阅读说明：本技术 考虑客流和节能的轨道交通快慢车时刻表优化方法 (Passenger flow and energy-saving rail transit fast and slow vehicle timetable optimization method ) 是由 叶茂 张人杰 殷世松 何赏璐 张子翰 程慧 赵一凡 芦永玖 于 2021-05-31 设计创作，主要内容包括：本发明涉及一种考虑客流和节能的轨道交通快慢车时刻表优化方法,属于轨道交通技术领域。包括S1对模型算法所需的快车、慢车的运营数据、线路数据、客流数据进行清洗、预处理；S2基于S1中的长短距离OD客流量计算快车、慢车开行比例,根据S1中的线路最大断面客流量P计算快慢车开行对数和开行周期时间H；S3、基于S1、S2的数据建立快车、慢车时刻表的数学模型；S4引入多种列车运行约束以及列车速度-距离关系,并将多目标模型化为单目标模型；S5算法参数初始化,将S3中的决策变量转化为染色体进行编码,利用遗传算法求取全局最优解,得到此种场景下的快车、慢车最优时刻表。本发明解决了动态客流与列车运力不匹配的问题。(The invention relates to a method for optimizing a schedule of a fast and slow rail transit vehicle in consideration of passenger flow and energy conservation, and belongs to the technical field of rail transit. S1, cleaning and preprocessing operation data, line data and passenger flow data of fast cars and slow cars required by a model algorithm; s2, calculating the driving proportion of fast and slow vehicles based on the long and short distance OD passenger flow in S1, and calculating the driving logarithm of the fast and slow vehicles and the driving cycle time H according to the maximum section passenger flow P of the line in S1; s3, establishing mathematical models of the fast and slow vehicle schedules based on the data of S1 and S2; s4, introducing various train operation constraints and train speed-distance relations, and modeling multiple targets into a single-target model; initializing parameters of an S5 algorithm, converting decision variables in S3 into chromosomes for encoding, and solving a global optimal solution by using a genetic algorithm to obtain an optimal schedule of fast and slow vehicles in the scene. The invention solves the problem that the dynamic passenger flow is not matched with the train capacity.)

1. A rail transit fast and slow train schedule optimization method considering passenger flow and energy conservation is characterized in that a train schedule is modeled, and the method comprises the following steps:

s1, cleaning and preprocessing operation data, line data and passenger flow data of fast cars and slow cars required by a model algorithm, dividing an operation day into a plurality of time periods comprising peaks and plateaus based on passenger flow change characteristics, counting OD passenger flow data according to the divided time periods respectively, and calculating the maximum section passenger traffic P of the line and the occupation ratio rho of a long-distance and short-distance travel passenger group;

s2, calculating the driving proportion of fast and slow vehicles based on the long and short distance OD passenger flow in S1, calculating the driving logarithm of fast and slow vehicles according to the maximum section passenger flow P of the line in S1, and calculating the driving cycle time H of fast and slow vehicles;

s3, establishing a mathematical model of the fast and slow vehicle schedules based on the data of S1 and S2: the method comprises the steps of taking the minimum waiting time of a passenger platform and the minimum energy consumption of train operation as targets, and taking departure intervals and stop time of different trains as decision variables to carry out modeling;

s4, introducing various train operation constraints and train speed-distance relations, and modeling multiple targets into a single-target model by using a linear weighting method;

and S5, initializing algorithm parameters, converting decision variables in the S3 into chromosomes for encoding, solving a global optimal solution by using a genetic algorithm, and finally obtaining an optimal schedule of fast and slow vehicles in the scene.

2. The method for optimizing the schedule of the rail transit fast and slow vehicles considering passenger flow and energy conservation as claimed in claim 1, wherein S1 specifically comprises the following steps:

s101, collecting and processing operation data, line data and passenger flow data of fast cars and slow cars required by a model algorithm, wherein the operation data of the fast cars and the slow cars comprises stop schemes, crossing schemes, train capacity, running time of two trains in each interval and original schedule data of the fast cars and the slow cars; the line data includes site information data; the passenger flow data is the OD passenger flow of the rail transit;

s102, dividing an operation day into a plurality of time intervals including peak and flat peaks based on passenger flow change characteristics, counting OD passenger flow data according to the divided time intervals respectively, and calculating the maximum section passenger flow P of a line and the proportion rho of a long-distance and short-distance travel passenger group, wherein the method specifically comprises the following steps:

wherein p is_ijThe OD passenger flow from the station i to the station j all day, i is the starting station, and j is the target station.

3. The method for optimizing the schedule of the rail transit fast and slow vehicles considering passenger flow and energy conservation as claimed in claim 1, wherein S2 specifically comprises the following steps: .

