## 6 Conclusions  
Bus rescheduling is a critical approach to ensuring the operation of a public transit system. When disruptions occur, the most useful methods for restoring operation schedules are rearranging, canceling, or reassigning trips. However, combinations of the above meth  
Figure 8: Optimization scheme of the DP-LNS algorithm.  
Figure 7: Visualization of local schedule. (**a**) Scheme of the MA. (**b**) Scheme of the greedy algorithm. (**c**) Scheme of the greedy-LNS algorithm. (**d**) Scheme of the DP-LNS algorithm.  
ods are various and intricate. In this paper, we construct a transit rescheduling optimization model based on the connection network. Studies have focused on the successful operation of subsequent trips. However, changes in service frequency caused by delays or cancellations also need to be considered, as these alterations can detrimentally affect passengers' travel experiences. Therefore, we introduce the deviation from departure intervals and construct the ISCR model to ensure both service capability and regularity, which makes the optimal scheme more achievable and reliable.  
The challenges lie in comprehensively considering the hysteresis effects of disruptions and efficiently solving the NP-hard problem and the proposed nonlinear model. Therefore, we propose combining domain knowledge by designing the DP-LNS algorithm. Dynamic programming decomposes the problem and then makes decisions for sub-stages by incorporating the effects of previous stages, which helps overcome long-term issues. Moreover, the LNS algorithm is improved to solve the problem and guarantee the sufficient capability and regularity of the transit service. Finally, we conduct several computational experiments based on an actual public transit scenario in Shenzhen, China. The results reveal that the DP-LNS algorithm effectively reduces the number of canceled trips to facilitate the recovery of transit operations. Moreover, DP-LNS also ensures service regularity through the modification of departure intervals. In conclusion, our method achieves the best rescheduling performance when compared to other approaches.  
However, this paper only analyzes rescheduling on a single line. The coordination of multiple lines would further expand the solution space because of the increased availability of resources, which could enable higher-quality solutions to be achieved. In addition, adding a feedback mechanism could improve our algorithm, and considering a multi-layer model will be a topic of our future research.  
Conceptualization, S.D. and J.Z.; methodology, S.D.; software, S.D.; validation, Z.H. and J.Z.; formal analysis, S.D. and J.Z.; investigation, S.D.; resources, Z.H.; data curation, S.D.; writing--original draft preparation, S.D. and J.Z.; writing--review and editing, S.D., J.Z., and J.X.; visualization, S.D.; supervision, Z.H.; project administration, J.Z. All authors have read and agreed to the published version of the manuscript.  
Not applicable.  
The data presented in this study are available on request from the corresponding author (accurately indicate status).  
The authors would like to thank the support from the Science and Technology Planning Project of Guangdong Province (No. 2023B1212060029) and the Science and Technology Program of Shenzhen (No. JSGG20220831094604008). The authors wish to thank the anonymous referees for their valuable comments.  
The authors report there are no competing interests to declare.  
The following abbreviations are used in this manuscript:  
\begin{tabular}{l l} VRSP & Vehicle rescheduling problem \\ CN & Connection network \\ ISCR & Integrated service capability and regularity model \\ DP & Dynamic programming \\ LNS & Large neighborhood search \\ \end{tabular}