Urban Rail Transit Train Timetable Optimization Method and System Considering Passenger Flow Distribution

Abstract

This invention provides a method and system for optimizing urban rail transit train timetables considering passenger flow allocation, belonging to the field of urban rail transit operation management technology. This invention establishes a timetable optimization model considering both long / short routes and express / local train modes, taking into account constraints such as train intervals, train service frequencies, and train origin and destination points. With the objective of minimizing total passenger travel time and company vehicle-kilometer costs, a multi-objective timetable optimization model based on long / short routes and express / local train modes is constructed. A passenger flow allocation model is established based on passenger choice behavior analysis under express / local train operation conditions, considering the influencing factors of passenger route selection under express / local train operation and analyzing passenger route selection behavior. The invention also discusses in detail the possible transfers and choice behaviors that passengers may exhibit during their travels and establishes a passenger flow allocation model.

Description

Technical Field

[0001] This invention relates to the field of urban rail transit operation management technology, specifically to a method and system for optimizing urban rail transit train timetables that takes into account passenger flow distribution. Background Technology

[0002] As the urban rail transit network expands, its spatial and temporal distribution becomes uneven, and the station-to-station operation model often fails to fully meet the diverse travel needs of passengers. Therefore, researching express and local train operation schemes under multi-route systems can effectively match capacity and demand, saving passengers' travel time. Faced with multi-route express and local train operation models, passengers exhibit diverse travel choices. For example, passengers may decide their travel route based on the type of train stopping at their destination. Thus, train operation schemes and timetables directly impact passenger flow allocation. Consequently, to meet passenger travel needs as much as possible, the result of passenger flow allocation affects the optimization of train operation plans. Currently, to achieve synergistic optimization of these two aspects, a "two-layer model" is primarily used to address this problem. By establishing a passenger transfer network and searching for effective paths, passenger travel choices are reflected. A two-layer programming model is constructed to achieve synergistic optimization of express and local train operation schemes and passenger flow allocation results. In the upper-layer model, based on the passenger flow allocation results of the lower-layer model, the cross-sectional passenger flow is calculated. The constraint that the cross-sectional passenger flow is lower than the transport capacity is used to achieve feedback between the upper and lower-layer models. Taking the train operation scheme combining express and local trains with multiple routes as the research object, a lower-level model is established based on the generalized cost of passenger travel origin and destination. The turnaround stations of local trains, the stopping schemes of express trains, and the operating frequencies of different types of trains are optimized. The feedback between the upper and lower level models is reflected by minimizing the generalized cost of passenger travel origin and destination and minimizing the enterprise's operating costs.

[0003] Most existing research, both domestically and internationally, focuses on optimizing train timetables under the operation organization modes of express and local trains, with few studies considering more complex transportation organization modes such as express and local trains and express and local trains simultaneously. Furthermore, for the two-level programming model established to solve train operation schemes, few studies link the upper and lower level models through constraints. Summary of the Invention

[0004] The purpose of this invention is to provide an urban rail transit train timetable optimization method and system that constructs a two-level planning model combining long and short routes and express and local train modes, and reflects the feedback of the optimization results of the lower-level model to the optimization results of the upper-level model through constraints in the upper-level model, so as to solve at least one of the technical problems existing in the above-mentioned background art.

[0005] To achieve the above objectives, the present invention adopts the following technical solution:

[0006] On the one hand, the present invention provides a method for optimizing urban rail transit train timetables considering passenger flow distribution, comprising:

[0007] To minimize the total travel time for passengers and the vehicle-kilometer cost for enterprises, a multi-objective timetable optimization model based on long and short routes and express and slow train modes is constructed.

[0008] Considering the factors influencing passenger route selection under express and local train operations, this paper analyzes the possible transfers and route selection behaviors of passengers during their travels and establishes a passenger flow allocation model.

[0009] Based on the passenger flow allocation model, the average passenger waiting time is obtained and used to form a constraint on the multi-objective timetable optimization model by associating it with the departure interval through adjustable parameters; the number of trains and express stations is determined, the initial number of trains in each time period is generated, and the upper bound of the departure interval is updated.

[0010] The lower limit of train departure interval is updated based on passenger waiting time; if it exceeds the maximum departure interval, a disturbance is set.

[0011] The multi-objective timetable optimization model is solved based on the number of trains and the lower bound of the departure interval to obtain the timetable. The passenger flow allocation model is run based on the passenger flow and the solved timetable to obtain the new average passenger waiting time and update the number of trains in each time period. The process continues until the number of updates that satisfy the upper bound of the departure interval and the lower bound of the train departure interval is reached, and the final optimal timetable is output.

[0012] Furthermore, a multi-objective timetable optimization model based on long and short routes and express and local train modes is constructed. The constraints include train arrival and departure safety interval constraints, section running time constraints, train origin and destination constraints, train type and stop variable constraints, train stop constraints, non-continuous departure constraints for express trains and short routes, train service frequency constraints, and model feedback constraints.