S201, calculating the driving pair number and the driving proportion of the fast vehicle and the slow vehicle under the scene based on the result in the S1, wherein the calculation formula is as follows:

m_s＝m_e*N；

in the formula: m is_eM is the minimum number of unit hour drops of express trains_sThe minimum throwing quantity in unit hour of the slow vehicle is obtained; c_eThe passenger capacity of a single fast vehicle, N is the ratio of slow vehicles to fast vehicles, and N is a positive integer;

s202, calculating the cycle time H for running a group of fast cars and slow cars under the scene according to the result of S201:

4. the method for optimizing the schedule of the rail transit fast and slow vehicles considering passenger flow and energy conservation as claimed in claim 1, wherein S3 specifically comprises the following steps:

s301, establishing time interval relation models of fast vehicles and slow vehicles in different proportions according to the result in the S1;

s302, dividing all trains into five types, namely, Case1, Case2, Case3, Case4 and Case 5;

and (3) Casel: the first type of train is a majority of slow trains, and is not adjacent to fast trains all the time during operation;

case 2: the second type of train is a slow train in the period, the slow train starts two shifts earlier than the fast train, and the fast train is adjacent to the second type of train after the fast train crosses the previous slow train;

case 3: the third type of train is a slow train which is arranged in front of the fast train and can be crossed by the fast train at the crossing station;

case 4: the fourth type of train is the only express train in the cycle;

case 5: the fifth type of train is a slow train which is arranged behind the fast train;

s303, calculating the interval time of the adjacent trains leaving different stations according to the types

The separation time between the first type of train and the second type of train is equal to the departure interval, and is represented as:

whereinThe time when the train k leaves the station i;

the third kind of train is over-ridden by express trains at the over-ride station, and the interval time needs to be discussed separately, wherein Z_-Representing a set of station numbers before an overrun station, Z₊Representing a station number set after the station is crossed; i is_eSet of numbers representing express trains, I_sThe number set representing the slow car, the interval time can be expressed as:

the fourth type of train stops only at the express station, and the interval time can be expressed as:

the interval time of the fifth type train is as follows:

s304: calculating the platform waiting time of passengers riding different types of trains;

s305: and according to the train division of S302, respectively calculating the total train energy consumption E of different types of trains during the operation.

5. The method for optimizing the schedule of the rail transit fast and slow vehicles considering passenger flow and energy conservation as claimed in claim 1, wherein S4 specifically comprises the following steps:

s401, converting the multi-target problem into a single-target problem by using a linear weighting method, firstly, normalizing T and E:

s402, introducing coefficient sigma₁Representing the degree of importance of passenger waiting time, introducing a coefficient sigma₂Representing the important degree of train operation energy consumption, introducing driving constraints for ensuring the safe operation of the train, and constructing a schedule optimization model for reducing the waiting time of passenger platforms:

Min F＝σ₁*η_T+σ₂*η_E

wherein h is_minTo a minimum departure interval, h_maxAt a maximum departure interval, d_minTo minimum station-stopping interval, d_maxAt a maximum station-stopping interval, θ_safeFor a safe interval of time, theta_aIn order to cross the minimum interval time, H is train departure cycle time, S is train running distance, t is train running time, V is train running speed, and a is train running acceleration.

6. The method for optimizing the schedule of the rail transit fast and slow vehicles considering passenger flow and energy conservation as claimed in claim 1, wherein S5 specifically comprises the following steps:

s501, initializing parameters: setting the maximum number pop _ size of the population scale, randomly generating individuals of departure intervals and station stop time, then setting the maximum evolution algebra max _ generation, and setting an evolution algebra counter to be 1;

s502, encoding and initial solution: coding variable departure intervals and stop times, and forming genes of chromosomes by using random initial values; judging whether the variable departure interval meets the constraint condition, and if so, entering S503; if not, regenerating the initial solution;

s503, calculating and selecting: calculating fitness values of all chromosomes; selecting chromosomes by roulette; if the fitness of the chromosome of the generation is higher than that of the previous generation, the chromosome of the generation is kept; if lower than the previous generation, retaining the previous generation chromosome;

s504, reproduction: the current chromosome generates next generation individuals through crossing and mutation behaviors; if each individual meets the constraint condition, turning to S505, and if not, reproducing the individual again;

s505, if the current evolution algebra is equal to max _ generation, stopping circulation to obtain an optimal solution; if not, return to S503.

7. The method for optimizing a schedule of fast and slow rail transit vehicles considering passenger flow and energy saving according to claim 4, wherein the platform waiting time for passengers riding different types of trains in S304 is calculated as follows:

firstly based on OD passenger flow lambda_ijAnd OD statistical time interval t_hComputingThe amount of passengers arriving at the station within the time is calculated, and the amount Q of the passengers staying caused by the k-crossing of the express train is calculated_ij，q_jIs a 0, 1 variable for indicating whether the target station is a express stop or not, and the calculation formula is as follows:

the passenger platform waiting time calculation formulas of the first type train and the second type train are as follows:

in the formula (I), the compound is shown in the specification,representing the platform waiting time of passengers from station i to station j taking a k vehicle;

the waiting time of the passenger platform of the third type of train is calculated in the following mode:

the passenger platform waiting time of the fourth type of train is:

the passenger platform waiting time of the fifth type of train is as follows:

the total passenger platform wait time T is calculated as:

in the formula, i and j respectively represent the numbers of a starting station and a target station of the travel of the passenger, k is the number of a train on which the passenger takes,representing the platform waiting time for a passenger from station i to station j and riding in car k.

