CN112149889A - Rail transit operation line and frequency collaborative optimization method considering passenger flow distribution - Google Patents

Rail transit operation line and frequency collaborative optimization method considering passenger flow distribution Download PDF

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CN112149889A
CN112149889A CN202010969081.1A CN202010969081A CN112149889A CN 112149889 A CN112149889 A CN 112149889A CN 202010969081 A CN202010969081 A CN 202010969081A CN 112149889 A CN112149889 A CN 112149889A
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rail transit
urban rail
passenger
frequency
station
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CN112149889B (en
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周宇
王云
闫学东
商攀
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Beijing Jiaotong University
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    • 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
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Abstract

The invention provides a rail transit operation line and frequency collaborative optimization method considering passenger flow distribution. The method comprises the following steps: the method comprises the steps of establishing and solving a mixed integer nonlinear programming model for urban rail transit operation lines and operation frequency collaborative optimization according to constraint sets and objective functions of urban rail transit operation cost and passenger trip cost, and obtaining optimized urban rail transit operation lines and operation frequency schemes. The invention comprehensively considers the factors of urban rail transit operation network connectivity, passenger path distribution, safe departure interval and the like, can effectively balance the operation cost and the passenger trip cost, improves the urban rail transit operation efficiency and enhances the riding satisfaction of the passengers.

Description

Rail transit operation line and frequency collaborative optimization method considering passenger flow distribution
Technical Field
The invention relates to the technical field of urban rail transit management, in particular to a rail transit operation line and frequency collaborative optimization method considering passenger flow distribution.
Background
Urban rail transit has the advantages of large transportation capacity, high speed, high punctuality, energy conservation, environmental protection, high safety and the like, is one of the main traveling modes of urban residents in China at present, and plays a role in supporting urban circulation and playing a leading role. In an urban rail transit system, an operation route is generally fixed and unchangeable as medium and long-term planning content based on infrastructure such as a given station and a given rail in a period of time. However, in order to meet the increasing demand of urban trips, new infrastructures such as stations and rails need to be continuously constructed, and therefore, the corresponding operation routes also need to be re-planned and set.
The urban rail transit line operation scheme mainly comprises two parts of main contents: firstly, setting lines, namely definitely opening the number of the lines, wherein each line comprises the number of stations and the trend thereof; and secondly, setting the starting frequency, namely determining the departure frequency of each open circuit. The total length of the operation line and the fixed cost thereof are determined by the line arrangement, and meanwhile, the total travel time and the total transfer times of passengers are influenced. The frequency of opening settings affects the cost of operation and the waiting time of passengers at the origin or transfer stations. How to balance the total operating cost of a company with the total trip cost of passengers is required to depend on the path distribution result of the passengers in the urban rail transit network.
In some operation route planning methods in the prior art, company operation cost and passenger trip cost cannot be considered at the same time, and it is difficult to couple passenger path distribution results, so that collaborative optimization of route design, frequency setting and passenger distribution cannot be realized. Therefore, how to formulate an operation route planning method to ensure that the total trip demand of the passengers can be ensured while the operation cost of the company is reduced, and the high-quality trip demand of short trip time and less transfer of the passengers is realized is a problem to be solved urgently.
Disclosure of Invention
The embodiment of the invention provides a rail transit operation line and frequency collaborative optimization method considering passenger flow distribution, and aims to overcome the problems in the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme.
A rail transit line of operation and frequency collaborative optimization method considering passenger flow distribution comprises the following steps:
step S1, generating urban rail transit operation network connectivity constraint conditions according to the urban rail transit physical network and the passing interval information of the candidate operation routes;
step S2, generating maximum and minimum operation frequency constraint conditions of a single operation line and maximum total operation frequency constraint conditions of all operation lines in an interval according to the safe departure interval information of the single operation line and the interval;
step S3, generating passenger path distribution constraint conditions according to information such as passenger candidate paths;
step S4, generating whether the operation scheme meets the constraint condition of the passenger allocation result according to the urban rail transit operation line, the operation frequency and the passenger path allocation information;
step S5, generating a target function based on weighted urban rail transit operation cost and passenger trip cost according to the urban rail transit operation route, the operation frequency and the passenger path distribution information;
step S6, forming a constraint set from all the above constraints, where the constraint set includes: the method comprises the following steps of determining whether the urban rail transit operation network connectivity constraint condition, the maximum and minimum operation frequency constraint condition of a single operation line, the maximum total operation frequency constraint condition of all operation lines in an interval, the passenger path allocation constraint condition and the operation scheme meet the passenger allocation result constraint condition or not.
Establishing a mixed integer nonlinear programming model for urban rail transit operation routes and operation frequency collaborative optimization according to the constraint set and the objective function based on the weighted urban rail transit operation cost and the passenger trip cost;
and S7, solving the mixed integer nonlinear programming model for the urban rail transit operation line and the operation frequency collaborative optimization to obtain an optimized urban rail transit operation line and operation frequency scheme.