[0013] Furthermore, the model feedback constraints include: the feedback constraints formed between the multi-objective timetable optimization model and the passenger flow allocation model.

[0014]

[0015] Where i and m are the sequence numbers of any two trains, and k is the station sequence number. Let m be the departure time of train m at station k. Let be the departure time of train i at station k. Let k be the average waiting time for passengers at station k. This indicates whether train i leaves station k earlier than train m, where M is a constant.

[0016] Furthermore, the method for determining the short-route candidate set includes: utilizing the cross-sectional passenger flow data of each section along the route { Using this as the basic data, the variance of cross-sectional passenger flow under each route scheme is calculated. This is used to determine the short-route plan candidate set { }

[0017] Furthermore, the steps for solving the candidate set of short-circuit routes are as follows:

[0018] Input the number of stations N on the line and the cross-sectional passenger flow data for each section. and the ratio of large and small routes operating. : ;

[0019] Based on the constraints, enumerate the shortest route schemes [ , The route lengths are checked, and the shorter route options that meet the constraints are retained to form an initial set of route option candidates. The constraints are as follows: ;

[0020] Calculate the variance of passenger flow cross-sections for a single long-distance route:

[0021]

[0022] Calculate the variance of passenger flow cross-sections for the route plan Including: Short-distance route sections are [ , ],Will middle Partially according to : The proportions were allocated to the long-distance and short-distance routes respectively; the passenger flow at each cross-section of the long-distance and short-distance routes was calculated separately. , Calculate the variance of passenger flow cross-sections for both large and small routes. , Calculate the mean of the cross-sectional passenger flow variance for this route plan. This will be used as an evaluation indicator for the route plan;

[0023] Traverse the initial set of alternative route plans and determine their applicability. ,Will Record the short-distance route plans and identify those that meet the criteria. Arrange the routes in ascending order and select the top 3 to form a candidate set of smaller route options. .

[0024] Further analysis of passenger route selection behavior includes:

[0025] Trains are divided into two types: express trains and local trains. Local trains have two arrival scenarios: direct to the destination station or not direct to the destination station. Express trains include the station before the destination station and the station after the destination station. When an express train goes directly to the station before or after the destination station, passengers may take the express train first and then transfer to a local train.

[0026] The probability of route selection is calculated using a multinomial Logit model:

[0027]

[0028] in It is the passenger who chooses the route The probability, It is the passenger's choice of route The waiting time It is the passenger's choice of route The time spent in the car Representative path Does a transfer exist? If so, set the value to 1. , and It is the regression coefficient.

[0029] Secondly, the present invention provides an urban rail transit train timetable optimization system that considers passenger flow distribution, comprising:

[0030] The first building module is used to construct a multi-objective timetable optimization model based on long and short routes and express and slow train modes, with the goal of minimizing the total travel time of passengers and the cost per vehicle kilometer for enterprises.

[0031] The second construction module is used to consider the influencing factors of passenger route selection under express and local train operations, analyze the possible transfers and route selection behaviors of passengers during the travel process, and establish a passenger flow allocation model.

[0032] The update module is used to obtain the average passenger waiting time based on the passenger flow distribution model, and form a constraint on the multi-objective timetable optimization model by associating it with the departure interval through adjustable parameters; determine the number of trains and express stations, generate the initial number of trains for each time period, and update the upper bound of the departure interval; update the lower bound of the train departure interval based on the passenger waiting time, and set a disturbance if it exceeds the maximum departure interval.

[0033] The solution module is used to solve a multi-objective timetable optimization model based on the number of trains and the lower bound of the departure interval to obtain the timetable; based on the number of passengers and the solved timetable, it runs a passenger flow allocation model to obtain a new average passenger waiting time and updates the number of trains in each time period; until the number of updates of the upper bound of the departure interval and the lower bound of the train departure interval is satisfied, the final optimal timetable is output.

[0034] Thirdly, the present invention provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the urban rail transit train timetable optimization method considering passenger flow allocation as described above.

[0035] Fourthly, the present invention provides a computer program product, including a computer program that, when run on one or more processors, is used to implement the urban rail transit train timetable optimization method considering passenger flow allocation as described above.

[0036] Fifthly, the present invention provides an electronic device, comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the urban rail transit train timetable optimization method considering passenger flow allocation as described above.

[0037] The beneficial effects of this invention are as follows: The established bi-level programming model considers both fast and slow train patterns and large and small traffic patterns. By reflecting the feedback of the optimization results of the lower-level model to the optimization results of the upper-level model through the constraints in the upper-level model, a bi-level programming model is constructed based on this feedback mechanism. It adopts a simplified approach, dividing a complex model into two upper and lower-level models, which can significantly reduce the solution time of the model while ensuring a high-quality solution.

[0038] The advantages of additional aspects of the invention will be set forth more clearly in the following description or will be learned by practice of the invention. Attached Figure Description

[0039] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0040] Figure 1 This is a functional principle block diagram of the two-layer planning model described in an embodiment of the present invention.

