# Coordinated Optimization of Feeder Flex-Route Transit Scheduling for Urban Rail Systems
## 6 Conclusions  
This paper examines the \"last mile\" travel demand characteristics and transfer behaviors of passengers using urban rail transit, explores the operational organization and connectivity between buses and urban rail transit, and proposes a strategy to convert conventional buses into flex-route transit for improved connectivity. Without requiring the introduction of a new feeder line, this approach simultaneously meets existing bus travel demand and accommodates urban rail transit passengers with short-distance travel needs.  
Drawing from conventional fixed-point and fixed-line bus timetable preparation methods, this study summarizes the process of flex-route transit path planning and station timetable development for urban rail transit connectivity. For a multi-vehicle flex-route transit service system, a collaborative optimization scheme for transit operations is developed. By examining passenger transfer behaviors and the operational characteristics of both transit systems, this research introduces a collaborative optimization method for feeder FRT scheduling and route planning. The methodology employs a mixed integer nonlinear programming approach to optimize departure intervals, vehicle deployment, and scheduling strategies.  
Simulation experiments based on real-world urban transit scenarios are conducted to validate the proposed model. Considering relevant operational characteristics and applicability, the optimal departure interval, departure frequency, number of operating vehicles, and station departure times for flex-route transit are determined. The findings suggest that optimizing departure intervals and vehicle scheduling reduces passenger waiting times and operational costs while ensuring high service reliability.  
This study establishes a theoretical foundation and a practical framework for automated scheduling in feeder transit systems. Future research could expand upon this work by investigating larger-scale collaborative networks, integrating diverse vehicle types, and implementing dynamic pricing and subsidy strategies to enhance system efficiency and promote equity in public transportation.  
The authors confirm their contribution to the paper as follows: Conceptualization: [PERSON]; Methodology: [PERSON] and [PERSON]; Software: [PERSON] and Z.H.; Validation: [PERSON] and Q.L.; Formal Analysis: [PERSON]; Data Curation: [PERSON] and Q.L.; Writing--Original Draft: [PERSON] and [PERSON]; Writing--Review and Editing: [PERSON] and [PERSON]; Visualization: [PERSON] and Q.L.; Supervision: [PERSON]; Project Administration: [PERSON]; Funding Acquisition: [PERSON] and Z.H. All authors have read and agreed to the published version of the manuscript.  
This research is supported by the Open Project of Anhui Provincial Key Laboratory of Urban Rail Transit Safety and Emergency Management, Hefei University (No. 2024 GD0007), the Anhui Provincial Housing and Urban-Rural Development Science and Technology Program Project (No. 2024-YF090) and the Hefei University Talent Research Fund Project (No. 24 RC26).  
Not applicable.  
Data Availability Statement: Data are contained within the article.  
The authors declare no conflicts of interest.