CN108515988B - Train operation diagram optimization method for improving passenger timeliness - Google Patents

Train operation diagram optimization method for improving passenger timeliness Download PDF

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CN108515988B
CN108515988B CN201810005843.9A CN201810005843A CN108515988B CN 108515988 B CN108515988 B CN 108515988B CN 201810005843 A CN201810005843 A CN 201810005843A CN 108515988 B CN108515988 B CN 108515988B
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孙帮成
杨欣
王洪伟
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CRRC Industry Institute Co Ltd
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    • B61RAILWAYS
    • B61LGUIDING RAILWAY TRAFFIC; ENSURING THE SAFETY OF RAILWAY TRAFFIC
    • B61L27/00Central railway traffic control systems; Trackside control; Communication systems specially adapted therefor
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Abstract

The invention discloses a train operation diagram optimization method for improving passenger timeliness, and belongs to the technical field of urban rail transit operation diagram optimization. The method comprises the following steps: step 1, calculating the number of people waiting for a train i at a station n
Figure DDA0001538577760000011
Step 2, determining the number of people on the train when the train i arrives at the station n
Figure DDA0001538577760000012
Step 3, calculating the number of passengers getting off when the train i arrives at the station n
Figure DDA0001538577760000013
Step 4, determining the number of passengers getting on the train when the train i arrives at the station n
Figure DDA0001538577760000014
And 5, calculating the waiting time W of passengers at the station to obtain a model of the waiting time of all passengers on the whole line with constraints. The method can be used for optimizing the train operation diagram, reducing the waiting time of passengers and improving the satisfaction degree of the passengers.

Description

Train operation diagram optimization method for improving passenger timeliness
Technical Field
The invention relates to a train running chart optimization method for improving passenger timeliness, in particular to an urban rail transit train running chart optimization method for reducing passenger average waiting time, and belongs to the technical field of urban rail transit running chart optimization.
Background
In recent years, along with the rapid development of urban rail transit, the passenger satisfaction problem of a rail transit system is emphasized. The urban rail transit system has the characteristics of large passenger flow and small departure interval, and passengers are sensitive to waiting time, so that an important index for measuring the satisfaction degree of the passengers is the waiting time of the passengers. The primary method of reducing passenger waiting time is to optimize the train operating map.
At present, research on optimization of train operation diagrams has been accumulated to a certain extent theoretically, more researches on reduction of passenger waiting time and conversion of the passenger waiting time are needed, and less researches on reduction of station passenger waiting time are needed. In the peak period, passengers often wait for at least two trains at a station to get on the train, and the waiting time is prolonged to cause inconvenience to the passengers, so that the satisfaction degree of the passengers in the rail transit system is reduced.
Disclosure of Invention
The invention aims to provide a train running chart optimization method for improving passenger timeliness, and particularly relates to an urban rail train running chart optimization method for reducing passenger average waiting time. The method is used for optimizing the train operation diagram, reducing the waiting time of passengers and improving the satisfaction degree of the passengers.
The purpose of the invention is realized by the following technical scheme:
a train diagram optimization method for improving passenger aging comprises the following steps:
step 1, calculating the number of people waiting for a train i at a station n
Figure GDA0002901836990000021
Wherein I represents a train index, I is 1,2, …, I; i is the number of trains; n represents a station index, i.e., N is 1,2, …, N; n is the number of stations;
when i is 1, namely the first train arrives at the station, the initial waiting number of each station is the number of the station-entering persons in the time h, namely the number of the station-entering persons
Figure GDA0002901836990000022
h is taken as a departure time interval, taunThe passenger arrival rate for station n;
when i is more than or equal to 2, the number of waiting persons at the station is the sum of the number of entering persons from the departure of the train i-1 from the station n to the arrival of the train i at the station n and the number of remaining persons at the platform when the train i-1 departs from the station n;
Figure GDA0002901836990000023
wherein h is the departure time interval of the station n; x is the number ofnStation stop time for n stations;
Figure GDA0002901836990000024
the number of passengers getting on the train at the station n for the train i-1;
Figure GDA0002901836990000025
the number of persons waiting for the train i-1 at the station n;
step 2, determining the number of people on the train when the train i arrives at the station n
Figure GDA0002901836990000026
When the train i arrives at the station n, the number of people on the train comprises the accumulated sum of the difference values of the number of people getting on the train and the number of people getting off the train from the first station to the station;