Preferably, the step S1 specifically includes the following steps:
s11: representing the urban rail transit physical network interval set as A; the urban rail transit candidate operation route set is represented as M;
s12: using a correlation matrix
Figure BDA0002683409690000031
The method comprises the steps of representing whether a candidate operation line M belongs to M and passes through a section a belongs to A, if so, the candidate operation line M belongs to M and passes through the section a
Figure BDA0002683409690000032
Otherwise, then
Figure BDA0002683409690000033
S13: the connectivity constraint condition of the urban rail transit operation network is represented as follows:
Figure BDA0002683409690000034
wherein x ismThe decision variables represent whether the urban rail transit candidate operation route M belongs to M and is operated in the final operation scheme; when x ismWhen 1, it represents open; when x ismWhen not equal to 1, no line is opened.
Preferably, the step S2 specifically includes the following steps:
s21: the maximum and minimum operating frequency constraints of the single operating line are expressed as:
Figure BDA0002683409690000035
Figure BDA0002683409690000036
wherein the content of the first and second substances,
Figure BDA0002683409690000037
and
Figure BDA0002683409690000038
respectively representing the maximum and minimum running frequency of the urban rail transit candidate operation line M belonging to M;
fmthe decision variable represents the running frequency of the urban rail transit candidate operation line M belonging to M;
s22: the maximum total open frequency constraint condition of all the operation lines in the interval is represented as follows:
Figure BDA0002683409690000039
wherein the content of the first and second substances,
Figure BDA00026834096900000310
and the maximum driving frequency of the urban rail transit physical network interval a epsilon A is represented.
Preferably, the step S3 specifically includes the following steps:
the passenger path assignment constraint is expressed as:
Figure BDA00026834096900000311
Figure BDA00026834096900000312
wherein the set N represents the set of urban rail transit stations, and the set KrsRepresenting all candidate path sets of passengers from the station r to the station s to the station N in the urban rail transit physical network;
Figure BDA0002683409690000041
the decision variable represents whether the passenger goes from the station r to the station s to the station M to the candidate operation line M when the passenger uses the candidate operation line M to the station r to the station s to the station M
Figure BDA0002683409690000042
When, use is indicated; when in use
Figure BDA0002683409690000043
When, it is not used;
Figure BDA0002683409690000044
the decision variable represents whether the passenger goes from the station r to the station s to the candidate path KrsWhen is coming into contact with
Figure BDA0002683409690000045
When, it indicates that it is allocated; when in use
Figure BDA0002683409690000046
And (4) indicating that the passenger is not allocated, and each passenger can be allocated to only one candidate path.
Preferably, the step S4 specifically includes the following steps:
s41: the constraint condition for matching the urban rail transit operation line scheme and the passenger path distribution is expressed as follows:
Figure BDA0002683409690000047
s42: the constraint conditions for matching the urban rail transit operation frequency scheme with the passenger path distribution are represented as follows:
Figure BDA0002683409690000048
wherein the parameter drsRepresenting passenger demands from station r e N to station s e N;
parameter(s)
Figure BDA0002683409690000049
The kth ∈ K indicating that the passenger goes from the station r ∈ N to the station s ∈ NrsWhether the candidate path passes through the interval a ∈ A or not, when
Figure BDA00026834096900000410
When, it means passing; when in use
Figure BDA00026834096900000411
When, it means not going through;
the parameter W represents the passenger carrying capacity per train of urban rail transit.
Preferably, the step S5 specifically includes the following steps:
s51: according to the urban rail transit operation line, the operation frequency and the passenger path distribution information, a target function based on weighted urban rail transit operation cost is generated and is expressed as follows:
Figure BDA00026834096900000412
wherein the parameter cfixRepresents the fixed cost of the operating line per unit length;
parameter laThe length of an urban rail transit physical network interval a belonging to A is represented;
parameter cm,fRepresenting the operation cost of the operation line M belonging to M for single operation;
s52: generating an objective function based on the weighted passenger travel costs, expressed as:
Figure BDA0002683409690000051
wherein the parameters
Figure BDA0002683409690000052
And represents the average speed of the running of the urban rail transit train.
Preferably, the mixed integer nonlinear programming model for the urban rail transit service line and the operation frequency collaborative optimization in the step S6 is represented as:
Figure BDA0002683409690000053
subject to
Figure BDA0002683409690000054
Figure BDA0002683409690000055
Figure BDA0002683409690000056
Figure BDA0002683409690000057
Figure BDA0002683409690000058
Figure BDA0002683409690000059
Figure BDA00026834096900000510
Figure BDA00026834096900000511
Figure BDA00026834096900000512
Figure BDA00026834096900000513
Figure BDA00026834096900000514
Figure BDA00026834096900000515
wherein, the parameters alpha, beta and gamma are weight coefficients;
the objective function of the mixed integer nonlinear programming model is to minimize the total operation cost of urban rail transit operation cost and minimize the passenger trip cost.
