Urban public bicycle dispatching optimization method

Leasing number forecast model

MSWK is an improved method for predicting lease/return bicycle quantity based on KNN algorithm. Analysed the amount of leasing in a similar time period to predict future leasing. Weather, temperature, humidity, winds speed, and visibility are measured in five indicators.

In the measurement of the similarity of weather, the weather is split into five levels and assigned corresponding values. The exact values are shown in Table 2.

The quantified weather conditions at p and q for two days t is denoted by $W_{D_p^t}$ and $W_{D_q^t}$, respectively, and the weather similarities for t in p and q are defined as follows (Eq. (3.11)): (3.11)${\displaystyle {\lambda }_1=\frac{1}{2\pi {\sigma }_1}{e}^{-\frac{{\left(W_{D_p^t}-W_{D_q^t}\right)}^2}{{\sigma }_1^2}}}$

The temperatures of the p and q two days t periods are denoted by $F_{D_p^t}$ and $F_{D_q^t}$. The temperature similarities of the t time periods in p and q are defined as follows (Eq. (3.12)): (3.12)${\displaystyle {\lambda }_2=\frac{1}{2\pi {\sigma }_2}{e}^{-\frac{{\left(F_{D_p^t}-F_{D_q^t}\right)}^2}{{\sigma }_2^2}}}$

The three dimensions of humidity, wind speed, and visibility are represented by a 3-D Gaussian kernel function, and $H_{D_p^t},S_{D_p^t},V_{D_p^t}$ represents the humidity, wind speed, and visibility of the t time period in p, respectively. The humidity, wind speed, and visibility similarity of p and q periods in t are defined as follows (Eq. (3.13)): (3.13)${\displaystyle {\lambda }_3=\frac{1}{2\pi \sigma }{e}^{-\left(\frac{{\left(H_{D_p^t}-H_{D_q^t}\right)}^2}{{\sigma }_3^2}+\frac{{\left(S_{D_p^t}-S_{D_q^t}\right)}^2}{{\sigma }_4^2}+\frac{{\left(V_{D_p^t}-V_{D_q^t}\right)}^2}{{\sigma }_5^2}\right)}}$

In order to simplify the calculation, the temperature, humidity, wind speed, and visibility are normalized and all σ₁, σ₂, σ₃, σ₄, σ₅ are set to 1, thereby simplifying the calculation; finally, by weighting the above three similarity indexes, p and q can be obtained. The overall similarity indicator at time t as follows (Eq. (3.14)): (3.14)${\displaystyle M\left(D_p^t,D_q^t;a\right)={\delta }_w\left(D_p^t,D_q^t\right)\sum _{i=1}^3{a}_i{\lambda }_i}$

Where ${\delta }_w\left(D_p^t,D_q^t\right)$ is a judgment function, when both p and q are working days or all non-working days, ${\delta }_w\left(D_p^t,D_q^t\right)=1$, otherwise ${\delta }_w\left(D_p^t,D_q^t\right)=0$. If you want to predict the amount of rent in the t time period in q, select the most similar K days and use the MSWK algorithm to calculate the predicted value. The specific Eq. (3.15) is as follows: (3.15)${\displaystyle s_i\cdot pd\left(D_q^t;a\right)=\frac{\sum _{p=1}^{K}M\left(D_p^t,D_q^t;a\right)s_i\cdot pd\left(D_p^t\right)}{\sum _{p=1}^{K}M\left(D_p^t,D_q^t;a\right)}}$

Returning number forecast model

After a user rents a bicycle, they often return the bicycle to an adjacent site within a certain period of time. Therefore, there is a need for prediction data of the number of bicycles based on neighbouring sites, which is used to predict the number of bicycles returned to the site. Bicycles rented from site i during time t may be returned to site j adjacent to i during time t or t+1. For the forecast of the number of return bicycles within the lease time t period, it is necessary to first estimate the number of bicycles rented from the site i and at the site j within the time period t. The specific Eq. (3.16) is as follows: (3.16)${\displaystyle e_{ij}^t=s_i\cdot pd\left(t\right)\frac{e_{ij}\cdot f}{s_i\cdot pd}}$