[0041] Figure 2 This is a flowchart of the urban rail transit train timetable optimization method considering passenger flow allocation as described in an embodiment of the present invention. Detailed Implementation

[0042] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0043] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0044] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, and / or groups thereof.

[0045] To facilitate understanding of the present invention, the present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. However, the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0046] Those skilled in the art should understand that the accompanying drawings are merely schematic diagrams of embodiments, and the components in the drawings are not necessarily essential for implementing the present invention.

[0047] Example 1

[0048] In this embodiment 1, a system for optimizing urban rail transit train timetables considering passenger flow allocation is first provided, including: a first construction module, used to construct a multi-objective timetable optimization model based on long-distance and short-distance routes and express / local train modes, with the goal of minimizing the total passenger travel time and the company's vehicle-kilometer cost; a second construction module, used to consider the influencing factors of passenger route selection under express / local train operation, analyze the possible transfers and route selection behaviors of passengers during their travel, and establish a passenger flow allocation model; and an update module, used to obtain the average passenger waiting time based on the passenger flow allocation model, and to construct a multi-objective timetable optimization model by associating it with the departure interval through adjustable parameters. The timetable optimization model is constrained as follows: The number of trains and express stations is determined, generating the initial number of trains for each time period, and updating the upper bound of the departure interval; the lower bound of the train departure interval is updated based on passenger waiting time, and a perturbation is set if the maximum departure interval is exceeded; a solution module is used to solve the multi-objective timetable optimization model based on the number of trains and the lower bound of the departure interval to obtain the timetable; a passenger flow allocation model is run based on passenger flow and the solved timetable to obtain a new average passenger waiting time, and the number of trains for each time period is updated; the process continues until the upper and lower bounds of the departure interval are satisfied, and the final optimal timetable is output.

[0049] In this embodiment 1, the above-described system is used to implement a method for optimizing urban rail transit train timetables that takes into account passenger flow distribution.

[0050] Among them, a multi-objective timetable optimization model based on long and short routes and express and slow train modes is constructed. The constraints include train arrival and departure safety interval constraints, section running time constraints, train origin and destination constraints, train type and stop variable constraints, train stop constraints, non-continuous departure constraints for express trains and short routes, train service frequency constraints, and model feedback constraints.

[0051] The model feedback constraints include the constraints formed by the feedback between the multi-objective timetable optimization model and the passenger flow allocation model.

[0052]

[0053] Where i and m are the sequence numbers of any two trains, and k is the station sequence number. Let m be the departure time of train m at station k. Let be the departure time of train i at station k. Let k be the average waiting time for passengers at station k. This indicates whether train i leaves station k earlier than train m, where M is a constant.

[0054] The methods for determining the short-route candidate set include: utilizing the cross-sectional passenger flow of each section along the route { Using this as the basic data, the variance of cross-sectional passenger flow under each route scheme is calculated. This is used to determine the short-route plan candidate set { }

[0055] The steps for solving the short-routes candidate set are as follows:

[0056] Input the number of stations N on the line and the cross-sectional passenger flow data for each section. and the ratio of large and small routes operating. : ;

[0057] Based on the constraints, enumerate the shortest route schemes [ , The route lengths are checked, and the shorter route options that meet the constraints are retained to form an initial set of route option candidates. The constraints are as follows: ;

[0058] Calculate the variance of passenger flow cross-sections for a single long-distance route:

[0059]

[0060] Calculate the variance of passenger flow cross-sections for the route plan Including: Short-distance route sections are [ , ],Will middle Partially according to : The proportions were allocated to the long-distance and short-distance routes respectively; the passenger flow at each cross-section of the long-distance and short-distance routes was calculated separately. , Calculate the variance of passenger flow cross-sections for both large and small routes. , Calculate the mean of the cross-sectional passenger flow variance for this route plan. This will be used as an evaluation indicator for the route plan;

[0061] Traverse the initial set of alternative route plans and determine their applicability. ,Will Record the short-distance route plans and identify those that meet the criteria. Arrange the routes in ascending order and select the top 3 to form a candidate set of smaller route options. .

[0062] Passenger route selection behavior analysis includes:

[0063] Trains are divided into two types: express trains and local trains. Local trains have two arrival scenarios: direct to the destination station or not direct to the destination station. Express trains include the station before the destination station and the station after the destination station. When an express train goes directly to the station before or after the destination station, passengers may take the express train first and then transfer to a local train.

[0064] The probability of route selection is calculated using a multinomial Logit model:

[0065]

[0066] in It is the passenger who chooses the route The probability, It is the passenger's choice of route The waiting time It is the passenger's choice of route The time spent in the car Representative path Does a transfer exist? If so, set the value to 1. , and It is the regression coefficient.

