CN110390421B - Space-time network-based method for coordinating and controlling passenger flow of congested subway line - Google Patents

Space-time network-based method for coordinating and controlling passenger flow of congested subway line Download PDF

Info

Publication number
CN110390421B
CN110390421B CN201910504530.2A CN201910504530A CN110390421B CN 110390421 B CN110390421 B CN 110390421B CN 201910504530 A CN201910504530 A CN 201910504530A CN 110390421 B CN110390421 B CN 110390421B
Authority
CN
China
Prior art keywords
passenger
time
train
station
network
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN201910504530.2A
Other languages
Chinese (zh)
Other versions
CN110390421A (en
Inventor
杨立兴
孟凡婷
高自友
李树凯
高原
阴佳腾
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Beijing Jiaotong University
Original Assignee
Beijing Jiaotong University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Beijing Jiaotong University filed Critical Beijing Jiaotong University
Priority to CN201910504530.2A priority Critical patent/CN110390421B/en
Publication of CN110390421A publication Critical patent/CN110390421A/en
Application granted granted Critical
Publication of CN110390421B publication Critical patent/CN110390421B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
    • G06Q10/047—Optimisation of routes or paths, e.g. travelling salesman problem
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0125—Traffic data processing

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Business, Economics & Management (AREA)
  • Human Resources & Organizations (AREA)
  • Theoretical Computer Science (AREA)
  • Strategic Management (AREA)
  • Economics (AREA)
  • Computer Hardware Design (AREA)
  • Entrepreneurship & Innovation (AREA)
  • Geometry (AREA)
  • Evolutionary Computation (AREA)
  • Development Economics (AREA)
  • Chemical & Material Sciences (AREA)
  • Analytical Chemistry (AREA)
  • General Engineering & Computer Science (AREA)
  • Game Theory and Decision Science (AREA)
  • Marketing (AREA)
  • Operations Research (AREA)
  • Quality & Reliability (AREA)
  • Tourism & Hospitality (AREA)
  • General Business, Economics & Management (AREA)
  • Train Traffic Observation, Control, And Security (AREA)

Abstract

The invention belongs to the technical field of urban rail transit, and relates to a method for coordinating and controlling passenger flow of a congested subway line based on a space-time network. Specifically, a train operation time-space network is constructed through a time discretization method on the premise that an operation diagram is determined, a passenger flow control problem is converted into a passenger travel time selection problem, and a mathematical optimization model accurately depicting the problem is established. And further converting the model into a travel shortest path selection problem based on individual passengers by means of a Lagrange relaxation method, designing an algorithm for solving the problem, and efficiently solving the rail transit line cooperative current limiting strategy under a set operation diagram.

