Train scheduling optimization method, device and equipment in subway network and storage medium

Abstract

This disclosure relates to a method, apparatus, equipment, and storage medium for optimizing train scheduling in a subway network. The method includes: acquiring subway network data within a specified time period, the network data including line information, train information, and passenger flow information; constructing an optimization model based on the network data, with the train departure intervals of each subway line in each direction of operation as the independent variable, the optimization model representing the total passenger waiting time consumed during the specified time period; and determining the target departure intervals of each train on each subway line in each direction of operation, based on pre-set constraints on the departure intervals, with the objective of minimizing the optimization model, the target departure intervals being used to formulate the train scheduling timetable for each subway line in each direction of operation within the specified time period. This enables overall optimization of train departure intervals in the subway network, thereby shortening passenger waiting times and improving subway operating efficiency.

Description

Technical Field

[0001] This disclosure relates to the field of computer technology, and in particular to a method, apparatus, equipment and storage medium for optimizing train scheduling in a subway network. Background Technology

[0002] Subways are a major mode of transportation today, helping to alleviate surface traffic congestion, promote coordinated regional economic development, and play an important role in improving people's lives. However, there is still much room for improvement in the passenger experience of subway services. For example, during peak hours, carriages are often overcrowded or passengers have to wait in queues for multiple trains to board; while during off-peak hours, long intervals between trains can lead to long waits, all of which result in a poor subway travel experience.

[0003] Train scheduling on subway lines typically uses timetables to control the departure times of each train and their arrival times at each station. Timetables are generally formulated based on time, space, and equipment constraints, such as limiting safe operating speeds, preventing rear-end collisions by ensuring sufficient headway, and limiting the number of trains operating on the line at any given time to the total number of trains.

[0004] Because current timetables are not based on actual passenger flow on the subway and typically only target a single line or direction of travel, lacking coordination between trains on different lines, the aforementioned poor riding experience is likely to occur. Therefore, optimizing train scheduling across the subway network to ensure passenger service quality, facilitate travel, and improve the subway riding experience is an urgent problem to be solved. Summary of the Invention

[0005] In view of this, this disclosure proposes a method, device, equipment and storage medium for optimizing train scheduling in a subway network, which can shorten the waiting time of passengers in the subway network, improve the efficiency of subway operation, and thus improve the quality of passenger service and the subway riding experience.

[0006] According to one aspect of this disclosure, a method for optimizing train scheduling in a subway network is provided, comprising: acquiring subway network data within a specified time period, the network data including line information, train information, and passenger flow information; the line information including: subway line number, direction of operation, transfer information between different subway lines, and station number of stations on the subway lines; the train information including: train number, train capacity, train running time between adjacent stations, and station dwell time of trains on different subway lines in different directions; and the passenger flow information including the number of passengers traveling from the subway within each unit time period of the specified time period. The number of passengers entering from any departure station in the network and heading to any destination station; based on the network data, an optimization model is constructed with the train departure interval of each subway line in each direction of operation in the subway network as the independent variable. The optimization model represents the total waiting time consumed by passengers waiting to board within the specified time period; based on the pre-set constraints on the departure interval, with the goal of minimizing the optimization model, the target departure interval of each train in each direction of operation in the subway network is determined. The target departure interval is used to formulate the timetable for train scheduling of each subway line in each direction of operation within the specified time period.

[0007] In one possible implementation, the step of constructing an optimization model based on the road network data, with the departure intervals of trains on each subway line in each direction of operation as independent variables, includes: determining, based on the passenger flow information, the transfer information, and the train capacity, the number of passengers remaining at each station when each train departs from each station in each direction of operation on each subway line, and the number of passengers entering the station between the arrival time of each train and the departure time of the previous train in each direction of operation on each subway line; and constructing an optimization model based on the number of passengers remaining at each station when each train departs from each station in each direction of operation on each subway line, and the arrival time and departure time of each train at each station in each direction of operation on each subway line. The model calculates the waiting time of passengers stranded after a train departs from each station. Based on the number of passengers entering each station from the departure of the previous train to the arrival of each train in each direction of travel on each metro line, the arrival time of each train at each station, and the time intervals between the arrival time of each train and the departure time of the previous train, the model constructs the waiting time for newly arriving passengers before each train arrives at each station in each direction of travel on each metro line. The arrival time is constructed based on the independent variable parameter representing the departure interval, the dwell time, and the inter-station travel time. The departure time is constructed based on the arrival time and the dwell time. The optimization model includes the sum of the waiting time and the waiting time for entering the station.

[0008] In one possible implementation, the number of passengers remaining at station x when train i departs from station x in any direction of travel on any metro line includes: the difference between the number of passengers on the platform when train i arrives at station x and the number of passengers boarding when train i departs from station x, where 1 ≤ i ≤ I, I is the total number of trains in any direction of travel on any metro line, and 1 ≤ x ≤ N, N is the total number of stations on any metro line; wherein, the number of passengers on the platform when train i arrives at station x is based on the number of passengers remaining at station x when train i-1 departs from station x and the number of passengers boarding from station i-1 to station x. The number of passengers entering the x-th station during the period is determined by the number of passengers boarding when the i-th train leaves the x-th station. The number of passengers boarding when the i-th train leaves the x-th station is determined by the number of passengers on the platform when the i-th train arrives at the x-th station, the train capacity, the number of passengers on the i-th train when it arrives at the x-th station, and the number of passengers disembarking when the i-th train arrives at the n-th station. The number of passengers already on the i-th train when it arrives at the i-th station is determined by the number of passengers boarding and disembarking at each station the i-th train has passed through. The number of passengers disembarking when the i-th train arrives at the n-th station is determined by the passenger flow information and the transfer information.

[0009] In one possible implementation, the transfer information includes: direct transfer information and indirect transfer information between subway lines in the subway network. The direct transfer information includes the station number of a transfer station on any subway line for direct transfer to another subway line, and the indirect transfer information includes the station number of a transfer station on any subway line for indirect transfer to another subway line. The number of passengers entering station x in any direction of travel on any subway line from the departure of train i-1 from station x to the arrival of train i at station x is based on the number of passengers entering station x in any direction of travel on any subway line from station x. The total number of destination stations reachable from the departure point and the passenger flow information during the period from the departure of train i-1 from station x to the arrival of train i at station x are determined. Specifically, the total number of destination stations reachable from station x in any direction of travel includes all stations reachable from station x in any direction of travel on the metro line to which station x belongs, as well as all stations on other metro lines that can be transferred to after entering station x. The total number of stations on other metro lines that can be transferred to after entering station x is determined based on the direct transfer information, the indirect transfer information, and the line information.

[0010] In one possible implementation, the transfer information includes: direct transfer information, indirect transfer information, and transfer time information between subway lines in the subway network. The transfer time information includes the transfer time required to directly transfer from a transfer station on any subway line to a transfer station on another subway line. The method further includes: for any current subway line in the subway network, based on the transfer information, determining adjacent subway lines that can be directly transferred from the current subway line, the current transfer station on the current subway line and adjacent transfer stations on the adjacent subway lines, the transfer time required to transfer from the current transfer station to the adjacent transfer station, and the transfer time required to transfer from the adjacent transfer station to the current transfer station. The arrival time of train j at the current transfer station is determined based on the target departure interval between trains 1 to j in any direction of travel on the current metro line, the inter-station travel time of trains on the current metro line between adjacent stations, and the station dwell time of trains. 1 < j ≤ J, where J is the total number of trains in any direction of travel on the current metro line. Based on the arrival time of train j at the current transfer station and the transfer time required to transfer from the current transfer station to the adjacent transfer station, the first arrival time of passengers disembarking at the current transfer station at the adjacent transfer station is determined. Based on the first arrival time, the arrival time of passengers disembarking at the current transfer station at the adjacent transfer station is determined. The following trains are considered: the k-th train departing from the adjacent transfer station before the first arrival time in any direction of the adjacent metro line, and the (k+1)-th train departing from the adjacent transfer station after the first arrival time, where 1 ≤ k ≤ K, and K is the total number of trains in any direction of the adjacent metro line; based on the target departure interval between every two trains on the adjacent metro line, the inter-station running time and station dwell time of trains on the adjacent metro line, and the transfer time required to transfer from the adjacent transfer station to the current transfer station, the second transfer passenger who disembarks at the adjacent transfer station and arrives at the current transfer station before the departure time of the j-th train from the current transfer station is determined. The arrival time and the third arrival time of transfer passengers arriving at the current transfer station after the departure time of the j-th train; based on the departure times of the k-th train and the (k+1)-th train from the adjacent transfer station, the first arrival time, the second arrival time, the third arrival time, and the preset boundary threshold for the departure interval, the target departure intervals corresponding to the j-th train and the (j+1)-th train are optimized to obtain the optimized departure intervals corresponding to the j-th train and the (j+1)-th train; wherein, the optimized departure intervals corresponding to each train in any direction of operation of any metro line are used to formulate the scheduling timetable for each train in any direction of operation of any metro line.

[0011] In one possible implementation, optimizing the target departure intervals for trains j and j+1 based on the departure times of train k and train k+1 from the adjacent transfer station, the first arrival time, the second arrival time, the third arrival time, and a preset boundary threshold for departure intervals, to obtain the optimized departure intervals for train j and train j+1, includes: optimizing the target departure intervals for train j and train j based on the boundary threshold and the target departure intervals for train j and train j+1. The initial upper bound for increasing the target departure interval for train j is determined, along with an initial upper bound for decreasing it. Based on the departure time of train k+1 from the adjacent transfer station, the first arrival time, and the initial upper bound, a target upper bound for increasing the target departure interval for train j is determined. This target upper bound ensures that passengers transferring from the current transfer station to the adjacent transfer station do not miss train k+1. Based on the departure time of train k from the adjacent transfer station and the first arrival time, the target upper bound for increasing the target departure interval for train j is determined. A target reduction lower bound is defined for the target departure interval corresponding to train j, which is used to ensure that transfer passengers transferring from the current transfer station to the adjacent transfer station catch train k. Based on the target departure interval corresponding to train j, the second arrival time, and the initial reduction upper bound, a target reduction upper bound is determined for the target departure interval corresponding to train j, which is used to ensure that transfer passengers arriving at the current transfer station at the second arrival time do not miss train j. Based on the target departure interval corresponding to train j and the third arrival time, a target increase lower bound is determined for the target departure interval corresponding to train j, which is used to ensure that transfer passengers arriving at the current transfer station at the third arrival time catch train j. Based on the target increase upper bound, target increase lower bound, target reduction upper bound, and target reduction lower bound, the target departure intervals corresponding to train j and train j+1 are optimized to obtain the optimized departure intervals corresponding to train j and train j+1.

[0012] In one possible implementation, optimizing the target departure intervals corresponding to train j and train j+1 based on the target increase upper bound, target increase lower bound, target decrease upper bound, and target decrease lower bound for the target departure interval corresponding to train j, to obtain the optimized departure intervals corresponding to train j and train j+1, includes: when the target decrease lower bound is less than or equal to the target decrease upper bound, and the target increase lower bound is greater than the target increase upper bound, determining the difference between the target departure interval corresponding to train j and the target decrease lower bound as the optimized departure interval corresponding to train j; and determining the sum of the target departure interval corresponding to train j+1 and the target decrease lower bound as the optimized departure interval corresponding to train j+1; or, when the target increase lower bound is less than or equal to the target decrease upper bound, optimizing the target departure interval corresponding to train j and train j+1 based on the target increase upper bound, target decrease lower bound, and target decrease lower bound, optimizing the target departure interval corresponding to train j and train j+1 based on the target increase upper bound, target decrease lower bound, and target decrease lower bound; or, when the target increase lower bound is less than or equal to the target decrease lower bound, optimizing the target departure interval corresponding to train j and train j+1 based on the target decrease upper bound, optimizing the target departure interval corresponding to train j and train j+1 based on the target decrease lower ... If the target increase lower bound is less than or equal to the target increase upper bound, and the target decrease lower bound is greater than the target decrease upper bound, the sum of the target departure interval corresponding to the j-th train and the target increase lower bound is determined as the optimized departure interval corresponding to the j-th train, and the difference between the target departure interval corresponding to the (j+1)-th train and the target increase lower bound is determined as the optimized departure interval corresponding to the (j+1)-th train; or, if the target increase lower bound is less than or equal to the target increase upper bound, and the target decrease lower bound is less than or equal to the target decrease upper bound, the target departure intervals corresponding to the j-th train and the (j+1)-th train are optimized according to the minimum value between the target increase lower bound and the target decrease lower bound, to obtain the optimized departure intervals corresponding to the j-th train and the (j+1)-th train.

[0013] In one possible implementation, determining the target departure interval for each train on each metro line in each direction of operation in the metro network, based on preset constraints for departure intervals and with the objective of minimizing the optimization model, includes: generating an initial population based on preset constraints for departure intervals. The initial population comprises multiple individuals, each individual representing the departure interval corresponding to each train on each metro line in each direction of operation in the metro network. The constraints include: the sum of the target departure intervals for all trains on any metro line in any direction of operation equals the specified time period; and any target departure interval does not exceed a preset boundary threshold. Based on the initial population, the following M-round iterative processing is performed, where M is a positive integer: in the m-th round of iterative processing, the optimization model is used to calculate the target departure interval for each train on the m-th generation population. The total passenger waiting time corresponding to each of the μ individuals is calculated. Based on the total passenger waiting time corresponding to each of the μ individuals in the m-th generation population, y individuals are randomly selected from the m-th generation population, where 1 ≤ m ≤ M, the first generation population is the initial population, μ is a positive integer, and 1 ≤ y ≤ μ. The y individuals selected from the m-th generation population are processed using a preset crossover operator and / or mutation operator to obtain λ offspring individuals, where λ is a positive integer. μ offspring individuals are selected from the parent population formed by the λ offspring individuals and the μ individuals in the m-th generation population to obtain the (m+1)-th generation population. For the (M+1)-th generation population obtained after the M-th iteration, the individual with the smallest total passenger waiting time in the (M+1)-th generation population is determined as the target departure interval for each train on each subway line in each direction of operation in the subway network.

[0014] In one possible implementation, the mutation operator includes at least one of the following: a single-point mutation operator, a swap mutation operator, a flip mutation operator, and a translation mutation operator; wherein, the single-point mutation operator is used to perform a single-point mutation process to increase or decrease any departure interval in an individual and to perform the opposite single-point mutation process on adjacent departure intervals; the swap mutation operator is used to perform a swap process on any two departure intervals in the same direction of operation of the same metro line in an individual; the flip mutation operator is used to perform a flip process on at least two departure intervals in any interval in the same direction of operation of the same metro line in an individual; the translation mutation operator is used to perform a head-to-tail translation process on all departure intervals in the same direction of operation of the same metro line in an individual; and the crossover operator is used to perform a weighted summation process on every two individuals selected from the m-th generation population based on random numbers randomly selected from a specified range.