[0067] Example 2

[0068] like Figure 1 As shown in Example 2, a train timetable optimization method is proposed, which simultaneously considers both express and local train operation modes as well as long-distance and short-distance train operation modes. Specific research content includes: establishing a timetable optimization model considering both long-distance and express / local train modes, taking into account constraints such as train intervals, train service frequencies, and train origin and destination points, with the objective of minimizing total passenger travel time and company vehicle-kilometer costs; constructing a multi-objective timetable optimization model based on long-distance and express / local train modes; establishing a passenger flow allocation model based on passenger choice behavior analysis under express / local train operation conditions, considering the influencing factors of passenger route selection under express / local train operation, and analyzing passenger route selection behavior; and discussing in detail the possible transfers and choices passengers may make during their travels, and establishing a passenger flow allocation model.

[0069] In this embodiment, it is assumed that all express trains adopt the same stopping scheme, express trains pass slow trains without stopping at stations, all trains use the same model, and multi-formation trains are not considered.

[0070] Symbol explanation:

[0071] (1) Set

[0072] Train assembly,

[0073] Meet at the station.

[0074] Meet at the turnaround station

[0075] Meeting point for express trains at designated stops

[0076] (2) Index

[0077] Train Index

[0078] Station Index

[0079] (3) Parameters

[0080] Minimum train departure interval

[0081] Minimum train arrival interval

[0082] :train In the interval Interval running time

[0083] Minimum train stopping time

[0084] Interval length

[0085] Total passenger time on the train

[0086] Total passenger waiting time

[0087] , The weights of passengers and businesses in the objective function

[0088] (4) Variables

[0089] :train At the station Arrival time

[0090] :train At the station Departure time

[0091] : 0-1 variable, train At the station Whether to stop

[0092] : 0-1 variable, train Was it earlier than the train? Leaving the station If yes, it is 1; otherwise, it is 0.

[0093] : 0-1 variable, train Are the starting and ending points the same? If yes, it is 1; otherwise, it is 0.

[0094] : 0-1 variable, train Is it an express train?

[0095] : 0-1 variable, train Is it a slow train on a short route?

[0096] Objective function:

[0097] The optimization goals of urban rail transit operation organization are geared towards two main entities: the demand side and the supply side. The goal is to minimize passenger travel time and reduce enterprise operating costs.

[0098] In a multi-route express and local train transport organization model, the operation of express trains can increase passenger travel speed and save travel time for passengers traveling long distances; however, passengers at stations not covered by local trains or stations not visited by express trains experience relatively longer waiting times. Therefore, the transport organization of multi-route express and local trains must coordinate the overall travel efficiency of passengers across all stations to achieve the shortest total travel time for all passengers. Ultimately, the passenger's goal can be expressed as:

[0099] .

[0100] As the operating entity, urban rail transit operators must meet the diverse travel needs of passengers while also considering their own economic benefits. Enterprise costs typically consider both fixed and variable costs: fixed costs usually refer to the construction investment in the line, the cost of purchasing rolling stock, etc.; variable costs include train operating costs and station stopping costs, etc. Here, in this embodiment, we mainly consider the enterprise's variable costs, using the minimum total train operating distance as the objective function.

[0101]

[0102] The final objective function can be expressed as:

[0103]

[0104] Constraints:

[0105] (1) Train operation constraints

[0106] To ensure operational safety, various safety intervals between trains need to be established. In the time dimension, these mainly include the departure safety interval between any two trains, the arrival safety interval, and the following safety interval. Here, a train departure order variable is introduced to describe the train arrival and departure safety intervals:

[0107]

[0108]

[0109] Furthermore, the departure times of any two trains at the same station are always different, therefore:

[0110]

[0111] (2) Interval running time constraints

[0112] The travel time of a train within a section can generally be expressed as the difference between the arrival time at the next station and the departure time at the previous station:

[0113] (3) Train origin and destination constraints

[0114] Each train has one and only one distinct pair of stations as its origin and destination, and this pair of stations both belong to the originating and terminating station set. The constraint can be expressed as: ;

[0115] The station number corresponding to the train's origin station cannot be greater than the station number corresponding to the destination station, therefore:

[0116]

[0117] If a station is the originating or terminating station of a train, then the train must stop at that station. This constraint can be expressed as:

[0118]

[0119]

[0120] All trains pass through all stations outside their operating sections without stopping in the time dimension, therefore:

[0121]

[0122]

[0123] (4) Constraints on train type and station stop variables

[0124] If the train is a local train operating on a short route, it will stop at every station on the short route section, but will not stop on sections not shared with the main line. Sometimes, and It can be transformed into:

[0125]

[0126]

[0127]

[0128]

[0129] Similarly, if the train is an express train, it will stop at the mandatory stops and not at other stations.

[0130]

[0131]

[0132]

[0133]

[0134] (5) Train stopping constraints

[0135] If a train stops at a station, its dwell time must be considered. Conversely, if a train does not stop at a station, its dwell time at that station is 0. This constraint can be expressed as:

[0136]

[0137] (6) Consecutive departure constraints for express trains and short-haul routes

[0138] To ensure passenger service quality, during the study period, two express trains, two local trains on short routes, or an express train and a local train on short routes are not allowed to operate consecutively, as follows:

[0139]

[0140]

[0141]

[0142]

[0143] (7) Train service frequency constraints

[0144] The number of express trains and short-route trains should not be too large to avoid reducing the overall service level.