Among them, $s_i\cdot pd\left(t\right)$ is the predicted value of bicycle rental quantity from site i in time period t, e_ij⋅f is historical record of bicycle rental from site i and is still at site j. s_i⋅pd is historical total bicycle rental record from site i. Through the analysis of historical data, it is found that the user’s riding time law can be fitted by the 2-Gaussian function. Therefore, the riding time $D_{ij}\left(t\right)$between rental sites i and j can be estimated by Eq. (3.17): (3.17)${\displaystyle D_{ij}\left(t\right)=g_1\left(t;{\mu }_1,{\sigma }_1\right)+g_2\left(t;{\mu }_2,{\sigma }_2\right).}$

Assume that the user’s return time is evenly distributed, and the user’s behaviour of returning the leased bicycle is completed within the t time period or t+1-time period. During the time periods t and t+1, the user t₁ rents a bicycle from the site i at the moment, and the probability of returning the ticket at the site j at t₂ is as follows (Eqs. (3.18) and (3.19)): (3.18)${\displaystyle P_{ij}^t=\frac{1}{\left|t\right|}{\int }_0^{\left|t\right|}{\int }_0^{\left|t\right|-t_1^{{}^{\prime }}}d{t}_1^{{}^{\prime }}d{t}_2{D}_{ij}\left(t_2\right)}$ (3.19)${\displaystyle P_{ij}^{t+1}=\frac{1}{\left|t\right|}{\int }_0^{\left|t\right|}{\int }_{\left|t\right|-t_1^{{}^{\prime }}}^{+\infty }d{t}_1^{{}^{\prime }}d{t}_2{D}_{ij}\left(t_2\right).}$

Finally, considering the traffic patterns and the corresponding probabilities of the adjacent sites, the formula for predicting the number of return bicycles within the sites is obtained as follows: (3.20)${\displaystyle s_i\cdot dd\left(t\right)=\sum _{j\ne i}{e}_{ij}^t{P}_{ij}^t+e_{ij}^{t-1}{P}_{ij}^{t+1}.}$

So far, the demand ΔN of the site i at the time t in the future will be calculated by combining the demand for rental and return of the rental site i at the time t in the future. The specific formula is as follows: (3.21)${\displaystyle \Delta N=s_i\cdot dd\left(t\right)-s_i\cdot pd\left(t\right).}$

If ΔN is less than zero, it means that the site i will not be able to meet the user’s bicycle rental demand at the time t in the future, and it is necessary to dispatch the bicycle through dispatch (Feng, Zhu & Liu, 2018). If ΔN is greater than the number of parking spots at the leased site, it means that the site i at the time t in the future cannot satisfy the user’s demand for returning the car. It is necessary to reduce the number of bicycles by scheduling.

Data set introduction

Citi Bikes (Jiang et al., 2018) is a people-benefit project launched by the New York City Government. Figure 3 displays the spatial distribution of rental sites. Blue represents Manhattan, with 250 rental sites; green represents Brooklyn, with 77 sites. Each Citi Bicycle rental site has GPS location information, so it is not difficult to locate the rental site. The system records the user’s data onto each cycle. The package contains the location and time data onto the start and the end of the site, the entire riding process, the bicycle ID, and the user’s gender and birth date. This experiment will use the May 2016 rent-return dataset of New York public bicycles to conduct an experiment, a total of 96, and 1986 rent-return data. The dataset contains 16 fields, and the nine fields related to this experiment are shown in Table 4.