Preferably, the optimized urban rail transit service line and operation frequency plan in the step S7 includes the decision variable xmDecision variable fmDecision variables
Figure BDA0002683409690000061
Decision variables
Figure BDA0002683409690000062
The values of (1) include which candidate operation lines should be operated, how much frequency of the operated operation lines should be set, and the passenger path allocation result.
According to the technical scheme provided by the embodiment of the invention, the method provided by the embodiment of the invention comprehensively considers the practical factors such as the connectivity of the urban rail transit operation network, the passenger path distribution, the safe departure interval and the like, and can adapt to the change and the dynamically changed passenger flow of the urban rail transit physical network and improve the service efficiency and the level of the urban rail transit by optimizing the urban rail transit operation line and the operation frequency thereof.
Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
Fig. 1 is a flowchart of a method for collaborative optimization of urban rail transit operation routes and operation frequency in consideration of passenger path allocation according to the present invention.
Fig. 2 is a topological structure diagram of an urban rail transit physical network in the embodiment of the present invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals refer to the same or similar elements or elements having the same or similar function throughout. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
As used herein, the singular forms "a", "an", "the" and "the" are intended to include the plural forms as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprises" and/or "comprising," when used in this specification, specify the presence of stated features, integers, steps, operations, elements, and/or components, but do not preclude the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof. It will be understood that when an element is referred to as being "connected" or "coupled" to another element, it can be directly connected or coupled to the other element or intervening elements may also be present. Further, "connected" or "coupled" as used herein may include wirelessly connected or coupled. As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
For the convenience of understanding the embodiments of the present invention, the following description will be further explained by taking several specific embodiments as examples in conjunction with the drawings, and the embodiments are not to be construed as limiting the embodiments of the present invention.
Example one
The invention provides a collaborative optimization method for an operation route and an operation frequency in the field of urban rail transit operation management considering passenger path distribution, which can utilize a route operation scheme based on a mixed integer nonlinear programming model, so that the total company operation cost and the total passenger trip cost can be balanced while the passenger trip requirement is met. The method can comprehensively consider the practical factors of the connectivity of an operation network, the passenger path distribution, the safe departure interval and the like, and is completely close to the practical environment. The urban rail transit operation service level and efficiency can be improved, and the traveling satisfaction of passengers is enhanced.
The processing flow of the urban rail transit operation line and operation frequency collaborative optimization method considering passenger path distribution provided by the embodiment of the invention is shown in figure 1, and comprises the following processing steps:
step S1, generating urban rail transit operation network connectivity constraint conditions according to the input information of the urban rail transit physical network, the passing intervals of the candidate operation routes and the like;
step S2, generating maximum and minimum operation frequency constraint conditions of a single operation line and maximum total operation frequency constraint conditions of all operation lines in an interval according to the input information of the single operation line, the safe departure interval of the interval and the like;
step S3, generating passenger path distribution constraint conditions according to the input information such as the passenger candidate paths;
step S4, generating whether the operation scheme meets the constraint condition of the passenger allocation result according to the information of the urban rail transit operation line, the operation frequency, the passenger path allocation and the like;
step S5, generating a target function based on weighted urban rail transit operation cost and passenger trip cost according to the information of urban rail transit operation routes, operation frequency, passenger path distribution and the like;
step S6, forming a constraint set from all the above constraints, where the constraint set includes: the method comprises the following steps of determining whether the urban rail transit operation network connectivity constraint condition, the maximum and minimum operation frequency constraint condition of a single operation line, the maximum total operation frequency constraint condition of all operation lines in an interval, the passenger path allocation constraint condition and the operation scheme meet the passenger allocation result constraint condition or not.
Establishing a mixed integer nonlinear programming model for the urban rail transit operation line and the operation frequency collaborative optimization according to the constraint set and the objective function;
and S7, solving the mixed integer nonlinear programming model to obtain an optimized urban rail transit operation line and operation frequency scheme. The non-linear term in the original model exists in the passenger waiting time of the objective function and is a form of dividing a binary variable by a continuous variable. When a binary variable
Figure BDA0002683409690000081
Then, the non-linear term is also 0; when a binary variable
Figure BDA0002683409690000091
When the non-linear term is 1/fmIs a convex function. Therefore, the original model is converted into a mixed integer linear programming by using an external approximation method and adopting a cluster of linear function to approximate a convex function, and the existing commercial software is used for solving.
