**6. Conclusions**

The boom of station-free BSSs has increased customer convenience but also caused ine fficiency due to the excessive supply of bikes. It presents regulation challenges for city o fficials. What is the optimal fleet size of the station-free BSS which can fully meet the needs of users and make bicycles be used e fficiency as well? How should these bikes be spatially distributed on this supply scale? This paper, which is based on actual travel data from the station-free BSS in Shenzhen, proposes an algorithm to construct a travel chain and determine the optimal bike demands in di fferent spatial units.

Our results show that in Shenzhen city, only one-fifth of shared bikes is needed to meet the current usage demand if the bikes are used e fficiency. With a population of 12.52 million in Shenzhen in 2017, the average number of bikes per 1000 people is 13 vehicles, which is in the range of 10–30 vehicles/1000 people recommended by the Bike Sharing Planning Guide. Correspondingly, our optimized results increase the average usage number of each bikes from below 1 to above 4, which greatly improved the efficiency of shared bikes.

Our results also identify some areas with the high spatial requirements of cycling and the ideal spatial distribution of optimized bikes' initial positions. If the initial distribution is established according to this demand, the trips that occur throughout the day can be completed with as few bikes as possible without reducing the level of user satisfaction. Obviously, the spatial distribution of bikes will change dramatically at the end of the day. In response to this situation, the operator can relocate the bikes to the initial distribution using a static strategy at night. Thus, this approach establishes both a benchmark for the layout of station-free bikes and a target strategy for relocation.

The proposed HBOA is simple in principle, and the calculations are convenient to perform. Although the calculation results may not be optimal at all times, this information can be used to significantly improve the use e fficiency of shared bikes. Thus, the results could be used by companies to meet the maximum coverage demand with the smallest number of bikes and as a tool for urban planners to scientifically manage the station-free BSS. From the perspective of the city as a whole, the total supply of shared bicycles should be kept at an optimal level to improve the overall operational efficiency of the urban tra ffic system. In this sense, it is necessary to break the barriers between di fferent operators of the overall station-free BSS and enable users to rent and return bikes among di fferent station-free BSSs. The two-day analysis results reflected the stability of bike use patterns and some specific di fferences between working and non-working days. If long-term data from more companies could be analyzed, the results would be more reliable and further improve the system e fficiency by minimizing the size of the shared bike with the HBOA. In this case, additional physical infrastructure is not needed, but the current infrastructure could be more intelligently managed.

**Author Contributions:** Methodology, Zhihui Gu; Validation, Yu Chen; Data Curation, Yong Zhu and Wanyu Zhou; Writing—Review & Editing, Zhihui Gu and Yan Zhang.

**Funding:** This research was funded by the National Natural Science Foundation of China, gran<sup>t</sup> No. 51778366.

**Acknowledgments:** The authors would like to thank the anonymous reviewers and academic editors for their helpful comments on an earlier draft of this paper.

**Conflicts of Interest:** The authors declare no conflict of interest. The funders had no role in the design of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or in the decision to publish the results.
