## 6 Experimental Comparison and Analysis
### Experimental Design  
According to the relevant literature, a verification example and a test example are designed. For the verification example, through the combination of the number of workpieces \(n\), the number of machines \(m\), and the number of AGVs \(a\), a total of 36 sets of verification examples were randomly generated, and each set of examples was repeated three times, resulting in a total of 108 sets of examples. To further validate the practicality of our proposed approach, we designed the simulation environment based on real-world pulsating assembly flow shops. Specifically, we referenced production settings from aerospace manufacturing workshops, where AGVs are widely used for material handling in complex assembly processes. The simulation design in this study is carefully aligned with real-world manufacturing applications. The experimental settings, including the number of jobs \(n\) = {20, 30, 50, 100}, machines \(m\) = {4, 6, 8}, and AGVs \(a\) = {4, 6, 8}, were selected based on actual pulsating assembly flow shop configurations observed in industry. These values are also consistent with established benchmark problems in flow shop scheduling [27; 28; 29], ensuring that the proposed model and scheduling strategies are applicable to practical production scenarios. By incorporating realistic constraints and parameters, the proposedscheduling framework closely reflects real-world operations, strengthening its applicability and robustness.  
The selection of problem sizes in this study is based on real-world pulsating assembly flow shops, particularly in aerospace and automotive manufacturing. Small-scale instances (\(n=20\), \(30\)) represent low-volume, high-mix production environments, where customized products require frequent scheduling adjustments. Medium-scale instances (\(n=50\)) correspond to standard production lines with moderate batch sizes, while large-scale instances (\(n=100\)) reflect high-volume production workshops, where efficient AGV scheduling is crucial for maintaining throughput. These problem sizes were chosen to ensure that the proposed scheduling strategies remain applicable across various manufacturing scenarios, from flexible production lines to large-scale automated assembly systems.  
The parameter values of the production data in the example are set as follows: The processing time of each workpiece in different machines obeys the uniform distribution of [1; 99], that is, \(U\)[1; 99], which is commonly used in scheduling research to reflect variability in manufacturing tasks and the transportation time of the AGV between each workstation is scaled according to the station distance.  
The algorithm program and experimental environment were programmed in Python 3.9, and the experiment was carried out on the same computer. The computer configuration is 11 th Gen Intel(R) Core (TM) i7-1165G7 @ 2.80 GHz 2.80 GHz, 16.0 GB RAM.  
All algorithms were evaluated using the Relative Percentage Deviation (RPD), as shown in Equation (7). Among them, \(ObjVal_{alg}\) represents the target value calculated by an algorithm and \(ObjVal_{best}\) represents the optimal target value obtained by all algorithms in the entire experiment.  
\[RPD=\frac{ObjVal_{alg}-ObjVal_{best}}{ObjVal_{best}}\times 100\% \tag{7}\]