CN108399468A - It is a kind of based on vehicle when cost optimization operation Time segments division method - Google Patents

It is a kind of based on vehicle when cost optimization operation Time segments division method Download PDF

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CN108399468A
CN108399468A CN201810093910.7A CN201810093910A CN108399468A CN 108399468 A CN108399468 A CN 108399468A CN 201810093910 A CN201810093910 A CN 201810093910A CN 108399468 A CN108399468 A CN 108399468A
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巫威眺
靳文舟
李鹏
任婧璇
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South China University of Technology SCUT
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Abstract

The operation Time segments division method of cost optimization, includes the following steps when the invention discloses a kind of based on vehicle：Using log logistic statistical models to history journey time into fitting of distribution, calculates and give the journey time that direction of each dispatching a car under frequency has reliability；Using history passenger flow data and legal minimum departure frequency, the minimum Fleet size completed in this time window needed for transport task is calculated；To the initial time of the time window, with certain step-length, direction is slided along the time axis, calculates the minimum Fleet size of theory in each time window successively；Calculate fleet's service time totle drilling cost of operation Time segments division scheme, the i.e. accumulative total of day part duration and the product of corresponding theory minimum Fleet size；It is minimised as target with fleet's service time totle drilling cost, optimizing is carried out to whole day operation Time segments division scheme.Compared with traditional Time segments division method, method of the invention can be better achieved transport power and match with freight volume, and effectively reduce vehicle when cost.

Description

Operation time period division method based on vehicle-time cost optimization
Technical Field
The invention relates to the technical field of bus operation management, in particular to an operation time interval division method based on vehicle-time cost optimization.
Background
Public transport is a main trip mode of urban commuters and is also an efficient transportation mode for realizing sustainable development of urban traffic. Effective bus system planning involves several well-defined and interrelated sub-problems: planning a line; designing departure frequency; compiling a time schedule; vehicle dispatch and driver scheduling. The public transportation operation time interval division divides the whole day operation time interval into a plurality of stages, and aims to enable the inside of each time interval to have Transport capacity requirements which are as close as possible, so as to further establish a corresponding Scheduling scheme, and a public transportation management department can conveniently establish a timetable and configure vehicles and personnel [ Song Rui, He Shiwei, Yang Yongkai, and the like.
In the aspect of bus operation optimization, currently, research mainly focuses on scheduling schemes in a given operation period, and little attention is paid to operation period division. Bie [ Bie Y, Gong X, Liu Z. time of day inter-arrival partition for bus schedule using GPS data [ J ]. Transportation Research Part C generating technologies,2015,60: 443-. Shendong et al [ Shendong, Zhangui, Xujia ] Analysis of public transport system Engineering and Information Based on K-means clustering algorithm [ J ]. Transport transportation System Engineering and Information 2014,14(2):87-93. Shendong, Zhang Tonghui, Xu Jia. Homogeneous Bus Running time Bands base on K-means Algorithms [ J ]. Journal of transportation systems Engineering and Information Technology 2014,14(2):87-93.] use data pairs consisting of departure times and their corresponding travel times as vehicle-level task attributes and use the distance of clustering to evaluate the similarity between different vehicle-level tasks, and use the resulting boundaries as the dividing time points of the public transport operation period. The Optimization Method of the bus dispatching peak Curve [ J ]. southeast university newspaper (Natural science edition),2001,31 (3):40-43.Yang Xinmiao Wang Wei Yin Yang Wu Yong, A New Method for Transit Peak value Current Optimization [ J ], Journal of south university (Natural science edition),2001,31(3) ] on the basis of the line passenger data, the bus operation time is divided by using a Fisher clustering algorithm, so that the inside of the operation time has similar passenger demands. Mendes et al [ Mendes-MoreiraJ, Moreira-Matias L, Gama J, et al. valid the coverage of bus schedules. Amachine Learning approach [ J ] Information Sciences,2015,293(1):299 &. 313.] utilize the vehicle travel time data of a line all the year around to plot the daily travel time variation curve of the line, utilize the dynamic time bending distance to evaluate the similarity of travel time between dates, and perform cluster analysis on the travel time variation curve, thereby classifying the dates all the year around. The method has the principle that the change rules of the whole day travel time have similarity in the same type of date, and can provide reference for schedule formulation work in different types of dates so as to improve the reliability of the schedule.
In current actual operation, an administrator often performs time interval division by experience, and a time interval division method with general guidance significance is lacked. In the theoretical research aspect, the previous researches are all based on a single data source (passenger flow demand or vehicle travel time), a clustering algorithm is adopted, the space-time similarity of parameters is used as a division result, and the joint action of multi-source public transportation data (passenger demand and vehicle travel time) on time interval division is not considered, so that the defects of the following aspects exist: (1) the clustering algorithm (such as k-means) performs time interval division according to the rules of historical data, the considered influence factors are limited, and the classification number is usually set manually, so that the division result is too subjective and is not necessarily an optimal solution. (2) The single-parameter time interval division method ignores the fluctuation of other influence factors, so the vehicle journey time-based operation time interval division method is suitable for lines in which passenger requirements are stable and the vehicle journey time fluctuation is large in operation time intervals, such as non-important commuting lines running in urban areas; the operation time interval dividing method based on the passenger demands is suitable for lines with stable travel time and large passenger flow fluctuation, such as BRT lines with bus lanes. However, for most urban public transport lines, the passenger flow composition structure is complex, the running road condition is complex, and the passenger flow demand fluctuation and the travel time fluctuation are large. Since the traffic volume directly affects the vehicle stop time, there is a certain relationship between the travel time and the passenger demand [ Wu w., Liu r., Jin w. modeling bus bustling and holding control with vehicle timing and distributed sensing monitoring device [ J ]. Transportation Research Part B,2017,104:175 + 197 ], if the combined action of the two parameters of the passenger flow demand and the travel time can be captured at the same time, the bus operation period division scheme may be more reasonable.
In practical operation, an important index of time interval division is the minimum fleet size of the time interval, namely the minimum number of vehicles required for completing all transportation tasks in the time interval. Since the minimum fleet size is proportional to passenger demand and proportional to vehicle travel time, there may be situations where passenger demand increases and vehicle travel time decreases, but capacity demand does not change, and vice versa. For example: the passenger demand and the vehicle travel time in the two periods have great difference, and if the passenger demand and the vehicle travel time are processed by the traditional method, the result tends to divide the two periods into different operation periods, however, the capacity demands of the two periods may be the same, and from the viewpoint of fleet operation management, the two periods should be included into the same operation period. Therefore, from the perspective of fleet management, it is reasonable to use the transportation demand as the basis for time interval division, and when the line fleet is a single vehicle type, the time interval transportation demand is the minimum fleet size [ Salzborn F, Buckley D J.
