Hierarchical Vehicle Scheduling Research on Tide Bicycle-Sharing Traffic of Autonomous Transportation Systems

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Introduction
Nowadays, as the modern transportation systems (TSs) develop, problems among mobility services (MSs), e.g., congestion, route adjustment, user dispersion, and peaktime conficts have become commonplace [1][2][3] in terms of the adjustment of urban planning and the year-on-year increase in car ownership.Since the MS are fundamental in propelling current intelligent TS (ITS) evolving towards autonomous TS (ATS), they are also being renovated to assist the public on a daily basis and explore the advancement of ATS.Some theoretical development has revealed that the creation of shared transport, called bicycle-sharing, has efectively alleviated the "last mile" service (LMS), which is the most predominant pain point in the current MS [4] in terms of the most immediate interaction with users, and some emerging companies, e.g., Mobike have also taken this trend to a new level.However, bikes must be parked in GPSidentifed areas to address ill-posed problems in the case of illegal parking, vandalism, or theft.Since then, to avoid constant billing, users never consider the capacity of the parking area, resulting in an uneven spatial distribution of bikes, namely, some areas sufer a severe accumulation of bikes while others are "one bike is hard to fnd" [5].Terefore, scientifc and reasonable scheduling strategies are required to overcome the imbalance between the supply and demand of bikes and improve resource utilization.
Rebalancing and optimizing bicycle-sharing distribution constitutes the vehicle routing problem (VRP), and most current research is based on this theory.For instance, Caggiani et al. [6] proposed a decision support system for the reallocation problem by forecasting the demand for spatiotemporal bikes.Similar research can, accordingly, be divided into static and dynamic scheduling to optimize VRP models with diferent objectives.Specifcally, in static scheduling, Kadri et al. [7] and Dell'Amico et al. [8] developed optimization models for user satisfaction and operating cost, respectively.Yan et al. [9] investigated the deterministic and stochastic demand for bicycle-sharing in dynamic scheduling.In general, these methods assume that the overall supply and demand within a scheduling station are in equilibrium without supporting the mobility of bikes between zones.Moreover, limited open literature has reported that current research focuses too much on mathematical modeling, neglecting the analysis of actual demands.Terefore, these methods have encountered three challenges in practice, namely, slow convergence, high time complexity, and problematic application, from perspectives of fulflling the actual demands in real-time and adjusting scheduling as needed.
As current diversifed mobility demands tend to be managed and fulflled by more intelligent and automated systems with fewer human intervention [10], it is an urgent need to collaborate corresponding functions to renovate the conventional MS of ITS in the context of ATS [11], i.e., update the ability to sense user demands and rearrange system supplies [12,13].Hence, to promote the MS provided by ATS, this paper proposes a hierarchical autonomous vehicle scheduling model based on tide bicycle-sharing trafc, namely, HATB.Tis model uses GeoHash coding to divide the scheduling into three layers, i.e., top, middle, and bottom, corresponding to the scheduling terminus, area, and point.Based on the genetic algorithm (GA), the model can achieve hierarchical and dynamic scheduling of vehicles and routes to maximize user satisfaction, while minimizing operating costs.
Furthermore, in contrast to current studies on scheduling bikes in ITS, the HATB makes three main contributions to optimizing convergence speed, time complexity, and application difculties of actual scheduling.Te scheduling results based on actual orders ultimately demonstrate HATB can provide a rational reference for LMS in ATS and guide the development of bicycle-sharing regulation and operation.
Te overall structure of this paper is divided into fve sections.Section 2 introduces related solutions and emerging challenges.Te methodology relevant to HATB is described in Section 3. Section 4 elaborates on the scheduling results and superiority of the model.Finally, Section 5 summarizes this study and sketches future research directions.