Figure GDA0002901836990000027
wherein j also represents a station index, i.e., j is 1,2, …, N-1;
Figure GDA0002901836990000028
the number of passengers getting on the train i at the station j is shown;
Figure GDA0002901836990000029
the number of the passengers getting off the train i at the station j is shown;
step 3, calculating the number of passengers getting off when the train i arrives at the station n
Figure GDA00029018369900000210
According to the historical data, when the train i arrives at the station n, the number of people getting off the station is in direct proportion to the number of people getting on the station, so that the number of people getting off the station is determined
Figure GDA00029018369900000211
Figure GDA00029018369900000212
Where ρ isnThe ratio of the number of people getting off the bus to the number of people getting on the bus at the station n according to the historical data; the historical data is the data of the latest month;
step 4, determining the number of passengers getting on the train when the train i arrives at the station n
Figure GDA0002901836990000031
When the train i arrives at the station n, the number of passengers getting on the station
Figure GDA0002901836990000032
Number of people waiting at platform
Figure GDA0002901836990000033
And passenger carrying capacity C of traini(ii) related;
if the number of waiting persons at the station is larger than the remaining passenger carrying capacity of the train, the number of getting-on persons at the station
Figure GDA0002901836990000034
Remaining passenger carrying capacity for the train;
if the waiting number of people at the station is less than the remaining passenger carrying capacity of the train, the number of people getting on the train at the station
Figure GDA0002901836990000035
Is composed of
Figure GDA0002901836990000036
Wherein, CiRepresenting the passenger carrying capacity of the train i;
step 5, calculating the waiting time W of passengers at a station;
determining the number of waiting persons at station n
Figure GDA0002901836990000037
Number of people on vehicle
Figure GDA0002901836990000038
The number of people getting off
Figure GDA0002901836990000039
The number of persons getting on the bus
Figure GDA00029018369900000310
Then, from the arrival of one train at the station to the arrival of the next train at the station, the time is divided into three parts to calculate the waiting time of passengers: i.e. the time of alighting A1Getting-on time A2And a remaining time, wherein the remaining time period is divided into two parts to calculate passenger waiting time: i.e. waiting time A for passengers not getting on the train when the previous train leaves the station3And waiting time A of newly-entered passenger4
Figure GDA00029018369900000311
Figure GDA00029018369900000312
Figure GDA00029018369900000313
A4=τn(h-xn)2/2,
Wherein p isnThe ratio of the getting-off time to the stop time of the station n is obtained;
time for passenger waiting for train i at station n:
Wn i(h,xn)=A1+A2+A3+A4
Figure GDA0002901836990000041
the departure interval and the stop time are allowed to fluctuate, and a model of the waiting time of all passengers on the whole line with constraints is obtained:
Figure GDA0002901836990000042
Figure GDA0002901836990000043
wherein, taunThe arrival rate of passengers at station n, h is departure time interval, xnTime of standing at n stations, CiFor the passenger carrying capacity of train i, pnIs the ratio of the time of getting off to the time of stopping at the station n, rhonThe ratio of the number of getting-off passengers to the number of passengers on the train at station N, I is the number of trains, N is the number of stations, Z is an integer set, lhAnd uhMinimum and maximum values, respectively, allowed for departure time intervalsnAnd unRespectively the minimum and maximum allowed for the stop time.
The full-line all-passenger latency model with constraints can be solved by many existing sophisticated algorithms, such as genetic algorithms.
Advantageous effects
The invention is used for optimizing the train operation diagram, reducing the waiting time of passengers and improving the satisfaction degree of the passengers, and has the following advantages: (1) the train operation diagram is adjusted to improve the service quality and the passenger satisfaction of an operation company, and the cost is low; (2) the model is simple, easy to understand and calculate, and has strong applicability. (3) And a heuristic algorithm is adopted, and the computer simulation is used, so that the calculation speed is high.
Drawings
FIG. 1 is a schematic passenger waiting time diagram of the method of the present invention;
in the context of figure 1 of the drawings,
Figure GDA0002901836990000051
the time when the train i arrives at the station n,
Figure GDA0002901836990000052
in order to obtain the time for getting off the vehicle,
Figure GDA0002901836990000053
the time when the train i leaves the station n,
Figure GDA0002901836990000054
the time when the train i +1 arrives at the station n.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments, but is not limited thereto.
The invention provides a train operation diagram optimization method for improving passenger timeliness, which is characterized in that a mathematical model (namely waiting time of all passengers on the whole line with constraints) is established, and departure intervals and stop time of each station are adjusted to reduce the waiting time of the passengers.
