## 3 Results
### Emission-Centered Scenario  
In this section, we consider a scenario in which the weighting parameters are equals (\(\alpha=\beta=\gamma=1\), see Equation (5)) and the Group A hypothesis concerning the optimization parameters is selected. An analysis of the use of RAM on the computing machine has shown that the implementation of the method does not allow the use of more than 16 values of advance and/or equivalence ratio without reaching the limits of the available memory (256 GB) for the Group A parameters. Therefore, four values for the air to fuel equivalence ratio and four values for the relative spark advance are considered. Table 6 summarizes the discretization steps used in Section 3.2. Global results are presented in Table 7 and a comparison with the consumption-centered scenario is drawn in Figure 12 for the WLTC driving cycle. In this drawing, the performance index is represented by the normalized value of the component. For example, the performance index of the fuel is: \(\frac{\#_{fuel}}{\#_{fuel,ref}}\) (see Equation (5)). \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Variable** & **Steps** & **Min. Value** & **Max. Value** \\ \hline Optimization parameter & Group A & & not applicable \\ \hline Equivalence ratio & 0.005 & 0.993 & 1.008 \\ \hline Relative spark advance & \(10^{\circ}\) & \(-30^{\circ}\) & \(0^{\circ}\) \\ \hline Step time & \(1\,\mathrm{s}\) & & not applicable \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Discretization step size used in this section. Figure 11: Temperature evolution and catalyst efficiency for the consumption-centered strategy in the WLTC driving cycle. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Drive** & **Fuel Cons.** & **CO2** & **CO** & **HC** & **NOx** & **RAM** & **Calc.** \\
**Cycle** & **1/100 km** & **g/km** & **g/km** & **g/km** & **g/km** & **Gb** & **Time (h)** \\ \hline NEDC & 3.77 & 89 & 0.302 & 0.007 & 0.009 & 133 & 57 \\ WLTC & 4.52 & 106 & 0.306 & 0.007 & 0.008 & 155 & 95 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Performance of the emission-centered scenario. Aggregated results show that, whatever the driving cycle considered, a small increase in fuel consumption (between 3% to 5%) allows a great reduction in NO\({}_{x}\) emission (divided by a factor 20), thus passing the EURO6 rules (0.060 g/km). One can also notice that CO emissions increase, but still stay three times lower than EU limits. Let us take a deeper look at the results. Figures 13-17 shows the temporal evolution of key variables in the WLTC driving cycle. Figure 13 represents the variation of the state of charge of the battery. The lower bound (in blue line) corresponds to the strategy that maximizes the discharge of the battery (i.e., the all-electric mode), while the red curve represents its maximum charge (i.e., the engine is providing maximum power). Of course, because we are simulating a charge sustaining hybrid, the curve must converge at the end of the driving cycle. This surface defines the admissible operating area. The yellow line is the optimal trajectory regarding the objective function. We conclude that the first part of the driving cycle is made in all-electric mode. This is confirmed in Figure 14, where we observe that the urban part is driven with the electric motor alone. We also notice that when the IC engine is started, the electric motor runs in recovery mode, thus recharging the battery. We also observe in Figure 13 that the optimal strategy is not far from the maximum discharge rate. This is only due to the fact that the more aggressive part of the driving cycle happens at the end, which gives the right conditions for the ICE to develop high power and recharge the battery with the best global efficiency (see Figure 14). Figure 12: Comparison of the performance index in the WLTC driving cycle. Figure 13: SOC trajectory with the emission-centered strategy in the WLTC driving cycle. Figure 16: Control parameters with the emission-centered strategy in the WLTC driving cycle.