## 4 Case Study
### Results and Analysis
#### 4.2.1 Optimization Results  
Using the algorithm model, the two objectives of minimum carbon emission and maximum revenue were considered to be solved separately, and two optimization results were obtained. Then  
Figure 6 represents the optimal location of carbon emission, in which the solid points represent the classification and testing centers, and the hollow points represent the recycling and processing centers. In this figure, the \(X\)-axis indicates the longitude of the city, and the \(Y\)-axis indicates the latitude of the city. As shown in Figure 6, the optimal solution is: \begin{tabular}{c c c c c c c c c c c c c c c c} \hline
**1** & **1** & **1** & **0** & **1** & **0** & **0** & **0** & **1** & **1** & **1** & **1** & **0** & **0** & **0** & **0** & **1** & **0** \\ \hline \end{tabular}   
Corresponding the optimal solution to the selected city, the classification and testing center can be established in Changchun, Jilin, Siping, Tonghua and Baicheng, and the recycling and processing center can be established in Changchun, Jilin, Siping and Liaoyuan. Consequently, the carbon emissions of the recycling network can be minimized. The carbon emissions of each type are shown in Table 10. It can be seen from the table that the transport carbon emissions account for the largest part of the recycling carbon emissions, accounting for more than 95%, which reminds us that in the construction of the recycling network, we should pay more attention to the optimization of the route to reduce the transport carbon emissions. Figure 8 represents the optimal site selection of recovery income, in which the solid points represent the classification and testing centers, and the hollow points represent the recycling and processing centers. In this figure, the \(X\)-axis indicates the longitude of the  
Figure 8: Optimal site selection of recovery income. Figure 7: Recovery revenue target evolution results. city, and the \(Y\)-axis indicates the latitude of the city. As shown in Figure 8, the optimal solution is: \begin{tabular}{c c c c c c c c c c c c c c c c c} \hline \hline
**1** & **1** & **0** & **1** & **0** & **0** & **1** & **0** & **0** & **0** & **1** & **1** & **0** & **0** & **0** & **0** & **0** & **0** & **0** \\ \hline \hline \end{tabular}   
Corresponding the optimal solution to the selected city, the classification and testing center was established in Changchun, Jilin, Songyuan and Baishan, and the recycling and processing center was established in Jilin and Siping. At this time, the profit value of the recycling network could reach the maximum. The various benefit/cost values are shown in Table 11. It can be seen from the table that in the recovery cost, the recovery and processing cost accounts for the largest part, accounting for more than 90% of the total cost. In order to save cost and improve revenue, it is necessary to make a breakthrough in the recovery process. In addition, transportation cost is also a point that needs to be paid attention to. Reasonable planning of routes can save costs. Consider dual targets of carbon emissions and recycling revenue  
It can be seen from the single objective analysis above that the carbon emission target is mainly affected by transportation, so the appropriate increase of classification detection stations and recycling and processing stations can effectively reduce carbon emissions, while the recycling income is mainly affected by the processing cost, so the recycling task can be completed with fewer logistics facilities to get more benefits. To sum up, in order to achieve the dual goals of maximizing benefits and minimizing carbon emissions, it is necessary to balance the number and location of logistics facilities. Figure 9 shows the convergence record of logistics site selection in the process of dual-objective evolution. It can be seen that after 100 times of evolution, the algorithm completed the balance of the dual-objective. \begin{table} \end{table} 
Table 11: Revenue Target Results Table (Yuan). Figure 9: Dual-objective evolution results.