The step S1 specifically includes the following steps:
s11: representing the urban rail transit physical network interval set as A; the set of urban rail transit candidate operation routes is denoted as M. The interval a epsilon A represents a connection channel between adjacent stations.
S12: in order to represent the passing section condition of the candidate operation line of the urban rail transit, the incidence matrix is used
Figure BDA0002683409690000092
The method comprises the steps of representing whether a candidate operation line M belongs to M and passes through a section a belongs to A, if so, the candidate operation line M belongs to M and passes through the section a
Figure BDA0002683409690000093
Otherwise, then
Figure BDA0002683409690000094
S13: the connectivity constraint condition of the urban rail transit operation network is represented as follows:
Figure BDA0002683409690000095
wherein x ismThe decision variables represent whether the urban rail transit candidate operation route M belongs to M and is operated in the final operation scheme; when x ismWhen 1, it represents open; when x ismWhen not equal to 1, no line is opened.
The step S2 specifically includes the following steps:
s21: the maximum and minimum operating frequency constraints of the single operating line are expressed as:
Figure BDA0002683409690000096
Figure BDA0002683409690000097
wherein the content of the first and second substances,
Figure BDA0002683409690000098
and
Figure BDA0002683409690000099
respectively represent citiesThe rail transit candidate operation line M belongs to the maximum and minimum running frequency of M;
fmthe decision variable represents the running frequency of the urban rail transit candidate operation line M belonging to M;
s22: the maximum total operating frequency constraint condition of all the operating lines in the interval is represented as follows:
Figure BDA00026834096900000910
wherein the content of the first and second substances,
Figure BDA00026834096900000911
the maximum running frequency of the urban rail transit physical network interval a belonging to A is represented;
the step S3 specifically includes the following steps:
the passenger path assignment constraint is expressed as
Figure BDA0002683409690000101
Figure BDA0002683409690000102
Wherein the set N represents the set of urban rail transit stations, and the set KrsRepresenting all candidate path sets of passengers from the station r to the station s to the station N in the urban rail transit physical network;
Figure BDA0002683409690000103
the decision variable represents whether the passenger goes from the station r to the station s to the station M to the candidate operation line M when the passenger uses the candidate operation line M to the station r to the station s to the station M
Figure BDA0002683409690000104
When, use is indicated; when in use
Figure BDA0002683409690000105
When, it is not used;
Figure BDA0002683409690000106
the decision variable represents whether the passenger goes from the station r to the station s to the candidate path KrsWhen is coming into contact with
Figure BDA0002683409690000107
When, it indicates that it is allocated; when in use
Figure BDA0002683409690000108
Time, indicates not allocated. In addition, each passenger can only be assigned to one candidate route.
The step S4 specifically includes the following steps:
s41: the constraint condition for matching the urban rail transit operation line scheme with the passenger path distribution can be expressed as
Figure BDA0002683409690000109
S42: the constraint condition of matching the urban rail transit operation frequency scheme with the passenger path distribution can be expressed as
Figure BDA00026834096900001010
Wherein the parameter drsRepresenting passenger demands from station r e N to station s e N;
parameter(s)
Figure BDA00026834096900001011
The kth ∈ K indicating that the passenger goes from the station r ∈ N to the station s ∈ NrsWhether the candidate path passes through the interval a ∈ A or not, when
Figure BDA00026834096900001012
When it is used, it means passing, and vice versa,
Figure BDA00026834096900001013
when, it means not going through;
the parameter W represents the passenger carrying capacity per train of urban rail transit.
The step S5 specifically includes the following steps:
s51: the operation cost of the urban rail transit line can be expressed as
Figure BDA0002683409690000111
Wherein the parameter cfixRepresents the fixed cost of the operating line per unit length;
parameter laThe length of an urban rail transit physical network interval a belonging to A is represented;
parameter cm,fRepresenting the operation cost of the operation line M belonging to M for single operation;
s52: the passenger trip cost can be expressed as
Figure BDA0002683409690000112
Wherein the parameters
Figure BDA0002683409690000113
And represents the average speed of the running of the urban rail transit train.
The mixed integer nonlinear programming model for the urban rail transit service route and the operation frequency collaborative optimization in the step S6 is represented as:
Figure BDA0002683409690000114
subject to
Figure BDA0002683409690000115
Figure BDA0002683409690000116
Figure BDA0002683409690000117
Figure BDA0002683409690000118
Figure BDA0002683409690000119
Figure BDA00026834096900001110
Figure BDA00026834096900001111
Figure BDA00026834096900001112
Figure BDA00026834096900001113
Figure BDA0002683409690000121
Figure BDA0002683409690000122
Figure BDA0002683409690000123
wherein, the parameters alpha, beta and gamma are weight coefficients;
the objective function of the mixed integer nonlinear programming model is to minimize the total operation cost of urban rail transit operation cost and minimize the passenger trip cost.
