## 5 Experimental Results and Analysis
### Comparison Experiments  
The comparison algorithm selects the currently better multi-objective hybrid algorithms MOPSO-GA and MOGA-VNS. Using the same time, HV and IGD were used as experimental evaluation indicators for comparison. Test the solution performance of the algorithm proposed in this article. HV is used to evaluate the degree to which the target space is covered by an approximation set and is the most common evaluation index. A reference point is required. The three targets are normalized separately, and the reference point is set to (1.2, 1.2, 1.2). The HV value is the volume of the hypercube formed between the Pereto front (PF) and the reference point. The comparison of HV does not require a priori knowledge and does not require finding the true Pareto front. If a certain approximation set A completely dominates another approximation set B, then the supercapacity HV of A will be greater than that of B. Therefore, HV can be completely used for PF comparison. The HV calculation method is shown in Equation (24). \[HV(f^{ref},X)=\wedge\left(\underset{X_{n}\in X}{\cup}\left[f_{1}(X_{n}),f_{1} ^{ref}\right]\times\cdots\times\left[f_{m}(X_{n}),f_{m}^{ref}\right]\right) \tag{24}\]  
In Equation (24), \(f^{ref}\) represents the selected reference point and X represents the obtained approximation set, and the value obtained by summing its volumes is the HV index. IGD is similar to Generational Distance (GD), but takes into account both diversity and convergence. IGD starts from the real PF and finds the point closest to it in the PF. This paper selects the optimal PF calculated by running all algorithms 10 times as the optimal PF. If the IGD index is smaller, it means that it is closer to the optimal PF, which means that the diversity and convergence of the algorithm are better. The IGD calculation method is shown in Equation (25). \[IGD=\frac{\sum_{y\in PF^{*}}d(y,x)}{|PF^{*}|} \tag{25}\] \begin{table}
\begin{tabular}{c c c} \hline
**Experiment No.** & **Learning Rate (\(\alpha\))** & **Discount Rate (\(\beta\))** \\ \hline
1 & 0.001 & 0.95 \\
2 & 0.001 & 0.9 \\
3 & 0.001 & 0.85 \\
4 & 0.001 & 0.7 \\
5 & 0.01 & 0.95 \\
6 & 0.01 & 0.9 \\
7 & 0.01 & 0.85 \\
8 & 0.01 & 0.7 \\
9 & 0.05 & 0.95 \\
10 & 0.05 & 0.9 \\
11 & 0.05 & 0.85 \\
12 & 0.05 & 0.7 \\
13 & 0.1 & 0.95 \\
14 & 0.1 & 0.9 \\
15 & 0.1 & 0.85 \\
16 & 0.1 & 0.7 \\ \hline \end{tabular}
\end{table} 
Table 3: Orthogonal experiment details. In Equation (25), \(PF^{*}\) represents the optimal Pareto front, \(x\) represents the obtained approximation set, and \(d(y,x)\) represents each solution y in the true optimal PF. The solution \(x\) in PF that is closest to it is found, and its Euclidean distance is calculated. The HV and IGD indicators for 40 groups of test examples across four sizes are shown in Table 4. The bolded values represent the optimal results for each calculation example. From Table 4, it can be seen that in medium- and large-scale calculation examples, the algorithm proposed in this article performs significantly better compared to the two hybrid algorithms. Additionally, the larger the scale, the more pronounced the improvement. To visually compare the solution quality of MODRL-SIA and the comparison algorithm, the experimental results from LRPTW test examples at different scales are presented in Figure 5. The MODRL-SIA framework not only exhibits superior solution quality but also adeptly manages complex logistics challenges by dynamically adapting to varying operational conditions. This framework utilizes an advanced hybrid method that merges deep reinforcement learning with swarm intelligence algorithms, enabling efficient navigation through the complexities of logistics systems, including fluctuating demand, diverse  
Figure 4: Parameter tuning result schematic. delivery requirements, and variable transportation conditions. By optimizing routes and resource allocations intelligently, the MODRL-SIA framework reduces costs and boosts operational efficiency, offering a robust solution to the multifaceted challenges of modern logistics.