# A Deep Reinforcement Learning-Based Decision-Making Approach for Routing Problems
## 4 Experiments
### Generalization Study
#### 4.3.3 Generalization on Real-World Benchmarks  
To assess the actual routing performance of our approach on real-life scenarios, we apply models trained on synthetic datasets to tackle instances in real-world benchmarks, i.e., TSPLIB [36] and CVRPLIB [37]. To be more specific, we employ the models trained on TSP100 and CVRP100 with uniform distribution to solve instances in TSPLIB and CVRPLIB. The final experimental results are reported in Tables 3 and 4. For TSPLIB, our proposed approach achieves an optimality gap of 7.12%, outperforming AM, DACT, and POMO by  
Figure 5: Generalization results among DRL-based methods on TSPs and CVRPs with explosion node distribution.  
Figure 6: Generalization results among DRL-based methods on TSPs and CVRPs with implosion node distribution.  
a decrease of 20.28%, 16.27%, and 13.58%, respectively. Take rat99 as an example, DRL-DM attains a route length of 1232, which is 8.93%, 6.33%, and 4.63% shorter than that of AM, DACT, and POMO. As for CVRPLIB, the superiority of our proposed approach is also significant. The optimality gap of DRL-DM is 8.91%, which is 10.52%, 6.56%, and 3.91% lower than that of AM, DACT, and POMO. These excellent results demonstrate the potential of our proposed approach to handle a series of challenging and complicated routing problems in real-world scenarios.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Instance** & **Opt.** & **AM [22]** & **DACT [25]** & **POMO [23]** & **Ours** \\ \hline X-n101-k25 & 27,591 & 36,248 & 32,262 & 29,605 & 28,967 \\ X-n106-k14 & 26,362 & 27,936 & 27,568 & 27,323 & 27,296 \\ X-n110-k13 & 14,971 & 16,318 & 16,060 & 15,889 & 15,219 \\ X-n115-k10 & 12,747 & 14,056 & 13,990 & 13,946 & 13,834 \\ X-n120-k6 & 13,332 & 14,453 & 14,392 & 14,352 & 14,231 \\ X-n125-k30 & 55,539 & 72,349 & 70,676 & 69,562 & 62,384 \\ X-n129-k18 & 28,940 & 30,896 & 30,458 & 30,167 & 30,026 \\ X-n134-k13 & 10,916 & 13,561 & 13,288 & 13,107 & 12,805 \\ X-n139-k10 & 13,590 & 14,756 & 14,403 & 14,169 & 13,856 \\ X-n143-k7 & 15,700 & 18,137 & 18,003 & 17,915 & 17,623 \\ X-n153-k22 & 21,220 & 29,034 & 27,434 & 26,368 & 25,103 \\ X-n157-k13 & 16,876 & 21,966 & 20,345 & 19,265 & 18,236 \\ X-n181-k23 & 25,628 & 27,865 & 27,596 & 27,418 & 27,048 \\ X-n190-k8 & 16,980 & 23,028 & 21,443 & 20,387 & 19,339 \\ X-n200-k36 & 58,578 & 76,035 & 74,289 & 73,126 & 67,238 \\ \hline Avg. Gap & 0.00\% & 19.43\% & 15.47\% & 12.82\% & 8.91\% \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison results among DRL-based methods on CVRPLIB.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Instance** & **Opt.** & **AM [22]** & **DACT [25]** & **POMO [23]** & **Ours** \\ \hline eil51 & 426 & 439 & 438 & 436 & 427 \\ berlin52 & 7542 & 8361 & 8062 & 7864 & 7549 \\ st70 & 675 & 693 & 688 & 684 & 682 \\ rat99 & 1211 & 1342 & 1310 & 1289 & 1232 \\ KroA100 & 21,282 & 42,661 & 40,238 & 38,624 & 25,163 \\ KroB100 & 2  
Furthermore, the proposed DRL-DM framework is evaluated on real-world logistics scenarios in Xi'an City, China. Specifically, the model trained on TSP50 is deployed to service 50 spatially distributed customers across the main urban district. Figure 7 presents the routing outcomes generated by DRL-DM in comparison with three representative DRL-based baselines: POMO, DACT, and AM. As illustrated, DRL-DM achieves a tour length of 97.90 km, reflecting improvements of 0.90%, 1.54%, and 4.50% over POMO, DACT, and AM, respectively. These results underscore the practical effectiveness and superior route optimization capability of DRL-DM in addressing complex, real-world vehicle routing tasks.