Solving the mixed integer nonlinear programming model to obtain an optimized urban rail transit operation line and operation frequency scheme, wherein the scheme comprises the decision variable xmDecision variable fmDecision variables
Figure BDA0002683409690000124
Decision variables
Figure BDA0002683409690000125
The values of (1) include which candidate operation lines should be operated, how much frequency of the operated operation lines should be set, and the passenger path allocation result.
Example two
The embodiment provides an urban rail transit operation line and operation frequency collaborative optimization method considering passenger path distribution, which comprises the following steps;
s1, in this embodiment, the information of the topology structure of the urban rail transit physical network, such as the stations and the intervals, is shown in fig. 2, and includes 44 stations and 52 intervals, and the information of the given candidate operation route is shown in table 1 below:
TABLE 1
Figure BDA0002683409690000126
Figure BDA0002683409690000131
Generating connectivity constraint of the urban rail transit operation network according to the urban rail transit physical network and the candidate operation line information, wherein the specific implementation process is as follows;
s11: representing the urban rail transit physical network interval set as A; and representing the urban rail transit candidate operation route set as M.
S12: in order to represent the situation that the candidate operation line of urban rail transit passes through the interval, the incidence matrix is used
Figure BDA0002683409690000132
The method comprises the steps of representing whether a candidate operation line M belongs to M and passes through a section a belongs to A, if so, the candidate operation line M belongs to M and passes through the section a
Figure BDA0002683409690000133
Otherwise, it is 0.
S13: the connectivity constraint condition of the urban rail transit operation network is represented as follows:
Figure BDA0002683409690000134
wherein x ismThe decision variables represent whether the urban rail transit candidate operation route M belongs to M and is operated in the final operation scheme; when x ismWhen 1, it indicates "on", and when xmWhen not equal to 1, no line is opened.
S2, generating maximum and minimum operation frequency constraint conditions of a single operation line and maximum total operation frequency constraint conditions of all operation lines in an interval according to the input information of the single operation line, the safe departure interval of the interval and the like, wherein the specific implementation process is as follows;
s21: the maximum and minimum operating frequency constraints of the single operating line are expressed as:
Figure BDA0002683409690000135
Figure BDA0002683409690000141
wherein the content of the first and second substances,
Figure BDA0002683409690000142
and
Figure BDA0002683409690000143
respectively representing the maximum and minimum running frequency of the urban rail transit candidate operation line M belonging to M;
fmthe decision variable represents the running frequency of the urban rail transit candidate operation line M belonging to M;
s22: the maximum total open frequency constraint of all the operation lines in the interval is represented as:
Figure BDA0002683409690000144
wherein the content of the first and second substances,
Figure BDA0002683409690000145
and the maximum driving frequency of the urban rail transit physical network interval a epsilon A is represented.
S3, generating passenger path distribution constraint conditions according to the input information such as the passenger candidate paths, and the specific implementation process is as follows;
the passenger routing constraints are expressed as
Figure BDA0002683409690000146
Figure BDA0002683409690000147
Wherein the set N represents the set of urban rail transit stations, and the set KrsRepresenting all candidate path sets of passengers from the station r to the station s to the station N in the urban rail transit physical network;
Figure BDA0002683409690000148
the decision variable represents whether the passenger goes from the station r to the station s to the station M to the candidate operation line M when the passenger uses the candidate operation line M to the station r to the station s to the station M
Figure BDA0002683409690000149
When, use is indicated; when in use
Figure BDA00026834096900001410
When, it is not used;
Figure BDA00026834096900001411
the decision variable represents whether the passenger goes from the station r to the station s to the candidate path KrsWhen is coming into contact with
Figure BDA00026834096900001412
When, it indicates that it is allocated; when in use
Figure BDA00026834096900001413
The representation is not assigned, and each passenger can only be assigned to one candidate route.
S4, generating whether an operation scheme meets the constraint condition of a passenger allocation result according to the information of urban rail transit operation lines, operation frequency, passenger path allocation and the like, wherein the specific implementation process is as follows;
s41: the constraint condition for matching the urban rail transit operation line scheme with the passenger path distribution can be expressed as
Figure BDA00026834096900001414
S42: the constraint condition of matching the urban rail transit operation frequency scheme with the passenger path distribution can be expressed as
Figure BDA0002683409690000151
Wherein the parameter drsRepresenting passenger demands from station r e N to station s e N;
parameter(s)
Figure BDA0002683409690000152
The kth ∈ K indicating that the passenger goes from the station r ∈ N to the station s ∈ NrsWhether the candidate path passes through the interval a ∈ A or not, when
Figure BDA0002683409690000153
When it is used, it means passing, and vice versa,
Figure BDA0002683409690000154
when, it means not going through;
the parameter W represents the passenger carrying capacity per train of urban rail transit.