[0145]

[0146]

[0147] (8) Model linearization

[0148] In the train stop time constraint, there is a situation where two 0-1 variables are multiplied together, which is handled here.

[0149]

[0150]

[0151]

[0152]

[0153]

[0154] (9) Constraints for mutual feedback between upper and lower level models

[0155]

[0156] Where i and m are the sequence numbers of any two trains, and k is the station sequence number. Let m be the departure time of train m at the station. Let i be the departure time of train i at the station. Let k be the average waiting time for passengers at station k. This indicates whether train i left station k before train m, where M is a very large number.

[0157] The upper-level timetable model determines the train intervals at each station, while the lower-level model generates the average passenger waiting time at each station. To generate a timetable that is more conducive to passenger travel, at a given station, the train interval should be greater than or equal to the average passenger waiting time at that station multiplied by a certain constant. .

[0158] Once the lower-level model generates a new average passenger waiting time, the upper-level model can update departure times to meet passenger demand. It's worth noting that constants... This is a parameter that needs adjustment; it is related to passenger arrival patterns and train stopping patterns. If only trains stop at every station are running, and if passenger arrival follows a uniform distribution, then the constant... It is approximately equal to 2. This value will decrease if express or local trains or short-distance trains are operated. In addition, the number of trains should also be updated based on the average waiting time generated by the lower-level model. If the number of trains multiplied by the average departure interval is greater than the length of the study period, the upper-level model may encounter a situation where there is no feasible solution.

[0159]

[0160] Adding the above formula to the lower-level model enables updating the number of trains to be operated based on the average waiting time of passengers. Let T be the number of trains running and T be the length of the study period. This is the floor function.

[0161] Method for determining the short-route candidate set:

[0162] To avoid an excessive number of short-route schemes and an overly large solution space during the research process, some obviously unreasonable short-route schemes were first eliminated based on the cross-sectional passenger flow characteristics of the routes. The remaining short-route plans with better results were used as a candidate set for the solution process. Therefore, the candidate set of routes can be regarded as known conditions.

[0163] Utilizing the cross-sectional passenger flow of each section along the line { Using this as the basic data, the variance of cross-sectional passenger flow under each route scheme is calculated. This is used to determine the short-route plan candidate set { The solution steps are as follows:

[0164] Step 1: Input basic data

[0165] Input the number of stations N on the line and the cross-sectional passenger flow data for each section. and the ratio of large and small routes operating. : Here we take 3:1.

[0166] Step 2: Preliminary calculation of feasible short-route solutions

[0167] Based on the following constraints, we will enumerate the shortest route schemes [ , The following formula is used to check the route lengths, and the shorter route schemes that meet the constraints are retained to form the initial route scheme candidate set. .

[0168]

[0169] Step 3: Calculate the variance of passenger flow cross-sections for a single large-circuit route.

[0170]

[0171] Step 4: Calculate the variance of passenger flow cross-sections for the route plan.

[0172] (1) The short-distance section is [ , ],Will middle Partially according to : The proportions were allocated to long-haul and short-haul routes, respectively;

[0173] (2) Calculate the passenger flow at each section of the long route and the short route respectively. , ;

[0174] (3) Calculate the variance of passenger flow cross-sections for large and small routes using the following formulas respectively. , ;

[0175]

[0176]

[0177] (4) Calculate the mean of the cross-sectional passenger flow variance for this route plan. This will be used as an evaluation indicator for the route plan.

[0178] Step 5: Traverse the initial set of route selection options and perform route selection suitability assessments. ,Will Record the short-distance route plans and identify those that meet the criteria. Arrange the routes in ascending order and select the top 3 to form a candidate set of smaller route options. .

[0179] Passenger transfer behavior analysis:

[0180] When urban rail transit lines introduce express and local trains, passengers will have to choose between taking the express or local train, potentially involving transfers from an express train in the forward direction to a local train, from an express train in the reverse direction to a local train, or from a local train to an express train. The specific details are as follows:

[0181] Scenario 1: Express train transferring to a local train in the forward direction. In this case, although the express train cannot go directly to the final destination D, it can go directly to the station A before the final destination. Therefore, the passenger may first take the express train to express station A, and then transfer to the local train to reach the final destination D.

[0182] Scenario 2: Express train transfer to local train in reverse. In this case, although the express train cannot go directly to the final destination D, it can go directly to the next station after the final destination, B. Therefore, the passenger may first take the express train to express station B, and then transfer to the local train in reverse to reach the final destination D.