In view of the above, the invention provides an operation time interval division method based on vehicle-time cost optimization for the first time from the perspective of fleet management and control. The minimum fleet scale of different times in an operation period is calculated by utilizing passenger flow demand and travel time information and combining an inverse difference function model and a sliding time window model, a period division scheme time division point is used as a decision variable, an operation period division optimization model with the minimum fleet operation time cost as a target is established, and the theoretical minimum fleet scale corresponding to each period is obtained so as to provide direct reference for subsequent schedule compilation and driver scheduling.
Disclosure of Invention
The invention aims to overcome the defects in the prior art and provides an operation time interval dividing method based on vehicle-time cost optimization.
In order to realize the purpose, the invention adopts the following technical scheme:
an operation time interval dividing method based on vehicle-time cost optimization comprises the following steps:
s1, performing distribution fitting on the historical travel time by using a log-logistic statistical model, and calculating the travel time with reliability in each departure direction at a given departure time on the basis of the distribution model obtained by fitting;
s2, calculating the number of operation vehicles needed in a time window which takes the departure time of the first bus as the starting time and the time when each terminal station reaches the vehicle transceiving balance as the ending time by using the historical passenger flow data and the legal lowest departure frequency, namely, finishing the minimum fleet scale needed by the transportation task in the time window;
s3, sliding along the direction of a time axis in a set step length from the starting time of a time window, wherein the width of the time window is constantly changed along with the change of the time for each terminal station to reach the vehicle transceiving balance; calculating the theoretical minimum fleet scale in each time window in sequence; the theoretical minimum fleet scale is a plurality of rolling applications of the calculated minimum fleet scale in step S2 according to a time window;
s4, calculating the total cost of the fleet operation time of the operation time interval division scheme, namely the accumulated sum of the products of the duration of each time interval and the corresponding theoretical minimum fleet scale;
and S5, optimizing the whole-day operation time period division scheme by taking the minimization of the total cost of the fleet operation time in the step S4 as a target.
As a preferred technical solution, the step S1 specifically includes the following steps:
s11, collecting GPS data of the bus, wherein the GPS data records the all-day spatial position information of the bus, and the starting time and the arrival time of each bus task executed by the bus are extracted by utilizing a GIS system in combination with the spatial positions of the first station and the last station, and the difference between the arrival time and the starting time is the travel time of the bus task; the GPS data is converted into waybill data, and each waybill data comprises the following information: the train number task ID, the vehicle ID, departure time, arrival time and travel time;
s12, combining GPS data with a GIS system to perform sectional statistics of vehicle travel time, and performing log-logistic distribution fitting on historical travel time data of departure in each time period by an equidistant time period of 600S;
the probability distribution function of the log-logistic distribution is as follows:
wherein l is the vehicle travel time, α is the range parameter, β is the shape parameter, θ is the set reliability level;
s13, calculating the travel time value when the reliability is larger than theta: under the condition that the distribution probability is known, the travel time which arrives at the terminal station on time with the probability larger than theta is taken as the theta quantile of the travel time, and the following calculation formula is specifically adopted:
wherein,the vehicle travel time indicates the reliability of the vehicle from the station s at the departure time t.
As a preferred technical solution, the step S2 specifically includes the following steps:
s21, calculating the cross-section passenger flow in one direction of a time window by using historical actual operation data, wherein the cross-section passenger flow refers to the number of passengers passing through one stop in one direction of the line in one time window of the line;
s211, all train number tasks in a time window are taken;
s212, adopting an OD reverse-pushing technology, extracting passenger OD information carried by each train number by utilizing the vehicle ID, departure time and arrival time information in the waybill data and combining the vehicle ID and card swiping time information in passenger IC card swiping data;
s213, calculating the cross section passenger flow of each station in the two directions of the line;
s214, determining the maximum section passenger flow, wherein the maximum section passenger flow is the maximum value of the station section passenger flow in one direction in one time window;
s215, calculating the average value of the maximum section passenger flow in the same time window on different dates;
s22, calculating the minimum departure frequency to ensure the bus service level; the ratio of the maximum section passenger flow to the single-vehicle passenger carrying capacity in a time window is the number of departure vehicles in the time window, the ratio of the number of departure vehicles in the time window to the width of the time window is the corresponding minimum departure frequency, and the calculated minimum departure frequency is not less than the statutory minimum departure frequency; the following calculation formula is provided:
wherein,represents the time window [ t, t + max (L)s t)]Minimum departure frequency, max (L), internally from the direction of origin of station ss t) Represents the maximum width of the time window;represents the time window [ t, t + max (L)s t)]The section passenger flow of the internal slave station s in the direction of the station i; fmRepresenting a statutory minimum departure frequency; c represents the maximum load capacity of the bicycle, namely the number of seats plus the number of standing passengers; lambda [ alpha ]tRepresents the legal passenger capacity coefficient at the time t, and is more than 0 and more than lambdat≤1；
S23, calculating the minimum fleet size: in a time window with the departure time of the first vehicle as the starting time and the maximum value of travel time in two directions as the width, subtracting the number of vehicles which arrive at the terminal station in the time window and can execute the task of the next vehicle number of the arriving station from the number of vehicles which arrive at the terminal station in the two directions; time windowThe calculation formula of the minimum required fleet size is as follows:
wherein, t0Which represents the starting moment of the time window,represents t0The maximum value of the travel time of the vehicles which start from the two stations a and b and arrive at the terminal station in the corresponding direction at the moment,represents t0The minimum value of the travel time of the vehicles which start from the two stations a and b and arrive at the terminal station in the corresponding direction at the moment,represents the maximum value of the two-way minimum departure frequency assuming the minimum departure frequencies in both directions to be the same, inAt the moment, the two terminals a and b reach the vehicle transceiving balance.
As a preferred technical solution, the step S3 specifically includes the following steps:
s31, pair t0Sliding along the time axis direction, wherein the sliding step length is delta t; using a new t for each sliding0RecalculationAndsliding until the operation time is finished;
and S32, calculating the theoretical minimum fleet size in each time window by the method about the minimum fleet size in the step S2, and acquiring a theoretical minimum fleet size data set.
Preferably, in step S4, the minimum fleet size N of the p-th operation period is determined according to the period division schemepThat is, the maximum value of the theoretical minimum fleet scale at each moment in the p-th operation period is specifically as follows:
wherein,indicates the start time of the p-th operation period,indicating the end time of the p-th operating period.