S5, generating an objective function based on weighted urban rail transit operation cost and passenger trip cost according to the information of urban rail transit operation lines, operation frequency, passenger path distribution and the like
S51: the urban rail transit line operation cost based on weighting can be expressed as
Figure BDA0002683409690000155
Wherein the parameter cfixRepresents the fixed cost of the operating line per unit length;
parameter laThe length of an urban rail transit physical network interval a belonging to A is represented;
parameter cm,fRepresenting the operation cost of the operation line M belonging to M for single operation;
s52: the weighting-based passenger travel cost can be expressed as
Figure BDA0002683409690000156
Wherein the parameters
Figure BDA0002683409690000157
And represents the average speed of the running of the urban rail transit train.
S6, establishing a mixed integer nonlinear programming model for urban rail transit operation lines and operation frequency collaborative optimization according to the constraint set and the objective function, wherein the specific implementation process is as follows;
Figure BDA0002683409690000161
subject to
Figure BDA0002683409690000162
Figure BDA0002683409690000163
Figure BDA0002683409690000164
Figure BDA0002683409690000165
Figure BDA0002683409690000166
Figure BDA0002683409690000167
Figure BDA0002683409690000168
Figure BDA0002683409690000169
Figure BDA00026834096900001610
Figure BDA00026834096900001611
Figure BDA00026834096900001612
Figure BDA00026834096900001613
wherein, the parameters alpha, beta and gamma are weight coefficients;
the objective function is to minimize the weighted total operating cost and the passenger trip cost.
S7, solving the mixed integer nonlinear programming model to obtain an optimized urban rail transit operation line and operation frequency scheme as shown in the following table 2
TABLE 2
Figure BDA00026834096900001614
Figure BDA0002683409690000171
The invention can obtain the urban rail transit operation line and the operation frequency result thereof, and can also obtain the passenger path distribution result, thereby calculating the total operation cost and the total trip cost of the passengers, and the relationship between the total operation cost and the total trip cost of the passengers can be balanced according to different weight coefficient settings, as shown in the following table 3:
table 3:
Figure BDA0002683409690000172
Figure BDA0002683409690000181
in summary, the method of the embodiment of the invention comprehensively considers practical factors such as urban rail transit operation network connectivity, passenger path allocation, safe departure intervals and the like, and optimizes the urban rail transit operation lines and the operation frequency thereof, so that the method not only can adapt to the change of the urban rail transit physical network and the dynamically changed passenger flow, but also can improve the service efficiency and level of the urban rail transit. In addition, the total company operation cost and the total passenger trip cost are balanced, the in-car time, waiting time and transfer times of passengers can be effectively controlled, so that the convenience and satisfaction of passengers riding urban rail transit trip are improved to a great extent, the urban rail transit trip system is closer to the practical problem, and the practical application value is improved.
Those of ordinary skill in the art will understand that: the figures are merely schematic representations of one embodiment, and the blocks or flow diagrams in the figures are not necessarily required to practice the present invention.
From the above description of the embodiments, it is clear to those skilled in the art that the present invention can be implemented by software plus necessary general hardware platform. Based on such understanding, the technical solutions of the present invention may be embodied in the form of a software product, which may be stored in a storage medium, such as ROM/RAM, magnetic disk, optical disk, etc., and includes instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute the method according to the embodiments or some parts of the embodiments.
The embodiments in the present specification are described in a progressive manner, and the same and similar parts among the embodiments are referred to each other, and each embodiment focuses on the differences from the other embodiments. In particular, for apparatus or system embodiments, since they are substantially similar to method embodiments, they are described in relative terms, as long as they are described in partial descriptions of method embodiments. The above-described embodiments of the apparatus and system are merely illustrative, and the units described as separate parts may or may not be physically separate, and the parts displayed as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of the present embodiment. One of ordinary skill in the art can understand and implement it without inventive effort.
The above description is only for the preferred embodiment of the present invention, but the scope of the present invention is not limited thereto, and any changes or substitutions that can be easily conceived by those skilled in the art within the technical scope of the present invention are included in the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (8)

1. A rail transit operation line and frequency collaborative optimization method considering passenger flow distribution is characterized by comprising the following steps:
step S1, generating urban rail transit operation network connectivity constraint conditions according to the urban rail transit physical network and the passing interval information of the candidate operation routes;
step S2, generating maximum and minimum operation frequency constraint conditions of a single operation line and maximum total operation frequency constraint conditions of all operation lines in an interval according to the safe departure interval information of the single operation line and the interval;
step S3, generating passenger path distribution constraint conditions according to information such as passenger candidate paths;
step S4, generating whether the operation scheme meets the constraint condition of the passenger allocation result according to the urban rail transit operation line, the operation frequency and the passenger path allocation information;
step S5, generating a target function based on weighted urban rail transit operation cost and passenger trip cost according to the urban rail transit operation route, the operation frequency and the passenger path distribution information;
step S6, forming a constraint set from all the above constraints, where the constraint set includes: the method comprises the following steps of determining whether the urban rail transit operation network connectivity constraint condition, the maximum and minimum operation frequency constraint condition of a single operation line, the maximum total operation frequency constraint condition of all operation lines in an interval, the passenger path allocation constraint condition and the operation scheme meet the passenger allocation result constraint condition or not.