[0015] In one possible implementation, before processing the y individuals selected from the m-th generation population using a preset crossover operator and / or mutation operator, the method further includes: determining the mutation probability and crossover probability corresponding to the m-th iteration based on a first preset relationship between the number of iteration rounds and the mutation probability, and a second preset relationship between the number of iteration rounds and the crossover probability, and determining whether the mutation probability and crossover probability corresponding to the m-th iteration are greater than a random number randomly selected from a specified range; wherein, the first preset relationship indicates a negative correlation between the mutation probability and the number of iteration rounds, and the second preset relationship indicates a positive correlation between the crossover probability and the number of iteration rounds; if the mutation probability corresponding to the m-th iteration is greater than the random number, determining to process the y individuals selected from the m-th generation population using a preset mutation operator; if the crossover probability corresponding to the m-th iteration is greater than the random number, determining to process the y individuals selected from the m-th generation population using a preset crossover operator.

[0016] According to another aspect of this disclosure, an acquisition module is provided for acquiring subway network data within a specified time period. The network data includes line information, train information, and passenger flow information. The line information includes at least one of the following: subway line number, direction of operation, transfer information between different subway lines, and station number of stations on the subway lines. The train information includes at least one of the following: train number of trains on different subway lines in different directions of operation, train capacity, train running time between adjacent stations, and train stopping time at stations. The passenger flow information includes passenger flow data from any point on the subway network within each unit of the specified time period. The number of passengers entering the station from the departure station to any destination station; a construction module, used to construct an optimization model based on the network data, with the departure interval of trains on each subway line in each direction of operation in the subway network as the independent variable, the optimization model representing the total waiting time consumed by passengers waiting to board within the specified time period; an optimization module, used to determine the target departure interval of each train on each subway line in each direction of operation in the subway network based on the preset constraints for the departure interval, with the goal of minimizing the optimization model, the target departure interval being used to formulate the timetable for scheduling trains on each subway line in each direction of operation in the subway network within the specified time period.

[0017] According to another aspect of this disclosure, an electronic device is provided, comprising: a processor; a memory for storing processor-executable instructions; wherein the processor is configured to implement the above-described method when executing instructions stored in the memory.

[0018] According to another aspect of this disclosure, a non-volatile computer-readable storage medium is provided that stores computer program instructions thereon, wherein the computer program instructions, when executed by a processor, implement the above-described method.

[0019] According to another aspect of this disclosure, a computer program product is provided, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code, wherein when the computer-readable code is run in a processor of an electronic device, the processor in the electronic device performs the above-described method.

[0020] According to the embodiments of this disclosure, an optimization model is established based on the line information, train information, and passenger flow information of the entire subway network. Based on preset constraints, the optimized target departure interval is determined with the goal of minimizing the optimization model, that is, minimizing the total waiting time of passengers. This not only achieves the overall optimization of the train departure interval in the subway network, but also the overall optimization of the train scheduling timetable in the subway network. When using the scheduling timetable based on the target departure interval for train scheduling, the waiting time of passengers in the subway network can be shortened, the subway operation efficiency can be improved, and thus the passenger service quality and subway riding experience can be improved.

[0021] Other features and aspects of this disclosure will become clear from the following detailed description of exemplary embodiments with reference to the accompanying drawings. Attached Figure Description

[0022] The accompanying drawings, which are included in and form part of this specification, illustrate exemplary embodiments, features, and aspects of this disclosure together with the specification and serve to explain the principles of this disclosure.

[0023] Figure 1 A flowchart is shown for a train scheduling optimization method in a subway network according to an embodiment of the present disclosure.

[0024] Figure 2 A schematic diagram of a subway network according to an embodiment of the present disclosure is shown.

[0025] Figure 3 A schematic diagram of an individual according to an embodiment of the present disclosure is shown.

[0026] Figure 4a A schematic diagram illustrating the single-point mutation process of a single-point mutation operator according to an embodiment of the present disclosure is shown.

[0027] Figure 4b A schematic diagram illustrating the exchange processing procedure of an exchange mutation operator according to an embodiment of the present disclosure is shown.

[0028] Figure 4c A schematic diagram illustrating the flipping process of a flipping mutation operator according to an embodiment of the present disclosure is shown.

[0029] Figure 4d A schematic diagram illustrating the translation processing procedure of a translation mutation operator according to an embodiment of the present disclosure is shown.

[0030] Figure 5 A schematic diagram illustrating a train transfer coordination optimization process according to an embodiment of the present disclosure is shown.

[0031] Figure 6 This diagram illustrates the timing of passengers arriving at the current transfer station before and after a target departure interval optimization according to an embodiment of the present disclosure.

[0032] Figure 7 This diagram illustrates a train scheduling simulation optimization process in a simulation environment according to an embodiment of the present disclosure.

[0033] Figure 8 A schematic diagram of a subway network according to an embodiment of the present disclosure is shown.

[0034] Figure 9 A block diagram of a train scheduling optimization device in a subway network according to an embodiment of the present disclosure is shown.

[0035] Figure 10 A block diagram of an electronic device 1900 according to an embodiment of the present disclosure is shown. Detailed Implementation

[0036] Various exemplary embodiments, features, and aspects of this disclosure will now be described in detail with reference to the accompanying drawings. The same reference numerals in the drawings denote elements that have the same or similar functions. Although various aspects of the embodiments are shown in the drawings, they are not necessarily drawn to scale unless specifically indicated otherwise.

[0037] The term “exemplary” as used herein means “serving as an example, embodiment, or illustration.” Any embodiment illustrated herein as “exemplary” is not necessarily to be construed as superior to or better than other embodiments.

[0038] Furthermore, to better illustrate this disclosure, numerous specific details are set forth in the following detailed description. Those skilled in the art will understand that this disclosure can be practiced without certain specific details. In some instances, methods, means, components, and circuits well known to those skilled in the art have not been described in detail in order to highlight the main points of this disclosure.

[0039] It should be noted that in the description of this disclosure, terms such as "first," "second," and "third" are used to distinguish different objects, not to describe a specific order, nor should they be construed as indicating or implying relative importance or implicitly specifying the number of technical features indicated. In the description of this disclosure, "a plurality of" means two or more, unless otherwise explicitly defined.

[0040] The train scheduling optimization method in the subway network of this disclosure can be deployed on various terminal devices through software or hardware modifications. The terminal devices involved in this disclosure can refer to devices with wireless and / or wired connection functions. Wireless connection means that they can connect to other devices via wireless connection methods such as Wi-Fi and Bluetooth. The terminal devices involved in this disclosure can also communicate with other devices via wired connection functions. The terminal devices involved in this disclosure can be touchscreen, non-touchscreen, or screenless. Touchscreen devices can be controlled by clicking or swiping on the display screen using fingers or styluses. Non-touchscreen devices can connect to input devices such as mice, keyboards, and touch panels to control the terminal device. Screenless devices can be, for example, screenless Bluetooth speakers. For example, the terminal devices in this application can include, but are not limited to, user equipment (UE), mobile devices, user terminals, terminals, handheld devices, tablet computers, laptops, PDAs, and computing devices.

[0041] The train scheduling optimization method for the subway network in this disclosure can also be deployed on a server. This server can be located in the cloud or locally, and can be a physical device or a virtual device, such as a virtual machine or container. It has wireless communication capabilities, which can be configured in the server's chip (system) or other components. This can refer to a device with wireless connectivity, meaning it can connect to other servers or terminal devices via Wi-Fi, Bluetooth, or other wireless connection methods. The server involved in this disclosure can also have wired communication capabilities. For example, the server in this disclosure can be located in the cloud, communicating with terminal devices, receiving subway network data sent by the terminal devices, and using the train scheduling optimization method deployed on the server to output the target departure intervals for each train on each subway line in each direction of operation in the subway network. This output is then returned to the terminal devices, allowing them to use the target departure intervals returned by the server to formulate a train scheduling timetable for the subway network.

[0042] Figure 1 A flowchart illustrating a train scheduling optimization method in a subway network according to an embodiment of the present disclosure is provided. This method can be executed by the aforementioned terminal device or electronic device such as a server, etc. Figure 1 As shown, the method includes steps S11 to S13.

[0043] In step S11, the subway network data for a specified time period is obtained, including line information, train information and passenger flow information.

[0044] The route information includes: the subway line number, direction of operation, transfer information between different subway lines, and station numbers of stations on the subway lines. The subway line number identifies different subway lines; the direction of operation refers to the direction of train travel on the subway line, typically including the up and down directions; transfer information includes: direct transfer information, indirect transfer information, and transfer time information between subway lines in the subway network. Direct transfer information includes the station number of the transfer station on any subway line for direct transfer to another subway line; indirect transfer information includes the station number of the transfer station on any subway line for indirect transfer to another subway line; and transfer time information includes the transfer time from any subway line to the transfer station on the other subway line. The transfer time required to transfer to a transfer station on another subway line; the station number is used to identify different stations. The station number can include at least one of a global number and a local number (also known as a station line number). The global number of any station represents the unique number of any station in the entire subway network, and the local number of any station represents the unique number of any station on its respective subway line. The local numbers of stations on different subway lines may be the same, but the global number is unique. For transfer stations on subway lines, two transfer stations on two subway lines are physically adjacent and connected by transfer passages within the station. They can be regarded as two independent entities. Therefore, transfer stations on different subway lines can be represented by different global numbers and local numbers.

[0045] Let Set(l) = {1, 2, ..., L} be the set of subway lines in the subway network, L be the total number of lines in the subway network, and l ∈ Set(l) represent the line number of any subway line. The direction of travel is represented by d, which has two directions: up and down, with values ​​corresponding to 0 and 1 in Set(d) = {0, 1}, respectively. For any subway line l, Set(n)... l ={1,2,…,N l Let} be the set of local station numbers on subway line l, where N l Let represent the total number of stations on subway line l, and n represent the local station number, where n ∈ Set(n). l The sum of the number of stations on all subway lines in the entire subway network is... The global number s of each station can be arranged in ascending order by the line number to which the station belongs and the local number of the station, together forming the global number set Set(s).

[0046] by Figure 2For example, one type of subway network shown is as follows: Figure 2 The shown metro network includes three metro lines, numbered "1", "2", and "3" respectively. Each metro line has two directions of operation, represented by "0" and "1", and a total of 14 stations. The station numbers on metro line 1 are represented as: partial numbering. 线路编号 n l (Global IDs s) G For example, 1 1 (1 G ) represents the station on subway line 1 with a local number of 1 and a global number of 1. 3 2 (8 G ) represents the station on subway line 2 with a local number of 3 and a global number of 8, 4 3 (14 G ) represents the station on subway line 3 with a local number of 4 and a global number of 14, and so on; Figure 2 Transfer information between the three subway lines can include at least: station number 2 of the transfer station from subway line 1 to subway line 2. 1 (2 G Station number 2, the station for indirect transfer from Metro Line 1 to Metro Line 3. 1 (2 G Station number 3, the station on Metro Line 2 that connects directly to Metro Line 1. 2 (8 G Station number 4, the station for direct transfer from Metro Line 2 to Metro Line 3. 2 (9 G Station number 1 of the direct transfer station from Metro Line 3 to Metro Line 2. 3 (11 G Station number 1 of the indirect transfer station from Metro Line 3 to Metro Line 1. 3 (11 G ), from 2 1 (2 G Transfer to 3 2 (8 G The transfer time is reduced from 3 2 (8 G Transfer to 2 1 (2 G The transfer time is reduced from 4 2 (9 G Transfer to 1 3 (11 G The transfer time is from 1 3 (11 G Transfer to bus 4 2 (9G (Transfer time)

[0047] In practical applications, subway lines and stations can be identified by sequentially setting line numbers and station numbers. Furthermore, a conversion relationship can be established between the global and local station numbers, allowing for the mutual conversion of the global and local numbers of any station on any subway line. For example, the conversion relationship between the local station number n and the global station number s on subway line l can be expressed by formulas (1-1) and (1-2):

[0048]

[0049] l is to satisfy the inequality The maximum value at time (1-2)

[0050] in, This represents the cumulative total number of stations from subway line 1 to subway line l-1. Given the line number l to which a station belongs and the station's local number n, the global number s can be obtained using the formula (1-1) above. Formula (1-1) represents the sum of the total number of stations from subway line 1 to subway line l-1, plus the local number n on subway line l, as the global number of that station. For example, Figure 2 The global number of station 2 on Metro Line 3 is 12, which is equal to the total number of stations N on Metro Line 1. 1 =5 and the total number of stations on subway line 2, N 2 =5 plus n=2, that is, 12=N 1 +N 2 +n=5+5+2; When the global number is known, that is, when s is known, the above formula (1-2) can be used to calculate the subway line l to which the station belongs and the local number n of the station. For example, Figure 2 The station with global number 9 belongs to a metro line whose line number satisfies the inequality. The maximum value is 2, which means the subway line number of the station with global number 9 is 2. Substituting the line number 2 and the global number 9 into the above formula (1-2), we get the local number n as 4, that is, 4 = sN. 1 =9-5.

[0051] Optionally, the transfer information in the entire subway network can be represented by multiple transfer matrices, including: Direct Transfer Matrix (DTM), Availability Transfer Matrix (ATM), Transfer Arrival Matrix (PTM), and Transfer Duration Matrix (TTM). The Direct Transfer Matrix (DTM) is used to describe whether there is a direct transfer relationship between subway lines in the subway network and the station number of the transfer station when a direct transfer relationship exists. If two subway lines l1 and l2 transfer through transfer stations s1 (transfer station on l1) and s2 (transfer station on l2), then DTM(l1,l2) = s1 and DTM(l2,l1) = s2. If two subway lines l1 and l2 cannot transfer directly, DTM(l1,l2) = -1 and DTM(l2,l1) = -1. The Availability-to-Transfer (ATM) matrix describes the first step required for transferring between two subway lines in a subway network, along with the corresponding transfer station. For example, to reach line l3 from line l1, one must first pass through line l2. The first step is transferring from line l1 to line l2, and the corresponding transfer station is station s1 on line l1. Therefore, ATM(l1,l3) = DTM(l1,l2) = s1. The Transfer-to-Arrival (PTM) matrix describes the global station number reached in the first step of a transfer using the ATM matrix. Again, to reach line l3 from line l1, one must first pass through line l2. The first step is transferring from line l1 to line l2, and the station reached is station s2 on line l2. Thus, PTM(l1,l3) = DTM(l2,l1) = s2. The ATM and PTM matrices essentially describe the indirect transfer relationships between subway lines. The transfer time matrix TTM is used to record the transfer time required between two transfer stations on two subway lines. For example, TTM(l1,l2) can represent the transfer time from station s1 on l1 to station s2 on l2. This transfer time can be the average time.