As a preferred technical solution, the step S5 specifically includes the following steps:
s51, establishing a time interval division optimization model based on multi-source bus data and vehicle-hour cost optimization:
the constraints are as follows:
the formula (6) represents that the total cost of the operation time of the all-day bus fleet is minimized, namely the cumulative sum of the minimum fleet scale and the duty time is given as veh.h; equation (7) represents the shortest operation period length limit; the formula (8) ensures that the starting time of the first operation period is the starting time of the line operation time; the formula (9) ensures that the end time of the last operation period is the end time of the line operation time; the equation (10) ensures complete division of the line operation time period; the expression (11) represents a value range of the time division amountEnclosing; wherein k represents the number of divisions in the operating period of the whole day; l ismpRepresents a minimum operation period length; t issRepresenting a line operation starting time; t iseIndicating a line operation end time;indicating the start time of the first operational period,represents the end time of the kth operating period;
s52, solving the model by adopting a genetic algorithm, wherein the algorithm comprises the following specific steps:
② departure time from the line running start time TsStarting time, taking delta T as time increment, and sequentially and circularly executing the following steps until departure time is equal to line operation ending time TeUntil the end;
② calculating the travel time of the vehicle from the station s at the departure time t
③ calculating time windowThe inner maximum cross-section passenger flow volume;
④ calculating time windowMinimum departure frequency within;
⑤ calculating time windowInner theoretical minimum fleet size;
⑥ ends the above cycle;
⑦ obtaining a theoretical minimum fleet size data set n (T | T ∈ (T ∈)s,Te))}；
⑧ given time division scheme [ (t)s 1,te 1),...,(ts p,te p),...,(ts k,te k)]And obtaining the theoretical minimum fleet size N of each time intervalp；te 1Indicating the end time, t, of the first operating periods kRepresents a start time of a k-th operation period;
⑨ a genetic algorithm is used to optimize the time division scheme with the goal of minimizing the total cost of fleet operating time.
Compared with the prior art, the invention has the following advantages and effects: the traditional time interval division method with a single parameter (based on passenger flow or travel time) can only reflect the fluctuation rule of the parameter in the operation time interval. In actual operation, although the passenger flow has correlation with the fluctuation law of the travel time, the difference of the passenger flow and the travel time affects the optimal time interval division scheme. Compared with the traditional single-parameter time interval division method, the optimization model based on the multi-source public transportation information (two parameters of passenger flow demand and travel time) and the operation time cost can obtain a time interval division scheme, can also obtain the corresponding minimum fleet scale in a time interval, and fully reflects the matching relation between the transport capacity and the transport capacity, so that the potential value of data is deeply mined, and references of the time interval division scheme and fleet configuration are provided for a public transportation management department; compared with the traditional method for dividing the time intervals according to single parameters (passenger flow requirements or travel time data), the method can better reflect the transport capacity requirements in different time intervals, enables the transport capacity and the transport volume to be more matched, effectively reduces the vehicle-hour cost, and has scientific and practical significance; the maximum cross-section passenger flow and the travel time utilized in the calculation process can be obtained by calculating the IC card swiping data and the vehicle GPS data, and the method has accuracy and timeliness.
Drawings
Fig. 1 is a flowchart of an operation period division method based on vehicle-hour cost optimization according to this embodiment.
Fig. 2 is a bidirectional travel time scatter diagram and an equidistant time segment dividing line of 600s according to the present embodiment.
3(a) -3 (f) are a cumulative plot of travel time over 6 typical time periods and a log logistic distribution fitted cumulative distribution plot for the upstream portion of the line of this embodiment; wherein FIG. 3(a), FIG. 3(b), FIG. 3(c), FIG. 3(d), FIG. 3(e) and FIG. 3(f) are fitted cumulative profiles of travel time for uplink direction time periods and log logistic distributions for lines 06:30:00-06:40:00, 08:00:00-08:10:00, 10: 00-10:10:00, 14:00:00-14:10:00, 18:00:00-18:10:00 and 22:00:00-22:10:00, respectively.
FIG. 4 is a diagram of the bidirectional vehicle operation at a certain time interval (08:00:00-09:00:00) in the present embodiment.
Fig. 5 is a schematic diagram of the theoretical minimum fleet size calculation of this embodiment.
Fig. 6 is a schematic diagram of calculating the minimum fleet size of each time window by using a sliding time window according to the present embodiment.
Fig. 7 is a schematic diagram of the fleet operating time cost according to the embodiment.
Fig. 8(a) -8 (c) are the 87-way bus route map, the bidirectional average cross-section passenger flow and the bidirectional average travel time of the embodiment; fig. 8(a) is a map of the 87-way bus lines of the embodiment, fig. 8(b) is bidirectional average cross-section passenger flow of the 87-way bus lines of the embodiment, and fig. 8(c) is bidirectional average travel time of the 87-way bus lines of the embodiment.
FIG. 9 is a sliding step Δ t sensitivity analysis of the present embodiment.
Fig. 10 is a sensitivity analysis of the time division number parameter k for different passenger capacities of the single vehicle according to the present embodiment.
Fig. 11 is a sensitivity analysis of passenger capacity per car for different time period division numbers according to the present embodiment.
Fig. 12 is an optimal time division scheme for different passenger capacities of the single vehicle according to the embodiment.
Fig. 13 shows the optimal time division scheme and the time slot fleet size when the passenger capacity of a single vehicle is 60 according to the same method of the present embodiment.
Detailed Description
The following description of the embodiments of the present invention is provided in connection with the accompanying drawings and examples, but the invention is not limited thereto.
Examples
TABLE 1 list of parameters, meanings and units used in this example
As shown in fig. 1, an operation time division method based on vehicle-hour cost optimization includes the following steps:
s1, calculating the travel time with reliability in each departure direction at a given departure time by using the historical travel time data;
and S11, starting the vehicle from the starting station until the one-way transportation task is completed and the vehicle reaches the destination station, wherein the required time is the one-way travel time of the vehicle, including road running time, delay time and station stop time. The traffic state and the fluctuation of the time for getting on and off the bus lead to the randomness of the travel time of the bus. The GPS data records the all-day spatial position information of the bus, the GIS system is used for spatial matching by combining the spatial positions of the first station and the last station, the starting time and the arrival time of the bus for executing each bus task can be extracted, and the difference between the arrival time and the starting time is the travel time of the bus task. By using the method, the bus GPS data can be converted into the wayside list data, and each wayside list comprises the following information: train number task ID, vehicle ID, departure time, arrival time, and travel time. A scatter diagram is drawn by summarizing the vehicle travel times of the waybills and the corresponding departure times thereof on all the study dates as shown in fig. 2.
S12, in order to estimate the vehicle travel time at the given departure time, GPS data is combined with a GIS system to carry out sectional statistics of the vehicle travel time, and the sectional width selection problem is involved: if the segment width is too short, the number of sample points contained in each time interval is too small, and the distribution fitting is inaccurate; and if the segment width is too long, too many sample points are obtained, the travel time distribution is not concentrated, and the standard deviation of the travel time is too large. By combining the actual data quantity and the distribution condition thereof, the present embodiment divides the operation time period into equidistant time periods of 600s (10min), and it is more appropriate to use 600s (10min) as the segment width, and the vertical line in fig. 2 is the dividing line of the equidistant time periods of 600 s; statistical analysis of actual data shows that the vehicle single-pass operating time in a time period accords with log-logistic distribution [ Ashkar F, Mahdi S. matching the log-logistic distribution by genetic distributions [ J ]. Journal of Hydrology,2006,328(3):694 + 703 ]), and in the embodiment, the log-logistic distribution is fitted to the historical travel time data of departure in each time period.