Description

Space-time network-based method for coordinating and controlling passenger flow of congested subway line
Technical Field
The invention belongs to the technical field of urban rail transit, relates to a method for coordinating and controlling passenger flow of congested subway lines based on a space-time network, and particularly relates to a method for optimally controlling the passenger flow of the cooperation of the subway lines under a given operating diagram.
Background
At present, the urban rail transit system plays an increasingly important role in relieving traffic jam of a large city by the characteristics of punctuality, convenience, large capacity, low emission and the like. However, as the operation scale of subway systems expands, the demand of passengers on a subway as a trip mode in a large city also rapidly increases. Taking the beijing subway system as an example, the number of passengers in the beijing subway service has been on the rise sharply in recent years. According to statistics, the passenger flow total of Beijing subway in 2007 is only 5 hundred million people, and in 2016, the passenger flow total in year is over 35 hundred million people, which is nearly 7 times of the passenger flow total in 2007.
With the rapid increase of the demand of passengers, the congestion problem of the subway system becomes more and more serious. Especially in a modern large city where public transportation service plays a crucial role in resident travel, subway travel becomes the first choice for more and more passengers to commute in the morning and at night due to punctuality and rapidity, and further overcrowding of subway lines at the peak of the large city in the morning and at the night is caused. Relevant survey data show that at least 9 lines are in a congestion state in the morning and evening peak hours of Beijing, and taking eight-way lines of Beijing subway as an example, the full load rate of part of the lines exceeds 100%, so that the problem of overstock of passengers is serious. Passenger transships, can reduce subway operation's quality of service on the one hand, reduces the comfort level of track traffic trip, especially under the condition of big passenger flow, and some passengers need wait for the long time at the station and just can take the train, and the passenger trip is experienced and is declined, influences the appeal of subway trip. On the other hand, a large amount of platform passengers are overstocked, so that train operation delay is easily caused, passenger pushing phenomena are frequent, and the occurrence frequency of operation accidents and the safety risk of rail transit operation are increased. In actual operation, in order to solve the problem, current limiting measures are taken at partial sites, which is an effective means often adopted by railway operation departments; the method comprises the following steps: by closing part of station entrances, setting an out-station fence and closing part of automatic toll gate (AFC) to change the space-time distribution of passenger flow, the congestion condition of the passenger flow at busy stations is relieved. For example, in beijing subway line 13, six stations take current limiting measures in the morning and evening rush hour, and the congested passenger flow is transferred to the outside of the stations, so that the subway operation risk is reduced.
However, since there is a complex coupling relationship between the passenger flow and the train flow, in practice, the passenger flow control measures taken by the operation department are usually performed independently after being judged according to the expertise and experience, and the interaction relationship between the passenger flow and the train flow between different stations is not fully considered. At present, most of the existing current-limiting strategies are based on stations and platforms, and the individual trip behaviors of passengers on the whole subway line are less considered, so that the adopted control strategy is usually only a better control strategy of a single station, and the system optimal strategy of the whole subway operation system is difficult to achieve. And under the existing information technology, it becomes possible to conveniently acquire the travel behaviors of the passengers. In view of this, the present invention particularly provides an effective optimization method, which can cooperatively optimize the passenger flow control strategy of the whole subway line based on the travel selection of passengers.
Based on the current application situation, the invention considers the arriving dynamics of passengers, converts the passenger flow control problem into the passenger travel time selection problem by constructing a train operation spatio-temporal network on the premise of determining the operation diagram, constructs a strict mathematical optimization model and designs an effective solving algorithm. The method comprises the following steps: by means of time discretization, a time-space network of passengers and trains is constructed, train running tracks are described by adopting time-space paths, and arrival rules of the passengers are quantized by adopting time-related matrixes. Under the technical background, the passenger flow control problem is converted into a passenger path selection problem, the passenger requirements of all stations on a line are comprehensively considered, a space-time path shortest-path model is constructed, and a passenger flow cooperative optimization control method with the optimal system is designed and sought.
Disclosure of Invention
The invention aims to: the subway line cooperative passenger flow control optimization method under the established operation diagram is provided, the purpose of relieving platform congestion, reducing the waiting time of passengers, realizing the balanced configuration of rail traffic resources and improving the service quality of rail traffic is realized under the condition that the rail traffic operation diagram is not influenced. The invention takes into account, among other things, the dynamics of the passenger, including: passenger arrival time, train loading capacity, and passenger travel OD (origin-destination).
In order to achieve the purpose, the time is discretized, a train operation space-time network is constructed on the basis of the existing track traffic diagram, the train operation track is converted into a space-time track, a passenger trip selection optimization model is established, the track traffic resource allocation is optimized, and the cooperative current limiting of the whole line station and the system level optimization are achieved. In addition, the Lagrange relaxation idea is utilized to decompose the model, the original problem is converted into a series of mutually independent shortest-circuit problems related to passengers, optimization software and a heuristic algorithm based on Lagrange relaxation are respectively adopted to effectively solve the model, and the specific technical scheme is as follows.
A method for coordinating and controlling passenger flow of a congested subway line based on a space-time network comprises the following steps:
s1, establishing a passenger trip selection shortest-circuit optimization model based on a spatio-temporal network, which specifically comprises the following steps:
s11, constructing a spatio-temporal network
Discretizing the planned time interval of the train, converting the planned time interval into a series of time intervals with unit length delta, and adopting T ═ T { (T)0,t1,t2,…,tMDenotes the discretized time node, where t0For the start of the planned time period, tMIs the end time;
with time nodes as abscissa, station s of rail transit line1,s2,…,snAs a vertical coordinate, a coordinate plane is formed;
mapping the train running track to the coordinate plane to construct a space-time network;
s12, defining decision variables
Defining decision variables
Figure BDA0002091378010000031
Wherein the subscripts represent the spatio-temporal path (i, j, t, t ') indicating that passenger p leaves the i station at time t and arrives at the j station at time t';
and makes the following hypothetical decisions:
if passenger p selects spatiotemporal path (i, j, t, t'), then
Figure BDA0002091378010000032
If not, then,
Figure BDA0002091378010000033
wherein P belongs to P, and P is a passenger set in a planning time interval;
s13, determining constraint conditions
The constraint conditions include: based on passenger flow balance constraints and loading capacity constraints;
the flow balance constraint is expressed as formula (2) and is marked as constraint (2),
Figure BDA0002091378010000041
wherein, OpIs the origin of the passenger p,
Figure BDA0002091378010000042
the time when passenger p arrives at the origin station, A is the set of space-time arcs;
Figure BDA0002091378010000043
as virtual passenger arrival nodes, tMFor passenger arrival
Figure BDA0002091378010000044
The time of (d);
the loading capacity constraint is expressed as a formula (3) and is marked as a constraint (3),
Figure BDA0002091378010000045
wherein C is train loading capacity;
s14, constructing an objective function, and establishing a passenger trip selection shortest path optimization model based on a space-time network
The method specifically comprises the following steps:
s141, calculating waiting time of passenger p in spatio-temporal network
Figure BDA0002091378010000046
As shown in the formula (5),
Figure BDA0002091378010000047
wherein the content of the first and second substances,
Figure BDA0002091378010000048
a decision variable waiting at the origin for passenger p;
s142, the objective function is shown as formula (8),
Figure BDA0002091378010000049
wherein, wpComprises the following steps: the weight for any passenger p, as shown in equation (7),
Figure BDA00020913780100000410
wherein σ is a constant;
s143, the model based on the space-time network is shown as a formula (9),
Figure BDA00020913780100000411
；
s2, solving passenger trip selection shortest path optimization model based on space-time network
The method specifically comprises the following steps:
s21, initializing Lagrange multiplier muijtt′Making the iteration number n equal to 1;
s22, solving the optimal solution of the sub-problem model by using a label method, taking the optimal solution as a lower bound of the model solution based on the spatio-temporal network, and updating the lower bound LB (n);
s23, calculating an objective function (8) by adopting a step-by-step adjustment method, and updating an upper bound UB (n);
s24, updating Lagrange multiplier mu by using a sub-gradient methodijtt′；
S25, when either of the following two conditions is satisfied (i.e. condition (r) and-
Or ②), the iteration is stopped,
the conditions are as follows: the relative error of the upper and lower bounds is less than a given allowable error value ξ;
condition two: the iteration number n reaches the set maximum iteration number;
otherwise, the process returns to step S22 to continue the subsequent steps.
On the basis of the above technical solution, the obtaining of the subproblem model in step S22 specifically includes the following steps:
s221, introducing a Lagrange multiplier muijtt′And relaxing the loading capacity constraint into an objective function (8) to obtain a relaxation problem objective function shown as a formula (10),
Figure BDA0002091378010000051
s222, introducing intermediate variables
Figure BDA0002091378010000052
As shown in the formula (11),
Figure BDA0002091378010000053
by intermediate variables
Figure BDA0002091378010000054
Combining equations (10) and (11), further reducing the relaxation problem objective function to equation (12),
Figure BDA0002091378010000055
the model of the relaxation problem is then expressed as: considering equation (13) under the flow balance constraint described by equation (2),
Figure BDA0002091378010000061
s223, according to the mutual independence of the passenger path selection behaviors, further decomposing the formula (13) into a subproblem model selected by the p trips of each passenger, as shown in the formula (14),
Figure BDA0002091378010000062
。
on the basis of the above technical solution, the specific steps of step S23 are as follows:
counting passengers per train
Figure BDA0002091378010000063
Wherein k is the train number; according to the method of vehicle-by-vehicle and station-by-station, inquiring passenger selection behaviors which do not meet the loading capacity constraint, sequencing all passengers who select to take the train and get off after the station i according to the arrival time of the passengers at the starting station for the train k exceeding the loading capacity constraint when the train k exceeds the station i, and according to the first-in first-out principle, sequencing the exceeding part
Figure BDA0002091378010000064
Adjusting to k +1 times of train; and recalculating the train loading condition every time of adjustment until all the train loadings meet the loading capacity constraint, calculating an objective function (8) as a lower bound of the model solution based on the spatio-temporal network, and updating an upper bound UB (n).
On the basis of the above technical solution, the step S24 specifically includes the following steps:
s241, setting a gradient as shown in a formula (15),
Figure BDA0002091378010000065
s242, Lagrange multiplier muijtt′As shown in equation (16), update is performed:
Figure BDA0002091378010000066
wherein λ isnIs the iteration step size.
On the basis of the technical scheme, the iteration step length lambda isnGiven the standard step size, as shown in equation (17),
Figure BDA0002091378010000071
wherein, thetanThe value range is 0 < thetan≤2。
The invention has the following beneficial technical effects:
the method comprehensively considers factors such as train space-time tracks, dynamic requirements of all OD passengers, train loading capacity, passenger path selection, waiting time and the like under the established operation diagram, optimizes the travel behaviors of the passengers on the premise of not influencing the existing operation diagram, ensures safe and efficient operation of rail transit, reduces the waiting time of the passengers and balances the utilization of rail transit resources. Specifically, a train operation time-space network is constructed through a time discretization method on the premise that an operation diagram is determined, the passenger flow control problem is converted into a passenger travel time selection problem, and a mathematical optimization model accurately describing the problems is established. Further, the model is converted into a travel shortest path selection problem based on individual passengers by means of a Lagrange relaxation method, and an efficient algorithm for solving the problem is designed. The technology can efficiently solve the rail transit line cooperative current limiting strategy under a given operation diagram.