In the method of the present invention, a current time schedule of a suburban line is first obtained according to the operation data of the subway operation company, and the names of stations are represented by numbers as shown in table 1 below.
TABLE 1 Current time-schedule
Figure GDA0002901836990000055
Assuming that the passengers uniformly enter the station in the peak period, the passenger entering speed of each station is stable, but the values of the stations are different, and the entering speed of each station is shown in the following table 2.
Table 2 inbound rate per station for early peak
Figure GDA0002901836990000056
According to the historical data, the number of people getting off each station is in direct proportion to the number of people getting on the vehicle, and the number of people getting off and the number of people getting on each station in the early peak and the peak are counted to obtain the getting off proportion of each station, as shown in the following table 3.
TABLE 3 get-off ratio for each station
Figure GDA0002901836990000061
The departure interval h under the current schedule is 134s, the number I of trains is 20, the number N of stations is 13, and the passenger carrying capacity C of the trainsi1400 persons are taken.
According to the mathematical model established by the invention, the waiting time of the passengers under the current schedule is calculated.
Step 1, calculating the waiting number of people at station
Figure GDA0002901836990000062
When the first train arrives at a station, the initial number of waits at each station may be approximated as the number of inbound people at the station over a period of time, i.e., the number of inbound people at the station
Figure GDA0002901836990000063
h, taking an departure interval, and setting the current time table to be 134 s.
The number of waiting persons at the station is the sum of the number of persons who get in from the departure station n of the train i-1 to the arrival station n of the train i and the number of persons on the platform when the train i-1 departs from the station n.
Figure GDA0002901836990000064
Substituting the inbound rate τnDeparture interval h, stop time xnThe number of persons getting on the bus
Figure GDA0002901836990000065
The number of waiting persons at the station when each train arrives at the station is obtained. According to the analysis of the actual situation, when the first train arrives at the station, the number of the passengers getting on the train is the initial waiting number
Figure GDA0002901836990000066
Step 2, determining the number of people on the train when the train i arrives at the station n
Figure GDA0002901836990000067
When the train i arrives at the station n, the number of people on the train comprises the accumulated sum of the difference values of the number of people getting on the train and the number of people getting off the train from the first station to the station.
Figure GDA0002901836990000071
When the train arrives at the first station, the train arrives as an empty train, and the number of people on the train at the station is 0.
Step 3, calculating the number of passengers getting off when the train i arrives at the station n
Figure GDA0002901836990000072
According to the historical data, when the train i arrives at the station n, the number of people getting off the station is in direct proportion to the number of people getting on the station, so that the number of people getting off the station is determined
Figure GDA0002901836990000073
Figure GDA0002901836990000074
In the embodiment, the selected early peak is short in time, and the get-off ratio rho n is considered to be a fixed value when each train arrives at the same station. And (4) substituting the number of the passengers on the train at each station when the train arrives at the station, which is obtained by calculation in the step (2), into the getting-off proportion of each station to obtain the number of the passengers getting off at each station.
Step 4, determining the number of passengers getting on the train when the train i arrives at the station n
Figure GDA0002901836990000075
When the train i arrives at the station n, the number of passengers getting on the station
Figure GDA0002901836990000076
Number of people waiting at platform
Figure GDA0002901836990000077
And passenger carrying capacity C of trainiIt is related.
If the number of waiting persons at the station is larger than the remaining passenger carrying capacity of the train, the number of getting-on persons at the station
Figure GDA0002901836990000078
Remaining passenger carrying capacity for the train;
if the waiting number of people at the station is less than the remaining passenger carrying capacity of the train, the number of people getting on the train at the station
Figure GDA0002901836990000079
Is composed of
Figure GDA00029018369900000710
And (3) comparing the number of the waiting persons at the platform with the number of the remaining passenger carrying capacity of the train according to the number of the waiting persons at the platform when the train arrives at the station, which is calculated in the step (1), the number of the persons on the train when the train arrives at the station and the number of the persons off the station when the train arrives at the station, which is calculated in the step (3), and determining the number of the persons on the station.