8. The method for optimizing the schedules of fast and slow trains of rail transit in consideration of passenger flow and energy saving according to claim 4, wherein the step of calculating the total energy consumption E of trains of different types during operation in S305 is as follows:

(1): calculating the total number of people taking the K car at the station i

In the formula (I), the compound is shown in the specification,by different stations on arrival of different trainsThe number of people getting on the bus is counted;

number of passengers getting off at station iThat is, the number of passengers who want to go to station i among the passengers who take train k is expressed as:

(2): and (3) calculating and updating the passenger capacity of the train on different sections through the number of passengers getting on and off the train at different stations and the passenger capacity on the previous section:

(3): calculating to obtain the total mass of the trains running in different sections

Wherein m is_pAverage mass per passenger, m^kIs the no-load mass of train k; the operation energy consumption of each train in the interval i to i +1 is as follows:

the total energy consumption for train operation in one period is as follows:

in the formula (I), the compound is shown in the specification,the energy consumption generated when k vehicles run between the stations i and i +1 is calculated.

9. The method for optimizing the schedules of fast and slow trains in rail transit considering passenger flow and energy conservation as claimed in claim 4, wherein the time when the train k leaves the station i in S301Departure interval h with pre-sequence workshop_kAnd calculating the running time and the stop time of the train k in different intervals to obtain:

wherein, the time point of the departure of the last vehicle in the previous period is takenAt the time point of the start of the cycle

10. The method for optimizing the schedules of fast and slow vehicles in rail transit with consideration of passenger flow and energy conservation as claimed in claim 6, wherein the constraint condition in S502 is a minimum departure interval h_minMaximum departure interval h_maxMinimum stop interval d_minMaximum stop interval d_maxA safety interval time theta_safeMinimum overrun interval time theta_aAnd a train departure cycle time H.

Technical Field

The invention relates to a method for optimizing a schedule of a fast and slow rail transit vehicle in consideration of passenger flow and energy conservation, and belongs to the technical field of rail transit.

Background

Urban rail transit has become the main public transport mode in big cities, and with the development of urban scale, central cities tend to saturate, resulting in increasing long-distance travel passenger flow between urban centers and suburbs. Therefore, a novel train operation mode, namely a fast train and slow train combined operation mode, is developed. The mode is the combination of traditional slow cars and fast cars, wherein slow cars refer to trains stopping at stations, and fast cars refer to trains crossing stations. At the station where the express train is going over, the stop waiting time is 0, so that the time required for the express train to complete one trip is smaller compared with the traditional slow train.

With the expansion of the scale of the network, the passenger flow characteristics become more and more complex, similar to the conventional stop mode, the fast and slow modes also face the problem that the train capacity is put in and the line passenger flow characteristics are not matched, especially in the peak period, the schedule of the balanced departure interval cannot meet the change requirements of irregular passenger flow, the waste of energy consumption is easily caused, and meanwhile, the travel waiting time of passengers is increased. In addition, at present, the driving proportion of fast driving and slow driving is too single, the driving proportion of the same line under different scenes and dates is basically consistent, the formulation of the scheme lacks specificity, and the multi-dimensional passenger flow requirements under different scenes cannot be met. Therefore, for the combined operation mode of the express train and the slow train, the schedule optimization problem based on the passenger flow change characteristics is very important. At present, the combined operation mode of the express trains and the slow trains is researched more, but most of the combined operation mode is limited to the research on the stop scheme and the start scheme of the trains, and the research on the schedule optimization of the express trains and the slow trains is very rare.

Disclosure of Invention

The invention aims to overcome the problems in the prior art, provide a method for optimizing a schedule of a rail transit fast and slow vehicle in consideration of passenger flow and energy conservation, solve the problem that dynamic passenger flow is not matched with train capacity, quickly provide a schedule optimization scheme of a fast and slow vehicle combined operation mode on the premise of simultaneously considering passenger travel satisfaction and enterprise operation cost, and provide a basis for making an operation organization scheme.