Drawings
The invention has the following drawings:
FIG. 1 is a schematic diagram of rail transit operation;
FIG. 2 is a schematic diagram of a train operation spatiotemporal network structure based on time dispersion;
FIG. 3 is a schematic diagram of passenger arrival distribution at an early peak section of a Beijing subway eight-way line;
FIG. 4 is a schematic diagram of passenger travel path selection in the spatio-temporal network;
FIG. 5 is a schematic diagram of a train operation diagram and train loading conditions solved by CPLEX in example verification;
FIG. 6 is a statistical plot of individual passenger waiting times solved using CPLEX in example validation;
FIG. 7 is a schematic illustration of an actual passenger inbound distribution and a passenger inbound distribution under control for example verification;
FIG. 8 is a graph of iterative convergence of a design algorithm in an example verification.
Detailed Description
In order to more clearly illustrate the present invention, the present invention is further described below with reference to examples and the accompanying drawings.
The following describes the specific implementation of the proposed method in detail according to the two parts of model building and model solving. It is to be understood by persons skilled in the art that the following detailed description is illustrative and not restrictive, and is not to be taken as limiting the scope of the invention.
Establishing a model based on a space-time network
1. Building spatio-temporal networks
The method has the key technology that the rail transit running track is mapped into a space-time network and converted into a space-time track, so that the passenger flow control problem is converted into the passenger departure time selection problem, and a passenger trip selection shortest-path optimization model is established.
To achieve the above object, the present invention first discretizes the planning period under consideration, and converts the planning period into a series of time intervals of unit time length δ (i.e., discrete time steps). Here, T ═ T is used0,t1,t2,…,tMDenotes the discretized time node, i.e. the set of discrete time intervals, where t0For the start of the planned time period, tMIs the end time.
In actual operation, the train usually runs periodically based on a predetermined operation diagram according to the route shown in fig. 1, where s1,s2,…,snRepresenting a rail transit line stop. For convenience of description, the train operation trajectory may be mapped to a spatio-temporal network as shown in fig. 2, wherein the abscissa represents a time node, the ordinate represents a track traffic line station, and solid arrows connected by dotted arrows respectively represent trainsThe dashed arrow represents the stop arc of the train at the station.
Since the traveling demands of passengers are dynamically changed with time in reality, in order to describe the dynamic demand distribution of passengers, an eight-way line early peak part station passenger arrival statistical curve diagram (i.e. an early peak part station passenger arrival distribution diagram) shown in fig. 3 is given. As can be seen from the figure, the early peak passenger arrival is far beyond the peak flat period. In order to further characterize the dynamics of the passenger flow, the invention uses a time-dependent OD matrix P (t)k) Is shown at (t)k-1,tk]The trip demand of the passengers arriving in the time interval is shown in the formula (1),
Figure BDA0002091378010000091
wherein p isij(tk) Represents (t)k-1,tk]The number of passengers arriving at station i in time and traveling OD i → j. By means of the method, all passenger travel demands in the planning period can be represented dynamically.
On the basis of the construction of the spatio-temporal network, the subway line passenger flow control process can be represented as a selection process of individual passenger travel paths in the spatio-temporal network as shown in fig. 4. Specifically, by regarding a single passenger with different travel demands as a control unit, on the premise of considering the constraint of train loading capacity, the optimal passenger travel path of the system is found, so as to realize the balanced configuration of system resources. The solid black nodes in the figure are the time-space nodes (i.e., passenger arrival nodes) at which passengers arrive, the dashed arrows indicate that passengers are waiting at the origin (i.e., passenger waiting arc in fig. 4), and the solid arrows indicate that passengers leave the origin (i.e., passenger outgoing arc in fig. 4) in a corresponding train. On the basis of the technology, a shortest path model for passenger travel selection is constructed to seek an optimal full-line passenger flow cooperative control optimization method of the system.
2. Defining decision variables
Generally speaking, the passenger routing variables are binary variables, and the following decision variables are adopted by the invention to describe the routing behavior of the passenger.
Defining decision variables
Figure BDA0002091378010000092
And makes the following hypothetical decisions:
if passenger p selects spatiotemporal path (i, j, t, t'), then
Figure BDA0002091378010000093
If not, then,
Figure BDA0002091378010000094
the above decision variables
Figure BDA0002091378010000095
Reflecting the travel track of the passenger in different time dimensions, and indicating that the passenger waits at the station i or the station j when the station i is j (for example, the train does not depart or the train on which the passenger stops at the station); when i is not equal to j, the passenger is indicated to be in a running state by taking the train, and the passenger leaves the station i at the time t and arrives at the station j at the time t'; (i, j, t, t') (also called spatio-temporal arc segments) are: and the train running track in the space-time network is used for indicating that the train departs from the station i at the time t and arrives at the station j at the time t'.
3. Determining constraints
(1) Passenger-based flow balance constraints
After the passengers arrive at the starting station, the passengers need to wait at the station or take a train to go to the destination station, so that the optimal space-time path from the starting station to the destination station needs to be found for each passenger, based on the above consideration, a flow balance constraint is constructed, as shown in formula (2), and is marked as constraint (2),
Figure BDA0002091378010000101
wherein the left term of the equation represents the number of times that the passenger enters or exits the node j, OpIs the origin of the passenger p,
Figure BDA0002091378010000102