[0052] The train information includes: train numbers, train capacities, train travel time between adjacent stations, and train dwell time at stations for trains on different subway lines and in different directions. The train number identifies different trains on a subway line. The train capacity indicates the maximum number of passengers a single train can carry. It can be assumed that all trains on the same subway line and in the same direction have the same capacity. The train travel time between adjacent stations is the time the train spends traveling between two adjacent stations. The train dwell time at stations is the time the train spends stopping at a station. The train travel time between stations and dwell time on the same subway line and in the same direction can be fixed and known. For example, suppose... This represents the total number of trains on subway line l in the direction d of travel. The train number of the i-th train on this subway line can be represented by the departure order as follows: in This is the set of train numbers on the subway line l in the direction d of operation. Train capacity can be further subdivided according to the subway line and direction of operation, such as... This represents the train capacity on the subway line l in the direction d of travel, assuming... This represents the travel time between stations on subway line l in the direction d, from station n (locally numbered n) to station n+1 (locally numbered n+1). This represents the dwell time of a train on subway line l in the direction d at station n.

[0053] The aforementioned passenger flow information includes the number of passengers entering from any departure station in the subway network and heading to any destination station within each unit time period of a specified time period. Optionally, the passenger flow information can be described using an OD matrix, that is, the OD matrix can be used to record the number of passengers entering from any departure station in the subway network and heading to any destination station within each unit time period. The number of passengers entering the station will change over time. For example, OD(t,s1,s2) represents the number of passengers entering station s1 at time t and whose destination station is s2. Here, the minimum time unit related to time can be preset as τ. The number of passengers entering station s1 at time t and whose destination station is s2 can be understood as the number of passengers entering station s1 and whose destination station is s2 between time t-τ and time t. Time t-τ to time t is also a unit time period.

[0054] In practical applications, a specified time period can be understood as the time period of the scheduling schedule to be optimized. For example, a specified time period can be the entire day from 0:00 to 24:00, or it can be the morning peak period from 7:00 to 10:00 and the evening peak period from 5:00 to 8:00. The route information and train information are usually fixed within a certain historical period, while passenger flow information is variable. Passenger flow information within the same specified time period usually exhibits similar patterns of change. Therefore, the passenger flow information in the road network data can be the average of multiple sets of passenger flow information within the same specified time period in a historical period. For example, the average of passenger flow information from multiple Monday morning peak periods can be used as the passenger flow information in the road network data. This allows for the construction of a more adaptive optimization model using more stable passenger flow information, thereby obtaining a more accurate target departure interval.

[0055] This disclosure does not limit the acquisition method of the aforementioned road network data. For example, the road network data can be obtained from a third-party platform. In practical applications, if the acquired raw road network data does not meet the data standards required for executing the train scheduling optimization method, the acquired raw road network data can be preprocessed to make the processed road network data conform to the aforementioned data standards. For example, if the line number, train number, and station number are not arranged in sequence, the subway lines, stations, and stations can be renumbered in sequence. If the transfer information is not in the form of a transfer matrix and the passenger flow information is not in the form of an OD matrix, the transfer information and passenger flow information can be converted into the forms of a transfer matrix and an OD matrix, respectively. This disclosure does not limit the preprocessing method of the raw road network data, as long as it meets the data standards required for executing the train scheduling optimization method.

[0056] In step S12, based on the road network data, an optimization model is constructed with the train departure interval of each subway line in each direction of operation in the subway network as the independent variable. The optimization model represents the total waiting time consumed by passengers waiting to board the train within a specified time period.

[0057] In practical applications, based on the characteristics of subway train operation, and in order to simplify the construction of the optimization model, the embodiments of this disclosure propose the following assumptions: passenger flow follows the rule of first-come, first-served; when the remaining capacity of the train is insufficient, passengers are allocated boarding quotas according to the proportion of destination stations, and the train can be fully loaded but not overloaded; passenger waiting time is calculated from the time of passenger entry to the time of boarding, and the boarding time and alighting time are taken as the train's arrival time; the waiting time for passengers arriving during the train's stop is 0; the time required for passengers to alight and board is ignored, and passengers at the platform can board before departure, provided that the train's capacity limit is not exceeded.

[0058] The departure interval for any train is the time interval between the departure time of that train and the departure time of the previous train. Independent variable parameters representing the departure interval can be preset, for example, by setting... The independent variable parameter represents the departure interval of the i-th train on the running direction d of subway line l.

[0059] Considering that in reality, passengers waiting to board at any station usually include passengers who remain at the station after the previous train departs, as well as new passengers entering the station before a train that is about to arrive arrives, where passengers who remain can be understood as those who remain due to train capacity limitations, the optimization model in this embodiment includes the sum of the waiting time of passengers who remain at each station after each train departs in each direction of each metro line and the waiting time of new passengers entering the station before each train arrives in each direction of each metro line. In other words, the optimization model represents the total waiting time of passengers waiting to board within a specified time period.

[0060] Based on the above assumptions and settings, in one possible implementation, step S12 involves constructing an optimization model using the train departure intervals of each subway line in the subway network in each direction of operation as independent variables, based on the road network data. This model includes:

[0061] Step S121: Based on passenger flow information, transfer information and train capacity, determine the number of passengers remaining at each station when each train leaves each station in each direction of operation of each subway line, and the number of passengers entering the station between the arrival time of each train entering the station and the departure time of the previous train leaving the station in each direction of operation of each subway line.

[0062] Step S122: Based on the number of passengers waiting at each station when each train departs from each station in each direction of operation of each subway line, as well as the arrival time and departure time of each train at each station, construct the waiting time of passengers waiting at each station after each train departs from each station in each direction of operation of each subway line.

[0063] Step S123: Based on the number of passengers entering the station from the departure of the previous train to the arrival of each train in each direction of operation of each subway line, the arrival time of each train at each station, and the time intervals between the arrival time of each train and the departure time of the previous train, construct the waiting time for new passengers entering the station before each train arrives at each station in each direction of operation of each subway line.

[0064] The arrival time is constructed based on the independent variable parameter representing the departure interval, the stop duration, and the inter-station travel time, while the departure time is constructed based on the arrival time and the stop duration. For example, suppose... This represents the arrival time of the i-th train on the direction d of subway line l at station n. The departure time of the i-th train on the direction d of subway line l from station n can be represented by formula (2-1) to construct the arrival time. And the departure time is constructed using formula (2-2).

[0065]

[0066]

[0067] in, d∈Set(d), n∈Set(n) l , σ represents the departure time of the first train on the direction d of subway line l. This σ can be set according to a specified time period. For ease of calculation, σ can also be set to 0. This represents the cumulative interval between the departures of trains from train 1 to train i. The train on subway line l, traveling in the direction d, departs from station n. * to station n * Inter-station runtime between +1 The train on subway line l, traveling in the direction d, is at station n. * The duration of the stop, This represents the direction of travel d=0 (i.e., the train travels from station 1 to station N). l When traveling in the opposite direction, the travel time between stations and the dwell time from station 1 to station n-1 (i.e., the station with the local number n-1) are accumulated. This represents the direction of travel, d=1 (i.e., the train departs from station N). l When running towards station 1, for the distance from station n+1 to station N... l The station running time and station stop time are added together.

[0068] Formula (2-1) above represents the arrival time of train i at station n by summing the departure interval between every two trains from train i to train i, as well as the inter-station running time and stop time of train i at stations it passes through before entering station n. Formula (2-2) above represents the departure time of train i at station n by adding the stop time of train i at station n.

[0069] In one possible implementation, in step S121, the number of passengers remaining when the i-th train leaves the n-th station in any direction of travel on any metro line includes the difference between the number of passengers on the platform when the i-th train arrives at the x-th station and the number of passengers boarding when the i-th train leaves the x-th station, 1≤i≤I, where I is the total number of trains in any direction of travel on any metro line, 1≤x≤N, where N is the total number of stations on any metro line.

[0070] The number of passengers on the platform when the i-th train arrives at the n-th station is determined based on the number of passengers who were stranded when the (i-1)-th train left the x-th station and the number of passengers who entered the x-th station from the time the (i-1)-th train left the x-th station to the time the i-th train entered the x-th station.

[0071] The number of passengers boarding when train i departs from station x is determined based on the number of passengers on the platform when train i arrives at station i, the train capacity, the number of passengers on train i when train i arrives at station x, and the number of passengers disembarking when train i arrives at station x. The number of passengers already on train i when train i arrives at station i is determined based on the number of passengers boarding and disembarking at each station that train i has passed through. The number of passengers disembarking when train i arrives at station x is determined based on passenger flow information and transfer information.

[0072] To facilitate the explanation of the above process, let's assume that the local number of the x-th station on any subway line in any direction of operation is n. In the following text, station n refers to the x-th station. It should be understood that the local number of the x-th station on the same subway line may be different in different directions of operation. For example... Figure 2 The local number of the second station on Metro Line 2 in the direction of operation d=0 is 2, and the local number of the second station in the direction of operation d=1 is 4.

[0073] Where, assuming This represents the number of passengers stranded due to train capacity limitations when the i-th train on subway line l departs from station n (i.e., the x-th station on subway line l in the direction d) in the direction of travel. This represents the number of passengers on the platform when the i-th train on subway line l arrives at station n in the direction d. Let the number of passengers boarding the i-th train in the direction d of subway line l at station n be the number of passengers remaining. This can be expressed as formula (3):

[0074]

[0075] Formula (4) can be used to determine the number of passengers on the platform when the i-th train arrives at the x-th station, based on the number of passengers remaining when the (i-1)-th train leaves the x-th station and the number of passengers entering the x-th station from the departure of the (i-1)-th train from the departure of the x-th train to the arrival of the i-th train at the x-th station.

[0076]

[0077] in, This represents the number of passengers stranded when the (i-1)th train in the direction d of subway line l departs from station n (i.e., the number of passengers stranded when the (i-1)th train departs from station x). An initial value is set for this value. This represents the number of passengers entering station n along the direction of travel of subway line l from the departure of train i-1 from station n to the arrival of train i at station n (i.e., the number of passengers entering station x from the departure of train i-1 from station x to the arrival of train i at station x). This represents the number of people entering station n at time t on the direction of travel d of subway line l. Formula (4) above indicates that the number of people on the platform equals the sum of the number of people remaining on the platform and the number of people entering the station. Formula (5) can be used to calculate...

[0078]

[0079] Among them, s n,l RSN(l,d,n) represents the global number of station n on subway line l in the direction d, RSN(l,d,n) represents the set of global numbers of all destination stations that can be reached from station n on subway line l in the direction d. OD(t,s) n,l ,s * ) represents entering station s at time t. n,l And the destination station is s * The number of passengers, This represents entering station s at time t. n,l And the sum of the number of passengers going to all reachable destination stations. Formula (5) represents the number of passengers entering station s at time t. n,l The number of people entering the station is equal to the number of people entering the station at time t. n,l And the sum of the number of passengers going to all reachable destination stations.

[0080] Based on the above formulas (4) and (5), the above This can be expressed as formula (6):

[0081]

[0082] The above formula (6) can represent that the number of passengers entering the x station from the departure of the i-1th train from the x station to the arrival of the i-th train in any direction of operation of any metro line is determined based on all destination stations that can be reached from the x station in any direction of operation of any metro line and the passenger flow information from the departure of the i-1th train from the x station to the arrival of the i-th train in the x station.

[0083] The total number of destination stations reachable from station x in any direction of travel includes all stations reachable from station x in any direction of travel on the metro line to which station x belongs, as well as all stations on other metro lines that can be reached after entering station x. The number of stations on other metro lines that can be reached after entering station x is determined based on direct transfer information, indirect transfer information, and line information. It is understood that, based on the aforementioned line information, the global number of stations reachable from station x in any direction of travel on the metro line to which station x belongs can be obtained. Then, combining the aforementioned direct and indirect transfer information, the global number of all stations on other metro lines that can be reached after entering station x can be obtained. Thus, the global number of all destination stations reachable from station x can be obtained.

[0084] For example, the above RSN(l,d,n) can be expressed as formula (7-1):

[0085]

[0086] Where RSL(l,d,n) represents the global set of station numbers that can be reached from station n along the running direction d of metro line l to which station n belongs, [Set(l)-{l}] represents the set of metro lines in the metro network excluding metro line l, and s = s(n * ,l * () represents subway line l * Upper local number n * The global number of the station can be calculated using the formula (1-1) above. * ,l * ), Representative subway line l * The total number of stations on the ATM, l, l * () represents transferring from subway line l to subway line l * For transfer stations on metro line l, the above formula (7-1) represents the transfer from metro line l to metro line l. * ATM (l,l) at the transfer station on subway line l * When RSN(l,d,n) belongs to RSL(l,d,n), RSN(l,d,n) includes the metro line l. * The global number of all stations on the ATM, when ATM(l,l) * If a line is not part of RSL(l,d,n), then RSN(l,d,n) does not include that metro line l. * The global number of all stations. In the above formula (7-1), the addition operation represents the merging of two sets, and the subtraction operation represents the deletion of an element from one set from another.

[0087] The above RSL(l,d,n) can be represented as (7-2):

[0088]

[0089] Formula (7-2) above represents the direction of travel d=0 (i.e., the train travels from station 1 to station N). l When running in the direction of travel (l,d,n), RSL(l,d,n) includes stations n+1 to N on the metro line l to which station n belongs, in the direction of travel d. l The global number, in the direction of travel d=1 (i.e., the train departs from station N). l When running towards station 1, RSL(l,d,n) includes the global numbers of stations 1 to n-1 on the running direction d of the metro line l to which station n belongs.

[0090] Formula (8) can be used to determine the number of passengers boarding the i-th train when it leaves the x-th station, based on the number of passengers on the platform when the i-th train arrives at the x-th station (i.e., station n), the train capacity, the number of passengers on the i-th train when it arrives at the x-th station, and the number of passengers disembarking when the i-th train arrives at the x-th station.

[0091]

[0092] in, This represents the number of passengers on the i-th train when it arrives at station n (i.e., the x-th station) on subway line l in the direction d. This represents the number of passengers disembarking when the i-th train on subway line l arrives at station n in the direction d. This represents the number of passengers who can board the i-th train when it arrives at station n under the limitation of train capacity (that is, the remaining capacity of the i-th train). The above formula (8) represents the number of passengers who board the i-th train when it arrives at station x on the i-th train in the direction d of subway line l. Equal to the number of people on the platform The number of people who can board the train despite its capacity limitations The minimum value in the range. It should be understood that when any train arrives at the first station, the number of passengers getting off is 0 and the number of passengers on board is also 0.

[0093] Among them, the number of passengers on the i-th train when it arrives at the x-th station. It is determined based on the number of passengers boarding and alighting at each station the i-th train has passed through, or in other words, it is calculated by the number of passengers boarding and alighting at all platforms the i-th train passes through before arriving at the x-th station; for example, formula (9) can be used to calculate the number of passengers on the i-th train when it arrives at the x-th station (i.e., station n).

[0094] Formula (9) above represents the direction of travel d=0 (i.e., from station 1 to station N). l When traveling in the direction of (the vehicle's movement), the number of people on board It equals the cumulative difference between the number of passengers boarding and alighting from station 1 to station n-1, in the direction of travel d=0 (i.e., from station N). l When traveling towards station 1, the number of passengers on board Equal to station N l The cumulative difference between the number of passengers boarding and disembarking at station n+1.