The probability distribution function of the log-logistic distribution is as follows:
wherein l is the vehicle travel time, α is the range parameter, β is the shape parameter, theta is the reliability degree set according to the requirement;
s13, for the theoretical minimum fleet scale, under the condition that the departure frequency is unchanged, if the vehicle travel time is shortened, the actual required fleet scale is shortened, and the minimum fleet scale can still complete the transportation task; if the travel time is increased, the actually required fleet scale is larger than the minimum fleet scale, the minimum fleet scale cannot complete the transportation task, and the situation of insufficient transportation capacity occurs.
According to the distribution probability in step S12, a travel time value when the reliability is greater than θ is calculated, and a travel time value when the terminal arrives at the terminal on time with a probability greater than θ is taken as a θ quantile of the travel time (i.e., the vertical axis of the cumulative probability density map is a horizontal coordinate numerical point corresponding to θ), specifically, the following calculation formula is provided:
in this embodiment, in order to verify the reliability of the distribution fitting, the present embodiment performs Kolmogorov-Smirnov (K-S) verification on the data based on the fitting of the time period data, and as a result, as shown in table 2, it can be seen that the p value of the K-S verification is greater than 0.2 and the coefficient of solution R is greater than 0.2 in all time periods2It is also high, i.e., the vehicle travel times over the time periods conform to a log-logistic distribution, so the travel time distribution model fitted by this distribution is reliable. In order to visually display the log-logistic distribution fitting result, travel time data of a vehicle sent out in 6 representative time periods in the uplink direction are selected in the embodiment, and a graph 3 is drawn, wherein the graphs (a) to (f) are a travel time cumulative graph and a loglogistic distribution fitting cumulative distribution graph of 6 representative time periods in the uplink direction of the route; wherein, the travel time of the uplink direction time periods of the circuits of FIG. 3(a), FIG. 3(b), FIG. 3(c), FIG. 3(d), FIG. 3(e) and FIG. 3(f) are 06:30:00-06:40:00, 08:00:00-08:10:00, 10: 00-10:10:00, 14:00: 14:10:00, 18:00:00-18:10:00 and 22:00:00-22:10:00 respectivelyFitting the product graph and the logogic distribution to a cumulative distribution graph; in fig. 3(a) to 3(f), the horizontal axis represents the travel time, the vertical axis represents the corresponding cumulative distribution, the solid line represents the cumulative graph of the actual data, and the dotted line represents the log-logistic fitted cumulative distribution graph. The required buffer time with the travel time reliability larger than theta is calculated by utilizing the time distribution, and theta takes 95% in the embodiment. Therefore, based on the method, a data set of travel time of the bus is obtained, wherein the data set comprises three information of time interval starting time, time interval ending time and travel time, namely, the vehicles which are dispatched in the corresponding time interval have the probability that the travel time of the vehicles is less than or equal to a given buffering time value by 95%. It should be noted that, since the travel time includes the stop time of the station and the travel time between the stations, and the traffic volume directly affects the stop time of the vehicle, the travel time fitting here also reflects the fluctuation of the traffic to some extent.
TABLE 2 results of the distribution fitting verification of the time-segment data
S2, calculating the number of operation vehicles needed in a time window which takes the departure time of the first bus as the starting time and the time when each terminal station reaches the vehicle transceiving balance as the ending time by using the historical passenger flow data and the legal lowest departure frequency, namely, finishing the minimum fleet scale needed by the transportation task in the time window;
s21, calculating the cross-section passenger flow in one direction of a time window by using historical actual operation data, wherein the specific method comprises the following steps:
and S211, extracting all train number tasks in the time window. Taking a bus running diagram in a certain time period as an example shown in fig. 4, wherein the horizontal axis represents operation time, the vertical axis represents positions (terminal stations a and b), black oblique lines represent vehicles departing in a time window of 08:00-09:00, gray oblique lines represent vehicles departing outside the time window of 08:00-09:00, and the maximum cross-section passenger flow carried by the vehicles represented by the black running diagram is the maximum cross-section passenger flow in the time period of 08:00-09: 00.
And S212, extracting the OD information of the passengers carried by each train number. Passenger IC card swiping data comprises passenger card number information, passenger card swiping time information, passenger card swiping station information and passenger card swiping vehicle information, and does not comprise getting-off station information, for this reason, the embodiment utilizes OD reverse-push technology [ Chen J, Liu Z, Zhu S, et al. And (4) extracting passenger OD information carried by each train number by using the vehicle ID, departure time and arrival time information in the waybill data and combining the vehicle ID and card swiping time information in the passenger IC card swiping data.
And S213, calculating the cross-section passenger flow of each station in the two directions of the line. The cross-sectional passenger flow of each station in each direction is the sum of the number of all passengers before the boarding station (including the station) and after the alighting station (not including the station). For example, a public transportation OD matrix (as shown in table 3) having 10 stations and a certain time period in a certain departure direction, each row and column respectively represents a departure station and an arrival station, the numerical values in the table are the passenger flow volumes of the corresponding ODs in the certain time period in the certain direction of the line, and if the cross-sectional passenger flow of the fourth station (O4 or D4) needs to be calculated, the OD passenger flow volumes with the row numbers of O1-O4 and the column numbers of D5-D10 are accumulated.
TABLE 3 passenger OD matrix
And S214, the maximum value of the cross-section passenger flow of each station in a certain direction is the maximum cross-section passenger flow in the direction in the time window.
S215, calculating the average value of the maximum section passenger flow of the same time window on different dates.
The method can obtain the maximum section passenger flow data set which comprises three information of time window starting time, time window ending time and maximum section passenger flow, and lays a foundation for subsequent calculation of transportation capacity requirements.