the time when a passenger P arrives at an origin station, namely the departure time, P is a passenger set in a planning time interval, and A is a set of space-time arcs; in order to ensure the rationality of the constraint, a purpose station virtual node is specially added
Figure BDA0002091378010000103
Wherein the content of the first and second substances,
Figure BDA0002091378010000104
as virtual passenger arrival nodes, tMVirtual node arrival for passengers
Figure BDA0002091378010000105
Time of (d). Then the space-time arc segment
Figure BDA0002091378010000106
Represents passenger at tkConstantly driving away from the actual destination node DpAnd at tMTime of arrival at a virtual node
Figure BDA0002091378010000107
Note that from actual node DpTo the virtual node
Figure BDA0002091378010000108
Has a travel time of 0, i.e. tk＝tM。
(2) Load capacity constraint
The travel of passengers is limited by the constraint of train loading capacity, in order to ensure the reasonability of the model, the constraint of the loading capacity is established, as shown in formula (3), and is marked as constraint (3),
Figure BDA0002091378010000109
in principle, to ensure travel safety, the number of passengers on the train must not exceed the train loading capacity, reflected on the spatio-temporal network, i.e. the number of passengers with i ≠ j does not exceed the train loading capacity C, selecting the same path (i, j, t, t').
4. Constructing an objective function
As mentioned above, the present invention aims to guarantee: on the premise that the rail transit operation diagram is not influenced, the travel paths of passengers are optimized to reasonably distribute rail transit resources, the waiting time of the passengers is reduced, and the cooperative optimization control of subway line passenger flow is realized. The waiting time of the passenger p is the difference between the departure time and the arrival time of the passenger, as shown in the formula (4),
Figure BDA0002091378010000111
wherein the content of the first and second substances,
Figure BDA0002091378010000112
in order to be a waiting time for the passenger p,
Figure BDA0002091378010000113
the time at which passenger p leaves the origin station,
Figure BDA0002091378010000114
time of arrival at the origin for passenger p;
on a time discrete basis, the waiting time of the passenger p in the spatio-temporal network, i.e. the sum of all waiting arcs thereof, is multiplied by a discrete time step delta, as shown in equation (5),
Figure BDA0002091378010000115
wherein the content of the first and second substances,
Figure BDA0002091378010000116
a decision variable for passenger p to wait at the origin. Considering that the present invention aims to minimize the total waiting time of all passengers in the system, further, the waiting time t for all passengerswaitMake a calculation of the waiting time for all individual passengers
Figure BDA0002091378010000117
The addition of (b) is represented by the formula (6),
Figure BDA0002091378010000118
considering that if only the shortest total waiting time is pursued, the later passenger can take a car preferentially, and the first passenger waits, in order to ensure the passenger service to follow the principle of first-in first-out, the first passenger needs to be given a certain priority to ensure that the first passenger takes a train preferentially, and for the convenience of calculation, the following weight w is given to any passenger pp：
Figure BDA0002091378010000119
Wherein, the sigma is a given constant and is given according to specific requirements.
The invention aims to optimize the total waiting time of passengers, considers the first-in first-out principle and combines the formulas (6) and (7) to provide a model objective function shown in the formula (8),
Figure BDA00020913780100001110
in summary, the model based on the spatio-temporal network is represented as: equation (9) under the flow balance constraint of equation (2) and the load capacity constraint of equation (3),
Figure BDA00020913780100001111
second, solving model based on space-time network
The model solving based on the spatio-temporal network comprises three parts, namely, firstly, the model is needed to be decomposed, secondly, an iterative algorithm based on Lagrangian relaxation is designed, and finally, example verification is carried out.
1. Model decomposition based on Lagrange relaxation
To is coming toSolving the model based on the space-time network, analyzing that the loading capacity constraint (3) is difficult constraint and needs to be relaxed, and introducing a Lagrange multiplier mu to solve the problemijtt′,(i,j,t,t′)∈A。
By introducing lagrange multiplier muijtt′Relaxing the loading capacity constraint into a model objective function (8) to obtain a relaxation problem objective function as shown in a formula (10),
Figure BDA0002091378010000121
to simplify the description, intermediate variables are introduced
Figure BDA0002091378010000122
As shown in the formula (11),
Figure BDA0002091378010000123
by intermediate variables
Figure BDA0002091378010000124
Combining equations (10) and (11), the objective function of the relaxation problem is further simplified to equation (12),
Figure BDA0002091378010000125
the model of the relaxation problem can be expressed as: considering equation (13) under the flow balance constraint described by equation (2),
Figure BDA0002091378010000126
in the relaxation model (13), the routing behaviors of all passengers are independent from each other, so that the model can be further decomposed into a series of sub-problems (sub (p)) related to individual passengers to form a sub-problem model of the p travel selection of each passenger, as shown in formula (14),
Figure BDA0002091378010000131
from the sub-problem model equation (14), it can be seen that each sub-problem is a classical shortest-path problem that only considers the flow balance constraint, and it is solved precisely by the label method.
2. Solving algorithm
The subproblems obtained after the original problem is decomposed are classical shortest-path problems, and can be solved by means of a labeling method. The obtained relaxation problem objective function (12) can be regarded as the lower bound of the original problem solution, and in order to search the feasible solution of the original problem, the invention designs a gradual adjustment algorithm, and the solution obtained after relaxation is adjusted into the feasible solution, and the algorithm is divided into three parts.
1) Search for feasible solutions
Solving the optimal solution of the subproblems by using the shortest-path algorithm, and calculating the number of passengers on each train based on the optimal solution
Figure BDA0002091378010000132
Wherein k is the train number. Querying for passenger selection behavior that does not meet load-carrying capacity constraints on a car-by-car, station-by-station basis
Figure BDA0002091378010000133
For the train k beyond the loading capacity constraint, at the station i beyond the train k, sorting all passengers who choose to take the train and get off after the station i according to the arrival time of the passengers at the starting station, and according to the first-in first-out principle, sorting the exceeding part
Figure BDA0002091378010000134