[0183] Scenario 3: Transferring from a local train to an express train. A transfer from a local train to an express train may occur if the following conditions are met: First, the station type of the originating station O is not required, and the destination station D is an express train stop; second, when the passenger arrives at the station platform, the first train arriving is a local train. The second train to arrive was an express train. Finally, the express train Earlier than the slow train The train arrives at terminal station D (meaning the slower train has passed before the express train reaches its destination). In this case, passengers may first take the slower train. The express train stops at station A before reaching station D, then you can transfer to another express train. Arrived at station D.

[0184] Passenger choice behavior analysis:

[0185] First, trains are divided into two types: express trains and local trains. Local trains have two arrival options: direct to the destination station (referred to as direct) or not direct to the destination station (referred to as not direct). Express trains, on the other hand, have four arrival options: direct, direct to the station before the destination station (referred to as direct to the preceding station), direct to the station after the destination station (referred to as direct to the following station), and not direct. The reason for this division is that when an express train goes directly to the preceding or following station, passengers may first take the express train and then transfer to a local train.

[0186] The probability of route selection is calculated using a multinomial Logit model, as shown in the formula below.

[0187] ;

[0188] in It is the passenger who chooses the route The probability, This is the waiting time for passengers choosing route a. It is the time the passenger spends in the vehicle when choosing route a. This indicates whether path 'a' has a transfer; if it does, the value is 1. , and It is the regression coefficient.

[0189] Passenger flow allocation model construction:

[0190] The model's main assumptions include: passengers know the timetable information of the three trains they will be arriving at after arriving at the station; when passengers transfer from an express train to a local train, the destination station must be adjacent to the transfer station; when passengers transfer from a local train to an express train, they will transfer to the express train as late as possible in order to obtain a shorter waiting time; train capacity is unlimited; consecutive express trains or consecutive short-route trains are not allowed.

[0191] Based on the above assumptions and analysis, a passenger flow allocation model for express and slow trains is constructed, and the algorithm flow is as follows: Figure 2 As shown. The input to the algorithm is: train timetable data for both the up and down lines, including train number, express / local train type, arrival and departure times at each station, and whether each station stops; and passenger flow data for different time periods, including origin and destination stations, departure time, and number of passengers.

[0192] The algorithm outputs: the allocation results for both uphill and downhill directions, including passenger number, train number, forward transfer train number, reverse transfer train number, number of passengers, waiting time, on-train time, allocation type, origin and destination stations, train type, departure time, and arrival time; the cross-sectional passenger flow calculation results, which calculate the cross-sectional passenger flow of all sections at 15-minute intervals; and the train passenger flow allocation results, which calculate the cross-sectional passenger flow of all trains in each section.

[0193] Example 3

[0194] This embodiment 3 provides a non-transitory computer-readable storage medium for storing computer instructions. When executed by a processor, the computer instructions implement the urban rail transit train timetable optimization method considering passenger flow allocation as described above. The method includes:

[0195] To minimize the total travel time for passengers and the vehicle-kilometer cost for enterprises, a multi-objective timetable optimization model based on long and short routes and express and slow train modes is constructed.

[0196] Considering the factors influencing passenger route selection under express and local train operations, this paper analyzes the possible transfers and route selection behaviors of passengers during their travels and establishes a passenger flow allocation model.

[0197] Based on the passenger flow allocation model, the average passenger waiting time is obtained and used to form a constraint on the multi-objective timetable optimization model by associating it with the departure interval through adjustable parameters; the number of trains and express stations is determined, the initial number of trains in each time period is generated, and the upper bound of the departure interval is updated.

[0198] The lower limit of train departure interval is updated based on passenger waiting time; if it exceeds the maximum departure interval, a disturbance is set.

[0199] The multi-objective timetable optimization model is solved based on the number of trains and the lower bound of the departure interval to obtain the timetable. The passenger flow allocation model is run based on the passenger flow and the solved timetable to obtain the new average passenger waiting time and update the number of trains in each time period. The process continues until the number of updates that satisfy the upper bound of the departure interval and the lower bound of the train departure interval is reached, and the final optimal timetable is output.

[0200] Example 4

[0201] This embodiment 4 provides a computer program product, including a computer program that, when run on one or more processors, implements the urban rail transit train timetable optimization method considering passenger flow allocation as described above. The method includes:

[0202] To minimize the total travel time for passengers and the vehicle-kilometer cost for enterprises, a multi-objective timetable optimization model based on long and short routes and express and slow train modes is constructed.

[0203] Considering the factors influencing passenger route selection under express and local train operations, this paper analyzes the possible transfers and route selection behaviors of passengers during their travels and establishes a passenger flow allocation model.

[0204] Based on the passenger flow allocation model, the average passenger waiting time is obtained and used to form a constraint on the multi-objective timetable optimization model by associating it with the departure interval through adjustable parameters; the number of trains and express stations is determined, the initial number of trains in each time period is generated, and the upper bound of the departure interval is updated.

[0205] The lower limit of train departure interval is updated based on passenger waiting time; if it exceeds the maximum departure interval, a disturbance is set.