This paper uses the pre-processing program to process the leased data, it turned into the lease-return relationship between the least sites (Guo et al., 2017). It also generates a similarity matrix based on the rent-return relationship. The similarity calculation formula for the least sites is as follows (Eq. (4.4)): (4.4)${\displaystyle R_{ij}=\frac{Q_{ij}+Q_{ji}}{M}}$

Among them, R_ij represents the similarity between site i and site j; Q_ij represents the number of times to rent a bicycle from site i and site j to return the bicycle; Q_ji represents the number of times of renting a bicycle from site i and returning it at site j; M represents the time range in days. In this experiment, the data set was a total of 31 days in May 2016, so M = 31.The corresponding abstract network can be generated through the lease-return relationship (Fig. 4). Due to the dense population, dense sites, and prosperous business, the sites in Manhattan are more closely linked, and Brooklyn is a river is separated from Manhattan, so the connection between the two regional sites is sparse except for the leases along the river.

Experimental result

In the experiment, we first used the Gephi visualization network analysis platform to analyse the community structure in the data (Hu, An & Wang, 2018). The Gephi platform uses the integrated Fast Unfolding algorithm, it divides the public bicycle abstraction network according to the rules of public bicycle rental. The Fast Unfolding algorithm mainly includes two phases. The first phase is known as Modularity Optimization. The main part is to divide each node into the community, its neighbourhood nodes are located, so that the value of the module degree becomes larger; the second phase is called community. Aggregation is mainly to aggregate the communities divided in the first step into one site, that is, to rebuild the network based on the community structure generated in the previous step. Repeat the above process, until the structure of the network no longer changes (Fig. 5).

After the Fast Unfolding algorithm for the New York public bicycle rental site in this paper, Fig. 6 shows the internal community structure of the abstract network of New York’s public bicycles, where the dots represent sites, where the sites of different communities are represented by different colours, and the lines represent the relationships between the sites; obviously, six communities have more close contact with leases within the same community, and the links between different societies are relatively sparse. The results of the Fast Unfolding community discovery algorithm are mapped to map on New York (Fig. 7). Manhattan is a densely populated administrative district, and the vast majority of public bicycles in the area ride on the inside, so the Manhattan District is divided into five areas according to the law of rent. Brooklyn is structured in a district. Although the division results are relatively reasonable, there are still many abnormal sites. These abnormal sites are far away from their respective areas; the number of sites of each area is uniform.

CDoMO is based on community discovery algorithm, considering the regional scheduling workload factors. The regional scheduling workload is determined by estimated dispatch distance and the number of regional least sites. If the community finds out that there are abnormal sites, it will cause regional forecasting scheduling distance become larger, so that the variance between the scheduling distances will become larger. If there is a major difference in the number of sites between areas, the variance between the numbers of sites will increase. The goal of CDoMO is to optimize the variance of the distance between the regional scheduling, and optimize the variance of the number of sites. In the optimization process, the division results can be adjusted to make it more reasonable. The division process does not take into consideration the deficiencies in the workload balance in each scheduling area. After the community discovery algorithm based on multi-objective optimization solves the division model of the public bicycle scheduling area, the experimental results shown in Fig. 8 are obtained. By comparing the result shows that the sites along the Williamsburg Bridge and the riverside along Manhattan is divided into the same dispatch area, which is more n line with the rules of public bicycle rental and resolving the anomaly (Zhang et al., 2011). The difference between the number of sites and regional sites is too large (Manju & Fred, 2018).

In order to maintain the consistency of the experiment, the value of k in the classical clustering algorithm K-means algorithm is set to 6 (Lin & Song, 2017), and then the clustering is based on the same data set; the space area enclosed by the sites in each class as the scheduling area. In order to achieve regional division, the results of the regional division based on the clustering algorithm (Fig. 9). It was found that when the clustering number is k=6, the clustering algorithm achieves a poor regional division. The number of sites in the class represented by the red is very large, while the number of classes represented by purple and beige is very small, and the number of sites to vary greatly from the types. In addition, the boundaries of each scheduling area are unclear and are overlapped (Zhen et al., 2016).

