# Optimization of Multimodal Discrete Network Design Problems Based on Super Networks
## 6 Conclusions
\begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline
**Case** & \(\mathbf{\kappa}\) & \(\mathbf{\beta}\) & \(\gamma\) & \(\delta\) & \(\mathbf{\theta}\) & \(\mathbf{\tau}\) & **Optimization Schemes** & \(\mathbf{Z}\) \\ \hline
1 & 0.25 & 0.25 & 0.25 & 0.25 & 0.5 & 0.5 & (1,2), (2,3), (12,13), (15,16) & 56823.0 \\
2 & 0.25 & 0.25 & 0.25 & 0.25 & 0.9 & 0.1 & (1,2), (2,3), (12,13), (15,16), (17,20) & 78161.4 \\
3 & 0.25 & 0.25 & 0.25 & 0.25 & 0.1 & 0.9 & (1,2), (12,13), (15,16), (17,20) & 34684.6 \\
4 & 0.4 & 0.4 & 0.1 & 0.1 & 0.5 & 0.5 & (1,2), (2,3), (12,13), (15,16) & 62457.3 \\
5 & 0.4 & 0.4 & 0.1 & 0.1 & 0.9 & 0.1 & (1,2), (2,3), (12,13), (15,16), (17,20) & 84172.2 \\
6 & 0.4 & 0.4 & 0.1 & 0.1 & 0.1 & 0.9 & (1,2), (12,13), (15,16), (17,20) & 41435.1 \\
7 & 0.6 & 0.2 & 0.15 & 0.05 & 0.5 & 0.5 & (1,2), (2,3), (12,13), (15,16) & 65381.5 \\
8 & 0.6 & 0.2 & 0.15 & 0.05 & 0.9 & 0.1 & (1,2), (2,3), (12,13), (16,7) & 70242.2 \\
9 & 0.6 & 0.2 & 0.15 & 0.05 & 0.1 & 0.9 & (1,2), (2,3), (12,13), (15,16) & 62369.7 \\
10 & 0.2 & 0.6 & 0.05 & 0.15 & 0.5 & 0.5 & (1,2), (12,13), (15,16), (17,20) & 52854.8 \\
11 & 0.2 & 0.6 & 0.05 & 0.15 & 0.9 & 0.1 & (1,2), (2,3), (12,13), (15,16), (17,20) & 75254.6 \\
12 & 0.2 & 0.6 & 0.05 & 0.15 & 0.1 & 0.9 & (1,2), (12,13), (15,16), (17,20) & 30357.3 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Optimization results of the actual network under different weight coefficients. transportation network planning and construction can be obtained to provide comparison and reference for traffic planning departments, decision-makers, and researchers. (2) In the complicated urban transportation network formed by various modes, grasping the mutual influence between the operation of the multimodal transportation networks as a whole is helpful to improve the level of transportation management measures, and also conducive to giving full play to the advantages of various modes and coordinate the combination of various modes. These will bring great improvement to the transportation congestion, thus reducing vehicle delays and transportation costs. Certain disadvantages of the proposed methods need to be mentioned here. In this paper, only single OD is considered, and the passenger demand is determined. In future work, we will study the multimodal DNDP of multi-OD under uncertain demand. In addition, this paper only studies five representative travel modes: car, bus, and rail transit, walking, and bike-sharing. However, they can be subdivided into many types in real life. For example, the car model includes private cars, taxis, online car-hailing, etc. And electromobile, motorcycle and so on are also the travel modes that many people choose. Therefore, we can take these into account to improve the proposed model in future work. Conceptualization, C.C. and Y.Z. ; methodology, Y.Z. ; software, Z.F. ; validation, Y.Z., C.C. and Z.F. ; formal analysis, Y.Z. ; investigation, Y.Z. ; resources, C.C. ; data curation, Y.Z. ; writing--original draft preparation, Y.Z. ; writing--review and editing, Z.F. ; visualization, Y.Z. ; supervision, C.C. ; project administration, C.C. ; funding acquisition, C.C. All authors have read and agreed to the published version of the manuscript. This research was funded by Research Foundation of State Key Laboratory of Rail Traffic Control and Safety, Beijing Jiaotong University, China (RCS2021 ZZ002). This study did not involve humans or animals. This study did not report any data. The authors declare no conflict of interest.