[0095] Among them, the number of passengers disembarking when the i-th train arrives at the x-th station. It is determined based on passenger flow information and transfer information. In practical applications, passenger flow information can also include the number of people exiting each station in each unit time period within a specified time period. Thus, based on passenger flow information and transfer information, we can know the number of people getting off at station x when the i-th train arrives at station x (i.e., station n) and the number of people getting off at station x to transfer to other subway lines when station x is a transfer station. It should be understood that the number of people getting off at station 1 is 0 and the number of people boarding is the minimum value between the number of people on the platform and the train capacity.

[0096] In step S122, based on formula (10), the waiting time T1 of passengers left by any train in any direction of any metro line after leaving any station can be constructed according to the number of passengers left by each train in each direction of each metro line when they leave each station, as well as the arrival time and departure time of each train in each direction of each station. Then, the waiting time of passengers left by each train in each direction of each metro line after leaving each station can be accumulated to obtain the total waiting time.

[0097]

[0098] Formula (10) above represents the waiting time T1 of passengers stranded after the i-th train leaves station n on metro line l in the direction d. This is equal to the number of passengers stranded after the (i-1)-th train leaves the station. Arrival time of train i at station n Departure time of train i-1 from the station Difference between The product of.

[0099] In step S123, based on formula (11), the waiting time T2 of passengers entering the station for any train in any direction of any metro line can be constructed according to the number of passengers entering the station from the departure of the previous train to the arrival of each train in each direction of each metro line, the arrival time of each train at each station, and the time between the arrival time of each train and the departure time of the previous train. Then, the waiting time of newly entering passengers before each train arrives at each station in each direction of each metro line can be accumulated to obtain the total waiting time for entering the station.

[0100]

[0101] The above formula (11) represents the waiting time T2 of new passengers entering station n before the i-th train arrives on subway line l in the direction d. arrive Number of passengers entering the station at various times Arrival time The difference between time t (equivalent to the passenger's arrival time) and time t. The cumulative value of the product of, where, This can be understood as the waiting time of passengers entering the station at time t. As mentioned above, if we have a minimum time unit τ, then passengers entering the station at time t can be understood as passengers entering the station between time t-τ and time t.

[0102] Based on the above formulas (10) and (11), we can obtain the passenger waiting time for the i-th train at station n on the running direction d of subway line l, as shown in formula (12).

[0103]

[0104] The above formula (12) can be understood as the passenger waiting time. It consists of the sum of two parts: the first part is the waiting time of stranded passengers waiting for the i-th train, and the second part is the waiting time of newly arrived passengers waiting for the i-th train.

[0105] This allows us to track passenger wait times at various stations on different subway lines in different directions. By summing the results, we obtain the optimized model PWT as shown in formula (13):

[0106]

[0107] Formula (13) above represents the optimization model PWT, which includes: the waiting time of passengers stranded after each train leaves each station in each direction of operation on each metro line, and the waiting time of newly arriving passengers before each train arrives at each station in each direction of operation on each metro line. Step S13 can then be used to solve for the independent variable parameters in the optimization model. The parameter values ​​are used to obtain the target departure intervals of each train on each subway line in each direction of operation that minimizes the total passenger waiting time in the subway network.

[0108] In step S13, based on the pre-set constraints for the departure interval, with the goal of minimizing the optimization model, the target departure interval for each train on each subway line in each direction of operation in the subway network is determined. The target departure interval is used to formulate the scheduling timetable for trains on each subway line in each direction of operation in the subway network within a specified time period.

[0109] The constraints include: the sum of the target departure intervals for all trains on any subway line in any direction of travel is equal to the specified time period, and any target departure interval does not exceed a preset boundary threshold.

[0110] Here, the specified time period can be understood as the total duration of the timetable to be optimized. Assuming T represents the total duration of the timetable, the departure interval between any train and the previous train on metro line l in the direction d is... The following constraints can be satisfied between T and T: That is, the sum of the departure intervals of all trains on any subway line in any direction equals the total duration planned in the timetable. Among these, This represents the total number of trains on subway line l in the direction of travel d.

[0111] In light of real-world considerations regarding train operation safety (such as the train's safe operating speed not exceeding the upper limit and the departure interval not being too short to prevent rear-end collisions) and passenger waiting time, boundary thresholds can be set for the independent variable parameter of the departure interval. These boundary thresholds may include an upper bound. and the lower realm In other words, the departure interval of the i-th train on subway line l in the direction of travel d is... The following constraints must be met: It should be understood that those skilled in the art can set the above boundary thresholds according to actual needs. The boundary thresholds for different operating directions of different subway lines can be the same or different, and this disclosure does not limit this.

[0112] In one possible implementation, based on the above constraints, a genetic algorithm can be used to solve the optimization model. Specifically, in one possible implementation, step S13, based on the pre-set constraints for the departure interval and with the objective of minimizing the optimization model, determines the target departure interval for each train on each subway line in each direction of travel in the subway network, and may include:

[0113] Step S131: Based on the preset constraints for the departure interval, generate the first generation population. The first generation population includes multiple individuals, and each individual includes the departure interval corresponding to each train on each subway line in each direction of operation in the subway network.

[0114] Step S132: Based on the initial population described above, perform the following M rounds of iterative processing, where M is a positive integer:

[0115] In the m-th iteration, the optimization model is used to calculate the total waiting time of each of the μ individuals in the m-th generation population. Based on the total waiting time of each of the μ individuals in the m-th generation population, y individuals are randomly selected from the m-th generation population, where 1≤m≤M, the first generation population is the initial population, μ is a positive integer, and 1≤y≤μ.

[0116] Using a preset crossover operator and / or mutation operator, y individuals selected from the m-th generation population are processed to obtain λ offspring individuals, where λ is a positive integer;

[0117] Select μ offspring individuals from the parent population consisting of λ offspring individuals and μ individuals from the m-th generation population to obtain the (m+1)-th generation population.

[0118] Step S133: For the M+1 generation population obtained after the Mth iteration, the individual with the smallest total passenger waiting time in the M+1 generation population is determined as the target departure interval of each train on each subway line in each direction of operation in the subway network.

[0119] Optionally, in step S131, generating the initial population can be understood as the population initialization process in a genetic algorithm. This is done to ensure that the solutions generated by the optimization model are feasible solutions, i.e., satisfying the constraints. and Therefore, when generating the initial population, a uniform distribution method can be used to construct the individuals in the initial population, that is, the departure interval between every two trains on any subway line in any direction of operation is... Since a minimum time unit τ is preset, we can first take... The integer part of the result is used as the departure interval, and any possible decimal parts are accumulated. Each time the accumulated value reaches 1.0, the current departure interval is incremented by 1. For example, if calculating... If the value is 2.1, then the departure interval for trains 1 to 9 is 2, the departure interval for train 10 is 3, the departure interval for trains 11 to 19 is 2, the departure interval for train 20 is 3, and so on. This ensures that the constraint of the departure interval sum being T is satisfied, and also ensures that each independent variable parameter takes an integer value.

[0120] It should be understood that the above-described method for generating the first generation population is one possible implementation provided by the embodiments of this disclosure. In fact, those skilled in the art can customize the method for generating the first generation population according to actual needs, and the embodiments of this disclosure do not limit this.

[0121] Each individual in the population represents the departure interval of each train on each subway line in the subway network, in each direction of travel. That is, the code for each individual is composed of the departure intervals of all trains on all subway lines in the subway network. The departure intervals of any individual can be arranged sequentially according to the direction of travel, line number, and train number. For example, for... Figure 2 The subway line shown Figure 3 This shows a schematic diagram of an individual subway line, such as... Figure 3 As shown, this entity includes the departure intervals for all trains on three subway lines in both directions of travel. For example, This represents the departure interval of the first train on Metro Line 1 in the direction of d=0, and so on.

[0122] In step S132, those skilled in the art can customize the total number of iterations M according to actual needs, for example, 600 rounds can be set, and this embodiment of the present disclosure does not limit this. In the m-th iteration, the optimization model is used to calculate the total passenger waiting time corresponding to each of the μ individuals in the m-th generation population. This can be understood as the individual evaluation process in the genetic algorithm, that is, the optimization model is used to calculate the output value of the optimization model (i.e., the total passenger waiting time) for all individuals in the population to evaluate the individuals, and each individual corresponds to a total passenger waiting time.

[0123] In step S132, based on the total passenger waiting time corresponding to each of the μ individuals in the m-th generation population, y individuals are randomly selected from the m-th generation population. This can be understood as an individual selection process. Here, selection strategies known in the art can be used, such as the fitness ratio method, the k-ary tournament selection method, and the random traversal sampling method, to select y individuals with smaller total passenger waiting times from the m-th generation population. For example, the μ individuals can be sorted according to passenger waiting times, and y individuals can be selected from the μ individuals in ascending order. By selecting individuals with smaller total passenger waiting times, it is easier for excellent parent individuals to be inherited by their offspring.

[0124] In step S132, the mutation operator may include at least one of the following: a single-point mutation operator, an exchange mutation operator, a flip mutation operator, and a translation mutation operator; wherein, the single-point mutation operator is used to perform single-point mutation processing to increase or decrease any departure interval in an individual and to perform the opposite single-point mutation processing on adjacent departure intervals, wherein the degree of increase or decrease can be customized, for example, it can be set to increase by 1 or decrease by 1, wherein if the departure interval before performing the single-point mutation processing (i.e., increase or decrease) has reached the boundary threshold, the single-point mutation processing is extended to the next adjacent departure interval; the exchange mutation operator is used to perform exchange processing on any two departure intervals in the same direction of operation of the same metro line in an individual; the flip mutation operator is used to perform flip processing on at least two departure intervals in any section in the same direction of operation of the same metro line in an individual; the translation mutation operator is used to perform end-to-end translation processing on all departure intervals in the same direction of operation of the same metro line in an individual.

[0125] In practical applications, mutation operators can be randomly selected with different probabilities each time mutation processing is performed. These mutation operators can be operated on at departure intervals along the same route and in the same direction each time, without changing the feasibility of the departure interval. Traditional genetic algorithms only use single-point mutation operators, meaning each mutation operation only affects the departure intervals at two locations. This is not conducive to the algorithm's wide-area search of the solution space and makes it difficult to escape local optima. This embodiment enhances the algorithm's wide-area search capability in the solution space by adding three additional mutation operators (exchange mutation operator, flip mutation operator, and translation mutation operator).

[0126] For example, Figure 4a This illustrates the single-point mutation process of the single-point mutation operator. Figure 4b This illustrates the exchange processing procedure of the exchange mutation operator. Figure 4c This illustrates the flipping process of the flip mutation operator. Figure 4d The translation process of the translation mutation operator is shown, where, for example... Figure 4a As shown, a single-point mutation can be performed by subtracting 1 from a specific departure interval 28 and adding 1 to the adjacent departure interval 22, resulting in offspring individuals after this single-point mutation. Figure 4b As shown, any two departure intervals 23 and 22 on an individual can be swapped to obtain the offspring individual after the swap; as... Figure 4c As shown, multiple departure intervals within any interval of an individual (such as the interval circled in the circle) can be flipped to obtain offspring individuals after the flipping process; for example... Figure 4d As shown, all departure intervals corresponding to subway line 3 in the direction of operation 0 can be shifted two units to the right, one end to the other, to obtain the offspring individuals after the shifting process. The degree of shifting can be customized, and this embodiment does not limit it.

[0127] In step S132, the crossover operator is used to perform a weighted summation on every two individuals selected from the y individuals in the m-th generation population, based on random numbers randomly selected from a specified range. This ensures that all offspring generated by the crossover algorithm are feasible solutions. For example, the above crossover operator can be expressed as formula (14):

[0128]

[0129] Here, α represents a random number, with a specified range of values, such as (0,1), i.e., α∈(0,1). F1 and F2 represent any two individuals from the y individuals, which can be understood as two parent individuals. c1 and c2 represent two child individuals obtained by weighted summation of the two parent individuals F1 and F2. Considering that the result of the weighted summation may contain decimals, the child individuals obtained by weighted summation can be integerized. The method of integerization for child individuals is still to retain the integer part of the departure interval and accumulate the decimal part. When the decimal part accumulates to 1.0, the current departure interval is incremented by 1.

[0130] Considering that the crossover operator relies on parent individuals to generate offspring individuals and has stronger local search capabilities, while the mutation operator directly mutates genes in parent individuals and has stronger global search capabilities, in order to balance the global search capability in the early stage and the local search capability in the later stage, the embodiments of this disclosure adopt adaptive crossover and mutation probabilities to determine whether to use the crossover and mutation operators to perform crossover and mutation processing on the current generation of the population. In the early stage of population evolution, a strong wide-area search capability of the solution space is usually required, so a higher mutation probability and a lower crossover probability are needed in the early stage of population evolution. In the later stage of population evolution, a stronger local search capability of the solution space is needed, so a higher crossover probability and a lower mutation probability are needed in the later stage of population evolution. Therefore, the crossover probability can be gradually increased and the mutation probability can be gradually decreased as the number of iterations increases.

[0131] Based on this, in one possible implementation, before step S132 above processes multiple individuals selected from the m-th generation population using a preset crossover operator and / or mutation operator, the method further includes:

[0132] Based on the first preset relationship between the number of iteration rounds and the mutation probability, and the second preset relationship between the number of iteration rounds and the crossover probability, the mutation probability and crossover probability corresponding to the m-th iteration are determined, and it is determined whether the mutation probability and crossover probability corresponding to the m-th iteration are greater than a random number randomly selected from a specified range; wherein, the first preset relationship indicates that the mutation probability and the number of iteration rounds are negatively correlated, and the second preset relationship indicates that the crossover probability and the number of iteration rounds are positively correlated.

[0133] If the mutation probability corresponding to the m-th iteration is greater than the random number, the preset mutation operator is used to process the y individuals selected from the m-th generation population.

[0134] If the crossover probability corresponding to the m-th iteration is greater than the random number, the preset crossover operator is used to process the y individuals selected from the m-th generation population.

[0135] It should be understood that the first and second preset relationships described above can be customized in this embodiment. The first preset relationship simply needs to represent a negative correlation between the number of iterations and the mutation probability (i.e., the larger the number of iterations, the smaller the mutation probability), and the second preset relationship needs to represent a positive correlation between the number of iterations and the crossover probability (i.e., the larger the number of iterations, the greater the crossover probability). This embodiment does not impose any limitations on this. For example, formula (15-1) shows a first preset relationship provided by this embodiment, and formula (15-2) shows a second preset relationship provided by this embodiment:

[0136]

[0137]

[0138] Where m is the current iteration round number, P1 represents the mutation probability, and P2 represents the crossover probability. and For the initial and final values ​​of the custom mutation probability, and For the initial and final values ​​of the custom crossover probability, G start and G end These are the number of rounds to set the start and end adaptive crossover and mutation probabilities, respectively. For example, G can be set. start For 100, G end The value is 400, but this disclosure does not limit the implementation of the embodiments. Formulas (15-1) and (15-2) above represent the condition when the number of iterations m ≤ G. start When, the mutation probability is The crossover probability is When G start <m<G end The mutation probability decreases with increasing iteration number, while the crossover probability increases with increasing iteration number, when the iteration number m ≥ G. end When, the mutation probability is The crossover probability is

[0139] Specifically, if the mutation probability corresponding to the m-th iteration is less than or equal to the random number, then it is determined that the mutation operator will not be used to process the y individuals selected from the m-th generation population; if the crossover probability corresponding to the m-th iteration is less than or equal to the random number, then it is determined that the mutation operator will not be used to process the y individuals selected from the m-th generation population. It should be understood that in any iteration, it is possible that only the mutation operator is used to process the y individuals, or only the crossover operator is used to process the y individuals, or both the mutation and crossover operators are used to process the y individuals, or neither the mutation nor crossover operators are used to process the y individuals.

