=c_{2}=2.0\). The limited maximum flying speed \(v_{\max}\) is set to 100, and the number of particles \(l\) is 50. The number of undetermined parameters is 9, including \(\beta\), \(e\) in selecting kernel function type, parameters of each single kernel function \(a\), \(b\), \(d\), \(\sigma\), \(\tau\), \(\delta\), and SVR penalty factor \(C\), it is represented as the dimension of the particle space. The parameter of kernel function \(\sigma\) and penalty factor \(C\) are limited in the value range (\(-10\), \(10\)). The optimization steps are given as follows:  
1. randomly initialize the positions and speeds of all particles;
2. the fitness value of each particle is calculated according to the fitness function of driving decision problem;
3. respectively compare the fitness value of each particle with their own _Pbest_ and _Gbest_. If the fitness value is larger than _Pbest_, then update _Pbest_ with the fitness value. If the fitness value is larger than _Gbest_, then update _Gbest_ with the fitness value;
4. for each update, reset the SVR penalty factor \(C\) to create a larger research space for particles, avoid falling into the local area of current optimal value;
5. update the position and speed of each particle according to Formulas (8) and (9); and,
6. when the number of iterations reaches the maximum set, stop it and output the optimal parameters. Otherwise, return to Step 2. In this paper, set the training accuracy as the fitness function in the optimized process. In order to evaluate the predicting effect of model for each driving decision, the average absolute error \(E_{\text{M}}\) and relative mean square error \(E_{\text{R}}\) are selected as the comprehensive evaluation indexes.