## 5 Results
### Optimum Type Design Solutions  
Optimisation Results  
Regarding Scenario 1, Figure 8a,b illustrates the relation between the optimisation objectives and reveals the trade-offs among them. More specifically, Figure 8a reveals the conflicting relation between wear and comfort levels, where the increase of the RC index, which yields the increase of discomfort, leads to the decrease of tyre wear. At the same time, the conflicting relation of comfort and handling, captured by the optimisation in Figure 8b, serves as an indication of the validity of the results. In addition, the conflicting relation of the two objectives, handling and wear, with comfort reveal the linear relation between them, implying that increased levels of tyre deflections lead to increasing wear. Figure 9: Comparison of the optimum solutions obtained for the two optimisation cases (Class A and B road profiles) in Scenario 1: (**a**) TW vs. \(P\); (**b**) TW vs. \(c\); (**c**) TW vs. \(d\); (**d**) TW vs. \(b_{0}\); and (**e**) TW vs. \(r_{w}\). As far as the design variables are concerned, according to Figure 9a-e, the tyre pressure (\(P\)), the outside radius (\(d\)) and the chordwise curve (\(r_{w}\)) illustrate a conflicting relation with wear. For these, the algorithm has provided optimal alternatives ranging from the lower bound to the upper bound, which allowed capturing the conflicting relation between these variables and wear. On the other hand, the Pareto alternatives of tyre width (\(c\)) and crown thickness (\(b_{0}\)), as shown in Figure 9b,d, respectively, have not captured their relation with wear, as the algorithm converged close to one value. In the case of the tyre width, this value is different from the upper or lower bound, whereas the crown thickness alternatives have converged close to the lower bound trying to decrease the length of the tread (Figure 3a). However, both values are realistic according to the literature. Regarding the different road cases, Case 2 alternatives are providing larger values in all the objectives, as the more intense road roughness profile has increased discomfort, vehicle instability and tyre wear. Regarding the latter, according to Figure 8a, Case 2 Pareto alternatives have increased wear around \(\sim\)25% compared to Case 1, which illustrates how road profiles increase wear significantly if different tyre designs are adopted. In terms \begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Solution**} & \multicolumn{4}{c}{**Optimum Design Variables**} \\ \cline{2-5}  & \(K_{3}\)[N/m] & \(C_{min}\)[N/s] & \(C_{max}\)[N/s] & \(a_{f}\) [rad/sec] & **Threshold (\(c\))** \\ \hline
**PS** & 16,042 & 3675 & - & - & 6.0\% \\ \hline
**SH-2** & 43,181 & 2275 & 4394 & - & 9.5\% \\ \hline
**GH-2** & 16,160 & 2415 & 3327 & - & 3.0\% \\ \hline
**ADD** & 41,406 & 2452 & 4530 & - & 5.0\% \\ \hline
**PDD** & 15,534 & 1442 & 4045 & - & 5.0\% \\ \hline
**SH-PDD** & 42,281 & 2416 & 4749 & - & 5.0\% \\ \hline
**SH-ADD2** & 17,246 & 684 & 3515 & 23.5 & 15.0\% \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Common optimal suspension parameters among the two road profile cases for each suspension type. Figure 10: The tread profile induced to the tyre for the two common optimal tyre designs, after the vehicle is driven over the Class B S-path 20 times back and forth. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Solution**} & \multicolumn{4}{c}{**Optimum Design Variables**} \\ \cline{2-6}  & \(P\)[KPa] & \(c\)[m] & \(d\)[m] & \(b_{0}\)[m] & \(r_{w}\)[m] \\ \hline
**1** & 252 & 0.1889 & 0.2728 & 0.1215 & 0.1420 \\ \hline
**2** & 192 & 0.1883 & 0.2746 & 0.1206 & 0.1441 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Optimal tyre design variables of the identified common solutions among the two cases of different road profiles.