## 6 Analysis of Optimization Results  
In order to compare the performances of three types of connections (Type 1, Type 2, and Type 3), according to the range of the uncertain variables at the four spring heights shown in Table 2, the upper bound, middle value, and lower bound of each uncertain variable were selected as driving conditions 1-3, respectively. Comparisons were made among the three types of connections in the three driving conditions at each spring height, respectively. The results are shown in Tables 5-8. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Height (m)** & \(x_{1}\) **(mm)** & \(x_{2}\) **(mm)** \\ \hline \(H_{0}\) & 100 & 62 \\ \(H_{1}\) & 100 & 69 \\ \(H_{2}\) & 100 & 76 \\ \(H_{3}\) & 100 & 60 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Optimal geometric parameters of longitudinal-connected suspension at different spring heights based on the DL-MOPSO algorithm. Figure 4: **(a)** Pareto solution set of \(H_{0}\); **(b)** Pareto solution set of \(H_{1}\); **(c)** Pareto solution set of \(H_{2}\); and **(d)** Pareto solution set of \(H_{3}\). Based on Tables 5-8, the optimization rates of Type 3 relative to Type 1 and Type 2 are illustrated in Figure 5. The optimization rate refers to the reduction ratio of \(DLSC\) and \(a\) using Type 3 connection, compared with using Type 1 and Type 2 connections. As shown in the figures, with respect to different spring heights and driving conditions, compared with the two traditional types, the optimization rate of \(a\) is 1.44-35.1%. The \(DLSC\) optimization rate reaches 0.44-20.75% in most cases, except for a slight increase (1.04%) relative to Type 1 longitudinal connection in Condition 2, when the spring height is \(H_{0}\). The reason for the increase of \(DLSC\) is that the optimization in this paper targets the minimum evaluation functions corresponding to the variation intervals of \(DLSC\) and \(a\) when the uncertain variable is changing, so the optimization effect may not be desirable when the uncertain variables take a certain set of values. However, in most driving conditions, the DL-MOPSO algorithm proposed in this paper can guarantee the comprehensive driving performance of the semi-trailer with longitudinal-connected air suspensions. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{
\begin{tabular}{c} **Type of Longitudinal** \\ **Connection** \\ \end{tabular} } & \multirow{2}{*}{**Conditions**} & \multicolumn{2}{c}{**Uncertain Variables**} & \multicolumn{2}{c}{**Evaluation Criteria**} \\ \cline{3-6}  & & \(u_{1}\) & \(u_{2}\) & \(u_{3}\) & \(\alpha\) & \(DLSC\) \\ \hline \multirow{3}{*}{Type 1} & Condition 1 & 1 & 10 & 3735 & 0.04262 & 0.00662 \\  & Condition 2 & 3 & 30 & 5595 & 0.11011 & 0.02303 \\  & Condition 3 & 5 & 50 & 7455 & 0.3235 & 0.03932 \\ \hline \multirow{3}{*}{Type 2} & Condition 1 & 1 & 10 & 3735 & 0.03985 & 0.00533 \\  & Condition 2 & 3 & 50 & 5595 & 0.10722 & 0.01988 \\  & Condition 3 & 5 & 30 & 7455 & 0.29532 & 0.03437 \\ \hline \multirow{3}{*}{Type 3} & Condition 1 & 1 & 10 & 3735 & 0.03533 & 0.00525 \\  & Condition 2 & 3 & 50 & 5595 & 0.10236 & 0.01936 \\ \cline{1-1}  & Condition 3 & 5 & 30 & 7455 & 0.2518 & 0.03273 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Comparisons among the three types of connections at the spring height of \(H_{1}\).