Adjust to k +1 trains. And recalculating the train loading condition every time of adjustment until all the train loads meet the loading capacity constraint, obtaining a feasible solution of the problem, calculating an objective function (8), and updating the upper bound.
2) Updating lagrange multiplier muijtt′
Using a sub-gradient method, in accordance withUpdating the Lagrangian multiplier μ as followsijtt′。
First, a gradient is set, as shown in equation (15),
Figure BDA0002091378010000135
the definition of the method is that,
Figure BDA0002091378010000136
and representing the optimal solution of all the subproblems obtained by the nth iteration.
Lagrange multiplier muijtt′As shown in equation (16), update is performed:
Figure BDA0002091378010000141
wherein λ isnFor the iteration step, in the present invention, the iteration step λnGiven the standard step size, as shown in equation (17),
Figure BDA0002091378010000142
wherein, thetanThe value range is 0 < thetanLess than or equal to 2, is used for adjusting the step length and ensures the nonnegativity of the penalty value.
The specific steps for solving the algorithm are as follows,
step 1: (initialization). Initializing lagrange multiplier muijtt′Making the iteration number n equal to 1;
step 2: (calculate sub-problem optimal solution). Solving the optimal solution of the sub-problem model by using a shortest-path algorithm (namely a labeling method), and updating a lower bound LB (n);
step 3: (generating a feasible solution). And adjusting the generated infeasible solution into a feasible solution of the original problem according to the provided step-by-step adjustment method for searching the feasible solution, and updating the upper bound UB (n).
Step 4: (update multiplier). Using a sub-gradient methodUpdating the Lagrange multiplier muijtt′。
Step 5: (algorithm termination). The algorithm terminates when either of the following two conditions is satisfied.
(1) The relative error of the upper and lower bounds is less than a given allowable error value ξ;
(2) and the iteration reaches the set maximum iteration number.
Otherwise, returning to Step 2 and continuing to calculate n as n + 1.
3. Example verification
In order to more clearly illustrate the invention, the invention is further described below with reference to preferred examples and the accompanying drawings. A small-scale numerical example is designed to verify the inventive content, as shown in table 1, assuming that a one-way rail transit line with 6 stations runs 5 trains, a planning time domain (i.e. planning time interval) is 30min, which can be dispersed into 30 time intervals, a discrete step δ is 1min, and the dynamic arrival of passengers is given as follows:
(1) assuming that [5,15] is a peak time period, the arrival number of passengers per unit time among all trips OD is randomly given in an interval [20,40], and the passenger demand exceeds the loading capacity of a train;
(2) the rest time periods are peak-off time periods, and the arrival number of passengers per unit time among all trips OD is randomly given in the interval [5,10 ].
The number of passengers generated in the above manner may exceed the train capacity during peak hours. To ensure that passengers can ride the train during the scheduled time period, the train is finally operated according to the schedule shown in table 1, given that no passengers arrive at the station after the last train departure from the station, and finally the total number of passengers 6399.
TABLE 1 train timetable
Train numbering Station 1 Station 2 Station 3 Station 4 Station 5 Station 6
Train 1 (-,2) (4,5) (7,8) (11,12) (14,15) (17,-)
Train 2 (-,5) (7,8) (10,11) (14,15) (17,18) (20,-)
Train 3 (-,8) (10,11) (13,14) (17,18) (20,21) (23,-)
Train 4 (-,12) (14,15) (17,18) (21,22) (24,25) (27,-)
Train 5 (-,15) (17,18) (20,21) (24,25) (27,28) (30,-)
According to the given train timetable and passenger arrival data, firstly, a CPLEX solver is used for solving a model (9) to obtain a passenger travel selection scheme and a train running loading condition under a cooperative passenger flow control strategy, and the total waiting time of the passengers is calculated to be 15102 min. In order to better show the obtained travel plan and the retention situation of passengers, a train operation diagram, a passenger getting on/off situation of each station and a train loading situation of each station are given as shown in fig. 5. According to the path selection of the passengers, the specific waiting time of each passenger can be obtained, and as shown in fig. 6, the statistical data shows that the waiting time of most passengers at the starting station is short, and the passengers can travel by the train quickly. To better verify the effectiveness of the present invention, CPLEX is used to simulate the travel of passengers without control measures (riding rules on duty) (shown by black solid blocks in fig. 7, corresponding passenger inbound distribution, i.e. legend is no control), and compare with the above passenger inbound scheme (shown by black open blocks in fig. 7, corresponding passenger inbound distribution, i.e. legend is under control) obtained by solving the model (9) under the cooperative passenger flow control strategy. In the two situations, as shown in fig. 7, the obtained passenger inbound distribution can find that the inbound time of the passenger is greatly different from the inbound distribution without control.
In order to further verify the effectiveness of the designed calculation method, the algorithm designed by the application is used for solving the problem, the algorithm can be converged to a better solution within a short time (7.3s), the difference between the total waiting time of the passenger, which is 15180min, and the optimal solution obtained by the CPLEX solver is only 78min, and the convergence condition of the algorithm is shown in FIG. 8. Further, the passenger riding conditions and the passenger waiting time levels obtained by the two methods are compared, as shown in tables 2 and 3. It can be seen from the two tables that although there is some difference between the calculation method and the CPLEX solution result (as shown in bold font part in table 2), the flow control measures are similar from the global perspective, and the solution obtained by the calculation method is close to the optimal solution in terms of the total waiting time, and can be quickly solved in a short time, thereby verifying the effectiveness of the calculation method provided by the invention.
TABLE 2 passenger loading scheme comparison table obtained by two methods
Figure BDA0002091378010000161
TABLE 3 passenger waiting time statistical table obtained by two solving methods
Figure BDA0002091378010000162
It should be understood that the above-mentioned embodiments of the present invention are only examples for clearly illustrating the present invention, and are not intended to limit the embodiments of the present invention, and it will be obvious to those skilled in the art that other variations or modifications may be made on the basis of the above description, and all embodiments may not be exhaustive, and all obvious variations or modifications may be made within the scope of the present invention.
Those not described in detail in this specification are within the knowledge of those skilled in the art.

