## 3 Driver-Inspection Vehicle Automatic Scheduling Method
### Dynamic Automatic Scheduling Algorithm Based on Multi-Objective Optimization  
In managing the relocation of customs inspection vehicles, the scheduling system must optimize multiple objectives simultaneously, including minimizing vehicle waiting time, optimizing relocation paths, maximizing resource utilization, and balancing driver workload. These objectives often conflict, making the pursuit of an optimal balance a central challenge for this algorithm. To address the multi-objective optimization problem, this study adopts a hybrid intelligent optimization algorithm framework that combines the advantages of Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and Differential Evolution (DE) algorithms. This combination ensures both a robust global search capability and an effective local optimization capability. In the dynamic automatic scheduling algorithm based on multi-objective optimization, Pareto selection is employed to identify and maintain a set of solutions that are not strictly dominated by any other solutions across all objectives. Specifically, the algorithm integrates multi-objective optimization techniques with Pareto optimal selection to generate and filter effective scheduling schemes. The specific steps and combinations of the algorithm are outlined as follows:  
**Step 1: Initial population generation. **  
The initial population is generated based on random initialization and diversity control [34]. Heuristic generation methods, based on established rules or strategies, are employed to enhance the quality of initial solutions. In vehicle scheduling problems, initial solutions can be derived using known priority rules or simple scheduling strategies, improving the quality and optimizing overall efficiency. The scheduling problem is represented as the vector \(X=[x_{1},x_{2},\cdots,x_{n}]\), where each element \(x_{i}\) represents the specific scheduling order of the \(i\)-th inspection vehicle. To avoid generating infeasible solutions, an integer encoding method is adopted, with each \(x_{i}\) value range corresponding to the set of possible vehicle sequences [35]. The initial population is generated through random initialization, denoted as \(P(0)\). Specifically, the initialization method is:  
\[P(0)=\left\{X^{1},X^{2},\cdots,X^{N}\right\} \tag{14}\]  
where \(N\) represents the population size to ensure diversity, \(X^{i}\) represents the \(i\)-th individual in the population, and each individual's value on each objective function is calculated, including vehicle allocation, path selection, resource allocation, and driver tasks [36]. To elucidate the operation of the genetic algorithm's operation, it provides a detailed account of chromosomes within the optimization framework. Each chromosome represents a potential solution to the scheduling problem and comprises several key components:  
Vehicle priorities: each chromosome encodes the priorities of vehicles waiting for inspection, ensuring that higher-priority vehicles are scheduled first based on their urgency and inspection requirements. Optimal scheduling path: the chromosome includes a sequence of scheduled actions for each vehicle, detailing the path from the arrival point to the inspection yard, influenced by capacity and vehicle types. Driver assignments: each chromosome encodes driver assignments for each vehicle, considering driver skills, current workloads, and availability to ensure optimal matching. Resource allocation: elements indicating the allocation of resources (e.g., inspection lanes and equipment) necessary for processing each vehicle are incorporated into the chromosomes. Performance metrics: additional components may include fitness scores reflecting the expected performance of the scheduling plan encoded within the chromosome, facilitating the selection process during genetic operations. By structuring the chromosome in this manner, the genetic algorithm effectively explores a diverse solution space, enabling continuous evolution and enhancement of scheduling efficiency across successive generations.