Establishing a mixed integer nonlinear programming model for urban rail transit operation routes and operation frequency collaborative optimization according to the constraint set and the objective function based on the weighted urban rail transit operation cost and the passenger trip cost;
and S7, solving the mixed integer nonlinear programming model for the urban rail transit operation line and the operation frequency collaborative optimization to obtain an optimized urban rail transit operation line and operation frequency scheme.
2. The method according to claim 1, wherein the step S1 specifically comprises the steps of:
s11: representing the urban rail transit physical network interval set as A; the urban rail transit candidate operation route set is represented as M;
s12: using a correlation matrix
Figure FDA0002683409680000021
The method comprises the steps of representing whether a candidate operation line M belongs to M and passes through a section a belongs to A, if so, the candidate operation line M belongs to M and passes through the section a
Figure FDA0002683409680000022
Otherwise, then
Figure FDA0002683409680000023
S13: the connectivity constraint condition of the urban rail transit operation network is represented as follows:
Figure FDA0002683409680000024
wherein x ismThe decision variables represent whether the urban rail transit candidate operation route M belongs to M and is operated in the final operation scheme; when x ismWhen 1, it represents open; when x ismWhen not equal to 1, no line is opened.
3. The method according to claim 2, wherein the step S2 specifically comprises the steps of:
s21: the maximum and minimum operating frequency constraints of the single operating line are expressed as:
Figure FDA0002683409680000025
Figure FDA0002683409680000026
wherein the content of the first and second substances,
Figure FDA0002683409680000027
and
Figure FDA0002683409680000028
respectively representing the maximum and minimum running frequency of the urban rail transit candidate operation line M belonging to M;
fmthe decision variable represents the running frequency of the urban rail transit candidate operation line M belonging to M;
s22: the maximum total open frequency constraint condition of all the operation lines in the interval is represented as follows:
Figure FDA0002683409680000029
wherein the content of the first and second substances,
Figure FDA00026834096800000210
and the maximum driving frequency of the urban rail transit physical network interval a epsilon A is represented.
4. The method according to claim 1, wherein the step S3 specifically includes the following steps:
the passenger path assignment constraint is expressed as:
Figure FDA00026834096800000211
Figure FDA0002683409680000031
wherein the set N represents the set of urban rail transit stations, and the set KrsRepresenting all candidate path sets of passengers from the station r to the station s to the station N in the urban rail transit physical network;
Figure FDA0002683409680000032
the decision variable represents whether the passenger goes from the station r to the station s to the station M to the candidate operation line M when the passenger uses the candidate operation line M to the station r to the station s to the station M
Figure FDA0002683409680000033
When, use is indicated; when in use
Figure FDA0002683409680000034
When, it is not used;
Figure FDA0002683409680000035
the decision variable represents whether the passenger goes from the station r to the station s to the candidate path KrsWhen is coming into contact with
Figure FDA0002683409680000036
When, it indicates that it is allocated; when in use
Figure FDA0002683409680000037
And (4) indicating that the passenger is not allocated, and each passenger can be allocated to only one candidate path.
5. The method according to claim 1, wherein the step S4 specifically comprises the steps of:
s41: the constraint condition for matching the urban rail transit operation line scheme and the passenger path distribution is expressed as follows:
Figure FDA0002683409680000038
s42: the constraint conditions for matching the urban rail transit operation frequency scheme with the passenger path distribution are represented as follows:
Figure FDA0002683409680000039
wherein the parameter drsRepresenting passenger demands from station r e N to station s e N;
parameter(s)
Figure FDA00026834096800000310
The kth ∈ K indicating that the passenger goes from the station r ∈ N to the station s ∈ NrsWhether the candidate path passes through the interval a ∈ A or not, when
Figure FDA00026834096800000311
When, it means passing; when in use
Figure FDA00026834096800000312
When, it means not going through;
the parameter W represents the passenger carrying capacity per train of urban rail transit.
6. The method according to claim 1, wherein the step S5 specifically comprises the steps of:
s51: according to the urban rail transit operation line, the operation frequency and the passenger path distribution information, a target function based on weighted urban rail transit operation cost is generated and is expressed as follows:
Figure FDA0002683409680000041
wherein the parameter cfixRepresents the fixed cost of the operating line per unit length;
parameter laThe length of an urban rail transit physical network interval a belonging to A is represented;
parameter cm,fRepresenting the operation cost of the operation line M belonging to M for single operation;
s52: generating an objective function based on the weighted passenger travel costs, expressed as:
Figure FDA0002683409680000042
wherein the parameters
Figure FDA0002683409680000043
And represents the average speed of the running of the urban rail transit train.