Step 5 calculating passenger waiting time W of station
Determining the number of waiting persons at station n
Figure GDA0002901836990000081
Number of people on vehicle
Figure GDA0002901836990000082
The number of people getting off
Figure GDA0002901836990000083
The number of persons getting on the bus
Figure GDA0002901836990000084
Then, from the arrival of one train at the station to the arrival of the next train at the station, the time is divided into three parts to calculate the waiting time of passengers: i.e. the time of alighting A1Getting-on time A2And a remaining time, wherein the remaining time period is divided into two parts to calculate passenger waiting time: i.e. waiting time A for passengers not getting on the train when the previous train leaves the station3And waiting time A of newly-entered passenger4
Figure GDA0002901836990000085
Figure GDA0002901836990000086
Figure GDA0002901836990000087
A4=τn(h-xn)2/2,
Time for passenger waiting for train i at station n:
Wn i(h,xn)=A1+A2+A3+A4
Figure GDA0002901836990000088
full line all passenger waiting time:
Figure GDA0002901836990000089
based on the above data and the model proposed by the present invention, the waiting time of the passenger on the current schedule is 33966 Reh.
The heuristic algorithm-genetic algorithm is used for adjusting departure intervals and stop time, optimizing a train operation diagram and reducing the waiting time of passengers, and the method specifically comprises the following steps:
step 1 chromosomal coding
In the present example, there are N decision variables, one chromosome Yk=(y1,y2,y3,......yN) One feasible solution (h, x) for the surrogate model1,x2,x3,......xN-1) One gene of the chromosome corresponds to one decision variable of the corresponding position. At the same time, each gene of the chromosome is converted into a binary-coded representation.
Step 2 initialization population
The population size pop _ size is set, and pop _ size chromosomes Y satisfying the constraint condition are randomly generatedk=(y1,y2,y3,......yN)。
Step 3 fitness evaluation
In the embodiment of the present invention, an objective function W (h, x) is selected as a fitness function, and it should be noted that a genetic algorithm is usually used to solve the maximum value of the objective function, but the minimum value of the objective function needs to be solved in this embodiment, so that the objective function is processed to obtain the fitness function eval (y) ═ a-W (h, x), where a is a sufficiently large constant, so that the value of the fitness function is always a positive value.
Step 4 selection
Selection of pop _ size outstanding chromosomes using a roulette algorithmEntering the next generation population. Calculating probability P of each chromosome according to fitness value of each chromosomekUpdating the chromosome probability, order
Figure GDA0002901836990000091
k
1,2, pop size, randomly generating a c e (0,1)]Will satisfy c ∈ (P)k-1,Pk]Chromosome Y ofkAnd (6) selecting.
Step 5 intersection
Defining a cross probability PcrossRandomly generating a real number r epsilon (0,1) if r<PcrossAnd selecting two chromosomes to exchange genes after the cross point, otherwise, not crossing. If the newly generated chromosome meets the constraint condition, replacing the original chromosome with the new chromosome; otherwise, the original chromosome is kept unchanged.
Step 6 mutation
Defining a probability of variation PmRandomly generating a real number s epsilon (0,1) if s < PmA binary-coded chromosome is selected for mutation, otherwise no mutation is performed. If the newly generated chromosome meets the constraint condition, replacing the original chromosome with the new chromosome; otherwise, the original chromosome is kept unchanged.
Defining the iteration number max _ generation, and repeating the step 3-6 until the iteration number max _ generation is reached.
According to the model provided by the invention, a genetic algorithm is adopted to adjust departure intervals and station-stopping time, the optimized departure intervals are 120s, and the optimized schedule is shown in the following table 4:
TABLE 4 optimized timetable
Figure GDA0002901836990000101
According to the optimized schedule, the waiting time of the passengers is 27309 people h. Compared with the current schedule, the passenger waiting time of the optimized schedule is reduced by (33966-.