1.1.Related Works.In the transport domain, LMS refers to the direct interaction between the end of public transport and users, which often sufers from scattered users, peaktime conficts, and uneven distribution.As an efective way to cope with the LMS problems, bicycle-sharing has become a non-negligible component of urban transport.For example, Cheng et al. [14] have demonstrated that bicyclesharing increases the proportion of green transport in cities and solves the low efciency at the end of the travel chain.
In general, current research on bike-sharing mainly focuses on its development status and travel characteristics, but few on its scheduling.Researchers like Soriguera and Jiménez-Meroño [15], Gimon [16], and Lu et al. [17] concur that even while bicycle-sharing has considerable quantities, the spatio-temporal diferences in user demands, no fxed parking area, and fewer available bikes may lead to a more signifcant overall imbalance.Terefore, it is vital to take efective scheduling strategies to rebalance and optimize the distribution of bikes, thereby addressing difculties in management and operation.In this context, scheduling bicycle-sharing can be regarded as a heuristic algorithmbased, e.g., GA, ant colony algorithm (ACO), and vehicle routing problem (VRP) [18][19][20], which can be classifed as static or dynamic scheduling according to diferent strategies and objectives.
Dynamic scheduling mainly focuses on peak time and relies on user demands.For instance, a mathematical model for dynamic scheduling is created by Zhang et al. [21] based on the parking area's actual capacity and users' predicted arrival times.Shui and Szeto [22] partition peak time to optimize scheduling routes by regarding scheduling in each time interval as static scheduling.Chiariotti et al. [23] propose that scheduling bikes can dynamically determine the scheduling time through historical orders.In general, dynamic scheduling lessens operating costs' impact on operators by prescheduling bikes to avoid a shortage occurs.However, based on the uncertain use of bikes, frequent scheduling with complex constraints is necessary, which may lead to higher operating costs and slower convergence, thus making it challenging to fulfll user demands in realtime.
Another more common scheduling strategy is static scheduling during of-peak time.For example, Lang [24] provides a multiwarehouse model based on the Tabu search algorithm to minimize scheduling distance and improve scheduling efciency and robustness.Bae and Moon [25] use a dual time window with customer service levels to reduce total transport and labor costs.Since static scheduling only considers the predicted demands of stations, increasing more bikes for stations to guarantee user demands means that the time complexity of the heuristic algorithm grows exponentially.Moreover, to fulfll the actual demands, the allocated bikes by these studies may exceed the station's capacity.
Besides, such above-given studies are mainly applied to typical scenarios, as presented in Figure 1, where a single scheduling station serves one zone and only the routes within the scheduling zone are considered.It is often limited in actual scheduling by the service range of the station, which needs to frequently adjust the boundaries of this scheduling zone, thus leading to some research on hierarchical scheduling strategies.By defning scheduling priorities based on demand intensity, Sakakibara et al. [26] and Ni et al. [27] highlight the feasibility and reliability of hierarchical scheduling.In order to illustrate the fexibility, Zhang [28] and Ma et al. [29] set stations with similar demands in the same layer in accordance with the spatio-temporal characteristics of bikes.However, the defnition of hierarchies in these methods is too subjective and not clear, making it difcult to implement in practice.
In summary, whilst a considerable body of research has been carried out on VRP, much less fts the spatial-temporal and cross-regional mobility characteristics of bicyclesharing.In addition, it seems to be a common problem that existing studies focus more on mathematical modeling 2 Journal of Advanced Transportation but neglect the analysis of actual demands.When scheduling according to the above-given methods, three challenges in terms of the problematic application in practice, namely, the high time complexity of models and slow convergence for algorithms, are increasingly apparent.
Particularly driven by diverse and emerging technologies and demands, ITS is evolving into ATS, which illustrates that MS should be autonomously fulflled and managed by more intelligent systems with fewer human intervention [30].Terefore, it is an urgent need to study and improve the monolithic strategies and rationalize the actual demands to achieve hierarchical and autonomous scheduling of bicyclesharing, thus rationally guiding the provision of the LMS by ATS.

The HATB Methodology
Tis section uses three subsections to present the framework, hypotheses, and construction of the proposed HATB.

Model Framework.
As existing scheduling methods, in general, require frequently adjusting boundaries and increasing vehicles to alleviate the diference between bikes' supply and demand, which may inevitably increase transport time and costs; the scheduling framework can be set up as a hierarchical scheduling structure, i.e., a top-middlebottom hierarchy of scheduling terminus-area-point.
However, since current hierarchical methods have a subjective defnition of their hierarchies, geocode can ensure the objective; e.g., what3words [31] uses fxed 3m × 3m squares to divide the earth, and pluscode [32] represents each latitude and longitude level by 2-bit code, whose length range in levels 1 to 3 jumps from 110km and 5.5km to 275m.
Tese geocodes, accordingly, have good accuracy but loss fexibility; they may not meet the actual scheduling requirements.
Terefore, GeoHash encoding, proposed by Morton [33], can be used to better support efective and efcient scheduling.Its maximum length of 12 bits can represent a geographic location with arbitrary precision.For example, the GeoHash strings WX4ER and WX4G2 represent two regions of Beijing (China), where each character is a certain rectangular area.Moreover, the order information (Data Sources: https://biendata.xyz/competition/mobike/) on bicycle-sharing, as extracted in Table 1, also indicates the feasibility of dividing the scheduling layer via GeoHash.
Te coding defnition, as described in Table 1, illustrates that the 7-bit string matches the characteristics of actual bike stops, namely, area size, and the 5-bit string suits for vehicles to dispatch bikes in light of their loading capacity, i.e., 400 bikes.Terefore, the overall framework of the proposed hierarchical scheduling model, called HATB, can be obtained as presented in Figure 2. In general, this framework is characterized by a number of scheduling areas in each of the three layers, namely, bike stops consist of the bottom layer of scheduling, while the top and middle layers likewise have demands and capacity restrictions for bikes, and hence, the scheduling within the same layers is regional scheduling for seeking optimization.

Model Hypotheses.
Considering the complexity of actual scheduling, the proposed HATB in this paper defnes the following hypotheses and the frequency of scheduling as once in the morning peak and once in the evening peak, respectively.
(1) All scheduling vehicles own the same attributes (2) In each scheduling route, the vehicle departs from one scheduling terminus (area) and returns to this place after deploying bikes to corresponding areas (points) contained (3) Fuel consumption and vehicle loss should be considered (4) Each scheduling area can only be served once (5) Te actual orders determine the scheduling demand (6) All scheduling tasks are required to be completed within the specifed scheduling cycle (7) Te scheduling areas and points have sufcient space to accommodate the bikes deployed in or out during a scheduling cycle 2.3.Model Construction.Based on the above-given hypotheses and the actual operations of bike-sharing, considering only the operating costs will gradually lose customers, and weighing only user satisfaction runs counter to the essence of business proftability.Hence combining these two factors, this paper constructs a regional scheduling model for bikes to minimize operating costs (F 1 ) and maximize user satisfaction (F 2 ).min: Te parameters z and μ indicate that bike-sharing operators need to adjust the weight coefcients of operating and penalty costs according to their own emphasis.

F 1 : Te Objective of Minimizing Operating Costs.
Te actual operation costs need to consider both fxed and fexible costs, as summarized in equation ( 2), which is determined jointly by the value of scheduling vehicles [34], the unit transport cost (i.e., vehicle loss: 1 CNY/km, fuel consumption: 1 CNY/km, and labor cost: 100 CNY/person), and the scheduling distance.4) suggests that each area can only be served once; equation (5) shows that the transport distance must not exceed the maximum scheduling distance; equation (6) points that the number of bikes loaded by the vehicle must not exceed its maximum capacity, namely, 400; equation ( 7) means x t ij as 0-1 variable; equation (8) proves that the number of bikes deployed by the vehicle is a non-negative integer.

F 2 : Te Objective of Maximizing User Satisfaction.
User satisfaction can be improved by adding time window constraints, as described in equation (9), which means maximizing user satisfaction can equivalently transfer into minimizing the penalty cost of scheduling timeout.
Equation (10) indicates that the vehicle departs from the terminus at time zero; equation (11) means that the time calculation for a vehicle to arrive in an area; equation (12) demonstrates that the scheduling cannot arrive in area j from area i before ; equation (13) represents that vehicle needs to arrive in an area within the time window.
Te meaning of the parameters in the above-given equationsare shown in Table 2.

Case Study
Te highlights of HATB solving are illustrated in terms of algorithm settings, scheduling results, and model evaluation in this section.3, refects that the data are consistent with the "last mile" defnition [16], and hence, shows its reasonable usability according to prominent tidal characteristics.Tis paper proposes a GA with natural number encoding (NGA), as defned in Algorithm 1, to optimize the scheduling.In general, the frst and the last 0 s represent the scheduling terminus or area, [1, N] represents the zones that need to be scheduled, and other 0 s separate the routes of diferent vehicles, e.g., a chromosome example might be 0-3-0-1-2-5-7-0-4-8-6-0, namely, three vehicles serving eight zones.
Since the crossover and mutated sub chromosomes may lead to transport overload and overtime and the time window is more likely to be violated, the penalty factors for the two constraints are set to 10 and 500, respectively.