Algorithm performance comparison results

Built on the overall experimental results of the above three methods, it is found that the multi-objective optimization-based community discovery algorithm proposed to this paper can make the division of the areas consistent with the rules and make the regional scheduling workload as balanced as possible. In addition to the analysis of the overall distribution of provincial division space, the paper also compares and analyses the three dimensions of the regional rental site variance, the regional dispatch distance variance, and the estimated total dispatch distance. Figure 10 compares the variance between the numbers of sites. The data show that the variance between the CDoMO compared to the K-means algorithm is reduced by 63.31%, and the variance of the Fast Unfolding algorithm is reduced by 32.32%. Figure 11 compares the variance of the number of bicycles dispatched in the area. The data show that the variance of the CDoMO algorithm compared to the K-means algorithm is reduced by 88.06%, and the variance of the Fast Unfolding algorithm is reduced by 38.14%. Figure 12 compares the estimated total scheduled distances. The data show that the variance of the CDoMO algorithm is 55.17% compared with the K-means algorithm and 27.54% compared to the Fast Unfolding algorithm. When scheduling and partitioning based on multi-objective optimization algorithm, the estimated scheduling distance can be shortened, and the estimated scheduling distance is positively related to the actual scheduling distance, so the actual scheduling distance will also be shortened; in addition, the scheduling work of each area will also be made. Relatively balanced. Figure 13 is a comparative display of experimental results.

Data set introduction

First of all, the data set cited in this paper is from Chicago public bicycle data (Ye, Chu & Xu, 2015). The starting site is 2015-1-1, and the deadline is 2015-6-30. There are two quarters and six months of data, a total of 759,789 data records. This paper did some data pre-processing: Trips that did not include a start or end date were removed from the original table. Then, in order to ensure that the information of the data set more abundant, this paper decided to use the data set, distance information of each pair of source address and destination address. Finally, we utilize certain data pre-processing methods to remove weather and other data because it can be considered as an ideal condition. The dataset contains 12 fields, and the 10 fields related to this experiment are presented in the following Table 5.

Experimental result

Results of the Fast Unfolding community discovery algorithm can be mapped to Chicago map as the picture shows (Ye, Chu & Xu, 2015). In contrast, the division results are more uniform and reasonable, but there are too many abnormal sites in the middle. These abnormal sites are a long way from where they should have existed. The number of rental sites in a divided area is not particularly uniform (Fig. 14).

Based on CDoMO, in the optimization process, the division results are dynamically adjusted in time. Therefore, in this case, the division result is more reasonable, and the problem of scheduling balance, this algorithm obviously adds more consideration. It not only addresses the problem of abnormal sites, but also solves the problem of differences in the number of regional sites at the same time (Fig. 15). In order to make the experiment consistent, we set the value of k in the K-means algorithm as 5, and then we clustered the uniform data set. The results of the clustering are presented in the figure. This paper believes that the results obtained by the clustering algorithm are very poor, because the red sites represent a particularly large number of sites. The yellow site represents a particularly small number of rental sites. This shows that the various types of leases, the number of differences is too large, in addition, this algorithm also led to the border is not clear, and there is some inevitable overlap. In the actual scheduling work, this situation is not allowed, as showed in Fig. 16.

Algorithm performance comparison results

This paper will describe the quantified experimental results of the three methods, it compares the differences between them. It is easy to see that the algorithm proposed in this paper is optimal, compared to the other two algorithms. Figure 17 compares the difference between the numbers of sites. Compared to the K-means clustering algorithm and the Fast Unfolding community discovery algorithm, the variance of the CDoMO algorithm is reduced by 66.98% and 22.57%. Figure 18 in this paper compares the number of scheduled bicycles, it finds that the CDoMO algorithm set out in the present paper is an optimal algorithm. Similarly, opposed to the K-means clustering algorithm and the Fast Unfolding community finding algorithm, the variance is reduced by 83.77% and 48.72% (Fig. 19). Figure 20 compares the estimated total distance of scheduling with the other two algorithms, and the conclusion shows that the distance is decreased by 50.82% and 22.08%.

Then we can conclude that the CDoMO algorithm proposed in this paper: It effectively reduces the number of sites; it effectively reduced the variance in the number of bicycles dispatched; it effectively reduced the estimated total distance for scheduling.