## 4 Simulation and Result Discussion of the MOO Problem
### Simulation Analysis of NSGA-II  
MOO Simulation Model  
In order to guarantee the Pareto solution sets and evaluate the control effect of the strategies during deceleration braking, several simulations experiments were carried out to verify the feasibility and effectiveness of the system in MATLAB/Simulink and AVL-Cruise software. The main parameters used in the simulations are shown in Table 1.  
The API function provided by the Cruise software was used to develop vehicle control strategy on Simulink, while vehicle model development and the simulation calculation for vehicle performance were conducted on the Cruise. The vehicle control strategy was developed by the means of Simulink and the API function was provided by the Cruise. Vehicle model development and simulation calculations of vehicle performance are carried out on Cruise. The signals data such as traction and breaking, battery SoC, and \(V_{vch}\) were transferred via the interface of Cruise to Simulink. The analysis results were sent back to Cruise via the interface. Simulation on the power system was conducted in the Cruise model.  
In the model, the values of the output form a vector by a multiplexer. After completing the simulation step successfully, the output vector was transferred into the Matlab Workspace by the Matlab object \"Block Parameters: To Workspace,\" and Cruise could access it. The output values of the model had to be combined to a vector. Cruise got this vector and put its elements onto the data bus where they could be used by other components. The vehicle's dynamic model and regenerative braking control system were established in Cruise and Simulink, respectively, using a co-simulation model as seen in Figure 8.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Value** & **Parameter** & **Value** \\ \hline Full load weight (kg) & 1700 & Battery capacity (kWh) & 20 \\ Wheelbase (mm) & 2865 & Initial SoC (state of charge) & 0.8 \\ Distance from front axle to centroid (mm) & 1352 & Diameter of front wheel cylinder (mm) & 56.95 \\ Distance from rear axle to centroid (mm) & 1513 & Diameter of rear wheel cylinder (mm) & 33.82 \\ Centroid height (mm) & 500 & Diameter of master cylinder (mm) & 18 \\ Drag area (m\({}^{2}\)) & 1.66 & Effective radius of front brake rotor (mm) & 0.235 \\ Correction coefficient of rotating mass & 1.1 & Effective radius of rear brake rotor (mm) & 0.227 \\ Mechanical efficiency & 0.96 & Brake pedal leverage ratio & 3.5 \\ Transmission reduction ratio & 4.2 & Diameter of pedal travel simulator (mm) & 15 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Parameters of the multi-objective optimization (MOO) simulation model.  
Figure 8: Simulation platform of the R-EEV for the MOO problem.  
In order to verify the effectiveness of MOO algorithm, a co-simulation test was carried out based on the braking system model of R-EEV in the simulation environment. A customized typical deceleration braking (CTDB) was defined, as shown in Figure 9a. In simulations, the initial braking speed was set at 80 km/h. The braking strength increased slowly from 0 to 0.2 in 2 s and then increased quickly to 0.7 to simulate emergency braking conditions, and finally it stabilized at 0.5 until the vehicle speed was 0. A comprehensive driving cycle consisting of the CTDB, New European Drive Cycle (NEDC), China Light-duty Vehicle Test Cycle (CLTC), and World Light vehicle Test Procedure (WLTP) was set up, as shown in Figure 9b.  
Three different roads were assumed, namely, a dry asphalt surface with a high PTAC (\(\mu_{max\_h}\) = 0.9), dry cement surface with a medium PTAC (\(\mu_{max\_m}\) = 0.6), and wet cobblestone surface with a low PTAC (\(\mu_{max\_l}\) = 0.3), respectively.