Claims (4)

1. A method for coordinating and controlling passenger flow of a congested subway line based on a space-time network is characterized by comprising the following steps:
s1, establishing a passenger trip selection shortest-path optimization model based on a spatio-temporal network, and specifically comprising the following steps:
s11, constructing a spatio-temporal network
Discretizing the planned time interval of the train, converting the planned time interval into a series of time intervals with unit length delta, and adopting T ═ T { (T)0,t1,t2,…,tMDenotes the discretized time node, where t0For the start of the planned time period, tMIs the end time;
with time node T as abscissa, station s of rail transit line1,s2,…,snAs a vertical coordinate, a coordinate plane is formed;
mapping the train running track to the coordinate plane to construct a space-time network;
s12, defining decision variables
Defining decision variables
Figure FDA0003463219270000011
Wherein the subscript indicates the spatio-temporal path ijtt ', i.e. indicates that passenger p leaves station i at time t and arrives at station j at time t';
and makes the following hypothetical decisions:
if passenger p selects spatio-temporal path ijtt', then
Figure FDA0003463219270000012
If not, then,
Figure FDA0003463219270000013
wherein P belongs to P, and P is a passenger set in a planning time interval;
s13, determining constraint conditions
The constraint conditions include: based on passenger flow balance constraints and loading capacity constraints;
the flow balance constraint is expressed as formula (2) and is marked as constraint (2),
Figure FDA0003463219270000014
wherein, OpIs the origin station of the passenger p,
Figure FDA0003463219270000015
the time when passenger p arrives at the origin station, A is the set of space-time arcs;
Figure FDA0003463219270000016
as virtual passenger arrival nodes, tMFor passenger arrival
Figure FDA0003463219270000017
The time of (d);
the loading capacity constraint is expressed as a formula (3) and is marked as a constraint (3),
Figure FDA0003463219270000021
wherein C is the train loading capacity;
s14, constructing an objective function, and establishing a passenger trip selection shortest path optimization model based on a space-time network
The method specifically comprises the following steps:
s141, calculating waiting time of passenger p in spatio-temporal network
Figure FDA0003463219270000022
As shown in the formula (5),
Figure FDA0003463219270000023
wherein the content of the first and second substances,
Figure FDA0003463219270000024
a decision variable waiting at the origin for passenger p;
s142, the objective function is shown as formula (8),
Figure FDA0003463219270000025
wherein, twaitWaiting time for all passengers, wpAs a weight for any passenger p, as shown in equation (7),
Figure FDA0003463219270000026
wherein σ is a constant;
s143, the model based on the space-time network is shown as a formula (9),
Figure FDA0003463219270000027
；
s2, solving passenger trip selection shortest path optimization model based on space-time network
The method specifically comprises the following steps:
s21, initializing Lagrange multiplier muijtt′Making the iteration number n equal to 1;
s22, solving the optimal solution of the sub-problem model by using a label method, taking the optimal solution as a lower bound of the model solution based on the spatio-temporal network, and updating the lower bound LB (n);
s23, calculating an objective function (8) by adopting a step-by-step adjustment method, and updating an upper bound UB (n);
s24, updating Lagrange multiplier mu by using a sub-gradient methodijtt′；
S25, when either of the following two conditions is satisfied, stopping the iteration,
the method comprises the following steps: the relative error of the upper and lower bounds is less than a given allowable error value ξ;
condition two: the iteration number n reaches the set maximum iteration number;
otherwise, if n is n +1, the process returns to step S22, and the subsequent steps are continued;
the obtaining of the subproblem model in step S22 specifically includes the following steps:
s221, introducing a Lagrange multiplier muijtt′And relaxing the loading capacity constraint into an objective function (8) to obtain a relaxation problem objective function shown as a formula (10),
Figure FDA0003463219270000031
s222, introducing intermediate variables
Figure FDA0003463219270000032
As shown in the formula (11),
Figure FDA0003463219270000033
by intermediate variables
Figure FDA0003463219270000034
Combining equations (10) and (11), the objective function of the relaxation problem is further simplified to equation (12),
Figure FDA0003463219270000035
the model of the relaxation problem is then expressed as: considering equation (13) under the flow balance constraint described by equation (2),
Figure FDA0003463219270000036
s223, according to the mutual independence of the passenger path selection behaviors, further decomposing the formula (13) into a subproblem model selected by the p trips of each passenger, as shown in the formula (14),
Figure FDA0003463219270000041
2. the method for the coordinated control of the passenger flow of the congested subway line based on the spatio-temporal network as claimed in claim 1, wherein: the specific steps of step S23 are as follows:
counting passengers per train
Figure FDA0003463219270000042
Wherein k is train number; according to the method of vehicle-by-vehicle and station-by-station, inquiring passenger selection behaviors which do not meet the loading capacity constraint, sequencing all passengers who select to take the train and get off after the station i according to the arrival time of the passengers at the starting station for the train k exceeding the loading capacity constraint when the train k exceeds the station i, and according to the first-in first-out principle, sequencing the exceeding part
Figure FDA0003463219270000043
Adjusting to k +1 times of trains; and recalculating the train loading condition every time of adjustment until all the train loadings meet the loading capacity constraint, calculating an objective function (8) as a lower bound of the model solution based on the spatio-temporal network, and updating an upper bound UB (n).
3. The method for coordinating and controlling the passenger flow of the congested subway line based on the spatio-temporal network as claimed in claim 2, wherein: the step S24 specifically includes the following steps:
s241, setting a gradient as shown in a formula (15),
Figure FDA0003463219270000044
s242, Lagrange multiplier muijtt′As shown in equation (16), update is performed:
Figure FDA0003463219270000045
wherein λ isnIs the iteration step size.
4. The method for coordinating and controlling the passenger flow of the congested subway line based on the spatio-temporal network as claimed in claim 3, wherein: the iteration step λnGiven the standard step size, as shown in equation (17),
Figure FDA0003463219270000046
wherein, thetanValue range of 0<θn≤2。
CN201910504530.2A 2019-06-12 2019-06-12 Space-time network-based method for coordinating and controlling passenger flow of congested subway line Active CN110390421B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN201910504530.2A CN110390421B (en) 2019-06-12 2019-06-12 Space-time network-based method for coordinating and controlling passenger flow of congested subway line