The above is only a preferred embodiment of the present invention, and is not intended to limit the present invention, and various modifications and changes will occur to those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (3)

1. A train diagram optimization method for improving passenger aging is characterized by comprising the following steps:
step 1, calculating the number of people waiting for a train i at a station n
Figure FDA0002901836980000011
Wherein I represents a train index, I is 1,2, …, I; i is the number of trains; n represents a station index, i.e., N is 1,2, …, N; n is the number of stations;
when i is 1, namely the first train arrives at the station, the initial waiting number of each station is the number of the station-entering persons in the time h, namely the number of the station-entering persons
Figure FDA0002901836980000012
h is taken as a departure time interval, taunThe passenger arrival rate for station n;
when i is more than or equal to 2, the number of waiting persons at the station is the sum of the number of entering persons from the departure of the train i-1 from the station n to the arrival of the train i at the station n and the number of remaining persons at the platform when the train i-1 departs from the station n;
Figure FDA0002901836980000013
wherein h is the departure time interval of the station n; x is the number ofnStation stop time for n stations;
Figure FDA0002901836980000014
for train i-1 number of persons getting on at station n;
Figure FDA0002901836980000015
the number of persons waiting for the train i-1 at the station n;
step 2, determining the number of people on the train when the train i arrives at the station n
Figure FDA0002901836980000016
When the train i arrives at the station n, the number of people on the train is the accumulated sum of the difference values of the number of people getting on the train and the number of people getting off the train from the first station to the station;
Figure FDA0002901836980000017
wherein j also represents a station index, i.e., j is 1,2, …, N-1;
Figure FDA0002901836980000018
the number of passengers getting on the train i at the station j is shown;
Figure FDA0002901836980000019
the number of the passengers getting off the train i at the station j is shown;
step 3, calculating the number of passengers getting off when the train i arrives at the station n
Figure FDA00029018369800000110
According to the historical data, when the train i arrives at the station n, the number of people getting off the station is in direct proportion to the number of people getting on the station, so that the number of people getting off the station is determined
Figure FDA0002901836980000021
Figure FDA0002901836980000022
Where ρ isnThe ratio of the number of people getting off the bus to the number of people getting on the bus at the station n according to the historical data;
step 4, determining the number of passengers getting on the train when the train i arrives at the station n
Figure FDA0002901836980000023
When the train i arrives at the station n, the number of passengers getting on the station
Figure FDA0002901836980000024
Number of people waiting at platform
Figure FDA0002901836980000025
And passenger carrying capacity C of traini(ii) related;
if the number of waiting persons at the station is larger than the remaining passenger carrying capacity of the train, the number of getting-on persons at the station
Figure FDA0002901836980000026
Remaining passenger carrying capacity for the train;
if the waiting number of people at the station is less than the remaining passenger carrying capacity of the train, the number of people getting on the train at the station
Figure FDA0002901836980000027
Is composed of
Figure FDA0002901836980000028
Wherein, CiRepresenting the passenger carrying capacity of the train i;
step 5, calculating the waiting time W of passengers at a station;
determining the number of waiting persons at station n
Figure FDA0002901836980000029
Number of people on vehicle
Figure FDA00029018369800000210
The number of people getting off
Figure FDA00029018369800000211
The number of persons getting on the bus
Figure FDA00029018369800000212
Then, the time for the passenger to wait for train i at station n is calculated:
Figure FDA00029018369800000213
wherein p isnThe ratio of the getting-off time to the stop time of the station n is obtained;
the departure interval and the stop time are allowed to fluctuate, and the waiting time of all passengers on the whole line with the constraint is obtained:
Figure FDA00029018369800000214
Figure FDA00029018369800000215
wherein, taunThe arrival rate of passengers at station n, h is departure time interval, xnTime of standing at n stations, CiFor the passenger carrying capacity of train i, pnIs the ratio of the time of getting off to the time of stopping at the station n, rhonThe ratio of the number of getting-off passengers to the number of passengers on the train at station N, I is the number of trains, N is the number of stations, Z is an integer set, lhAnd uhMinimum and maximum values, respectively, allowed for departure time intervalsnAnd unRespectively the minimum and maximum allowed for the stop time.
2. The method for optimizing the train operation diagram for improving the passenger aging according to claim 1, wherein the time for the passenger to wait for the train i at the station n in the step 5 is calculated by adopting the following method:
determining the number of waiting persons at station n
Figure FDA0002901836980000031
Number of people on vehicle
Figure FDA0002901836980000032
The number of people getting off
Figure FDA0002901836980000033
The number of persons getting on the bus
Figure FDA0002901836980000034
Then, from the arrival of one train at the station to the arrival of the next train at the station, the time is divided into three parts to calculate the waiting time of passengers: i.e. the time of alighting A1Getting-on time A2And a remaining time, wherein the remaining time period is divided into two parts to calculate passenger waiting time: i.e. waiting time A for passengers not getting on the train when the previous train leaves the station3And waiting time A of newly-entered passenger4
Figure FDA0002901836980000035
Figure FDA0002901836980000036
Figure FDA0002901836980000037
A4=τn(h-xn)2/2,
Wherein p isnFor getting-off time and stop time of station nA ratio;
Figure FDA0002901836980000038
Figure FDA0002901836980000039
3. the method of claim 1, wherein the historical data is data of a last month.
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