In order to solve the technical problems, the invention provides a rail transit fast and slow train schedule optimization method considering passenger flow and energy conservation, which models a train schedule and comprises the following steps:

s1, cleaning and preprocessing operation data, line data and passenger flow data of fast cars and slow cars required by a model algorithm, dividing an operation day into a plurality of time periods comprising peaks and plateaus based on passenger flow change characteristics, counting OD passenger flow data according to the divided time periods respectively, and calculating the maximum section passenger traffic P of the line and the occupation ratio rho of a long-distance and short-distance travel passenger group;

s2, calculating the driving proportion of fast and slow vehicles based on the long and short distance OD passenger flow in S1, calculating the driving logarithm of fast and slow vehicles according to the maximum section passenger flow P of the line in S1, and calculating the driving cycle time H of fast and slow vehicles;

s3, establishing a mathematical model of the fast and slow vehicle schedules based on the data of S1 and S2: the method comprises the steps of taking the minimum waiting time of a passenger platform and the minimum energy consumption of train operation as targets, and taking departure intervals and stop time of different trains as decision variables to carry out modeling;

s4, introducing various train operation constraints and train speed-distance relations, and modeling multiple targets into a single-target model by using a linear weighting method;

and S5, initializing algorithm parameters, converting decision variables in the S3 into chromosomes for encoding, solving a global optimal solution by using a genetic algorithm, and finally obtaining an optimal schedule of fast and slow vehicles in the scene.

Further, S1 specifically includes the following steps:

s101, collecting and processing operation data, line data and passenger flow data of fast cars and slow cars required by a model algorithm, wherein the operation data of the fast cars and the slow cars comprises stop schemes, crossing schemes, train capacity, running time of two trains in each interval and original schedule data of the fast cars and the slow cars; the line data includes site information data; the passenger flow data is the OD passenger flow of the rail transit;

s102, dividing an operation day into a plurality of time intervals including peak and flat peaks based on passenger flow change characteristics, counting OD passenger flow data according to the divided time intervals respectively, and calculating the maximum section passenger flow P of a line and the proportion rho of a long-distance and short-distance travel passenger group, wherein the method specifically comprises the following steps:

wherein p is_ijThe OD passenger flow from the station i to the station j all day, i is the starting station, and j is the target station.

Further, S2 specifically includes the following steps: .

S201, calculating the driving pair number and the driving proportion of the fast vehicle and the slow vehicle under the scene based on the result in the S1, wherein the calculation formula is as follows:

in the formula: m is_eM is the minimum number of unit hour drops of express trains_sThe minimum throwing quantity in unit hour of the slow vehicle is obtained;

C_ethe passenger capacity of a single fast vehicle, N is the ratio of slow vehicle to fast vehicle, and N is positiveAn integer number;

s202, calculating the cycle time H for running a group of fast cars and slow cars under the scene according to the result of S201:

further, S3 specifically includes the following steps:

s301, establishing time interval relation models of fast vehicles and slow vehicles in different proportions according to the result in the S1;

s302, dividing all trains into five types, namely, Case1, Case2, Case3, Case4 and Case 5;

case 1: the first type of train is a majority of slow trains, and is not adjacent to fast trains all the time during operation;

case 2: the second type of train is a slow train in the period, the slow train starts two shifts earlier than the fast train, and the fast train is adjacent to the second type of train after the fast train crosses the previous slow train;

case 3: the third type of train is a slow train which is arranged in front of the fast train and can be crossed by the fast train at the crossing station;

case 4: the fourth type of train is the only express train in the cycle;

case 5: the fifth type of train is a slow train which is arranged behind the fast train;

s303, calculating the interval time of the adjacent trains leaving different stations according to the types

The separation time between the first type of train and the second type of train is equal to the departure interval, and is represented as:

whereinK is for trainThe time of starting the station i;

the third kind of train is over-ridden by express trains at the over-ride station, and the interval time needs to be discussed separately, wherein Z_-Representing a set of station numbers before an overrun station, Z₊Representing a station number set after the station is crossed; i is_eSet of numbers representing express trains, I_sThe number set representing the slow car, the interval time can be expressed as:

the fourth type of train stops only at the express station, and the interval time can be expressed as:

the interval time of the fifth type train is as follows:

s304: calculating the platform waiting time of passengers riding different types of trains;

s305: and according to the train division of S302, respectively calculating the total train energy consumption E of different types of trains during the operation.

Further, S4 specifically includes the following steps:

s401, converting the multi-target problem into a single-target problem by using a linear weighting method, firstly, normalizing T and E:

s402, introducing coefficient sigma₁Characterizing passengersImportance of latency, introducing a factor σ₂Representing the important degree of train operation energy consumption, introducing driving constraints for ensuring the safe operation of the train, and constructing a schedule optimization model for reducing the waiting time of passenger platforms:

Min F＝σ₁*η_T+σ₂*η_E

wherein h is_minTo a minimum departure interval, h_maxAt a maximum departure interval, d_minTo minimum station-stopping interval, d_maxAt a maximum station-stopping interval, θ_safeFor a safe interval of time, theta_aIn order to cross the minimum interval time, H is train departure cycle time, S is train running distance, t is train running time, V is train running speed, and a is train running acceleration.

Further, S5 specifically includes the following steps:

s501, initializing parameters: setting the maximum number pop _ size of the population scale, randomly generating individuals of departure intervals and station stop time, then setting the maximum evolution algebra max _ generation, and setting an evolution algebra counter to be 1;

s502, encoding and initial solution: coding variable departure intervals and stop times, and forming genes of chromosomes by using random initial values; judging whether the variable departure interval meets the constraint condition, and if so, entering S503; if not, regenerating the initial solution;

s503, calculating and selecting: calculating fitness values of all chromosomes; selecting chromosomes by roulette; if the fitness of the chromosome of the generation is higher than that of the previous generation, the chromosome of the generation is kept; if lower than the previous generation, retaining the previous generation chromosome;

s504, reproduction: the current chromosome generates next generation individuals through crossing and mutation behaviors; if each individual meets the constraint condition, turning to S505, and if not, reproducing the individual again;

s505, if the current evolution algebra is equal to max _ generation, stopping circulation to obtain an optimal solution; if not, return to S503.

Further, the platform waiting time for passengers riding different types of trains in S304 is calculated as follows:

firstly based on OD passenger flow lambda_ijAnd OD statistical time interval t_hComputingThe amount of passengers arriving at the station within the time is calculated, and the amount Q of the passengers staying caused by the k-crossing of the express train is calculated_ij，q_jIs a 0, 1 variable for indicating whether the target station is a express stop or not, and the calculation formula is as follows:

the passenger platform waiting time calculation formulas of the first type train and the second type train are as follows:

in the formula (I), the compound is shown in the specification,representing the platform waiting time of passengers from station i to station j taking a k vehicle;

the waiting time of the passenger platform of the third type of train is calculated in the following mode:

the passenger platform waiting time of the fourth type of train is:

the passenger platform waiting time of the fifth type of train is as follows:

the total passenger platform wait time T is calculated as:

in the formula, i and i respectively represent the numbers of the starting station and the target station of the passenger trip, k is the number of the train on which the passenger takes,representing the platform waiting time for a passenger from station i to station j and riding in car k.

Further, the step of calculating the total train energy consumption E of the trains of different types during operation in S305 is as follows:

(1): calculating the total number of people taking the K car at the station i

In the formula (I), the compound is shown in the specification,by different stations on arrival of different trainsThe number of people getting on the bus is counted;

number of passengers getting off at station iThat is, the number of passengers who want to go to station i among the passengers who take train k is expressed as:

(2): and (3) calculating and updating the passenger capacity of the train on different sections through the number of passengers getting on and off the train at different stations and the passenger capacity on the previous section:

(3): calculating to obtain the total mass of the trains running in different sections

Wherein m is_pAverage mass per passenger, m^kIs the no-load mass of train k; the operation energy consumption of each train in the interval i to i +1 is as follows:

the total energy consumption for train operation in one period is as follows:

in the formula (I), the compound is shown in the specification,the energy consumption generated when k vehicles run between the stations i and i +1 is calculated.

Further, in S301Time of departure of train k from station iDeparture interval h with pre-sequence workshop_kAnd calculating the running time and the stop time of the train k in different intervals to obtain:

wherein, the time point of the departure of the last vehicle in the previous period is takenAt the time point of the start of the cycle

Further, the constraint condition in S502 is a minimum departure interval h_minMaximum departure interval h_maxMinimum stop interval d_minMaximum stop interval d_maxA safety interval time theta_safeMinimum overrun interval time theta_aAnd a train departure cycle time H.

Compared with the prior art, the invention has the following beneficial effects: 1. according to passenger flow characteristic changes in different scenes, a passenger flow arrival rate is drawn up, a train schedule optimization model in an express train mode and a slow train mode is established by taking the passenger flow arrival rate as a data base and considering passenger flow requirements and train energy consumption, a genetic algorithm is adopted for solving, and finally schedules in different time periods of one day are linked to obtain an optimized full-day fast and slow train running schedule.

2. The travel time of passengers can be shortened, the energy consumption of train operation is reduced, the train transportation benefit is improved, and reference and basis are provided for the application of the fast and slow train operation modes.

3. By utilizing the fast and slow vehicle timetable optimization technology suitable for multiple scenes, scientific and reasonable driving schemes can be respectively formulated according to scenes with different passenger flow characteristics, such as peak/average peak, working day/weekend/holiday and the like, so that the traveling comfort of passengers under different passenger flow demand conditions is improved.

4. The fast and slow vehicle schedule optimization technology can reasonably configure the line transportation capacity resources, improve the matching degree between the transportation capacity and the passenger flow demand, and further reduce the waste of the transportation capacity resources; meanwhile, the invention can reduce the energy consumption of the train in the interval operation and reduce the operation cost of enterprises.

5. The schedule optimization problem in the combined operation mode of the fast and slow vehicles is considered, and compared with the traditional fast and slow vehicle schedules with balanced departure intervals, the schedule optimization method has better matching property and adaptability to irregular passenger flows, enables the transport capacity to be accurately released, and reduces the waste of resources.

