## 6 Conclusions  
The seismic retrofit decision on transportation network is a stochastic optimization problem with high dimensional uncertainty. Most current approaches use heuristic algorithms combined with MCS to find the optimal solutions, but still face terrible computational pressure. To address the issue, this paper introduces an efficient alternative methodology that can greatly reduce the computational burden of the retrofit problem. Based on the idea of feature subset selection, the proposed method transforms the complex stochastic optimization problem into the joint importance-ranking problem of bridge sets. Different from traditional importance-based methods, the proposed method integrates the uncertainty of multiple damage states as well as their effects on network functionality. More importantly, it considers the interactive effect between candidate components. The proposed method is applied to the mitigation problem of seismic emergency risk on a hypothetical transportation network. The results show that, based on only a small set of stochastic samples, the MI- and JMI-based approaches both perform excellently in risk mitigation and the JMI-based strategy provides a great approximation to the real optimal solution. Overall, compared with enumeration and heuristic optimization methods, the proposed method could provide reliable and stable retrofit advice for decision makers with high efficiency, which results in a good engineering application prospect, especially for large-scale transportation networks with high computational complexity. In addition, this study still has some limitations to be further expanded, for instance, to incorporate seismic analysis of complex components and to explore the impact of the correlation effect between earthquake intensities. Investigation, K.L. and C.Z. ; Methodology, K.L. and C.Z. ; Project administration, C.Z. ; Software, K.L. ; Supervision, C.Z. and X.M. ; Validation, K.L. ; Writing--original draft, K.L. ; Writing--review and editing, C.Z. and X.M. All authors have read and agreed to the published version of the manuscript. \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{**ID of Selected Bridges \(B_{m}\)=\([B_{1},B_{2},\ldots,B_{m}]\)**} \\ \cline{2-5} \(m\) & \multicolumn{3}{c}{**Case 1**} & \multicolumn{3}{c}{**Case 2**} \\ \cline{2-5}  & **Optimal** & **JMI-Based** & **Optimal** & **JMI-Based** \\ \hline
1 & 9 & 9 & 9 & 9 \\ \hline
2 & 9 & 9 & 9 & 5, 9 \\ \hline
3 & 2, 5, 9 & 2, 5, 9 & 5, 9 & 1, 5, 9 \\ \hline
4 & 2, 4, 5, 9 & 2, 4, 5, 9 & 2, 5, 8, 9 & 1, 5, 8, 9 \\ \hline
5 & 2, 4, 5, 9 & 2, 4, 5, 8, 9 & 1, 2, 5, 8, 9 & 1, 2, 5, 8, 9 \\ \hline
6 & 1, 2, 4, 5, 8, 9 & 1, 2, 4, 5, 8, 9 & 1, 2, 4, 5, 8, 9 & 1, 2, 4, 5, 8, 9 \\ \hline
7 & 1, 2, 3, 4, 5, 8, 9 & 1, 2, 3, 4, 5, 8, 9 & 1, 2, 3, 4, 5, 8, 9 & 1, 2, 3, 4, 5, 8, 9 \\ \hline
8 & 1, 2, 3, 4, 5, 8, 9 & 1, 2, 3, 4, 5, 8, 9 & 1, 2, 3, 4, 5, 6, 8, 9 & 1, 2, 3, 4, 5, 6, 8, 9 \\ \hline
9 & 1, 2, 3, 4, 5, 6, 7, 8, 9 & 1, 2, 3, 4, 5, 6, 7, 8, 9 & 1, 2, 3, 4, 5, 6, 7, 8, 9 \\ \hline \multicolumn{5}{c}{**Case 3**} & \multicolumn{3}{c}{**Case 4**} \\ \cline{2-5} \(m\) & \multicolumn{3}{c}{**Optimal**} & \multicolumn{3}{c}{**JMI-Based**} \\ \cline{2-5}  & 1 & 9 & 9 & 2 & 2 \\ \hline
2 & 5, 9 & 5, 9 & 2, 4 & 2, 4 \\ \hline
3 & 1, 5, 9 & 1, 5, 9 & 2, 4, 8 & 2, 4, 8 \\ \hline
4 & 1, 3, 5, 9 & 1, 3, 5, 9 & 2, 4, 6, 8 & 2, 4, 8, 9 \\ \hline
5 & 1, 3, 5, 9 & 1, 3, 5, 9 & 2, 4, 6, 8, 9 & 2, 4, 6, 8, 9 \\ \hline
6 & 1, 3, 5, 7, 8, 9 & 1, 3, 5, 7, 8, 9 & 2, 4, 5, 6, 8, 9 & 2, 4, 5, 6, 8, 9 \\ \hline
7 & 1, 2, 3, 5, 7, 8, 9 & 1, 2, 3, 5, 7, 8, 9 & 1, 2, 4, 5, 6, 8, 9 & 2, 4, 5, 6, 8, 9, 10 \\ \hline
8 & 1, 2, 3, 4, 5, 7, 8, 9 & 1, 2, 3, 4, 5, 7, 8, 9 & 1, 2, 4, 5, 6, 8, 9, 10 & 1, 2, 4, 5, 6, 8, 9, 10 \\ \hline
9 & 1, 2, 3, 4, 5, 6, 7, 8, 9 & 1, 2, 3, 4, 5, 6, 7, 8, 9 & 1, 2, 3, 4, 5, 6, 8, 9, 10 & 1, 2, 3, 4, 5, 6, 8, 9, 10 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Optimal and JMI-based seismic retrofit strategies.