Scheduling Results
. A total of 220 scheduling areas in the morning peak are used as HATB test cases to obtain the optimal hierarchical scheduling routes, as shown in Figure 3 and Tables 4 and 5.

Journal of Advanced Transportation
As described in the previous section, regional scheduling is applied for each layer.Note that, each scheduling area has a positive or negative raw demand that refects the redundancy or scarcity of bikes.Furthermore, scheduling prioritizes selfsatisfaction in the route, namely, redundancy supports scarcity, and hence, route demand indicates the self-satisfaction gap for corresponding regional scheduling.
Terefore, the experimental results can be summarized as the total scheduling distance for optimal routes in the entire Beijing is around 719.5 km.As for satisfying the demands, 17 vehicles required to participate in the scheduling to deploy bikes.Moreover, using route one in Table 4 as an example, the scheduling can be summarized as a vehicle departing from the scheduling terminus and returning to the terminus after completing regional scheduling sequentially and autonomously in accordance with the area-point (middle-bottom) hierarchy.In addition, the routes' information in reality for Table 5 is mapped to Table 6 via GeoHash.

Model Evaluation.
To further verify the reliability of this model, Figure 4 shows the comparison for iteration between the HATB and other models proposed in the literature with similar objectives.Specifcally, based on the GA, Gao et al. [35] provided a promising perspective on improving operation efciency by reducing operating costs and service quality during peak times to minimize the total operating  a0-a11-a4-a18-a17-a9-a1-a12-a15-a19-a5-a0 170 (a0) Te proposed HATB converged at the 64 th generation, and the total time cost is 148.9 s, with an average running time of 15 s per generation.Due to the diferent objectives, only the convergence speed of the above models is compared.It can be seen from Figure 4 that the HATB signifcantly outperforms the model proposed in the existing literature.Such a result indicates that this model is more proper for practical scheduling applications since it optimizes with higher convergence speed and lower time complexity.

Conclusion and Future Works
Even though the emerging and diversifed technologies and demands are driving TS to renovate conventional MS to be selfactuating, the current bicycle-sharing scheduling and maintenance rely on manual experience, which lacks scientifc guidance and efciency.Terefore, to achieve sustainable development, operators urgently need to develop a rational scheduling strategy to balance the distribution conficts and supply user demands in time.
Terefore, this paper proposes a hierarchical scheduling model, called HATB, to address the unsolved issues by current studies in terms of slow convergence, high time complexity, and problematic application, and hence, to support the rational and autonomous provision of LMS.In summary, according to bicycle-sharing properties, namely, spatio-temporal characteristics, cross-regional mobilities, and actual demands, HATB takes 220-morning peak areas as tests to validate its improved validity, feasibility, and efciency for practical application.
As compared to the similarly used methods, HATB can, accordingly, obtain the following improvements.A hierarchical framework is frst designed through GeoHash encoding to solve the cross-regional mobility of bikes and reduce the time complexity of global optimization.Next, a GA for regional scheduling is built by combining the tidal characteristics of bicycle-sharing to minimize operating costs and maximize user satisfaction, which signifcantly accelerates the algorithm's convergence.Last, the use of actual orders considerably enhances the ability in the practical application of instant response to any regional scheduling demand.
Tis work was carried out as a preliminary to obtain the present results.However, there are still problems such as the inability to adapt scheduling throughout 24 hours or the lack of comprehensive constraints.As the closure of this study, one recommendation for further research is to use a form of "GA + Tabu" algorithm to exploit its global search capability and thus improve the big data processing capability.Another research direction is adding weather and road characteristics to optimize the model reliability further.

Table 1 :
Te order information of corresponding GeoHash string length.

Table 3 :
Examples of user travel characteristics.Te experiment data comes from the 2017 Mobike cup algorithm challenge, which involves 3,214,096 orders and 485,465 bikes (10 th May 2017-23 rd May 2017).Te characterized user travel, as presented in Table

Table 5 :
Examples of hierarchical autonomous scheduling results for route one.

Table 6 :
Te mapped scheduling results with examples of route one (Table5).
[37]s.Angeloudis et al.[36]achieved user appeal increase by ofering a new method of planning bike routes and distributions.Moreover, Zhao et al.[37]optimized the total scheduling distance to accommodate large-scale scheduling via an ACO.