## 6 Example Solution and Analysis
### Sensitivity Analysis  
#### 6.3.1 Effectiveness of Improved Grey Wolf Algorithm  
To verify the superiority of our algorithm, we compared it with three other traditional search optimization algorithms: the traditional grey wolf algorithm, ant colony algorithm, and large neighborhood search algorithm. Furthermore, to ensure that the other three algorithms would not fall into the local optimal solution as a result of logical defects, we also improved those three comparison algorithms. The algorithm parameters and improvements are as follows. First, for the ant colony algorithm, an improved ant colony algorithm strategy, with the adaptive-adjusting pheromone volatile factor, is introduced, and the global performance of the algorithm is improved by adaptively changing pheromone volatile factor \(\rho\). Letting \(\rho\) start with \(\rho(t_{0})\)\(=1\), \(\rho\) performs an adaptive adjustment according to the following formula:  
\[\rho_{(t)}=\left\{ \begin{array}{ll}0.95\rho(t-1)\,if\ 0.95\rho(t-1)\geq\rho_{ \min}\\ \rho_{\min}\,\ \ \ \ \ \text{otherwise}\end{array} \right.\]  
After conducting multiple calculations, we established the following parameters for the adaptive ant colony algorithm to ensure the optimal results. The concentration weight of the pheromone (alpha) and the heuristic information weight (beta) are 1 and 2, respectively. These values balance the effects of the pheromone and heuristic information during the search process. Meanwhile, the evaporation rate of the pheromones (rho) is set to 0.5, regulating the persistence and update speed of the pheromones. We also set the exploration probability (q0) to 0.9, encouraging the ants to choose the optimal solution. To determine when the algorithm should stop searching, we used a convergence criterion of 0.001. The search process terminates when the difference between a newly generated solution, and the current best solution is smaller than this value. Moreover, we introduced the static weighted average strategy [37] to the grey wolf algorithm, assigning weights to the three head wolves to show the hierarchical structure of \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Region**} & **IGWO Logistics** & **Traditional Distribution** & **IGWO Carbon** & **Traditional Distribution** \\  & **Cost/RMB** & **Method Logistics Cost/RMB** & **Emissions/t** & **Method Carbon Emissions/t** \\ \hline Region 1 & 3443.01 & 3720.26 & 0.574 & 1.34 \\ Region 2 & 3170.29 & 3783.01 & 0.584 & 1.362 \\ Region 3 & 3011.86 & 3011.86 & 1.11 & 1.11 \\ Region 4 & 2735.10 & 2735.10 & 1.008 & 1.008 \\ Region 5 & 2960.33 & 2960.33 & 1.091 & 1.091 \\ Region 6 & 2787.20 & 3035.86 & 0.480 & 1.119 \\ Region 7 & 3815.46 & 4514.45 & 0.714 & 1.507 \\ Total & 21,923.25 & 23,760.87 & 5.561 & 8.537 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparison table of new and old transportation methods. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Region** & **Total Demand/Piece** & **Delivery Method** \\ \hline Region 1 & 58 & Vans \\ Region 2 & 48 & Vans \\ Region 3 & 72 & Refrigerated trucks \\ Region 4 & 61 & Refrigerated trucks \\ Region 5 & 79 & Refrigerated trucks \\ Region 6 & 50 & Vans \\ Region 7 & 62 & Vans \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Regional demand table. the pyramid. The alpha wolves were assigned a weight of 0.5, beta wolves 0.3, and delta wolves 0.2. Lastly, to expedite the convergence of the large-scale neighborhood search algorithm, we used the C-W saving method to construct an initial solution. The number of iterations, numIterations, was set to 300, while the neighborhood size was defined as 100, indicating the number of paths that require modification during each search. Additionally, we set the tabu length to 13, dictating the duration that a path cannot be revisited.