[0206] The multi-objective timetable optimization model is solved based on the number of trains and the lower bound of the departure interval to obtain the timetable. The passenger flow allocation model is run based on the passenger flow and the solved timetable to obtain the new average passenger waiting time and update the number of trains in each time period. The process continues until the number of updates that satisfy the upper bound of the departure interval and the lower bound of the train departure interval is reached, and the final optimal timetable is output.

[0207] Example 5

[0208] This embodiment 5 provides an electronic device, including: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the urban rail transit train timetable optimization method considering passenger flow allocation as described above. The method includes:

[0209] To minimize the total travel time for passengers and the vehicle-kilometer cost for enterprises, a multi-objective timetable optimization model based on long and short routes and express and slow train modes is constructed.

[0210] Considering the factors influencing passenger route selection under express and local train operations, this paper analyzes the possible transfers and route selection behaviors of passengers during their travels and establishes a passenger flow allocation model.

[0211] Based on the passenger flow allocation model, the average passenger waiting time is obtained and used to form a constraint on the multi-objective timetable optimization model by associating it with the departure interval through adjustable parameters; the number of trains and express stations is determined, the initial number of trains in each time period is generated, and the upper bound of the departure interval is updated.

[0212] The lower limit of train departure interval is updated based on passenger waiting time; if it exceeds the maximum departure interval, a disturbance is set.

[0213] The multi-objective timetable optimization model is solved based on the number of trains and the lower bound of the departure interval to obtain the timetable. The passenger flow allocation model is run based on the passenger flow and the solved timetable to obtain the new average passenger waiting time and update the number of trains in each time period. The process continues until the number of updates that satisfy the upper bound of the departure interval and the lower bound of the train departure interval is reached, and the final optimal timetable is output.

[0214] In summary, the urban rail transit train timetable optimization method and system considering passenger flow allocation described in this invention simultaneously considers express and local train modes as well as long-distance and short-distance train modes. A two-layer planning model for the timetable considering passenger flow allocation is established. The upper-layer model is used to obtain train operation schemes and timetables with the objective of minimizing passenger travel time and train travel distance. By analyzing passenger travel choice behavior, the passenger flow allocation model constructed based on the solution results of the upper-layer model serves as the lower-layer planning model. Simultaneously, the passenger waiting time obtained from the lower-layer model can be used as a constraint on the upper-layer model through an adjustable parameter associated with the departure interval, i.e., C * WT (waiting time) ≤ departure interval, thus completing the feedback between the upper and lower-layer models. This achieves comprehensive optimization of passenger flow allocation, long-distance and short-distance train modes, and express and local train timetable compilation problems. Compared with other studies, it covers a wider range, fully considers various constraints in actual train operation, and significantly accelerates the solution speed while ensuring the quality of the scheme. Compared with other existing technologies, the present invention has a more specific feedback effect between the passenger flow allocation of the lower-level model and the solution of the multi-route express and local train timetable of the upper-level model. This is reflected in the waiting time of passengers. The solution results of the lower-level model can be fed back to the upper-level model in the form of constraints for subsequent iterative optimization.

[0215] This invention offers two main methods for optimizing train operation plans: First, establishing a single model. This model places passengers and train operators in a game-theoretic relationship, seeking an equilibrium point between them. The objective functions are train operator operating costs and passenger travel costs, with constraints including transport capacity, throughput capacity, passenger demand, train configuration, and route planning. Second, establishing a two-level programming model. The upper level aims to minimize passenger travel costs and train operator operating costs, while the lower level optimizes the traffic allocation balancing problem.

[0216] Regarding algorithmic computation, those skilled in the art can design algorithms adapted to the model based on the size of the solution space. They can use the first derivative to find the minimum value or choose a branch and bound algorithm to solve integer programming problems. However, as the solution space increases and the model becomes more complex, traditional methods become too time-consuming and inefficient. Therefore, in practical applications, heuristic algorithms such as genetic algorithms, simulated annealing algorithms, and ant colony algorithms can be used to solve the problem.

[0217] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0218] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0219] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0220] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0221] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solutions disclosed in the present invention, various modifications or variations that can be made by those skilled in the art without creative effort should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing train timetable of urban rail transit considering passenger flow distribution, characterized in that, include: To minimize the total travel time for passengers and the vehicle-kilometer cost for enterprises, a multi-objective timetable optimization model based on long and short routes and express and slow train modes is constructed. A multi-objective timetable optimization model based on long and short routes and express / local train patterns is constructed. Constraints include train arrival / departure safety interval constraints, section travel time constraints, train origin / destination point constraints, train type and stop variable constraints, train stop constraints, non-contiguous departure constraints for express and short routes, train service frequency constraints, and model feedback constraints. Model feedback constraints include the constraints that allow the multi-objective timetable optimization model and the passenger flow allocation model to interact. ； where i and m and k are the indices of any two trains and stations, is the departure time of train m at station k, is the departure time of train i at station k, is the average waiting time of passengers at station k, denotes whether train i leaves station k earlier than train m, and M is a constant. Considering the factors influencing passenger route selection under express and local train operations, this paper analyzes the possible transfers and route selection behaviors of passengers during their travels and establishes a passenger flow allocation model. Based on the passenger flow allocation model, the average passenger waiting time is obtained and used to form a constraint on the multi-objective timetable optimization model by associating it with the departure interval through adjustable parameters; the number of trains and express stations is determined, the initial number of trains in each time period is generated, and the upper bound of the departure interval is updated. The lower limit of train departure interval is updated based on passenger waiting time; if it exceeds the maximum departure interval, a disturbance is set. The multi-objective timetable optimization model is solved based on the number of trains and the lower bound of the departure interval to obtain the timetable. The passenger flow allocation model is run based on the passenger flow and the solved timetable to obtain the new average passenger waiting time and update the number of trains in each time period. The process continues until the number of updates that satisfy the upper bound of the departure interval and the lower bound of the train departure interval is reached, and the final optimal timetable is output.

