## 4 Simulation and Result Discussion of the MOO Problem
### Results Analysis Based on Pareto Solution Sets  
As we know, the theory of Pareto optimality can reflect the essential characteristic of the MOO problem better. Therefore, the evolutionary algorithm based on the Pareto principle is proposed to solve the MOO problem. The existence of the optimal solution sets was further studied, and a group of non-inferior Pareto solution sets was obtained. The conflicting relationship among the three objectives is shown in Figure 10. The four evaluation indexes of BP, RBLE, BCLR, and CRBP were comparatively analyzed. The optimization results are summarized in Table 2.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Item (High Adhesion)** & **Solution 1 (Best BP)** & **Solution 2 (Lowest RBL)** & **Solution 3 (Lowest BCLR)** & **Solution 4 (Best CRBP)** \\ \hline \([\mu_{\mu,\mu},\mu_{\mu,\mu_{\mu},\mu_{\mu,\mu}}]\) & [0.17, 0.51, 0.44, 0.77] & [0.21, 0.48, 0.24, 0.49] & [0.22, 0.62, 0.29, 0.78] & [0.18,0.53, 0  
The results of the experiment on the high tire-road adhesion condition were taken as an example for discussion and analysis. As shown in Table 3 and Figure 10, the conflict was reflected as the following aspects: (1) Under the best BP (S1), \(I_{bp\_cyc}=0.0407\) with a best braking performance, \(I_{bcl\_cyc}=2.9\) with a better battery state of health (SOH). However, \(I_{rble\_cyc}=0.76\) with the worst braking recovery efficiency. The worse \(I_{crbr\_cyc}=0.61\) was caused by the worst indicator \(I_{rble\_cyc}\). A similar situation manifested under the lowest BCLR (S3). (2) Under the lowest RBLE (S2), \(I_{rble\_cyc}=0.68\) with the best braking recovery efficiency. However, \(I_{bp\_cyc}=0.0473\) with the worst braking performance and \(I_{bcl\_cyc}=11.7\) with the worst battery SOH, which caused the worst \(I_{crbr\_cyc}\). (3) Under the best CRBP (S4), although none of the three indicators were optimal, they were suboptimal and made the best \(I_{crbr\_cyc}\). The performance optimization of one single target may inevitably damage the other targets. The optimization results should be multiple sets of solutions rather than a single optimal solution. Each point represents a set of alternatives. BP, RBLE, and BCLR present a clear conflict, and three optimization objectives cannot be optimal at the same time. Since reducing regenerative braking efficiency tends to extend the battery life, the battery RCC is limited to the maximum. The braking work-point on high regenerative braking will switch to low regenerative braking on the \(I\) curve to ensure braking performance better, which means the high braking performance reduces the regenerative braking efficiency to a certain extent and causes the conflict. The above obtained Pareto optimal solution sets consist of a series of discrete points. It needs only one index to show optimal values and evaluation index more clearly. Therefore, averaging method is  
Figure 10: Distribution of the Pareto optimal solution in objective space: (**a**) \(\mu_{mx\_h}=0.9\); (**b**) \(\mu_{mx\_m}=0.6\); and (**c**) \(\mu_{mx\_l}=0.3\). \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Item**} & \multicolumn{4}{c}{**Optimization Variables**} & \multicolumn{4}{c}{**Evaluation Indexes**} \\ \cline{2-9}  & \(\mu_{\varphi,J}\) & \(\mu_{\varphi,h}\) & \(\mu_{w,J}\) & \(\mu_{w,h}\) & \(I_{bp\_cyc}\) & \(I_{rble\_cyc}\) & \(I_{bcl\_cyc}\) & \(I_{crbr\_cyc}\) \\ \hline First generation & 0.20 & 0.40 & 0.40 & 0.60 & 0.443 & 79.4\% & 16.1\% & 0.32 \\ Last generation & 0.10 & 0.53 & 0.28 & 0.65 & 0.428 & 75.1\% & 11.2\% & 0.71 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Results of the variables. adopted to fit the discrete optimal points into optimal value.