## 5 Experiments
### Experimental Result  
In this section, all methods are evaluated using six datasets of varying sizes, and the statistical outcomes are presented in Table 8. The table includes the size of each dataset, the type of dataset, and the performance of several approaches. We conducted model testing on datasets 1234 and 1236 using 100, 200, and 400 nodes, respectively. Let us take the dataset 1236, which consists of 100 nodes, as an example. The values of \(-3.61\%\), \(-4.01\%\), \(-3.99\%\), \(-3.00\%\), \(1.76\%\), \(-4.81\%\), \(-5.13\%\), \(-1.02\%\), \(-6.39\%\), \(-6.00\%\) and \(-6.02\%\), represent the percentage difference from the solution of the DRL method. Our strategy surpasses other strategies by 2.91%, 2.49%, 6.83%, 1.69%, 1.35%, 5.73%, 2.56%, 3.62%, 8.73%, 0.43%, and 0.39%, respectively. Simultaneously, it is evident that as the sample size increases to 400, the effectiveness of employing the complex rollout baseline and critic baseline strategies for convergence deteriorates considerably compared to using the simple exponential baseline strategy. In fact, the impact may even be twice as severe, suggesting that the complex baseline strategy is not suitable for use at 400 nodes and beyond. A comprehensive analysis of the tabulated data reveals the following: First, the hybrid approach based on strategy optimization and attention mechanisms exhibits significant advantages in small- to medium-scale problems, achieving performance improvements of up to 8.73% over conventional DRL methods. Second, the method that incorporates a rollout mechanism coupled with an exponential decay strategy demonstrates superior scalability in large-scale scenarios, effectively controlling cost escalation and enhancing computational efficiency. Moreover, the improved approach shows markedly higher stability under different random seed settings compared to DRL, thereby validating its robustness in complex problem settings. Additionally, in performance comparisons for large-scale problems, the PGDD algorithm proposed in this section--which integrates strategy pruning with efficient exploration--significantly alleviates the computational complexity issues inherent in DRL. In addition, this section also provides the evaluation performance and evaluation duration of each model on a 400-node dataset at the conclusion of training, as presented in Table 9.  
Evidently, our model exhibits a smaller standard deviation (STD) on the same data, indicating enhanced stability. Although the evaluation time is marginally longer compared to other methods, it remains within the range of a few tens of milliseconds, thereby substantiating the efficiency of our model. In summary, in terms of cost efficiency and stability, the proposed Ours/Exponential algorithm in this section is the most outstanding, ensuring extremely low cost while maintaining minimal solution variability. In contrast, the benchmark algorithm AM/Exponential achieves a relatively balanced performanceacross cost, evaluation time, and stability, which may render it more suitable for practical applications requiring high performance in both cost and speed. In order to further demonstrate the performance of the proposed model in dealing with real datasets, we adjust the Solomon datasets RC201, RC202, and RC203 to meet the model input requirements, as displayed in Table 10. Figure 5 show that our model is still superior to other algorithms and can search for a better path.