6. Based on the passenger flow multidimensional characteristics under multiple scenes, the fast and slow train timetable can make corresponding timetables for different scenes, and compared with a fast and slow train mode with a fixed proportion in the traditional scheme, the fast and slow train timetable has higher adaptability to the passenger flow requirements of different scenes and has important guiding significance for scientific and reasonable making of a train operation scheme.

7. The traditional fast and slow train optimization scheme focuses on considering the total trip time of passengers, the description of the total waiting time of the passengers at the platform is fuzzy, the waiting time of the passenger platform and the energy consumption of train operation are minimized, the satisfaction degree of detained passengers and the operation cost of enterprises are deeply considered, the trip satisfaction degree of the passengers is improved, the operation cost of the enterprises is reduced, and great economic benefits are brought.

Drawings

The invention will be described in further detail with reference to the following drawings and detailed description, which are provided for reference and illustration purposes only and are not intended to limit the invention.

FIG. 1 is a schematic diagram of the steps of the method for optimizing the schedule of the rail transit fast and slow vehicles considering passenger flow and energy conservation;

FIG. 2 is a schematic diagram of one driving cycle of the fast and slow vehicles according to the present invention;

FIG. 3 is a schematic diagram showing statistics of all possible ratios of fast cars and slow cars in the present invention;

wherein, fig. 3(a) is a schematic diagram of the ratio statistics of fast cars and slow cars when N is 1,

fig. 3(b) is a diagram showing the statistics of the ratio of fast cars to slow cars when N is 2,

fig. 3(c) is a diagram illustrating the statistics of the ratio of fast cars to slow cars when N is 3,

FIG. 3(d) is a diagram showing the statistics of the ratio of fast cars to slow cars when N > 3;

FIG. 4 is a schematic diagram of the calculation of time intervals between different trains in the present invention;

FIG. 5 is a schematic diagram of the division of the train interval operation time period in the invention;

FIG. 6 is a schematic flow chart of a genetic optimization algorithm used in the present invention;

fig. 7 is a diagram of the optimized train operation in the embodiment of the present invention.

Detailed Description

In order to make the technical means, the creation characteristics, the achievement purposes and the effects of the invention easy to understand, the invention is further explained below by combining the specific drawings.

The invention relates to a passenger flow and energy-saving rail transit fast and slow train timetable optimization method, which models a train timetable, and comprises the following steps as shown in figure 1:

s1, cleaning and preprocessing operation data, line data and passenger flow data of fast cars and slow cars required by a model algorithm, dividing an operation day into a plurality of time periods comprising peaks and plateaus based on passenger flow change characteristics, counting OD passenger flow data according to the divided time periods respectively, and calculating the maximum section passenger traffic P of the line and the occupation ratio rho of a long-distance and short-distance travel passenger group;

s2, calculating the driving proportion of fast and slow vehicles based on the long and short distance OD passenger flow in S1, calculating the driving logarithm of fast and slow vehicles according to the maximum section passenger flow P of the line in S1, and calculating the driving cycle time H of fast and slow vehicles;

s3, establishing a mathematical model of the fast and slow vehicle schedules based on the data of S1 and S2: the method comprises the steps of taking the minimum waiting time of a passenger platform and the minimum energy consumption of train operation as targets, and taking departure intervals and stop time of different trains as decision variables to carry out modeling;

s4, introducing various train operation constraints and train speed-distance relations, and modeling multiple targets into a single-target model by using a linear weighting method;

and S5, initializing algorithm parameters, converting decision variables in the S3 into chromosomes for encoding, solving a global optimal solution by using a genetic algorithm, and finally obtaining an optimal schedule of fast and slow vehicles in the scene.

S1 specifically includes the following steps:

s101, collecting and processing operation data, line data and passenger flow data of fast cars and slow cars required by a model algorithm, wherein the operation data of the fast cars and the slow cars comprises stop schemes, crossing schemes, train capacity, running time of two trains in each interval and original schedule data of the fast cars and the slow cars; the line data includes site information data; the passenger flow data is the OD passenger flow of the rail transit;

s102, dividing an operation day into a plurality of time intervals including peak and flat peaks based on passenger flow change characteristics, counting OD passenger flow data according to the divided time intervals respectively, and calculating the maximum section passenger flow P of a line and the proportion rho of a long-distance and short-distance travel passenger group, wherein the method specifically comprises the following steps:

wherein rho is the proportion of the passenger group for long-distance and short-distance travel, and p is_ijThe OD passenger flow from the station i to the station j all day, i is the starting station, and j is the target station.

As shown in figures 2-4 of the drawings,

s2 specifically includes the following steps:

as shown in fig. 3, in S201, the driving pair and the driving ratio of the fast vehicle and the slow vehicle in this scenario are calculated based on the result in S1, and the calculation formula is as follows:

m_s＝m_e*N；

in the formula:m_em is the minimum number of unit hour drops of express trains_sThe minimum throwing quantity in unit hour of the slow vehicle is obtained;

C_ethe passenger capacity of a single fast vehicle, N is the ratio of slow vehicles to fast vehicles, and N is a positive integer.