S22, the departure frequency in a time window is determined by the maximum cross-section passenger flow, and under the condition of the given single-car bearing capacity, the minimum departure frequency in a certain time window must be ensured to meet the maximum cross-section passenger flow requirement of a line [ Lampkinw, Saalmans P D. the signals of routes, service frequencies, and schedules for an urban bus intersection: A case study [ J ] Journal of the Operational research facility, 1967,18(4):375- ]. Too low departure frequency increases the waiting time of passengers, so the public transportation management department generally sets the statutory minimum departure frequency to ensure the public transportation service level. The ratio of the maximum section passenger flow to the single-vehicle passenger carrying capacity in a certain time window is the number of departure vehicles in the time window, the ratio of the number of departure vehicles in the time window to the width of the time window is the corresponding minimum departure frequency, and the calculated minimum departure frequency is not less than the legal minimum departure frequency. The specific calculation method can be calculated by using the following formula [ Lampkin W, Saalmans P D.the design of routes, servicefrequencies, and schedules for an a microbial bus understandating: A case study [ J ]. Journal of the Operational Research facility, 1967,18(4):375 and 397 ]:
wherein,is represented in a time windowMinimum departure frequency, max (L), internally from the direction of origin of station ss t) Represents the maximum width of the time window;represents the time window [ t, t + max (L)s t)]The section passenger flow of the internal slave station s in the direction of the station i; fmRepresenting a statutory minimum departure frequency; c represents the maximum load capacity of the bicycle, namely the number of seats plus the number of standing passengers; lambda [ alpha ]tRepresents the legal passenger capacity coefficient at the time t, and is more than 0 and more than lambdat≤1。
And S23, for the circulating or returning line with only one terminal station, calculating the theoretical minimum fleet scale required for completing the line transportation task according to the travel time of the first vehicle returning to the station and the minimum departure frequency, wherein the terminal station vehicle receiving and sending balance time is the time for the first vehicle to return to the station. For a bus line with bidirectional departure, according to the one-way travel time and the minimum departure frequency of the vehicles sent from a parking lot in two directions, the theoretical minimum fleet scale required for completing the bidirectional transportation task and the time (Ceder, available. public transportation planning and operation) required for the bidirectional station to reach the transceiving balance can be calculated by utilizing an inverse difference function model].Elsevier,2007.]. In this embodiment, the two-way departure bus route is taken as an example to calculate the theoretical minimum fleet scale of the route, and in order to simplify the calculation, the minimum departure frequency in two directions is assumed to be the same, and is a larger value of the two-way minimum departure frequencyAt t0At the time, the travel time of the vehicle from the a station to the b station isThe operation time from the b site to the a site isThus, inAt the moment, the two terminals a and b reach the vehicle transceiving balance, and the number of the vehicles put into operation at the moment isThe minimum fleet size required to complete the transportation task within this time window. Under the condition of no increase of departure frequency and travel time, the fleet scale can continue to complete the next operation task, and the fleet scale can utilize an inverse difference function model (Ceder, avishai].Elsevier,2007.]And (6) performing calculation. For the premise assumption of this embodiment, the calculation method of the fleet scale can be simplified as follows: and in a time window with the departure time of the first vehicle as the starting time and the maximum value of the travel time in the two directions as the width, subtracting the number of vehicles which arrive at the terminal station in the time window and can execute the task of the next vehicle number of the arriving station from the number of vehicles which arrive at the terminal station in the two directions. Time windowThe calculation formula of the minimum required fleet size is as follows:
wherein, t0Which represents the starting moment of the time window,represents t0The maximum value of the travel time of the vehicles which start from the two stations a and b and arrive at the terminal station in the corresponding direction at the moment,represents t0The minimum value of the travel time of the vehicles which start from the two stations a and b and arrive at the terminal station in the corresponding direction at the moment,represents the maximum value of the two-way minimum departure frequency assuming the minimum departure frequencies in both directions to be the same, inAt time, both terminals a, bThe vehicle transceiving balance is achieved.
As shown in fig. 5, the schematic diagram of calculating the minimum fleet size of each time window by using sliding time windows is shown, the lower half part of fig. 5 is a public transportation operation diagram in a certain time period, and the upper half part is a corresponding bidirectional accumulated inverse difference function (i.e. a function of the number of operating vehicles changing with time), wherein the horizontal axis represents operation time, the vertical axis represents a terminal a and a terminal b, and the black vertical line is a starting time t0The vertical dotted line is at t0The time of the vehicle sent by the b arrives at the a station, and the vertical line is at the t0The time of the vehicle from a arrives at b, and the solid inclined line represents the time windowInternally emitted vehicle travel map, the oblique dashed lines representing time windowsAnd (4) externally sending a vehicle operation diagram. The time window is completed in this example, as calculated by equation (4)The number of vehicles for the inner transportation task is 7 veh.
S3, sliding along the direction of a time axis in a set step length from the starting time of a time window, wherein the width of the time window is constantly changed along with the change of the time for each terminal station to reach the vehicle transceiving balance; calculating the theoretical minimum fleet scale in each time window in sequence; the theoretical minimum fleet scale is a plurality of rolling applications of the calculated minimum fleet scale in step S2 according to a time window;
s31, pair t0Sliding along the time axis direction, wherein the sliding step length is delta t; using a new t for each sliding0RecalculationAndsliding until the operation time is finished; FIG. 6 is a schematic diagram of a calculation process of adjacent sliding time windows, wherein the horizontal axis represents operation time, the vertical axis represents fleet scale, and the step diagram of dotted lines represents time windowsInner two-way cumulative inverse difference function, solid line ladder diagram being time windowThe two-way accumulated inverse difference function in the inner part has horizontal thick dotted line with two corresponding horizontal coordinates as time windowThe corresponding ordinate of the starting time and the ending time of the time window is the minimum calculated fleet scale of the time window, and the same principle is applied to horizontal thick solid lines. In the present embodiment, the time windowThe minimum fleet size is 7/veh, the time windowThe minimum fleet size of (2) is 8/veh.
And S32, calculating the theoretical minimum fleet size in each time window by the method about the minimum fleet size in the step S2, and obtaining a minimum fleet size data set.
S4, calculating the total cost of the fleet operation time of the operation time interval division scheme, namely the accumulated sum of the products of the duration of each time interval and the corresponding theoretical minimum fleet scale;
minimum fleet size N for a certain operational period p given a time division schemepI.e. the maximum value of the theoretical minimum fleet size at each moment in time period p. FIG. 7 is a schematic representation of fleet operating time cost, with the horizontal axis representing operating time, the vertical axis representing minimum fleet size, and the horizontal line with circles as endpoints representing a time windowThe time points of the transverse shaft corresponding to the two end points are time windowsThe vertical axis value corresponding to the horizontal line is the minimum fleet size required by the time windowThe vertical dashed line is the split time point between the operation periods. The minimum fleet size of each operating period is the maximum value of the minimum fleet size required for each time window covered by the period, i.e., the upper bound of the diagonally shaded part of each operating period in fig. 7, and the specific calculation formula is as follows:
wherein,indicates the start time of the p-th operation period,indicating the end time of the p-th operating period.
And S5, optimizing the whole-day operation time period division scheme by taking the minimization of the total cost of the fleet operation time in the step S4 as a target.
S51, from the perspective of fleet management and control, the present embodiment proposes a time division optimization model based on the goal of minimizing the total fleet operation time cost (unit is, vehicle × hour, veh · h), where the fleet time cost reflects the variable cost of bus operation, and the fixed cost of the vehicle is not considered here, because this Part of the cost can be approximately ignored in the long run [ Wu w., liur., Jin w.design route scheduling scheme for transit network with safety control indexes [ J ]. Transportation Research Part B,2016,93: 495-. The fleet operation time cost of a time period is defined as the product of the fleet size and the length of the time period, and the total fleet operation time cost is the accumulation of the fleet operation time costs of each time period. In fig. 7, the cumulative fleet operating time cost is the area of the diagonally shaded portion in fig. 7. The time interval division scheme optimizing process is a process of searching the operation time interval division point with the minimum shadow area under the condition of meeting the constraint condition. In order to facilitate fleet management, the minimum value of the operation time interval length is generally required to be set, in actual operation, a vehicle can quit operation when reaching a terminal station (including an uplink terminal station and a downlink terminal station), the shortest operation time length of the vehicle is one-way travel time, and for convenient calculation, the shortest operation time length is specified as the larger value of the average value of the uplink one-way time and the average value of the downlink one-way time. After the shortest operation period length is determined, the theoretical maximum period division number is also determined.