[0140] In step S132, after obtaining λ offspring individuals through crossover or mutation, any known evolutionary strategy in the art can be used to select the next generation population. That is, μ offspring individuals are selected from the parent population consisting of λ offspring individuals and μ individuals from the m-th generation population to obtain the (m+1)-th generation population. For example, a (μ+λ) evolutionary strategy can be used, where the population size remains μ in each generation, and after each round of mutation and / or crossover, λ offspring individuals are generated, which, together with the μ individuals from the m-th generation population, form (μ+λ) individuals. The selection strategy for individuals in the next generation population can include selecting μ individuals with smaller total passenger waiting times from (μ+λ) individuals in the parent population, thus obtaining the (m+1)th generation population. Here, an optimization model can be used to calculate the total passenger waiting time corresponding to each of the above λ offspring individuals. Then, based on the total passenger waiting time corresponding to each of the (μ+λ) individuals, the (μ+λ) individuals are sorted, and μ individuals are selected from the (μ+λ) individuals in ascending order to form the (m+1)th generation population.

[0141] In step S133, after the Mth iteration, the M+1th generation population can be obtained. The optimization model can be used to calculate the total passenger waiting time for each individual in the M+1th generation population, and the individual with the smallest total passenger waiting time is determined as the target departure interval for each train on each subway line in each direction of operation in the subway network.

[0142] As mentioned above, train scheduling on subway lines generally uses timetables. Therefore, after obtaining the target departure intervals of each train on each subway line in each direction of operation in the subway network, a timetable for scheduling trains on each subway line in each direction of operation within a specified time period can be formulated based on the target departure intervals. This allows for the use of optimized timetables to schedule each train on each subway line in each direction of operation within a specified time period, thereby reducing the waiting time for passengers to board trains in the subway network.

[0143] According to the embodiments of this disclosure, an optimization model is established based on the line information, train information, and passenger flow information of the entire subway network. Based on preset constraints, the optimized target departure interval is determined with the goal of minimizing the optimization model, that is, minimizing the total waiting time of passengers. This not only achieves the overall optimization of the train departure interval in the subway network, but also the overall optimization of the train scheduling timetable in the subway network. When using the scheduling timetable based on the target departure interval for train scheduling, the waiting time of passengers in the subway network can be shortened, the subway operation efficiency can be improved, and thus the passenger service quality and subway riding experience can be improved.

[0144] Considering that in actual practice, when train scheduling is carried out based on the above timetable, there may be situations where trains on two subway lines connected by a transfer station fail to coordinate passenger flow upon arrival at the transfer station, resulting in longer waiting times for transfer passengers to board. For example, when passengers arrive at a transfer station on one subway line from a transfer station on another subway line, the previous train on that subway line has just left the transfer station. Therefore, in one possible implementation, this disclosure embodiment also provides a method such as... Figure 5 The train transfer coordination optimization process shown above further optimizes the target departure interval obtained in step S13 using the aforementioned transfer information. Figure 5 As shown, after obtaining the target departure intervals of each train on each subway line in each direction of operation in the subway network, the method further includes steps S14 to S19.

[0145] In step S14, for any current subway line in the subway network, based on the transfer information, determine the adjacent subway lines that can be directly transferred from the current subway line, the current transfer station on the current subway line and the adjacent transfer station on the adjacent subway line, the transfer time required to transfer from the current transfer station to the adjacent transfer station, and the transfer time required to transfer from the adjacent transfer station to the current transfer station.

[0146] In practical applications, for example, the target departure interval of trains on each subway line in the subway network can be optimized sequentially according to the line numbering order and the order of operation direction of the subway lines in the subway network; of course, the departure interval of trains on a certain subway line in the subway network can also be optimized according to actual needs, and this disclosure does not limit this.

[0147] In this context, the metro line currently undergoing optimization within the metro network is called the current metro line. The metro lines from which one can directly transfer are called adjacent metro lines. The station on the current metro line used for transferring to the adjacent metro line is called the current transfer station. The station on the adjacent metro line connected to the current transfer station is called the adjacent transfer station. It can be understood that, based on the above transfer information, one can obtain the adjacent metro lines of any current metro line, the current transfer station on the current metro line and the adjacent transfer stations on the adjacent metro lines, the transfer time required to transfer from the current transfer station to the adjacent transfer station, and the transfer time required to transfer from the adjacent transfer station to the current transfer station.

[0148] For ease of understanding, in this embodiment of the disclosure, the current subway line is represented as l0, and the adjacent subway line is represented as l. ω The current transfer station is indicated as Adjacent transfer stations are represented as From the current transfer station Transfer to the adjacent transfer station The required transfer time is expressed as TTM(l0,l) ω From the adjacent transfer station l ω The transfer time required to reach the current transfer station l0 is expressed as TTM(l) ω ,l0), the current direction of travel of the train on the subway line is d.

[0149] In step S15, based on the target departure interval between every two trains from the first train to the jth train in any direction of operation of the current metro line l0, the inter-station running time of trains on the current metro line l0 between adjacent stations, and the station dwell time of trains, the arrival time of the jth train at the current transfer station is determined. The arrival time is 1 < j ≤ J, where J is the total number of trains running in any direction on the current subway line.

[0150] The arrival time of the j-th train at the current transfer station can be determined by referring to the formula (2-1) above. Arrival time Specifically, the target departure interval between every two trains from train 1 to train j, and the departure interval of train j upon entering the current transfer station can be set. The inter-station travel time and stop time of the train passing through the previous stations are added together to obtain the arrival time of the j-th train at the current transfer station. Arrival time Arrival time It can be used as the j-th train to reach the current transfer station. The time when passengers alight.

[0151] In step S16, the arrival time of the j-th train at the current transfer station is determined. And the transfer time TTM(l0,l) required to transfer from the current transfer station to the adjacent transfer station. ω ), determine the arrival time of train j at the current transfer station. Passengers disembarking at the current time arrive at the adjacent transfer station. First arrival time

[0152] Among them, the first arrival time This is equivalent to the j-th train arriving at the current transfer station. Arrival time With the current transfer station Transfer to the adjacent transfer station Required transfer time TTM(l0,l) ω ), that is,

[0153] In step S17, based on the first arrival time Identify adjacent subway lines ω At the first arrival time in any direction of travel Previously leaving the adjacent transfer station The kth train and the first arrival time Then leave the adjacent transfer station The (k+1)th train, 1≤k≤K, where K is the total number of trains in any direction of travel on the adjacent subway line.

[0154] It is understandable that, given the target departure interval of trains in any direction of operation of the adjacent metro line, the travel time between two adjacent stations, and the dwell time at each station, the arrival time of each train in any direction of operation of the adjacent metro line at the adjacent transfer station can be calculated by referring to the above formulas (2-1) and (2-2). By taking the arrival and departure times and combining them with the first arrival time, we can determine that the departure time is exactly at [time missing]. Previously leaving the adjacent transfer station The kth train and in Then leave the adjacent transfer station The k+1th train.

[0155] In step S18, based on the target departure interval between every two trains on the adjacent metro line, the inter-station running time of trains on the adjacent metro line between two adjacent stations and the station dwell time of trains, and the data from the adjacent transfer station... Transfer to the current transfer station The required transfer time is determined from the adjacent transfer station. Get off the train and leave the current transfer station on the jth train. Arrive at the current transfer station before the departure time. The second arrival time of transfer passengers and the departure time of the jth train from the current transfer station. Arrive at the current transfer station after the departure time. The third arrival time for connecting passengers.

[0156] The above formula (2-2) can be used to calculate the arrival time of the j-th train at the current transfer station. Arrival time and at the current transfer station The dwell time is used to calculate the departure time of the j-th train from the current transfer station. Departure time The time of arrival is approaching. The departure time is obtained by adding the stop duration to the stop duration.

[0157] Among them, the method based on adjacent subway lines can be achieved by referring to the above formula (2-1). ω The target departure interval between every two trains, and adjacent subway lines. ω The train's travel time between two adjacent stations and its dwell time at each station are used to calculate the adjacent metro line l. ω Trains in any direction of travel arrive at the adjacent transfer station. The arrival times can then be used to transfer trains to adjacent transfer stations. Arrival time plus transfer time from adjacent stations Transfer time TTM(l) required to reach the current transfer station ω (l0) , to obtain the arrival times of each train at adjacent transfer stations Passengers disembarking now arrive at their current transfer station. The arrival time, and then combined with the departure time of the j-th train from the current transfer station. Departure time It can be determined from the adjacent transfer station Get off the bus and just at Arrived at the current transfer station Second arrival time And in Then arrive at the current transfer station The third arrival time

[0158] Step S19: Based on the departure time and first arrival time of train k and train (k+1) from the adjacent transfer station... The second arrival time, the third arrival time, and the preset boundary threshold for the departure interval are used to optimize the target departure intervals for the j-th train and the (j+1)-th train, respectively, to obtain the optimized departure intervals for the j-th train and the (j+1)-th train respectively. Among them, the optimized departure intervals for each train in any direction of operation on any metro line are used to formulate the departure timetable for each train in any direction of operation on any metro line.

[0159] Specifically, formula (2-2) above can be used to calculate the departure time of train k from the adjacent transfer station based on the arrival times of train k and train k+1 at the respective adjacent transfer station and the stop time of the trains at the adjacent transfer station. Departure time And the (k+1)th train departs from the adjacent transfer station Departure time d ω It represents a certain direction of operation of an adjacent subway line.

[0160] In one possible implementation, step S19 above optimizes the target departure intervals for trains j and j+1 based on the departure time, first arrival time, second arrival time, and third arrival time of train k and train k+1, as well as a preset boundary threshold for the departure interval, to obtain the optimized departure intervals for train j and train j+1, including:

[0161] Step S191: Based on the boundary threshold and the target departure intervals corresponding to the j-th train and the (j+1)-th train, determine the initial upper bound for increasing the target departure interval and the initial upper bound for decreasing the target departure interval corresponding to the j-th train.

[0162] As mentioned above, the boundary threshold includes an upper bound. and the lower realm Let the target departure interval for the j-th train be represented as... The target departure interval for the (j+1)th train is represented as follows: It should be understood that the train interval on any metro line should also be within the range constrained by the above-mentioned boundary threshold. Therefore, the initial upper bound of the increase in the target train interval corresponding to the j-th train can be calculated using formula (16-1). And the initial upper bound for reducing the target departure interval corresponding to the j-th train is calculated using formula (16-2).

[0163]

[0164]

[0165] Among them, the initial upper bound is added. This constraint limits the increase in the target departure interval to no more than Initial decrease upper bound The amount used to constrain the reduction in the target departure interval cannot exceed This ensures that the optimized departure interval obtained by increasing or decreasing the target departure interval remains within the range constrained by the boundary threshold.

[0166] Step S192: Based on the departure time of the (k+1)th train from the adjacent transfer station... First arrival time and the initial upper bound Determine the upper bound of the target increase for the target departure interval corresponding to the j-th train. This is used to ensure that passengers transferring from the current transfer station to an adjacent transfer station do not miss the k+1th train;

[0167] Formula (17-1) can be used to determine the target increase upper bound pos for the target departure interval corresponding to the j-th train. max :

[0168]

[0169] Step S193: Based on the departure time of the k-th train from the adjacent transfer station... and the first arrival time Determine the lower bound of the target reduction for the target departure interval corresponding to the j-th train (neg). min The goal is to reduce the lower bound (neg). min This is used to ensure that passengers transferring from the current transfer station to an adjacent transfer station catch the kth train.

[0170] Formula (17-2) can be used to determine the lower bound of the target reduction for the target departure interval corresponding to the j-th train. min :

[0171]

[0172] in, The target reduction lower bound for the target departure interval corresponding to the (j-1)th train is calculated. Since there is no target departure interval between the 1st train and the 0th train, it is not necessary to use formula (17-2) to update the target reduction lower bound for the target departure interval corresponding to the 1st train.

[0173] Step S194, based on the target departure interval corresponding to the j-th train. Second arrival time and the initial decreasing upper bound Determine the upper bound of the target reduction for the target departure interval corresponding to the j-th train (neg). max The target decreases the upper bound to make the second arrival time... Arrive at the current transfer station Transfer passengers will not miss the jth train;

[0174] Formula (18-1) can be used to determine the upper bound of the target reduction of the target departure interval corresponding to the j-th train, neg. max :

[0175]

[0176] Step S195, based on the target departure interval corresponding to the j-th train. and the third arrival time Determine the target increase lower bound pos for the target departure interval corresponding to the j-th train. min The goal is to increase the lower bound pos. min Used to enable arrival at the third time Arrive at the current transfer station The transferring passengers just happened to catch the jth train;

[0177] Formula (18-2) can be used to determine the target increase lower bound pos for the target departure interval corresponding to the j-th train. min :

[0178]

[0179] in, Add a lower bound to the target departure interval corresponding to the calculated (j-1)th train. Since there is no target departure interval between the first train and the 0th train, it is not necessary to use formula (18-2) to update the target lower bound of the target departure interval corresponding to the first train.

[0180] Step S196: Increase the upper bound pos according to the target departure interval corresponding to the j-th train. max The goal is to increase the lower bound pos. min The target decreases the upper bound (neg) max and the target decreases the lower bound (neg) min The target departure intervals for train j and train j+1 are optimized to obtain the optimized departure intervals for train j and train j+1.