2. The urban rail transit train timetable optimization method considering passenger flow distribution according to claim 1, characterized in that, The methods for determining the short-route candidate set include: utilizing the cross-sectional passenger flow of each section along the route { Using this as the basic data, the variance of cross-sectional passenger flow under each route scheme is calculated. This is used to determine the short-route candidate set { The short-routes candidate set is used to solve the multi-objective timetable optimization model.

3. The urban rail transit train timetable optimization method considering passenger flow distribution according to claim 2, characterized in that, The steps for solving the short-routes candidate set are as follows: Input the number of stations N on the line and the cross-sectional passenger flow data for each section. and the ratio of large and small routes operating. : ; Based on the constraints, enumerate the shortest route schemes [ , The route lengths are checked, and the shorter route options that meet the constraints are retained to form an initial set of route option candidates. ; The constraints are as follows: ; Calculate the variance of passenger flow cross-sections for a single long-distance route: ； Calculate the variance of passenger flow cross-sections for the route plan Including: Short-distance route sections are [ , ],Will middle Partially according to : The proportions were allocated to the long-distance and short-distance routes respectively; the passenger flow at each cross-section of the long-distance and short-distance routes was calculated separately. , Calculate the variance of passenger flow cross-sections for both large and small routes. , Calculate the mean of the cross-sectional passenger flow variance for this route plan. This will be used as an evaluation indicator for the route plan; among which, ； ； Iterate through the initial set of alternative route plans, assess their suitability, and then... Record the short-distance route plans and identify those that meet the criteria. Arrange the routes in ascending order and select the top 3 to form a candidate set of smaller route options. .

4. The urban rail transit train timetable optimization method considering passenger flow distribution according to claim 1, characterized in that, Passenger route selection behavior analysis includes: Trains are divided into two types: express trains and local trains. Local trains have two arrival scenarios: direct to the destination station or not direct to the destination station. Express trains include the station before the destination station and the station after the destination station. When an express train goes directly to the station before or after the destination station, passengers may take the express train first and then transfer to a local train. The probability of route selection is calculated using a multinomial Logit model: ； in It is the passenger who chooses the route The probability, This is the waiting time for passengers choosing route a. It is the time the passenger spends in the vehicle when choosing route a. This indicates whether path 'a' has a transfer; if it does, the value is 1. , and It is the regression coefficient.

5. A system for optimizing urban rail transit train timetables based on the method described in any one of claims 1-4, characterized in that, include: The first building module is used to construct a multi-objective timetable optimization model based on long and short routes and express and slow train modes, with the goal of minimizing the total travel time of passengers and the cost per vehicle kilometer for enterprises. The second construction module is used to consider the influencing factors of passenger route selection under express and local train operations, analyze the possible transfers and route selection behaviors of passengers during the travel process, and establish a passenger flow allocation model. The update module is used to obtain the average passenger waiting time based on the passenger flow distribution model, and to form a constraint on the multi-objective timetable optimization model by associating it with the departure interval through adjustable parameters; determine the number of trains and the number of express stations, generate the initial number of trains for each time period, and update the upper bound of the departure interval; The lower limit of train departure interval is updated based on passenger waiting time; if it exceeds the maximum departure interval, a disturbance is set. The solution module is used to solve a multi-objective timetable optimization model based on the number of trains and the lower bound of the departure interval to obtain the timetable; based on the number of passengers and the solved timetable, it runs a passenger flow allocation model to obtain a new average passenger waiting time and updates the number of trains in each time period; until the number of updates of the upper bound of the departure interval and the lower bound of the train departure interval is satisfied, the final optimal timetable is output.

6. A computer program product, characterized in that, The method includes a computer program that, when run on one or more processors, implements the urban rail transit train timetable optimization method considering passenger flow allocation as described in any one of claims 1-4.

7. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement the urban rail transit train timetable optimization method considering passenger flow allocation as described in any one of claims 1-4.

8. An electronic device, characterized in that, include: The device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the urban rail transit train timetable optimization method considering passenger flow allocation as described in any one of claims 1-4.

Images