S202, calculating the cycle time H for running a group of fast cars and slow cars under the scene according to the result of S201:

s3 specifically includes the following steps:

s301, according to the result in the S1, establishing time interval relation models of fast trains and slow trains with different proportions, and the time of the train k leaving the station iDeparture interval h with pre-sequence workshop_kAnd calculating the running time and the stop time of the train k in different intervals to obtain:

wherein, the time point of the departure of the last vehicle in the previous period is takenAt the time point of the start of the cycleArrival time of i station k trainCalculations can also be made in a similar way.

S302, dividing all trains into five types, namely, Case1, Case2, Case3, Case4 and Case 5;

case 1: the first type of train is a majority of slow trains, and is not adjacent to fast trains all the time during operation; train 5, train 6 …, train N +1 in fig. 2;

case 2: the second type of train is a slow train in the period, the slow train starts two shifts earlier than the fast train, and the fast train is adjacent to the second type of train after the fast train crosses the previous slow train; i.e. train 1 in fig. 2;

case 3: the third type of train is a slow train which is arranged in front of the fast train and can be crossed by the fast train at the crossing station; i.e. train 2 in fig. 2;

case 4: the fourth type of train is the only express train in the cycle; i.e. train 3 in fig. 2;

case 5: the fifth type of train is a slow train which is arranged behind the fast train; i.e. train 4 in fig. 2.

As shown in fig. 4, S303, calculating the time intervals between adjacent trains leaving different stations according to the categories

The separation time between the first type of train and the second type of train is equal to the departure interval, and is represented as:

whereinThe time when the train k leaves the station i;

the third kind of train is over-ridden by express trains at the over-ride station, and the interval time needs to be discussed separately, wherein Z_-Representing a set of station numbers before an overrun station, Z₊Representing a station number set after the station is crossed; i is_eSet of numbers representing express trains, I_sThe number set representing the slow car, the interval time can be expressed as:

the fourth type of train stops only at the express station, and the interval time can be expressed as:

the interval time of the fifth type train is as follows:

s304: calculating the platform waiting time of passengers riding different types of trains in the following specific calculation mode:

firstly based on OD passenger flow lambda_ijAnd OD statistical time interval t_hComputingThe amount of passengers arriving at the station within the time is calculated, and the amount Q of the passengers staying caused by the k-crossing of the express train is calculated_ij，q_jIs a 0, 1 variable for indicating whether the target station is a express stop or not, and the calculation formula is as follows:

the passenger platform waiting time calculation formulas of the first type train and the second type train are as follows:

in the formula (I), the compound is shown in the specification,representing the platform waiting time of passengers from station i to station j taking a k vehicle;

the waiting time of the passenger platform of the third type of train is calculated in the following mode:

when a third type of train passes through the cross station and the express train runs in front of the cross station, passengers taking the third type of train need to additionally consider passengers detained by the express train;

the passenger platform waiting time of the fourth type of train is:

the passenger platform waiting time of the fifth type of train is as follows:

the total passenger platform wait time T may be calculated as:

in the formula, i and j respectively represent the numbers of a starting station and a target station of the travel of the passenger, k is the number of a train on which the passenger takes,representing the platform waiting time for a passenger from station i to station j and riding in car k.

As shown in fig. 5, S305: according to the train division of S302, the total train energy consumption E of different types of trains in the running period is respectively calculated, and the calculation steps are as follows:

(1): calculating the total number of people taking the K car at the station i

In the formula (I), the compound is shown in the specification,by different stations on arrival of different trainsThe number of people getting on the bus is counted;

number of passengers getting off at station iThat is, the number of passengers who want to go to station i among the passengers who take train k is expressed as:

(2): the passenger capacity of the train on different sections can be calculated and updated through the number of passengers getting on and off the train at different stations and the passenger capacity on the previous section:

(3): calculating to obtain the total mass of the trains running in different sections

Wherein m is_pAverage mass per passenger, m^kIs the no-load mass of train k; the operation energy consumption of each train in the interval i to i +1 is as follows:

the total energy consumption for train operation in one period is as follows:

in the formula (I), the compound is shown in the specification,the energy consumption generated when k vehicles run between the stations i and i +1 is calculated.

S4 specifically includes the following steps:

s401, converting the multi-target problem into a single-target problem by using a linear weighting method, firstly, normalizing T and E:

s402, introducing coefficient sigma₁Representing the degree of importance of passenger waiting time, introducing a coefficient sigma₂Representing the important degree of train operation energy consumption, introducing driving constraints for ensuring the safe operation of the train, and constructing a schedule optimization model for reducing the waiting time of passenger platforms:

Min F＝σ₁*η_T+σ₂*η_E

wherein h is_minTo a minimum departure interval, h_maxAt a maximum departure interval, d_minTo minimum station-stopping interval, d_maxAt a maximum station-stopping interval, θ_safeFor a safe interval of time, theta_aFor exceeding the minimum time interval, the 5 th constraint indicates that the sum of all departure intervals equals to the departure of one trainA cycle time H; s is train running distance, t is train running time, V is train running speed, a is train running acceleration, and the last six equations are the relationship between train running speed and distance calculated based on Newton' S theorem.