[0181] In one possible implementation, the above-mentioned upper bound pos is added based on the target departure interval corresponding to the j-th train. max The goal is to increase the lower bound pos. minThe target decreases the upper bound (neg) max and the target decreases the lower bound (neg) min The target departure intervals for train j and train j+1 are optimized to obtain the optimized departure intervals for train j and train j+1, including:

[0182] The target decreases by a lower bound, neg min Less than or equal to the upper bound of the target reduction (neg) max Furthermore, the target is increased by a lower bound pos. min Increase the upper bound pos if it is greater than the target. max In this case, the target departure interval corresponding to the j-th train is compared with the target reduction lower bound neg. min The difference is determined as the optimized departure interval corresponding to the j-th train, and the target departure interval corresponding to the (j+1)-th train is the lower bound of the target reduction, neg. min The sum is determined as the optimized departure interval for the (j+1)th train; or,

[0183] Increase the lower bound pos for the target min Less than or equal to the target plus an upper bound of pos max And the target decreases the lower bound neg min The upper bound of the target is reduced by neg. max In this case, the target departure interval corresponding to the j-th train is increased by a lower bound of pos. min The sum is determined as the optimized departure interval corresponding to the j-th train, and the target departure interval corresponding to the (j+1)-th train is increased by a lower bound pos. min The difference is determined as the optimized departure interval corresponding to the (j+1)th train; or,

[0184] Increase the lower bound pos for the target min Less than or equal to the target plus an upper bound of pos max And the target decreases the lower bound neg min Less than or equal to the upper bound of the target reduction (neg) max In this case, increase the lower bound pos based on the target. min With the target decreasing the lower bound, neg min The minimum value in the range is used to optimize the target departure intervals for train j and train j+1, resulting in the optimized departure intervals for train j and train j+1.

[0185] The optimization process for the target departure interval described above can be summarized as follows: if neg min ≤neg max And pos min >pos maxThis means that only the target departure interval corresponding to the j-th train can be reduced, then the optimized departure interval corresponding to the j-th train is: The optimized departure interval for the (j+1)th train is: If pos min ≤pos max And neg min >neg max This means that the target departure interval for the j-th train can only be increased, so the optimized departure interval for the j-th train is: The optimized departure interval for the (j+1)th train is: If neg min ≤neg max And pos min ≤pos max This means that the target departure interval for the j-th train can either be decreased or increased. In this case, we can choose the optimization method with smaller change. That is, if the target interval increases by a lower bound of pos... min Less than the target, reduce the lower bound (neg) min Then use the target to increase the lower bound pos. min Increase the target departure interval for the j-th train, that is, execute... and Conversely, if the target decreases the lower bound neg min Increase the lower bound pos if it is less than the target. min Then use the target to decrease the lower bound neg. min Reduce the target departure interval for the j-th train, that is, execute...

[0186] For example, Figure 6 This diagram illustrates the timing of passenger arrivals at the current transfer station before and after optimization of the target departure interval, as shown below. Figure 6 As shown, a certain subway line l k Before optimizing the target departure interval, transfer passengers arrive at the current metro line l at time t1. k At transfer station n on subway line l, at this time... k The (i-1)th train in the direction d=0 (departure time is...) Passengers who have already left transfer station n and need to wait for the i-th train in that direction for the transfer period have a waiting time of: Meanwhile, on subway line l k The i-th train in the direction d=1 (departure time is...) Passengers who have already left the transfer station and need to wait for the (i+1)th train in this direction will have a waiting time of: After optimizing the target departure interval using steps S14 to S19 of the embodiments of this disclosure, transfer passengers will arrive at subway line l earlier at time t2. k The transfer station n on the line means that originally, in the direction of d=1, one could only wait for the (i+1)th train. Passengers transferring can take the i-th train, which is an earlier one. Although the waiting time for transfer passengers in the d=0 direction is relatively shorter than... The increase in Δt = t1 - t2 resulted in a significant reduction in the waiting time for passengers transferring in the d = 1 direction. This effectively reduces the total waiting time for transfer passengers, which is the optimized total waiting time for transfer passengers between the two operating directions. Less than the total waiting time before optimization

[0187] In practical applications, after obtaining the optimized departure intervals for each train in any direction of operation on any metro line, a timetable for trains on that metro network in that direction of operation can be formulated based on the optimized departure intervals. This allows for the use of the timetable with optimized departure intervals to schedule each train on that metro line in that direction of operation, thereby reducing the waiting time for transfer passengers, improving metro operating efficiency, and enhancing the passenger experience.

[0188] According to the embodiments of this disclosure, by further optimizing the target departure interval using transfer information, an optimized departure interval is obtained. This enables train scheduling using the timetable established by the optimized departure interval, allowing trains on two subway lines connected by the transfer station to form passenger flow coordination when arriving at the transfer station. This reduces situations where passengers have just transferred and the previous train has just departed, thus reducing the waiting time for transfer passengers.

[0189] This disclosure proposes a train scheduling optimization method for a subway network. It explicitly utilizes train and passenger flow information at the same transfer station on different subway lines to efficiently optimize the network timetable, aiming to enhance the operational coordination between trains on different lines in the subway network to minimize the total passenger waiting time. This disclosure uses a refined time-varying OD matrix that more closely resembles real-world scenarios as the passenger flow data input to the optimization model. It also designs a train transfer coordination optimization process (i.e., steps S14 to S19 above) specifically for the characteristics of subway network train scheduling problems, significantly improving the population convergence speed. Furthermore, during the population iteration update process, adaptive crossover and mutation probabilities are used to balance global and local search capabilities, which can significantly shorten the total passenger waiting time.

[0190] This disclosure implements a train scheduling optimization method based on refined time-varying OD matrix passenger flow data to coordinate train scheduling in a subway network. It makes several improvements to the basic genetic algorithm framework to address the characteristics of the subway network train scheduling problem, adds a train transfer coordination optimization process, and further optimizes the crossover and mutation processing in the traditional genetic algorithm, thereby significantly improving the performance of the genetic algorithm, effectively shortening the total waiting time for passengers, and improving the service quality for passengers. Specifically, it can explicitly utilize passenger flow and train information at transfer stations to form inter-line scheduling coordination to accelerate the search. It considers two scenarios: the coordination of passenger flow transferring on this line with trains on other lines, and the coordination of passenger flow transferring on other lines with trains on this line. With minimizing the total passenger waiting time as the optimization objective, it achieves collaborative optimization of train departure intervals across all lines in the entire subway network. Furthermore, it improves the basic genetic algorithm by adding a train transfer coordination optimization process, significantly increasing the algorithm's convergence speed. Secondly, it designs four different mutation operators and randomly selects operators for mutation operations based on probability. In addition, it uses adaptive crossover and mutation probabilities to achieve a balance between global exploration and local search capabilities in the heuristic algorithm. It can adapt to refined time-varying OD matrix passenger flow data, that is, it can handle passenger flow data containing origin and destination information that changes over time, providing greater guidance and reference for subway scheduling in reality. It is not limited by the network structure of the subway network; by adjusting the model parameters, it can be directly ported and adapted to new subway networks, exhibiting strong versatility and reusability.

[0191] This disclosure also provides a train scheduling simulation optimization process in a simulation environment. This process includes maintaining the OD matrix of passenger flow information, maintaining the number of passengers alighting, and simulating the total passenger waiting time. The simulation can be triggered sequentially by train arrival events, meaning the simulation calculation can be performed whenever a train arrives. Specifically, for example... Figure 7 As shown, at time At that time, for subway line l, when it arrives at station n in the direction of travel d... l train The following simulation calculation steps will be performed:

[0192] 1. Obtain the set of reachable stations RSN(l,d,n);

[0193] 2. Calculate using the set RSN(l,d,n) and OD matrix. and Number of arrivals at each time point

[0194] 3. According to and Calculate the number of people on the platform

[0195] 4. By the number of people on the vehicle Number of people getting off and the number of people on the platform Calculate the actual number of passengers on board If not all passengers can board the train, passengers who arrive at their destination earlier will board first, and passengers arriving at the same time will board in proportion to their destination.

[0196] 5. Calculate the number of people stranded on the platform. and the number of people on the vehicle

[0197] 6. Based on the number of people stranded on the platform and the number of arrivals Calculate passenger waiting time for trains Total time Accumulate it into the optimization model PWT;

[0198] 7. For each reachable station s G ∈RSN(l,d,n) performs the following operations:

[0199] 7.1 The target station for statistics is s G The actual number of passengers on board, e;

[0200] 7.2 Determine the destination station s G Do I need to transfer?

[0201] 7.3 If no transfer is required:

[0202] 7.3.1 Calculate the local number of the destination station using formula (1-2)

[0203] 7.3.2 Update the disembarkation variable

[0204] 7.4 If a transfer is required:

[0205] 7.4.1 Calculate the destination station s using formula (1-2) G Line l k ;

[0206] 7.4.2 Using ATM(l,l) k Get the global number of the transfer platform on line l.

[0207] 7.4.3 Calculate the local number of the alighting platform on line l using formula (1-2)

[0208] 7.4.4 Update the number of passengers getting off the bus variable.

[0209] 7.4.5 Using PTM(l,l) k Get the global number of the transfer platform after one transfer.

[0210] 7.4.6 Calculate the line number l reached after one transfer using formula (1-2). j ;

[0211] 7.4.7 Using TTM(l,l) j Get the transfer walking time t j ;

[0212] 7.4.8 Calculate passenger arrival route l j Transfer station time

[0213] 7.4.9 Update OD matrix data

[0214] Among them, steps (1) to (6) are simulation calculations of the total waiting time of passengers, and step (7) is the numerical maintenance of the number of passengers getting off the bus and the OD matrix. Specifically, steps (7.3) and (7.4.1) to (7.4.4) are simulation updates of the number of passengers getting off the bus, and steps (7.4.1) to (7.4.3) and (7.4.5) to (7.4.9) are simulation updates of the OD matrix.

[0215] The OD matrix only needs to be updated when passengers involve multiple transfer routes. This process divides a journey spanning multiple routes into multiple segments along the same route, and adds each segment back into the OD matrix. However, the exact arrival time of the next equivalent passenger flow can only be calculated by obtaining the actual departure times of passengers. Therefore, the equivalent segmentation must be calculated based on actual departure events during the simulation, and it is not possible to perform equivalent segmentation for all transfer passenger flows at the beginning. Figure 8 The image shows a travel route 1 in the subway network. G —15 G When passengers are on platform 1 G After boarding, the original route is divided into equivalent 1 G —3 G and 7 G —15 G Then passengers on platform 7 G After boarding, the original route was further divided into equivalent 1 G —3 G 7 G —9 G and 13 G —15 GUsing the equivalent segmentation method to process the OD matrix when calculating the total passenger waiting time will not affect the final result.

[0216] Figure 9 A block diagram of a train scheduling optimization device in a subway network according to an embodiment of the present disclosure is shown. Figure 9 As shown, the device includes:

[0217] The acquisition module 901 is used to acquire subway network data within a specified time period. The network data includes line information, train information, and passenger flow information. The line information includes at least one of the following: subway line number, direction of operation, transfer information between different subway lines, and station number of stations on the subway lines. The train information includes at least one of the following: train number, train capacity, train running time between adjacent stations, and train stopping time at stations on different subway lines in different directions. The passenger flow information includes the number of passengers entering from any departure station in the subway network and heading to any destination station within each unit time period of the specified time period.

[0218] The construction module 902 is used to construct an optimization model based on the road network data, with the train departure interval of each subway line in the subway network in each direction of operation as the independent variable. The optimization model represents the total waiting time of passengers waiting to board the train within the specified time period.

[0219] The optimization module 903 is used to determine the target departure interval of each train on each subway line in each direction of operation in the subway network based on the preset constraints for the departure interval and with the goal of minimizing the optimization model. The target departure interval is used to formulate the scheduling timetable of trains on each subway line in each direction of operation in the subway network during the specified time period.

[0220] In one possible implementation, the step of constructing an optimization model based on the road network data, with the departure intervals of trains on each subway line in each direction of operation as independent variables, includes: determining, based on the passenger flow information, the transfer information, and the train capacity, the number of passengers remaining at each station when each train departs from each station in each direction of operation on each subway line, and the number of passengers entering the station between the arrival time of each train and the departure time of the previous train in each direction of operation on each subway line; and constructing an optimization model based on the number of passengers remaining at each station when each train departs from each station in each direction of operation on each subway line, and the arrival time and departure time of each train at each station in each direction of operation on each subway line. The model calculates the waiting time of passengers stranded after a train departs from each station. Based on the number of passengers entering each station from the departure of the previous train to the arrival of each train in each direction of travel on each metro line, the arrival time of each train at each station, and the time intervals between the arrival time of each train and the departure time of the previous train, the model constructs the waiting time for newly arriving passengers before each train arrives at each station in each direction of travel on each metro line. The arrival time is constructed based on the independent variable parameter representing the departure interval, the dwell time, and the inter-station travel time. The departure time is constructed based on the arrival time and the dwell time. The optimization model includes the sum of the waiting time and the waiting time for entering the station.

[0221] In one possible implementation, the number of passengers remaining at station x when train i departs from station x in any direction of travel on any metro line includes: the difference between the number of passengers on the platform when train i arrives at station x and the number of passengers boarding when train i departs from station x, where 1 ≤ i ≤ I, I is the total number of trains in any direction of travel on any metro line, and 1 ≤ x ≤ N, N is the total number of stations on any metro line; wherein, the number of passengers on the platform when train i arrives at station x is based on the number of passengers remaining at station x when train i-1 departs from station x and the number of passengers boarding from station i-1 to station x. The number of passengers entering the x-th station during the period is determined by the number of passengers boarding when the i-th train leaves the x-th station. The number of passengers boarding when the i-th train leaves the x-th station is determined by the number of passengers on the platform when the i-th train arrives at the x-th station, the train capacity, the number of passengers on the i-th train when it arrives at the x-th station, and the number of passengers disembarking when the i-th train arrives at the n-th station. The number of passengers already on the i-th train when it arrives at the i-th station is determined by the number of passengers boarding and disembarking at each station the i-th train has passed through. The number of passengers disembarking when the i-th train arrives at the n-th station is determined by the passenger flow information and the transfer information.

[0222] In one possible implementation, the transfer information includes: direct transfer information and indirect transfer information between subway lines in the subway network. The direct transfer information includes the station number of a transfer station on any subway line for direct transfer to another subway line, and the indirect transfer information includes the station number of a transfer station on any subway line for indirect transfer to another subway line. The number of passengers entering station x in any direction of travel on any subway line from the departure of train i-1 from station x to the arrival of train i at station x is based on the number of passengers entering station x in any direction of travel on any subway line from station x. The total number of destination stations reachable from the departure point and the passenger flow information during the period from the departure of train i-1 from station x to the arrival of train i at station x are determined. Specifically, the total number of destination stations reachable from station x in any direction of travel includes all stations reachable from station x in any direction of travel on the metro line to which station x belongs, as well as all stations on other metro lines that can be transferred to after entering station x. The total number of stations on other metro lines that can be transferred to after entering station x is determined based on the direct transfer information, the indirect transfer information, and the line information.

[0223] In one possible implementation, the transfer information includes: direct transfer information, indirect transfer information, and transfer time information between subway lines in the subway network. The transfer time information includes the transfer time required to directly transfer from a transfer station on one subway line to a transfer station on another subway line. The device further includes:

[0224] The determination module is used to determine, based on the transfer information, any current subway line in the subway network, the adjacent subway lines that can be directly transferred from the current subway line, the current transfer station on the current subway line and the adjacent transfer station on the adjacent subway line, the transfer time required to transfer from the current transfer station to the adjacent transfer station, and the transfer time required to transfer from the adjacent transfer station to the current transfer station.