Establishing a time interval division optimization model based on multi-source bus data and vehicle-hour cost optimization:
the constraints are as follows:
wherein, the formula (6) represents that the total cost of the operation time of the whole-day bus fleet is minimized, namely the cumulative sum of the fleet scale and the on-duty time is given as veh.h; equation (7) represents the shortest operation period length limit; the formula (8) ensures that the starting time of the first operation period is the starting time of the line operation time; the formula (9) ensures that the end time of the last operation period is the end time of the line operation time; the equation (10) ensures complete division of the line operation time period; the formula (11) represents a value range of the time division amount; wherein k represents the number of divisions in the operating period of the whole day; l ismpRepresents a minimum operation period length; t issRepresenting a line operation starting time; t iseIndicating a line operation end time;indicating the start time of the first operational period,represents the end time of the kth operating period;
the operation time interval is a continuous and bounded time interval, the minimum time unit of the historical operation data is second, and the division space of the operation time interval by taking the second as a unit is large. Since the time nodes in the operation time interval division do not need to be excessively accurate, in order to reduce the solution space, the minimum time accuracy of the time interval division can be determined, for example, in the embodiment, the operation time interval is divided with 5 minutes as the time accuracy. The present embodiment represents the period division scheme as an integer type vector, each integer representing a period division time point (the few 5 minutes of a day) between two adjacent operation periods, and table 4 is an example of the period division scheme. The fleet operation time cost per time interval division scheme can be obtained by using the minimum fleet scale data set obtained as described above as an environment variable and using equation (6) as a calculation method. Table 4 shows a method for representing decision variables, which is a combinatorial optimization problem of feasible domain bounded integer programming because the decision variables can be all represented by integers.
TABLE 4 optimized decision variable representation method
S52, aiming at the problem of the combination optimization of the feasible domain bounded integer programming in the step S51, various intelligent Algorithms can be utilized to solve, the embodiment adopts a Genetic algorithm [ Zhou, Genetic algorithm principle and application [ M ]. the National defense industry Press,1999. Zhou Ming, Genetic Algorithms: Theory and Applications [ M ], National Defenend industry Press,1999 ], and the table 4 is pseudo code of the algorithm of the embodiment.
TABLE 5 Algorithm pseudocode for this example
Example analysis
In the present embodiment, the time division method was verified using 87 public transportation lines in Guangzhou city, 2016 vehicle GPS data and IC card swiping data in 5 months. The first and last stations of the bus line are respectively an airport road master station and an escape green garden master station, the total length is 17.4 kilometers, the bus line is connected with Guangzhou subway No. 1 line, No. 2 line and No. 6 line in urban functional areas such as Guangzhou city central business area, high-density residential areas, numerous hospital school parks and the like, and passenger flow composition and traffic state are complex. All operating vehicles of the bus line are provided with GPS equipment and completely record operating data, the data completeness is good, the accuracy is high, the card swiping rate of passengers in the bus line is over 95%, and the card swiping data of an IC card can completely reflect information required by the method of the invention, such as passenger flow space-time distribution and the like.
1. Data collection and processing
Fig. 8(a) is a map of the 87-way bus route of the embodiment, fig. 8(b) is a bidirectional average cross-section passenger flow of the 87-way bus route of the embodiment, and fig. 8(c) is a bidirectional average travel time of the 87-way bus route of the embodiment, and it can be seen from fig. 8(a) -8 (c) that the passenger flow and the travel time fluctuation of the bus route all day are large, and therefore, in order to make the operation period division scheme more accurate, it is necessary to capture the change rule of the passenger flow and the travel time at the same time.
According to Mendes' research, the influence of different date types on the operation of a public transportation system is great, and the public transportation operation time has a more similar time fluctuation rule in the same date type. Therefore, by taking the conclusion of Mendes as a reference, the method divides the actual bus operation data into two types of working days and non-working days, and extracts the data of the working days to verify the method of the embodiment.
2. Parameter setting and result analysis
In this embodiment, it is found through investigation that the theoretical maximum passenger capacity c of a single vehicle of 87 operating vehicles on the line is 100pax/veh, and the legal passenger capacity coefficient λtIn actual operation, different values can be obtained at different times, and for the convenience of calculation and comparison, it is assumed that the values are kept unchanged, namely, lambdatλ, for example, when λ is 0.4, the corresponding desired single-vehicle passenger capacity is c · λ 40/pax. In addition, the minimum departure frequency FmThe shortest operation time length L is 5 vehicles per hourmpIs 90/min.
The sliding step parameter Δ t is the sampling precision of the basic information in the method of the present embodiment, and fig. 9 shows the influence of the parameter on the system performance (λ ═ 0.6). As can be seen from fig. 9, the sliding step length is within an interval of 0 to 6 minutes, the operation time cost of the obtained optimal scheme fleet is stable, and when the sliding step length exceeds 6 minutes, the operation time cost of the optimal scheme fleet has a certain fluctuation, because when the sliding step length is set to be large (that is, data points in fig. 7 become sparse), some time windows with concentrated passenger flows may be divided into adjacent sliding time windows, which results in a minimum fleet size of the time windows and a reduction in the operation time cost of the fleet, however, at this time, the fleet size may not complete the transportation task of a peak time window, resulting in an excessive passenger carrying capacity of a single vehicle or a retention passenger in a station. During the sliding step change, the peak time window in the passenger flow concentration may appear in a sliding time window, which causes the fleet scale and the fleet operation time cost to be large, and thus the fleet operation time cost fluctuates dramatically when the sliding step is large. However, if Δ t is too small, the regular similarity between the passenger flow and the travel time of adjacent time windows is too large, and the complexity of the solution is increased. Therefore, the selection principle of the sliding step length parameter Δ t is to select a smaller value as much as possible on the premise of ensuring that the optimization calculation process is feasible, and in summary, the value Δ t of this embodiment is 5/min.