7. The method according to claim 1, wherein the mixed integer nonlinear programming model for the urban rail transit service line and frequency of operation collaborative optimization in the step S6 is represented as:
Figure FDA0002683409680000044
subject to
Figure FDA0002683409680000045
Figure FDA0002683409680000046
Figure FDA0002683409680000047
Figure FDA0002683409680000048
Figure FDA0002683409680000049
Figure FDA00026834096800000410
Figure FDA00026834096800000411
Figure FDA00026834096800000412
Figure FDA00026834096800000413
Figure FDA0002683409680000051
Figure FDA0002683409680000052
Figure FDA0002683409680000053
wherein, the parameters alpha, beta and gamma are weight coefficients;
the objective function of the mixed integer nonlinear programming model is to minimize the total operation cost of urban rail transit operation cost and minimize the passenger trip cost.
8. The method according to claim 1, wherein the optimized urban rail transit service line and frequency of operation scheme in the step S7 comprises the decision variable xmDecision variable fmDecision variables
Figure FDA0002683409680000054
Decision variables
Figure FDA0002683409680000055
The values of (1) include which candidate operation lines should be operated, how much frequency of the operated operation lines should be set, and the passenger path allocation result.
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Cited By (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113408790A (en) * 2021-05-31 2021-09-17 银江股份有限公司 Modular vehicle operation path and combination strategy collaborative optimization method and system
CN113822461A (en) * 2021-07-27 2021-12-21 深圳技术大学 Track traffic cross-line operation optimization method, system, equipment and storage medium
CN115809729A (en) * 2022-11-28 2023-03-17 北京交通大学 Urban rail transit hub transfer facility optimal configuration method considering newly added lines
CN116307441A (en) * 2022-11-28 2023-06-23 北京交通大学 Urban rail transit junction transfer facility optimal configuration method considering burst scene
WO2024045727A1 (en) * 2022-08-30 2024-03-07 比亚迪股份有限公司 Line network dispatching method and apparatus, medium, and electronic device

Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140357283A1 (en) * 2013-06-04 2014-12-04 King Abdulaziz City For Science And Technology Method of optimizing location and frequency assignment of cellular base stations
CN110533219A (en) * 2019-07-24 2019-12-03 北京交通大学 The last time-table optimization method of urban track traffic
CN110648022A (en) * 2019-09-18 2020-01-03 北京工业大学 Community public transport network and departure frequency synchronous optimization method considering station full coverage for connecting subways
CN111353639A (en) * 2020-02-26 2020-06-30 北京交通大学 Urban rail transit peak current limiting optimization method for coordinating train timetable

Patent Citations (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US20140357283A1 (en) * 2013-06-04 2014-12-04 King Abdulaziz City For Science And Technology Method of optimizing location and frequency assignment of cellular base stations
CN110533219A (en) * 2019-07-24 2019-12-03 北京交通大学 The last time-table optimization method of urban track traffic
CN110648022A (en) * 2019-09-18 2020-01-03 北京工业大学 Community public transport network and departure frequency synchronous optimization method considering station full coverage for connecting subways
CN111353639A (en) * 2020-02-26 2020-06-30 北京交通大学 Urban rail transit peak current limiting optimization method for coordinating train timetable

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
李正洋;赵军;彭其渊;: "考虑多交路多编组的城市轨道线路列车交路计划优化", 铁道学报, no. 06 *

Cited By (7)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113408790A (en) * 2021-05-31 2021-09-17 银江股份有限公司 Modular vehicle operation path and combination strategy collaborative optimization method and system
CN113822461A (en) * 2021-07-27 2021-12-21 深圳技术大学 Track traffic cross-line operation optimization method, system, equipment and storage medium
WO2024045727A1 (en) * 2022-08-30 2024-03-07 比亚迪股份有限公司 Line network dispatching method and apparatus, medium, and electronic device
CN115809729A (en) * 2022-11-28 2023-03-17 北京交通大学 Urban rail transit hub transfer facility optimal configuration method considering newly added lines
CN116307441A (en) * 2022-11-28 2023-06-23 北京交通大学 Urban rail transit junction transfer facility optimal configuration method considering burst scene
CN115809729B (en) * 2022-11-28 2023-08-22 北京交通大学 Urban rail transit junction transfer facility optimal configuration method considering newly-added line
CN116307441B (en) * 2022-11-28 2023-11-03 北京交通大学 Urban rail transit junction transfer facility optimal configuration method considering burst scene

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