# Multi-Class Freeway Congestion and Emission Based on Robust Dynamic Multi-Objective Optimization
## 5 Simulation
### Results
In the early stages of peak formation, the DFCM-RDNSGA-III algorithm begins to limit the ramp entry, so as to ensure the patency of the main road in the process of peak formation. After that, the ramp metering rate of the RDNSGA-III algorithm is still maintained at more than 60% within 5-15 min. At 15-20 min, it starts to limit the ramp entry, and the average ramp metering rate is set to 56%, while the ramp metering rate of the DFCM-RDNSGA-III algorithm is always set at about 50% during this period. Therefore, in the early peak formation process, the inflow of the DFCM-RDNSGA-III algorithm is maintained within the scope of environmental detection by limiting the ramp entry. While the ramp inflow in the RDNSGA-III algorithm is not restricted well in the early stage, the flow changes at the last and next time exceed the detection threshold. Therefore, within 20 min of peak formation, the control strategy is continuously adjusted before it starts to maintain stability. Similarly, RDNSGA-III has a certain conservative setting of VSL within 60 min to 75 min of peak dissipation. At the beginning of the peak dissipation process, the VSL is still controlled below 70 km/h. However, the DFCM-RDNSGA-III algorithm starts to maintain the VSL above 70 km/h after 60 min to 65 min of early peak dissipation process, therefore ensuring the rapid outflow of the main road in the process of peak dissipation. In general, the DFCM-RDNSGA-III algorithm has better control optimization stability than \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithms** & **Travel Time (h)** & **Ramp Queue (veh)** & **Traffic Emission (kg)** \\ \hline NSGA-III & 2002.48 & 37.15 & 194.62 \\ \hline RDNSGA-III & 1709.39 & 44.77 & 162.07 \\  & \(-14.64\%\) & \(+20.51\%\) & \(-16.72\%\) \\ \hline DFCM-RDNSGA-III & 1621.26 & 48.43 & 152.5 \\  & \(-19.04\%\) & \(+30.36\%\) & \(-21.64\%\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Comparison of algorithm results. the RDNSGA-III algorithm in the process of peak formation. The control strategy can be better dealt with in the process of peak formation, and solutions with better robustness can be generated under the same environmental sensitivity. Figures 6 and 7 show the heat map of car speed and car flow in each road section of the three algorithms, in which the ordinate denotes the main road section number link 1 to link 18, and the abscissa denotes the time interval. In Figure 6, the speed heat map, it can be noticed through comparison that in the process of peak formation, the speed of each road section in DFCM-RDNSGA-III can be maintained at a relatively high level compared with the other two algorithms, which can better help control the ramp metering rate. Therefore, the traffic efficiency and vehicle speed of the main road can be improved. As can be seen from the flow heat map in Figure 7, the overall process of traffic flow is smoother from link1 to link18 in the DFCM-RDNSGA-III algorithm. The flow variation in each road section is within 500 veh, and the flow difference between each road section is small. However, the traffic flow of the NSGA-III algorithm and the RDNSGA-III algorithm have quite obvious and abrupt variations in the ramp merging section, especially at the ramp merging part of link 10. The traffic flow of NSGA-III algorithm suddenly changes from 2000 veh to 3000 veh, and the traffic flow of RDNSGA-III algorithm also increases by more than 500 veh.