# Freeway Traffic Congestion Reduction and Environment Regulation via Model Predictive Control
## 6 Simulation Research
### Simulation Results  
It is assumed that all of vehicles are cars, and the compliance rate is 100%, namely \(a=0\). The parameters of MPC_CPDMO-NSGA-II are shown in Table 2, which are also referred by the authors of [7]. Table 2 gives the value of parameter use in the MPC_CPDMO-NSGA-II algorithm. It can be seen from Table 2 that the sampling period is set as 10 s, the control period is set as 1 min, the prediction \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Name** & **Value** & **Unit** & **Name** & **Value** & **Unit** \\ \hline \(\tau\) & 18 & s & \(\rho_{cr,m}\) & 33.5 & veh/km/lane \\ \(\kappa\) & 40 & veh/km/lane & \(\delta\) & 0.012 & - \\ \(v\) & 60 & km2/h & \(a_{m}\) & 1.636 & - \\ \(\rho_{\max}\) & 180 & veh/km/lane & \(v_{f,m}\) & 110 & km/h \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters of the METANET model. Figure 6: The freeway network with an on-ramp. Figure 7: The traffic demands of the mainline and the on-ramp. horizon and the control horizon are set as 15 min and 10 min respectively in this paper. Since the control period is set as 1 min, it means that the MPC_CPDMO-NSGA-II algorithm proposed in this paper is suitable for both the simulation experiment and on-line control on the small road network. For larger networks, since more computation time are required, other methods should be applied. The sampling period is also the prediction period of METANET model. In this paper, we will analyze the conditions of the freeway with fixed speed limit strategy firstly, so as to determine which segment requires freeway control strategy. Then, the proposed MPC_CPDMO-NSGA-II algorithm is used to solve freeway congestions in rush hours. The control strategy is an incorporation of VSL and RM strategy. In the proposed CPDMO-NSGA-II algorithm, the size of population is 160; the number of iterations is 50; and the number of clustering is 10. For comparison, a model predictive control based on single-objective optimization algorithm named as MPC_SOO, is used to solve the freeway control problem in this paper, and the single-objective optimization algorithm is genetic algorithm [28]. The performance indicator used in MPC_SOO is described as following:  
\[\min\quad J(k) =k_{1}J_{1}(k)-k_{2}J_{2}(k)+k_{3}J_{3}(k), \tag{38}\]  
where \(k_{1},k_{2},k_{3}\) are the weights, which are set as 0.4, 0.3, 0.3 respectively. To compare the result of the MPC_SOO algorithm and the MPC_CPDMO-NSGA-II algorithm under similar expert's experience, the weights of the \(k_{1},k_{2},k_{3}\) used in the MPC_SOO algorithm is set as the same value used in the TOPSIS method in the MPC_CPDMO-NSGA-II algorithm. In the MPC_SOO method, the single objective is set as the weight sum of the multiple objectives considered in the MPC_CPDMO-NSGA-II algorithm, and the weights used in the single objective in the MPC_SOO method is set as 0.4, 0.3, 0.3, which is the same value used in the TOPSIS method in the MPC_CPDMO-NSGA-II algorithm. The reason is that the result of the MPC_SOO method and the MPC_CPDMO-NSGA-II algorithm are compared under similar expert's experience. In order to distinctly analyze the trends of traffic variables, they are averaged before plotting every 2 min. 2.1 Results of Traffic Condition, Emissions and Fuel Consumption of the Freeway with Fixed Speed Limit  
In the whole simulation process, the fixed speed limit is directly implemented in VISSIM simulation environment, and minimum and maximum speed of the vehicle on each segment on the road is set at [60,100] km/h. In this part, we will discuss the results obtained from fixed speed limit strategy firstly. The Pareto fronts obtained by MPC_CPDMO-NSGA-II algorithm will be discussed in Section 6.2.2 secondly. The results obtained from MPC_SOO method and MPC_CPDMO-NSGA-II algorithm will be discussed in Section 6.2.3 thirdly. The results about traffic conditions obtained from fixed speed limit strategy, MPC_SOO method and MPC_CPDMO-NSGA-II algorithm will be discussed in Section 6.2.4.