[0225] The arrival time determination module is used to determine the arrival time of the jth train at the current transfer station based on the target departure interval between every two trains from the first train to the jth train in any direction of operation of the current metro line, the inter-station running time of the train between two adjacent stations on the current metro line, and the station dwell time of the train at the station, 1 < j ≤ J, where J is the total number of trains in any direction of operation of the current metro line.

[0226] The time determination module is used to determine the first arrival time of the transfer passengers who disembark when the j-th train arrives at the current transfer station and the transfer time required to transfer from the current transfer station to the adjacent transfer station, based on the arrival time of the j-th train arriving at the current transfer station and the transfer time required to transfer from the current transfer station to the adjacent transfer station.

[0227] The train determination module is used to determine, based on the first arrival time, the kth train that leaves the adjacent transfer station before the first arrival time and the k+1th train that leaves the adjacent transfer station after the first arrival time in any direction of operation of the adjacent metro line, where 1≤k≤K and K is the total number of trains in any direction of operation on the adjacent metro line.

[0228] The arrival time determination module is used to determine, based on the target departure interval between every two trains on the adjacent metro line, the inter-station running time of trains on the adjacent metro line between two adjacent stations and the station dwell time of trains at stations, and the transfer time required to transfer from the adjacent transfer station to the current transfer station, the second arrival time of transfer passengers who disembark at the adjacent transfer station and arrive at the current transfer station before the departure time of the j-th train from the current transfer station; and the third arrival time of transfer passengers who arrive at the current transfer station after the departure time of the j-th train from the current transfer station.

[0229] The target departure interval optimization module is used to optimize the target departure intervals corresponding to train j and train j+1 based on the departure time of train k and train k+1 from the adjacent transfer station, the first arrival time, the second arrival time, the third arrival time, and the preset boundary threshold for departure intervals, to obtain the optimized departure intervals corresponding to train j and train j+1. The optimized departure intervals corresponding to each train in any direction of operation on any metro line are used to formulate the scheduling timetable for each train in any direction of operation on any metro line.

[0230] In one possible implementation, optimizing the target departure intervals for trains j and j+1 based on the departure times of train k and train k+1 from the adjacent transfer station, the first arrival time, the second arrival time, the third arrival time, and a preset boundary threshold for departure intervals, to obtain the optimized departure intervals for train j and train j+1, includes: optimizing the target departure intervals for train j and train j based on the boundary threshold and the target departure intervals for train j and train j+1. The initial upper bound for increasing the target departure interval for train j is determined, along with an initial upper bound for decreasing it. Based on the departure time of train k+1 from the adjacent transfer station, the first arrival time, and the initial upper bound, a target upper bound for increasing the target departure interval for train j is determined. This target upper bound ensures that passengers transferring from the current transfer station to the adjacent transfer station do not miss train k+1. Based on the departure time of train k from the adjacent transfer station and the first arrival time, the target upper bound for increasing the target departure interval for train j is determined. A target reduction lower bound is defined for the target departure interval corresponding to train j, which is used to ensure that transfer passengers transferring from the current transfer station to the adjacent transfer station catch train k. Based on the target departure interval corresponding to train j, the second arrival time, and the initial reduction upper bound, a target reduction upper bound is determined for the target departure interval corresponding to train j, which is used to ensure that transfer passengers arriving at the current transfer station at the second arrival time do not miss train j. Based on the target departure interval corresponding to train j and the third arrival time, a target increase lower bound is determined for the target departure interval corresponding to train j, which is used to ensure that transfer passengers arriving at the current transfer station at the third arrival time catch train j. Based on the target increase upper bound, target increase lower bound, target reduction upper bound, and target reduction lower bound, the target departure intervals corresponding to train j and train j+1 are optimized to obtain the optimized departure intervals corresponding to train j and train j+1.

[0231] In one possible implementation, optimizing the target departure intervals corresponding to train j and train j+1 based on the target increase upper bound, target increase lower bound, target decrease upper bound, and target decrease lower bound for the target departure interval corresponding to train j, to obtain the optimized departure intervals corresponding to train j and train j+1, includes: when the target decrease lower bound is less than or equal to the target decrease upper bound, and the target increase lower bound is greater than the target increase upper bound, determining the difference between the target departure interval corresponding to train j and the target decrease lower bound as the optimized departure interval corresponding to train j; and determining the sum of the target departure interval corresponding to train j+1 and the target decrease lower bound as the optimized departure interval corresponding to train j+1; or, when the target increase lower bound is less than or equal to the target decrease upper bound, optimizing the target departure interval corresponding to train j and train j+1 based on the target increase upper bound, target decrease lower bound, and target decrease lower bound, optimizing the target departure interval corresponding to train j and train j+1 based on the target increase upper bound, target decrease lower bound, and target decrease lower bound; or, when the target increase lower bound is less than or equal to the target decrease lower bound, optimizing the target departure interval corresponding to train j and train j+1 based on the target decrease upper bound, optimizing the target departure interval corresponding to train j and train j+1 based on the target decrease lower ... If the target increase lower bound is less than or equal to the target increase upper bound, and the target decrease lower bound is greater than the target decrease upper bound, the sum of the target departure interval corresponding to the j-th train and the target increase lower bound is determined as the optimized departure interval corresponding to the j-th train, and the difference between the target departure interval corresponding to the (j+1)-th train and the target increase lower bound is determined as the optimized departure interval corresponding to the (j+1)-th train; or, if the target increase lower bound is less than or equal to the target increase upper bound, and the target decrease lower bound is less than or equal to the target decrease upper bound, the target departure intervals corresponding to the j-th train and the (j+1)-th train are optimized according to the minimum value between the target increase lower bound and the target decrease lower bound, to obtain the optimized departure intervals corresponding to the j-th train and the (j+1)-th train.

[0232] In one possible implementation, determining the target departure interval for each train on each metro line in each direction of operation in the metro network, based on preset constraints for departure intervals and with the objective of minimizing the optimization model, includes: generating an initial population based on preset constraints for departure intervals. The initial population comprises multiple individuals, each individual representing the departure interval corresponding to each train on each metro line in each direction of operation in the metro network. The constraints include: the sum of the target departure intervals for all trains on any metro line in any direction of operation equals the specified time period; and any target departure interval does not exceed a preset boundary threshold. Based on the initial population, the following M-round iterative processing is performed, where M is a positive integer: in the m-th round of iterative processing, the optimization model is used to calculate the target departure interval for each train on the m-th generation population. The total passenger waiting time corresponding to each of the μ individuals is calculated. Based on the total passenger waiting time corresponding to each of the μ individuals in the m-th generation population, y individuals are randomly selected from the m-th generation population, where 1 ≤ m ≤ M, the first generation population is the initial population, μ is a positive integer, and 1 ≤ y ≤ μ. The y individuals selected from the m-th generation population are processed using a preset crossover operator and / or mutation operator to obtain λ offspring individuals, where λ is a positive integer. μ offspring individuals are selected from the parent population formed by the λ offspring individuals and the μ individuals in the m-th generation population to obtain the (m+1)-th generation population. For the (M+1)-th generation population obtained after the M-th iteration, the individual with the smallest total passenger waiting time in the (M+1)-th generation population is determined as the target departure interval for each train on each subway line in each direction of operation in the subway network.

[0233] In one possible implementation, the mutation operator includes at least one of the following: a single-point mutation operator, a swap mutation operator, a flip mutation operator, and a translation mutation operator; wherein, the single-point mutation operator is used to perform a single-point mutation process to increase or decrease any departure interval in an individual and to perform the opposite single-point mutation process on adjacent departure intervals; the swap mutation operator is used to perform a swap process on any two departure intervals in the same direction of operation of the same metro line in an individual; the flip mutation operator is used to perform a flip process on at least two departure intervals in any interval in the same direction of operation of the same metro line in an individual; the translation mutation operator is used to perform a head-to-tail translation process on all departure intervals in the same direction of operation of the same metro line in an individual; and the crossover operator is used to perform a weighted summation process on every two individuals selected from the m-th generation population based on random numbers randomly selected from a specified range.

[0234] In one possible implementation, before processing the y individuals selected from the m-th generation population using a preset crossover operator and / or mutation operator, the method further includes: determining the mutation probability and crossover probability corresponding to the m-th iteration based on a first preset relationship between the number of iteration rounds and the mutation probability, and a second preset relationship between the number of iteration rounds and the crossover probability, and determining whether the mutation probability and crossover probability corresponding to the m-th iteration are greater than a random number randomly selected from a specified range; wherein, the first preset relationship indicates a negative correlation between the mutation probability and the number of iteration rounds, and the second preset relationship indicates a positive correlation between the crossover probability and the number of iteration rounds; if the mutation probability corresponding to the m-th iteration is greater than the random number, determining to process the y individuals selected from the m-th generation population using a preset mutation operator; if the crossover probability corresponding to the m-th iteration is greater than the random number, determining to process the y individuals selected from the m-th generation population using a preset crossover operator.

[0235] According to the embodiments of this disclosure, an optimization model is established by using the line information, train information, and passenger flow information of the entire subway network. Based on preset constraints, the optimized target departure interval is determined with the goal of minimizing the optimization model, that is, minimizing the total waiting time of passengers. This not only achieves the overall optimization of the train departure interval in the subway network, but also the overall optimization of the train scheduling timetable in the subway network. When using the scheduling timetable based on the target departure interval for train scheduling, the waiting time of passengers in the subway network can be shortened, the subway operation efficiency can be improved, and thus the passenger service quality and subway riding experience can be improved.

[0236] In some embodiments, the functions or modules of the apparatus provided in this disclosure can be used to perform the methods described in the above method embodiments. The specific implementation can be referred to the description of the above method embodiments, and for the sake of brevity, it will not be repeated here.

[0237] This disclosure also proposes a computer-readable storage medium storing computer program instructions that, when executed by a processor, implement the above-described method. The computer-readable storage medium can be volatile or non-volatile.

[0238] This disclosure also proposes an electronic device, including: a processor; and a memory for storing processor-executable instructions; wherein the processor is configured to implement the above method when executing the instructions stored in the memory.

[0239] This disclosure also provides a computer program product, including computer-readable code, or a non-volatile computer-readable storage medium carrying computer-readable code, wherein when the computer-readable code is run in a processor of an electronic device, the processor in the electronic device performs the above-described method.

[0240] Figure 10 A block diagram of an electronic device 1900 according to an embodiment of the present disclosure is shown. For example, the electronic device 1900 may be provided as a server or a terminal device. (Refer to...) Figure 10 The electronic device 1900 includes a processing component 1922, which further includes one or more processors, and memory resources represented by memory 1932 for storing instructions, such as application programs, that can be executed by the processing component 1922. The application programs stored in memory 1932 may include one or more modules, each corresponding to a set of instructions. Furthermore, the processing component 1922 is configured to execute instructions to perform the methods described above.

[0241] Electronic device 1900 may also include a power supply component 1926 configured to perform power management of electronic device 1900, a wired or wireless network interface 1950 configured to connect electronic device 1900 to a network, and an input / output interface 1958 (I / O interface). Electronic device 1900 can operate on an operating system, such as Windows Server, stored in memory 1932. TM Mac OS X TM Unix TM Linux TM FreeBSD TM Or similar.

[0242] In an exemplary embodiment, a non-volatile computer-readable storage medium is also provided, such as a memory 1932 including computer program instructions that can be executed by a processing component 1922 of an electronic device 1900 to perform the above-described method.

[0243] This disclosure can be a system, method, and / or computer program product. A computer program product may include a computer-readable storage medium having computer-readable program instructions loaded thereon for causing a processor to implement various aspects of this disclosure.

[0244] Computer-readable storage media can be tangible devices capable of holding and storing instructions for use by an instruction execution device. Computer-readable storage media can be, for example—but not limited to—electrical storage devices, magnetic storage devices, optical storage devices, electromagnetic storage devices, semiconductor storage devices, or any suitable combination thereof. More specific examples (a non-exhaustive list) of computer-readable storage media include: portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), static random access memory (SRAM), portable compact disc read-only memory (CD-ROM), digital multifunction disc (DVD), memory sticks, floppy disks, mechanical encoding devices, such as punch cards or recessed protrusions storing instructions thereon, and any suitable combination thereof. The computer-readable storage media used herein are not to be construed as transient signals themselves, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through waveguides or other transmission media (e.g., light pulses through fiber optic cables), or electrical signals transmitted through wires.

[0245] The computer-readable program instructions described herein can be downloaded from computer-readable storage media to various computing / processing devices, or downloaded via a network, such as the Internet, local area network, wide area network, and / or wireless network, to an external computer or external storage device. The network may include copper transmission cables, fiber optic transmission, wireless transmission, routers, firewalls, switches, gateway computers, and / or edge servers. A network adapter card or network interface in each computing / processing device receives the computer-readable program instructions from the network and forwards them to the computer-readable storage media in the respective computing / processing device.

[0246] Computer program instructions used to perform the operations of this disclosure may be assembly instructions, instruction set architecture (ISA) instructions, machine instructions, machine-dependent instructions, microcode, firmware instructions, status setting data, or source code or object code written in any combination of one or more programming languages, including object-oriented programming languages ​​such as Smalltalk, C++, etc., and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The computer-readable program instructions may execute entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving a remote computer, the remote computer may be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or may be connected to an external computer (e.g., via the Internet using an Internet service provider). In some embodiments, electronic circuitry, such as programmable logic circuitry, field-programmable gate arrays (FPGAs), or programmable logic arrays (PLAs), is personalized by utilizing the status information of the computer-readable program instructions to implement various aspects of this disclosure.

[0247] Various aspects of this disclosure are described herein with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this disclosure. It should 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-readable program instructions.

[0248] These computer-readable program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, or other programmable data processing apparatus to produce a machine such that, when executed by the processor of the computer or other programmable data processing apparatus, they create means for implementing the functions / actions specified in one or more blocks of the flowchart and / or block diagram. These computer-readable program instructions can also be stored in a computer-readable storage medium that causes a computer, programmable data processing apparatus, and / or other device to operate in a particular manner; thus, the computer-readable medium storing the instructions comprises an article of manufacture that includes instructions for implementing aspects of the functions / actions specified in one or more blocks of the flowchart and / or block diagram.

[0249] Computer-readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable data processing apparatus, or other device to produce a computer-implemented process, thereby causing the instructions executed on the computer, other programmable data processing apparatus, or other device to perform the functions / actions specified in one or more boxes of a flowchart and / or block diagram.

[0250] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present disclosure. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of an instruction containing one or more executable instructions for implementing a specified logical function. In some alternative implementations, the functions marked in the blocks may occur in a different order than those shown in the drawings. For example, two consecutive blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, may be implemented using a dedicated hardware-based system that performs the specified function or action, or using a combination of dedicated hardware and computer instructions.

[0251] The various embodiments of this disclosure have been described above. These descriptions are exemplary and not exhaustive, nor are they limited to the disclosed embodiments. Many modifications and variations will be apparent to those skilled in the art without departing from the scope and spirit of the described embodiments. The terminology used herein is chosen to best explain the principles, practical application, or technical improvements to the embodiments in the market, or to enable others skilled in the art to understand the embodiments disclosed herein.

