# Multi-Attribute Collaborative Optimization for Multimodal Transportation Based on User Preferences
## 5 Case Study
### Case Solution  
The GA-AFO hybrid algorithm was implemented using MATLAB 2023a and evaluated on a Windows 10 system equipped with a 2.40 GHz processor and 8.00 GB of RAM. Key parameters were configured as follows:  
Population size: 50 individuals;  
GA iterations (generations): 20 (evolutionary cycles of the genetic algorithm);  
AFO iterations (outer loop): 100 (outer optimization loop of the AFO algorithm);  
Crossover probability: 0.7;  
Mutation probability: 0.1. This configuration ensures a balance between exploration (via 20 GA generations) and exploitation (via 100 AFO outer-loop iterations), with the GA refining the population structure and the AFO component fine-tuning individual solutions. The GA-AFO algorithm, as well as the GA and AFO algorithms, each were executed 20 times independently. The best-performing run from each algorithm was selected for comparison, and the results are illustrated in Figure 8. It can be observed that all three algorithms are capable of obtaining the optimal solution. To further validate the efficiency \begin{table}
\begin{tabular}{c c c} \hline \hline
**Transportation Mode** & **Data Category** & **Value** \\ \hline Highway & Transportation cost (CNY (t/km)\({}^{-1}\)) & 0.3 \\  & Carbon emission factor (kg (t/km)\({}^{-1}\)) & 0.796 \\ Railway & Transportation cost (CNY (t/km)\({}^{-1}\)) & 0.2 \\  & Carbon emission factor (kg (t/km)\({}^{-1}\)) & 0.028 \\ Waterway & Transportation cost (CNY (t/km)\({}^{-1}\)) & 0.1 \\  & Carbon emission factor (kg (t/km)\({}^{-1}\)) & 0.04 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Characteristics and values of each transportation mode. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Transportation** & \multicolumn{3}{c}{**Highway**} & \multicolumn{3}{c}{**Railway**} & \multicolumn{3}{c}{**Waterway**} \\ \cline{2-10}
**Arc Segment** & **Distance/km** & **Capacity/t** & **Risk** & **Distance/km** & **Capacity/t** & **Risk** & **Distance/km** & **Capacity/t** & **Risk** \\ \hline (1, 2) & 400 & 160 & 20 & 312 & 180 & 12 & — & — & — \\ (1, 3) & 350 & 190 & 18 & — & — & — & 650 & 175 & 10 \\ (1, 4) & 435 & 168 & 10 & 424  
of these algorithms, we tested them on networks with varying numbers of nodes. All three algorithms were able to converge to the same optimal solution, and their iterative convergence processes are depicted in Figure 9. In the figure, the horizontal axis represents the number of nodes in the network, while the vertical axes denote the number of iterations and the iteration time required for the algorithms to converge, respectively. It can be seen that when the network is relatively small, the hybrid GA-AFO algorithm, due to the initial iterations of GA in its early stages, requires slightly more iterations to converge compared to the standalone GA and AFO algorithms. However, as the complexity of the network gradually increases, the number of iterations and the iteration time for both the GA and AFO algorithms rise sharply, whereas those for the hybrid algorithm increase at a much slower pace, maintaining a relatively stable state. This demonstrates the hybrid algorithm's excellent accuracy and efficiency. Table 4 presents the optimized transportation schemes and their corresponding performance indicators. The disparities among these schemes in terms of transportation cost, carbon emissions, travel duration, and risk exposure are visually illustrated in Figure 10. It is evident that each scheme exhibits distinct strengths and weaknesses. For instance, Scheme 7 achieves the lowest transportation cost, while maintaining moderate levels of carbon emissions and travel time, yet it incurs the highest transportation risk. In contrast, Scheme 2 leads in carbon efficiency and shortest delivery time, with its cost and risk profiles  
Figure 8: Comparison of the GA-AFO, AFO, and GA with 15 nodes. Figure 9: Comparison of the GA-AFO, AFO, and GA with different nodes. ranking second among all options.