As shown in fig. 6, S5 specifically includes the following steps:

s501, initializing parameters: setting the maximum number pop _ size of the population scale, randomly generating individuals of departure intervals and station stop time, then setting the maximum evolution algebra max _ generation, and setting an evolution algebra counter to be 1;

s502, encoding and initial solution: coding variable departure intervals and stop times, and forming genes of chromosomes by using random initial values; judging whether the variable departure interval meets the constraint condition, and if so, entering S503; if not, regenerating the initial solution; the constraint condition is the minimum departure interval h_minMaximum departure interval h_maxMinimum stop interval d_minMaximum stop interval d_maxA safety interval time theta_safeMinimum overrun interval time theta_aAnd a train departure cycle time H.

S503, calculating and selecting: calculating fitness values of all chromosomes; selecting chromosomes by roulette; if the fitness of the chromosome of the generation is higher than that of the previous generation, the chromosome of the generation is kept; if lower than the previous generation, retaining the previous generation chromosome;

s504, reproduction: the current chromosome generates next generation individuals through crossing and mutation behaviors; if each individual meets the constraint condition, turning to S505, and if not, reproducing the individual again;

s505, if the current evolution algebra is equal to max _ generation, stopping circulation to obtain an optimal solution; if not, return to S503.

Taking the ascending direction of Guangzhou subway number 14 line as an example for model verification:

the line adopts a fast/local mode to meet the requirements of long-distance travelers, and is provided with 13 stations. Wherein, the express stations are stations No. 1, 8, 12 and 13, and the rest are slow stations, wherein, the station No. 6A station is an waypoint. The full-day passenger flow was divided into peak and flat, the study was conducted with a peak period of 1 hour as the target, and the OD passenger flow was counted as shown in table 3. In the original driving plan, the ratio of fast cars to slow cars is fixed at 1: 4, one cycle of fast cars and slow cars is selected for case analysis, the running time and the retention time of a train interval are respectively shown in tables 1 and 2, and the rest parameters are H1380 s and H_min＝100s，h_max＝600s，θ_a＝65s，a₁＝lm/s²，a₃＝-0.8m/s²，m^k＝280000kg，m_p＝60kg，σ₁＝σ₂＝0.5。

TABLE 1

TABLE 2

λij	1	2	3	4	5	6	7	8	9	10	11	12	13
														1	0	1404	1104	1024	1092	552	252	1228	608	268	192	3032	432
2	0	0	120	288	192	136	4	72	28	32	8	44	0
														3	0	0	0	308	144	116	20	92	32	20	12	68	8
4	0	0	0	0	152	196	16	132	32	24	16	124	12
														5	0	0	0	0	0	100	32	124	36	28	8	100	32
6	0	0	0	0	0	0	20	228	32	16	8	56	0
														7	0	0	0	0	0	0	0	52	12	0	4	36	4
8	0	0	0	0	0	0	0	0	124	52	56	624	96
														9	0	0	0	0	0	0	0	0	0	20	20	328	32
10	0	0	0	0	0	0	0	0	0	0	16	92	16
														11	0	0	0	0	0	0	0	0	0	0	0	88	16
12	0	0	0	0	0	0	0	0	0	0	0	0	40
														13	0	0	0	0	0	0	0	0	0	0	0	0	0

TABLE 3

First, the schedule optimization method of the present invention is examined. For the schedule optimization scheme, in order to compare with the actual case, the logarithm of the open rows, the proportion of the open rows, and the open period need to be controlled to be fixed variables, that is, the variables are set to be the same as the case. The resulting original departure intervals in the cycle are shown in table 4, and the stop times and the optimized schedule are shown in table 5. The optimized fast and slow vehicle running chart is shown in fig. 7.

TABLE 4

TABLE 5

Compared with the waiting time before optimization, the total waiting time of the optimized passengers at the platform is reduced by 464716s (about 20.3%), the total energy consumption of the optimized train operation is reduced by 831010284J (about 1.4%), in addition, the waiting time of the platform of the passengers is reduced by about 23% because the destinations of some passengers are at slow stations and cannot take fast cars. The result shows that the invention can effectively reduce the waiting time of the passenger platform, especially the waiting time of the passengers detained by the express train, and can improve the travel satisfaction of the passengers.

In addition, through the calculation of the OD passenger flow, the ratio of long-distance traveling passengers to short-distance traveling passengers in the OD passenger flow in the time interval is about 1: 1, so that the driving ratio of fast and slow vehicles of 1: 4 cannot well match the passenger flow in the time interval. By the model method, the driving proportion of the fast and slow trains in different time periods can be adjusted, schedule optimization is further carried out, and train capacity delivery benefits are improved.