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN201910504530.2A CN110390421B (en) 2019-06-12 2019-06-12 Space-time network-based method for coordinating and controlling passenger flow of congested subway line

Publications (2)

Publication Number Publication Date
CN110390421A CN110390421A (en) 2019-10-29
CN110390421B true CN110390421B (en) 2022-05-10

Family

ID=68285495

Family Applications (1)

Application Number Title Priority Date Filing Date
CN201910504530.2A Active CN110390421B (en) 2019-06-12 2019-06-12 Space-time network-based method for coordinating and controlling passenger flow of congested subway line

Country Status (1)

Country Link
CN (1) CN110390421B (en)

Families Citing this family (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN111353639B (en) * 2020-02-26 2022-04-12 北京交通大学 Urban rail transit peak current limiting optimization method for coordinating train timetable
CN111967134B (en) * 2020-07-10 2023-12-12 北京交通大学 Underground logistics system optimization control method based on subway collinear co-vehicle
CN111860991B (en) * 2020-07-13 2022-07-08 清华大学深圳国际研究生院 Unmanned vehicle distribution path planning method
CN112613659B (en) * 2020-12-23 2022-11-15 东南大学 New energy freight charging station site selection-path optimization method based on three-dimensional space-time network
CN112918523B (en) * 2021-02-25 2023-05-02 北京电子科技职业学院 Passenger flow collaborative accurate control method for crowded subway line based on train schedule optimization
CN112991801B (en) * 2021-03-05 2022-03-11 合肥工业大学 Optimal safety path obtaining method based on time-varying road condition
CN113112055A (en) * 2021-03-22 2021-07-13 北京交通大学 Dynamic distribution and operation plan integrated optimization method for subway passenger and cargo shared carriage
CN114394135B (en) * 2021-11-08 2023-01-17 北京交通大学 Train operation diagram and path selection optimization method based on multi-granularity time-space network
CN114819327A (en) * 2022-04-20 2022-07-29 东南大学 Collection and bulk integration electric vehicle path optimization method based on high-dimensional network

Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104537439A (en) * 2014-12-29 2015-04-22 中南大学 Minimal-cost path and mixed path distribution method for alleviating track traffic congestion
CN106779190A (en) * 2016-12-02 2017-05-31 东南大学 A kind of urban track traffic passenger trip route suggesting method and system
CN107705039A (en) * 2017-10-27 2018-02-16 华东交通大学 Urban track traffic for passenger flow Precise control method and system based on passenger flow demand
CN107704950A (en) * 2017-09-14 2018-02-16 北京交通大学 A kind of city rail train figure optimization method based on trip requirements and energy saving of system
CN108053062A (en) * 2017-12-11 2018-05-18 北京航空航天大学 A kind of customization public bus network generation method based on multi-source data
CN109257287A (en) * 2017-07-13 2019-01-22 华为技术有限公司 A kind of shortest path determines method and controller

Patent Citations (6)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104537439A (en) * 2014-12-29 2015-04-22 中南大学 Minimal-cost path and mixed path distribution method for alleviating track traffic congestion
CN106779190A (en) * 2016-12-02 2017-05-31 东南大学 A kind of urban track traffic passenger trip route suggesting method and system
CN109257287A (en) * 2017-07-13 2019-01-22 华为技术有限公司 A kind of shortest path determines method and controller
CN107704950A (en) * 2017-09-14 2018-02-16 北京交通大学 A kind of city rail train figure optimization method based on trip requirements and energy saving of system
CN107705039A (en) * 2017-10-27 2018-02-16 华东交通大学 Urban track traffic for passenger flow Precise control method and system based on passenger flow demand
CN108053062A (en) * 2017-12-11 2018-05-18 北京航空航天大学 A kind of customization public bus network generation method based on multi-source data

Non-Patent Citations (2)

* Cited by examiner, † Cited by third party
Title
城市轨道交通列车运行图优化模型与算法研究;黄航飞;《中国优秀硕士学位论文全文数据库工程科技II辑》;20181115(第11期);第C033-6页 *
考虑旅客需求的停站方案与列车运行图一体化模型与算法;刘璐等;《铁道科学与工程学报》;20190228;第16卷(第2期);第518-527页 *

Also Published As

Publication number Publication date
CN110390421A (en) 2019-10-29

Similar Documents

Publication Publication Date Title
CN110390421B (en) Space-time network-based method for coordinating and controlling passenger flow of congested subway line
Wang et al. Passenger demand oriented train scheduling and rolling stock circulation planning for an urban rail transit line
Wang et al. Passenger-demands-oriented train scheduling for an urban rail transit network
CN111401614B (en) Dynamic passenger flow distribution method and system for urban rail transit
Yuan et al. Integrated optimization of train timetable, rolling stock assignment and short-turning strategy for a metro line
Malandri et al. Recovery time and propagation effects of passenger transport disruptions
CN112085641B (en) High-speed railway passenger flow distribution method based on train operation scheme
Yin et al. Hybrid demand‐driven and cyclic timetabling considering rolling stock circulation for a bidirectional railway line
CN108537408B (en) Road network cooperative current limiting modeling and evaluation method integrating station entering and transfer control
WO2019003672A1 (en) Transit demand forecasting device and transit demand forecasting method
D’Acierno et al. Assumptions and simulation of passenger behaviour on rail platforms
Cats et al. Effect of real-time transit information on dynamic passenger path choice
CN115809729B (en) Urban rail transit junction transfer facility optimal configuration method considering newly-added line
Drabicki et al. Mitigating bus bunching with real-time crowding information
CN111724076A (en) Regional multi-type rail transit passenger flow dynamic distribution method under operation interruption condition
Li et al. Metro Timetabling for Time‐Varying Passenger Demand and Congestion at Stations
CN112465205A (en) Single-line multi-station cooperative current limiting rail transit train running density optimization method
CN114841556A (en) Rail transit cross-line operation transportation plan evaluation system and method
Meschini et al. A frequency based transit model for dynamic traffic assignment to multimodal networks
Gong et al. Equity-oriented train timetabling with collaborative passenger flow control: a spatial rebalance of service on an oversaturated urban rail transit line
Yuan et al. Decomposition and approximate dynamic programming approach to optimization of train timetable and skip-stop plan for metro networks
Zhang et al. Train rescheduling for large-scale disruptions in a large-scale railway network
Papola et al. Schedule-based transit assignment: new dynamic equilibrium model with vehicle capacity constraints
Huang et al. Optimizing train timetable based on departure time preference of passengers for high‐speed rails
Liu et al. Timetable scheduling for passenger-centric urban rail networks: Model predictive control based on a novel absorption model

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant