# Passenger Flow-Oriented Metro Operation without Timetables
## 3 Mathematical Description
### Objective Function
#### 4.1.3 Passenger-Train Interaction Section
A case study based on the Beijing Metro Line 19 has been carried out to validate the effectiveness of the proposed method. Compared with traditional periodic timetables, the passenger waiting time has been reduced in most scenarios and the flexibility of the operation has been significantly improved. The limitations found for this research were that no real-life passenger flow data were collected for the test, as the Beijing Metro Line is still under construction, and no other test metro systems were found for the proposed optimisation method. In future works, we aim to design more test instances for the proposed method and also to improve the computing time by integrating the genetic algorithm with a machine learning method such as the decision tree algorithm. Conceptualisation, L.H. and L.C. ; methodology, L.H. and L.C. ; software, L.H. ; validation, L.H., L.C., S.Y. and X.F. ; formal analysis, L.H. and L.C. ; investigation, L.H. and L.C. ; writing--original draft preparation, L.H. ; writing--review and editing, L.C. and J.L. ; supervision, L.C. and C.R. ; project administration, L.C. and C.R. ; funding acquisition, L.C. All authors have read and agreed to the published version of the manuscript. This research was funded by China Urban Sustainable Transport Research Centre under Grant No.2018 YFC0809900 and supported by project \"Research and Development of Intelligent Metro Network Operation Decision Support System\" by Hefei Metro. Not applicable. The authors declare no conflict of interest. ## References

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