Fig. 10 shows the effect of the passenger capacity of a single vehicle (c · λ) on the minimum fleet time cost, it can be seen from fig. 10 that an increase in the passenger capacity of a single vehicle leads to a decrease in the minimum fleet time cost for a certain number of divisions of the time interval, because the decrease in the fleet time cost is smaller for a certain maximum section passenger flow, according to equations (3) and (4), for a certain maximum section passenger flow, the higher the passenger capacity of a single vehicle, the lower the required departure frequency (the departure frequency is not lower than the legal minimum departure frequency), the smaller the minimum fleet size, and thus the lower the fleet time cost, however, as the passenger capacity of a single vehicle increases, the decrease in the fleet operation time cost is gradually decreased, such as k 6, the passenger capacity of a single vehicle changes from 40 to 50, the operating time cost is decreased by 125.25veh · h. when the passenger capacity of a single vehicle changes from 70 to 80, the operating time cost of the operating time can be reduced by only 30.15, according to 633, the following equation, the reason that ① is not reduced when the maximum section frequency of the maximum section is not greater than the minimum frequency of the maximum section and thus the frequency of the minimum frequency of the flat vehicle, the frequency of the minimum fleet operation.
FIG. 11 illustrates the effect of the number of time slots k on fleet time cost for different individual capacities (c.lambda.) it can be seen from FIG. 11 that the minimum fleet time cost generally decreases with increasing number of time slots, since more time slots with lower fleet size demand are divided as the number of divided time slots increases, thereby decreasing the operating time of a fleet with larger peak time slots and thus generally decreasing the minimum fleet time cost, however, as the number of divided time slots increases, the minimum fleet time cost remains unchanged or even increases, for two reasons, ①, when there are too many divided time slots, the minimum size of adjacent time slots is equal, resulting in invalid time slots dividing, resulting in unchanged fleet minimum fleet time cost, ②, due to the length L of the minimum operating time slot, LmpSuch that the length of some low fleet size demand periods is less than LmpThe operation time period cannot be divided more optimally, resulting in a change of the time division point of the optimal solution when the division number is small, a suboptimal solution is generated, and finally the minimum fleet time cost is increased.
Fig. 12 shows an optimal time division scheme and a minimum fleet scale for each time period under different individual passenger capacities, wherein dotted lines indicate time period division time points, and numbers between adjacent dotted lines indicate the minimum fleet scale for the time periods; it can be seen that the influence of the passenger capacity of a single vehicle on the fleet scale at the peak time of passenger flow is large, and the influence on the fleet scale at the peak time of passenger flow is small, because according to the formulas (3) and (4), the influence of the section passenger flow on the minimum fleet scale is larger than that of the vehicle travel time at the peak time of passenger flow, and the vehicle one-way time is a main determining factor of the minimum fleet scale at the peak time of passenger flow, so that the influence of the section passenger flow is reduced; under the condition of different passenger capacities of the single vehicles, the division quantity and the division time point of the optimal time period division scheme have certain difference, for the reasons, the influence of the section passenger flow on the scale of the motorcade is large in the passenger flow peak period, the influence on the scale of the motorcade is small in the passenger flow peak period, the length of the peak periods can be increased or even combined with each other along with the increase of the passenger capacity of the single vehicles, the time period division scheme is changed along with the change of the time period, and the time cost of the motorcade is reduced along with the change of the.
To verify the advantages of the method of this embodiment over the conventional method, fig. 13 shows the optimal time division schemes and the minimum fleet scale of each time period (for comparison, the number of time period divisions is set to 5), where the dotted lines in each time period division method represent time period division time points, and the numbers between adjacent dotted lines represent the minimum fleet scale of time periods, where method 1 is a time period division method according to line passenger flow (vehicle-hour cost 458veh · h), method 2 is a time period division method according to travel time (vehicle-hour cost 434.33veh · h), and the vehicle-hour cost obtained by the time period division method according to capacity requirement of this embodiment is 412.67veh · h. As can be seen from fig. 12, the time interval fleet scales of the optimal time interval division schemes obtained by the method 1 and the method 2 are the same, but the time interval division schemes are different because the time interval division schemes are different due to the fact that the fluctuation rule of the passenger flow section and the fluctuation rule of the travel time are different. The method of the embodiment accurately identifies the peak evening time periods between the peak of the capacity demand, such as the peak evening time period (11:00-14:20) and the peak evening time period (20:45-23:00), thereby reducing the vehicle-hour cost as a whole. The minimum fleet size of the adjacent time intervals in the method 1 and the method 2 is the same because the section passenger flow or the travel time between the two corresponding time intervals has larger difference, but as described above, the two time intervals with larger difference in the section passenger flow or the travel time may have the same transportation capacity requirement, and the experiment proves that the method of the embodiment can accurately divide the adjacent time intervals with different transportation capacity requirements.
In conclusion, the operation time interval division method based on vehicle-time cost optimization firstly matches passenger flow requirements and travel time, calculates the transport capacity requirements at all times of the day by using a sliding time window model and a backstepping function model, establishes an optimization model taking a time interval division scheme as a decision variable and taking minimum accumulated fleet operation time cost as an optimization target on the basis, and optimizes the time interval division scheme. Compared with the traditional method for dividing the time intervals according to a single parameter (passenger flow demand or travel time data), the method can better reflect the transport capacity demands in different time intervals and enables the transport capacity and the transport volume to be more matched, so that the method has more scientific and practical significance. The maximum section passenger flow and the travel time utilized in the calculation process can be obtained by calculating the IC card swiping data and the vehicle GPS data, and the method has accuracy and timeliness.
The above embodiments are preferred embodiments of the present invention, but the present invention is not limited to the above embodiments, and any other changes, modifications, substitutions, combinations, and simplifications which do not depart from the spirit and principle of the present invention should be construed as equivalents thereof, and all such changes, modifications, substitutions, combinations, and simplifications are intended to be included in the scope of the present invention.

Claims (6)

1. An operation time interval dividing method based on vehicle-time cost optimization is characterized by comprising the following steps:
s1, performing distribution fitting on the historical travel time by using a log-logistic statistical model, and calculating the travel time with reliability in each departure direction at a given departure time on the basis of the distribution model obtained by fitting;
s2, calculating the number of operation vehicles needed in a time window which takes the departure time of the first bus as the starting time and the time when each terminal station reaches the vehicle transceiving balance as the ending time by using the historical passenger flow data and the legal lowest departure frequency, namely, finishing the minimum fleet scale needed by the transportation task in the time window;
s3, sliding along the direction of a time axis in a set step length from the starting time of a time window, wherein the width of the time window is constantly changed along with the change of the time for each terminal station to reach the vehicle transceiving balance; calculating the theoretical minimum fleet scale in each time window in sequence; the theoretical minimum fleet scale is a plurality of rolling applications of the calculated minimum fleet scale in step S2 according to a time window;
s4, calculating the total cost of the fleet operation time of the operation time interval division scheme, namely the accumulated sum of the products of the duration of each time interval and the corresponding theoretical minimum fleet scale;
and S5, optimizing the whole-day operation time period division scheme by taking the minimization of the total cost of the fleet operation time in the step S4 as a target.
