# Multi-Class Freeway Congestion and Emission Based on Robust Dynamic Multi-Objective Optimization
## 5 Simulation
### Results  
Each experiment was run for 5 times and the results of the three indicators are the average results. The results of three objective functions, including travel time, ramp queue, and traffic emission of the three algorithms, NSGA-III, RDNSGA-III and DFCM-RDNSGA-III, are compared in Table 5. Among these three algorithms, a static optimization framework is adopted in algorithm NSGA-III to statically optimize the variable speed limit and metering rate in the whole simulation, while a dynamic optimization framework is adopted to dynamically optimize these variables according to the environmental changes in the RDNSGA-III algorithm and the DFCM-RDNSGA-III algorithm. It can be concluded from Table 5 that: (1) The travel time and traffic emission indicators performed the worst on the algorithm NSGA-III with a static optimization framework. Compared to NSGA-III, the two indicators decreased by 14.64% and 16.72%, respectively, in the algorithm RDNSGA-III, as well as 19.04% and 21.64%, respectively, in the algorithm DFCM-RDNSGA-III. (2) Although NSGA-III performs poorly on the travel time and traffic emission indicators, it performs the best on the aspect of the ramp queue indicator. Compared to NSGA-III, the ramp queue indicator increased by 20.51% and 30.36%, respectively, in the algorithm RDNSGA-III and DFCM-RDNSGA-III. \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Number**} & \multicolumn{2}{c}{**SC**} & \multicolumn{2}{c}{**DBI**} \\ \cline{2-5}  & **DFCM** & **FCM** & **DFCM** & **FCM** \\ \hline
1  
The above comparison results show that, under the control scheme of NSGA-III, which has a static optimization framework, the ramp-entering vehicles are not limited when the main road capacity is relatively tight. Therefore, the pressure on the main road will be aggravated due to the excessive ramp-entering, which increases the total travel time and traffic emissions but decreases the ramp queue. For the algorithms under robust dynamic optimization frameworks, including RDNSGA-III and DFCM-RDNSGA-III, although the ramp queue of the DFCM-RDNSGA-III algorithm is improved by 9% compared with the former, the travel time and traffic emission are both improved by more than 5%. The reason is that the inflow of part of the ramp vehicles to the main road is sacrificed in the DFCM-RDNSGA-III algorithm, contributing to the improved traffic efficiency of the main road and the reduced environmental pollution caused by gas emissions. The VSL and RM control schemes during the peak forming period and peak subsiding period of the RDNSGA-III and DFCM-RDNSGA-III algorithms are shown in Tables 6 and 7, while the niche detection threshold is set as \(\varepsilon=0.1\). The environment detection is carried out every 5 min. When it is detected that the environment has not changed, i.e., the threshold before and after the change is set within the predefined range, the optimization does not need to be performed again and the current control scheme continues to be used. This also means that the situation where the control scheme has not changed represents that the optimization need not to be restarted. Therefore, the robustness of the control scheme of the RDNSGA-III and DFCM-RDNSGA-III algorithms can be compared under the same environment detection threshold through the change of control schemes. A static framework is adopted in the basic algorithm NSGA-III to optimize the VSL and RM, so the change of the control scheme is not involved in it. The variation in traffic control schemes of the RDNSGA-III algorithm and the DFCM-RDNSGA-III algorithm according to the change of the environment in the processes of peak hour and dissipation hour are shown in Tables 6 and 7. It can be seen that the average ramp metering rate of the RDNSGA-III algorithm at the three on-ramps is 68% within 0 min to 5 min of the peak formation process, and the ramp metering rate of the DFCM-RDNSGA-III algorithm is 48%.