## 3 Driver-Inspection Vehicle Automatic Scheduling Method
### Dynamic Automatic Scheduling Algorithm Based on Multi-Objective Optimization
**Step 2: Pareto selection and non-dominated sorting. **  
The fitness of individuals is evaluated based on the objective functions [37]. Non-dominated sorting is performed on the individuals in the population \(P(0)\), assigning different levels of non-dominance to the individuals. The Pareto level of each individual \(r(x_{i})\) is determined by the number of individuals it dominates, with lower levels indicating a solution closer to the Pareto front. Level 1: contains all individuals not dominated by any other solution. Level 2: contains individuals only dominated by solutions in Level 1, and so on. The roulette wheel selection method is employed to select individuals based on their fitness values, calculated as follows:  
\[F(x)=\frac{f(X^{i})}{\sum_{j=1}^{N}f(X^{j})}=\frac{1}{1+r(x_{i})} \tag{15}\]  
where \(f(X)\) is the fitness function for an individual and \(r(x_{i})\) is the rank of an individual \(x\). An elite retention strategy ensures that the current optimal individuals directly progress to the next generation, preventing the loss of optimal solutions. For each individual on the Pareto front, its crowding distance is calculated to maintain population diversity. The crowding distance \(d(x_{i})\) is determined by measuring the distance between that individual and its nearest neighbors:  
\[d(x_{i})=\sum_{j=1}^{m}\left(\frac{f_{j}(x_{i+1})-f_{j}(x_{i-1})}{f_{j}^{ \text{max}}-f_{j}^{\text{min}}}\right) \tag{16}\]  
Step 3: Genetic operations and local search. Genetic operations, including crossover and mutation operations, are performed, alongside local search strategies, combining Particle Swarm Optimization (PSO) and Differential Evolution (DE) to enhance solution quality [38]. Crossover employs a combination of single-point and multi-point crossover methods, with a crossover probability of \(p_{c}\). New individuals are generated by the following formula:  
\[X^{new}=Cross(X^{i},X^{j}) \tag{17}\]  
where \(X^{i}\) and \(X^{j}\) are the parent individuals involved in crossover, and \(X^{new}\) is the offspring individual generated [39]. Mutation is achieved by randomly altering one or more genes of an individual to increase diversity, with a mutation probability of \(p_{m}\). The mutated individual is denoted as follows:  
\[X^{mut}=Mutate(X^{i}) \tag{18}\]  
where \(X^{i}\) is the individual undergoing mutation, and \(X^{mut}\) is the mutated individual [40]. In the case of single-point crossing, for each pair of parental chromosomes selected for crossing, a random crossing point is chosen. After this point, all genes of one parent are exchanged with the corresponding genes of the other parent. This method promotes the mixing of genetic information while maintaining some structural integrity of chromosomes. For multi-point crossing, after performing single-point crossing, multiple crossover points are selected within the chromosome. The segments between these points are exchanged between the two parents, allowing for greater variation and exploration of the solution space. In the combined strategy, single-point crossover is applied first, followed by multi-point crossover on the offspring generated from the first operation. This two-step process leverages the strengths of both methods, encouraging a broader search for optimal solutions while maintaining convergence. Regarding parameter settings, the crossover probability of both single-point and multi-point methods is uniformly set to 0.8 in this study. This ensures that a sufficient number of offspring inherit diverse features from their parents. By utilizing this combination of crossover methods, the genetic algorithms effectively explore the solution space while preserving high-quality genetic material from the parental chromosomes. PSO enables each particle to navigate in the solution space while continuously updating its position and velocity to converge on the optimal solution. The position of each particle in the solution space is denoted by \(d_{i}\), and its velocity is denoted by \(v_{i}\).