2. The operation period division method based on vehicle-hour cost optimization according to claim 1, wherein the step S1 specifically comprises the following steps:
s11, collecting GPS data of the bus, wherein the GPS data records the all-day spatial position information of the bus, and the starting time and the arrival time of each bus task executed by the bus are extracted by utilizing a GIS system in combination with the spatial positions of the first station and the last station, and the difference between the arrival time and the starting time is the travel time of the bus task; the GPS data is converted into waybill data, and each waybill data comprises the following information: the train number task ID, the vehicle ID, departure time, arrival time and travel time;
s12, combining GPS data with a GIS system to perform sectional statistics of vehicle travel time, and performing log-logistic distribution fitting on historical travel time data of departure in each time period by an equidistant time period of 600S;
the probability distribution function of the log-logistic distribution is as follows:
wherein l is the vehicle travel time, α is the range parameter, β is the shape parameter, θ is the set reliability level;
s13, calculating the travel time value when the reliability is larger than theta: under the condition that the distribution probability is known, the travel time which arrives at the terminal station on time with the probability larger than theta is taken as the theta quantile of the travel time, and the following calculation formula is specifically adopted:
wherein,the vehicle travel time indicates the reliability of the vehicle from the station s at the departure time t.
3. The operation period division method based on vehicle-hour cost optimization according to claim 1, wherein the step S2 specifically comprises the following steps:
s21, calculating the cross-section passenger flow in one direction of a time window by using historical actual operation data, wherein the cross-section passenger flow refers to the number of passengers passing through one stop in one direction of the line in one time window of the line;
s211, all train number tasks in a time window are taken;
s212, adopting an OD reverse-pushing technology, extracting passenger OD information carried by each train number by utilizing the vehicle ID, departure time and arrival time information in the waybill data and combining the vehicle ID and card swiping time information in passenger IC card swiping data;
s213, calculating the cross section passenger flow of each station in the two directions of the line;
s214, determining the maximum section passenger flow, wherein the maximum section passenger flow is the maximum value of the station section passenger flow in one direction in one time window;
s215, calculating the average value of the maximum section passenger flow in the same time window on different dates;
s22, calculating the minimum departure frequency to ensure the bus service level; the ratio of the maximum section passenger flow to the single-vehicle passenger carrying capacity in a time window is the number of departure vehicles in the time window, the ratio of the number of departure vehicles in the time window to the width of the time window is the corresponding minimum departure frequency, and the calculated minimum departure frequency is not less than the statutory minimum departure frequency; the following calculation formula is provided:
wherein,represents the time window [ t, t + max (L)s t)]Minimum departure frequency, max (L), internally from the direction of origin of station ss t) Represents the maximum width of the time window;represents the time window [ t, t + max (L)s t)]The section passenger flow of the internal slave station s in the direction of the station i; fmRepresenting a statutory minimum departure frequency; c represents the maximum load capacity of the bicycle, namely the number of seats plus the number of standing passengers; lambda [ alpha ]tRepresents the legal passenger capacity coefficient at the time t, and is more than 0 and more than lambdat≤1；
S23, calculating the minimum fleet size: in a time window with the departure time of the first vehicle as the starting time and the maximum value of travel time in two directions as the width, subtracting the number of vehicles which arrive at the terminal station in the time window and can execute the task of the next vehicle number of the arriving station from the number of vehicles which arrive at the terminal station in the two directions; time windowThe calculation formula of the minimum required fleet size is as follows:
wherein, t0Indicating the start of a time windowAt the moment of time, the time of day,represents t0The maximum value of the travel time of the vehicles which start from the two stations a and b and arrive at the terminal station in the corresponding direction at the moment,represents t0The minimum value of the travel time of the vehicles which start from the two stations a and b and arrive at the terminal station in the corresponding direction at the moment,represents the maximum value of the two-way minimum departure frequency assuming the minimum departure frequencies in both directions to be the same, inAt the moment, the two terminals a and b reach the vehicle transceiving balance.
4. The operation period division method based on vehicle-hour cost optimization according to claim 3, wherein the step S3 specifically comprises the following steps:
s31, pair t0Sliding along the time axis direction, wherein the sliding step length is delta t; using a new t for each sliding0RecalculationAndsliding until the operation time is finished;
and S32, calculating the theoretical minimum fleet size in each time window by the method about the minimum fleet size in the step S2, and acquiring a theoretical minimum fleet size data set.
5. The vehicle-hour-cost-optimization-based operation of claim 1The time division method is characterized in that in step S4, the minimum fleet size N of the p-th operation time interval is given by the time division schemepThat is, the maximum value of the theoretical minimum fleet scale at each moment in the p-th operation period is specifically as follows:
wherein,indicates the start time of the p-th operation period,indicating the end time of the p-th operating period.
6. The operation period division method based on vehicle-hour cost optimization according to claim 1, wherein the step S5 specifically comprises the following steps:
s51, establishing a time interval division optimization model based on multi-source bus data and vehicle-hour cost optimization:
the constraints are as follows:
the formula (6) represents that the total cost of the operation time of the all-day bus fleet is minimized, namely the cumulative sum of the minimum fleet scale and the duty time is given as veh.h; equation (7) represents the shortest operation period length limit; the formula (8) ensures that the starting time of the first operation period is the starting time of the line operation time; the formula (9) ensures that the end time of the last operation period is the end time of the line operation time; the equation (10) ensures complete division of the line operation time period; the formula (11) represents a value range of the time division amount; wherein k represents the number of divisions in the operating period of the whole day; l ismpRepresents a minimum operation period length; t issRepresenting a line operation starting time; t iseIndicating a line operation end time;indicating the start time of the first operational period,represents the end time of the kth operating period;
s52, solving the model by adopting a genetic algorithm, wherein the algorithm comprises the following specific steps:
① departure time from the line running start time TsStarting time, taking delta T as time increment, and sequentially and circularly executing the following steps until departure time is equal to line operation ending time TeUntil the end;
② calculating the travel time of the vehicle from the station s at the departure time t
③ calculating time windowThe inner maximum cross-section passenger flow volume;
④ calculating time windowMinimum departure frequency within;
⑤ calculating time windowInner theoretical minimum fleet size;
⑥ ends the above cycle;
⑦ obtaining a theoretical minimum fleet size data set n (T | T ∈ (T ∈)s,Te))}；
⑧ given time division scheme [ (t)s 1,te 1),...,(ts p,te p),...,(ts k,te k)]And obtaining the theoretical minimum fleet size N of each time intervalp；te 1Indicating the end time, t, of the first operating periods kRepresents a start time of a k-th operation period;
⑨ a genetic algorithm is used to optimize the time division scheme with the goal of minimizing the total cost of fleet operating time.
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CN109377759A (en) * 2018-11-28 2019-02-22 南京莱斯信息技术股份有限公司 A kind of method of fleet's journey time in acquisition discrete traffic flow
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CN110738425A (en) * 2019-10-17 2020-01-31 华北水利水电大学 course resource scheduling method for English collaboration writing teaching
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CN112580866B (en) * 2020-12-15 2021-06-25 北京化工大学 Bus route bunching optimization method based on whole-course vehicle and inter-vehicle combined scheduling
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