Claims

1. A method for optimizing train scheduling in a subway network, characterized in that, include: The system acquires subway network data for a specified time period. This network data includes line information, train information, and passenger flow information. The line information includes: subway line number, direction of travel, transfer information between different subway lines, and station number on each subway line. The train information includes: train number, train capacity, train travel time between adjacent stations, and train stop time at each station on different subway lines in different directions. The passenger flow information includes the number of passengers entering from any departure station and traveling to any destination station within each unit of the specified time period. Based on the road network data, an optimization model is constructed with the train departure interval of each subway line in each direction of operation in the subway network as the independent variable. The optimization model represents the total waiting time of passengers waiting to board the train within the specified time period. Based on the pre-set constraints for the departure interval, with the goal of minimizing the optimization model, the target departure interval for each train on each subway line in each direction of operation in the subway network is determined. The target departure interval is used to formulate the scheduling timetable for trains on each subway line in each direction of operation in the subway network during the specified time period. The transfer information includes: direct transfer information, indirect transfer information, and transfer time information between subway lines in the subway network. The transfer time information includes the transfer time required to directly transfer from a transfer station on any subway line to a transfer station on another subway line. The method further includes: For any current subway line in the subway network, based on the transfer information, determine the adjacent subway lines that can be directly transferred from the current subway line, the current transfer station on the current subway line and the adjacent transfer station on the adjacent subway line, the transfer time required to transfer from the current transfer station to the adjacent transfer station, and the transfer time required to transfer from the adjacent transfer station to the current transfer station; Based on the target departure interval between every two trains from the first train to the jth train in any direction of operation of the current metro line, the inter-station running time of trains on the current metro line between two adjacent stations, and the station dwell time of trains, the arrival time of the jth train at the current transfer station is determined, 1 < j ≤ J, where J is the total number of trains in any direction of operation of the current metro line. Based on the arrival time of the j-th train at the current transfer station and the transfer time required to transfer from the current transfer station to the adjacent transfer station, determine the first arrival time of the transfer passengers who disembark when the j-th train arrives at the current transfer station and arrive at the adjacent transfer station. Based on the first arrival time, determine the kth train that leaves the adjacent transfer station before the first arrival time and the (k+1)th train that leaves the adjacent transfer station after the first arrival time in any direction of operation of the adjacent metro line, where 1≤k≤K and K is the total number of trains in any direction of operation on the adjacent metro line. Based on the target departure interval between every two trains on the adjacent metro line, the inter-station running time of trains on the adjacent metro line between two adjacent stations and the station dwell time of trains, and the transfer time required to transfer from the adjacent transfer station to the current transfer station, the second arrival time of transfer passengers who get off at the adjacent transfer station and arrive at the current transfer station before the departure time of the j-th train from the current transfer station, and the third arrival time of transfer passengers who arrive at the current transfer station after the departure time of the j-th train from the current transfer station are determined. Based on the departure time of the k-th train and the (k+1)-th train from the adjacent transfer station, the first arrival time, the second arrival time, the third arrival time, and the preset boundary threshold for the departure interval, the target departure intervals corresponding to the j-th train and the (j+1)-th train are optimized to obtain the optimized departure intervals corresponding to the j-th train and the (j+1)-th train. Among them, the optimized departure intervals for each train in any direction of operation on any metro line are used to formulate the scheduling timetable for each train in any direction of operation on any metro line.

2. The method according to claim 1, characterized in that, The step of constructing an optimization model based on the road network data, with the train departure intervals of each subway line in each direction of operation in the subway network as independent variables, includes: Based on the passenger flow information, the transfer information, and the train capacity, determine the number of passengers remaining at each station when each train leaves each station in each direction of operation on each subway line, and the number of passengers entering the station between the arrival time of each train entering the station and the departure time of the previous train leaving the station on each direction of operation on each subway line. Based on the number of passengers waiting at each station when each train departs from each station in each direction of operation on each subway line, as well as the arrival time and departure time of each train at each station, the waiting time of passengers waiting at each station after each train departs from each station in each direction of operation on each subway line is constructed. Based on the number of passengers entering the station from the departure of the previous train to the arrival of each train in each direction of operation of each subway line, the arrival time of each train at each station, and the time intervals between the arrival time of each train and the departure time of the previous train, the waiting time for new passengers entering the station before each train arrives at each station in each direction of operation of each subway line is constructed. The arrival time is constructed based on the independent variable parameter representing the departure interval, the stop duration, and the inter-station running time; the departure time is constructed based on the arrival time and the stop duration; the optimization model includes the sum of the waiting time and the waiting time for entering the station.

3. The method according to claim 2, characterized in that, The number of passengers stranded when the i-th train leaves the x-th station in any direction of travel on any metro line includes the difference between the number of passengers on the platform when the i-th train arrives at the x-th station and the number of passengers boarding when the i-th train leaves the x-th station, 1≤i≤I, where I is the total number of trains in any direction of travel on any metro line, 1≤x≤N, where N is the total number of stations on any metro line. The number of passengers on the platform when the i-th train arrives at the x-th station is determined based on the number of passengers who were stranded when the (i-1)-th train left the x-th station and the number of passengers who entered the x-th station from the time the (i-1)-th train left the x-th station to the time the i-th train entered the x-th station. The number of passengers boarding when train i departs from station x is determined based on the number of passengers on the platform when train i arrives at station x, the train capacity, the number of passengers on train i when train i arrives at station x, and the number of passengers disembarking when train i arrives at station x. The number of passengers already on train i when train i arrives at station x is determined based on the number of passengers boarding and disembarking at each station that train i has passed through. The number of passengers disembarking when train i arrives at station x is determined based on the passenger flow information and the transfer information.

4. The method according to claim 2 or 3, characterized in that, The direct transfer information includes the station number of the transfer station on any metro line for direct transfer to another metro line, and the indirect transfer information includes the station number of the transfer station on any metro line for indirect transfer to another metro line. The number of passengers entering station x in any direction of operation of any metro line from the departure of train i-1 from station x to the arrival of train i at station x is determined based on all destination stations reachable from station x in any direction of operation of any metro line and passenger flow information from the departure of train i-1 from station x to the arrival of train i at station x. Wherein, all destination stations that can be reached from the x-th station in any direction of operation include: all stations that can be reached from the x-th station in any direction of operation on the metro line to which the x-th station belongs, as well as all stations on other metro lines that can be transferred to after entering the x-th station. The total number of stations on other metro lines that can be transferred to after entering the x-th station is determined based on the direct transfer information, the indirect transfer information, and the line information.

5. The method according to claim 1, characterized in that, The optimization of the target departure intervals for trains j and j+1, based on the departure times of train k and train k+1 from the adjacent transfer station, the first arrival time, the second arrival time, the third arrival time, and a preset boundary threshold for departure intervals, to obtain the optimized departure intervals for train j and train j+1, includes: Based on the boundary threshold and the target departure intervals corresponding to the j-th train and the (j+1)-th train, determine the initial upper bound for increasing the target departure interval and the initial upper bound for decreasing the target departure interval corresponding to the j-th train. Based on the departure time of the (k+1)th train from the adjacent transfer station, the first arrival time, and the initial upper bound, the target upper bound for the target departure interval corresponding to the jth train is determined. The target upper bound is used to ensure that transfer passengers transferring from the current transfer station to the adjacent transfer station do not miss the (k+1)th train. Based on the departure time of the kth train from the adjacent transfer station and the first arrival time, a target reduction lower bound for the target departure interval corresponding to the jth train is determined. The target reduction lower bound is used to ensure that transfer passengers transferring from the current transfer station to the adjacent transfer station catch the kth train. Based on the target departure interval corresponding to the j-th train, the second arrival time, and the initial reduction upper bound, the target reduction upper bound for the target departure interval corresponding to the j-th train is determined. The target reduction upper bound is used to ensure that transfer passengers arriving at the current transfer station at the second arrival time do not miss the j-th train. Based on the target departure interval corresponding to the j-th train and the third arrival time, a target increase lower bound for the target departure interval corresponding to the j-th train is determined. The target increase lower bound is used to ensure that the transfer passengers arriving at the current transfer station at the third arrival time catch the j-th train. Based on the target increase upper bound, target increase lower bound, target decrease upper bound, and target decrease lower bound for the target departure interval corresponding to train j, the target departure intervals corresponding to train j and train j+1 are optimized to obtain the optimized departure intervals corresponding to train j and train j+1.

6. The method according to claim 5, characterized in that, The optimization of the target departure intervals for train j and train j+1, based on the target increase upper bound, target increase lower bound, target decrease upper bound, and target decrease lower bound for the target departure interval corresponding to train j, yields the optimized departure intervals for train j and train j+1, including: When the target reduction lower bound is less than or equal to the target reduction upper bound, and the target increase lower bound is greater than the target increase upper bound, the difference between the target departure interval corresponding to the j-th train and the target reduction lower bound is determined as the optimized departure interval corresponding to the j-th train, and the sum of the target departure interval corresponding to the (j+1)-th train and the target reduction lower bound is determined as the optimized departure interval corresponding to the (j+1)-th train; or, If the target increase lower bound is less than or equal to the target increase upper bound, and the target decrease lower bound is greater than the target decrease upper bound, then the sum of the target departure interval corresponding to the j-th train and the target increase lower bound is determined as the optimized departure interval corresponding to the j-th train, and the difference between the target departure interval corresponding to the (j+1)-th train and the target increase lower bound is determined as the optimized departure interval corresponding to the (j+1)-th train; or, When the target increase lower bound is less than or equal to the target increase upper bound, and the target decrease lower bound is less than or equal to the target decrease upper bound, the target departure intervals corresponding to the j-th train and the (j+1)-th train are optimized based on the minimum value between the target increase lower bound and the target decrease lower bound, thus obtaining the optimized departure intervals corresponding to the j-th train and the (j+1)-th train.

7. The method according to claim 1, characterized in that, The determination of the target departure interval for each train on each subway line in each direction of travel in the subway network, based on the preset constraints for departure intervals and with the objective of minimizing the optimization model, includes: Based on the preset constraints for departure intervals, an initial population is generated. The initial population includes multiple individuals, and each individual includes the departure intervals corresponding to each train on each subway line in each direction of operation in the subway network. The constraints include: the sum of the target departure intervals corresponding to all trains on any subway line in any direction of operation is equal to the specified time period, and any target departure interval does not exceed the preset boundary threshold. Based on the initial population described above, perform the following M rounds of iterative processing, where M is a positive integer: In the m-th iteration, the optimization model is used to calculate the population in the m-th generation. The total passenger waiting time for each individual, based on the population in generation m. The total waiting time for each individual passenger is calculated by randomly selecting y individuals from the m-th generation population, where 1 ≤ m ≤ M, and the first generation population is the initial population. For positive integers, 1 ≤ y ≤ ; The y individuals selected from the m-th generation population are processed using a preset crossover operator and / or mutation operator to obtain... Individual offspring It is a positive integer; From the above The offspring individuals and the population in the m-th generation Selecting from the parent population consisting of individuals 1+1 offspring individuals are obtained to form the (m+1)th generation population. For the M+1th generation population obtained after the Mth iteration, the individual with the smallest total passenger waiting time in the M+1th generation population is determined as the target departure interval for each train on each subway line in each direction of operation in the subway network.

8. The method according to claim 7, characterized in that, The mutation operator includes at least one of the following: a single-point mutation operator, a swap mutation operator, a flip mutation operator, and a translation mutation operator; wherein, the single-point mutation operator is used to perform a single-point mutation process to increase or decrease any departure interval in an individual and to perform the opposite single-point mutation process on adjacent departure intervals; the swap mutation operator is used to perform a swap process on any two departure intervals in the same direction of operation of the same metro line in an individual; the flip mutation operator is used to perform a flip process on at least two departure intervals in any section in the same direction of operation of the same metro line in an individual; and the translation mutation operator is used to perform a head-to-tail translation process on all departure intervals in the same direction of operation of the same metro line in an individual. The crossover operator is used to perform a weighted summation on every two individuals selected from the y individuals in the m-th generation population, based on random numbers randomly selected from a specified range.

9. The method according to claim 7 or 8, characterized in that, Before processing the y individuals selected from the m-th generation population using preset crossover and / or mutation operators, the method further includes: Based on a first preset relationship between the number of iteration rounds and the mutation probability, and a second preset relationship between the number of iteration rounds and the crossover probability, the mutation probability and crossover probability corresponding to the m-th iteration are determined, and it is determined whether the mutation probability and crossover probability corresponding to the m-th iteration are greater than a random number randomly selected from a specified range; wherein, the first preset relationship indicates that the mutation probability and the number of iteration rounds are negatively correlated, and the second preset relationship indicates that the crossover probability and the number of iteration rounds are positively correlated; If the mutation probability corresponding to the m-th iteration is greater than the random number, it is determined that a preset mutation operator will be used to process the y individuals selected from the m-th generation population. If the crossover probability corresponding to the m-th iteration is greater than the random number, a preset crossover operator is used to process the y individuals selected from the m-th generation population.

10. A train scheduling optimization device for a subway network, characterized in that, include: The acquisition module is used to acquire subway network data within a specified time period. The network data includes line information, train information, and passenger flow information. The line information includes: subway line number, direction of operation, transfer information between different subway lines, and station number of stations on the subway lines. The train information includes: train number, train capacity, train running time between adjacent stations, and train dwell time at stations on different subway lines in different directions. The passenger flow information includes the number of passengers entering from any departure station in the subway network and heading to any destination station within each unit time period of the specified time period. The construction module is used to construct an optimization model based on the road network data, with the train departure interval of each subway line in the subway network in each direction of operation as the independent variable. The optimization model represents the total waiting time of passengers waiting to board the train within the specified time period. The optimization module is used to determine the target departure interval of each train on each subway line in each direction of operation in the subway network based on the preset constraints for the departure interval and with the goal of minimizing the optimization model. The target departure interval is used to formulate the scheduling timetable of trains on each subway line in each direction of operation in the subway network during the specified time period. The transfer information includes: direct transfer information, indirect transfer information, and transfer time information between subway lines in the subway network. The transfer time information includes the transfer time required to directly transfer from a transfer station on one subway line to a transfer station on another subway line. The device also includes: The determination module is used to determine, based on the transfer information, any current subway line in the subway network, the adjacent subway lines that can be directly transferred from the current subway line, the current transfer station on the current subway line and the adjacent transfer station on the adjacent subway line, the transfer time required to transfer from the current transfer station to the adjacent transfer station, and the transfer time required to transfer from the adjacent transfer station to the current transfer station. The arrival time determination module is used to determine the arrival time of the jth train at the current transfer station based on the target departure interval between every two trains from the first train to the jth train in any direction of operation of the current metro line, the inter-station running time of the train between two adjacent stations on the current metro line, and the station dwell time of the train at the station, 1 < j ≤ J, where J is the total number of trains in any direction of operation of the current metro line. The time determination module is used to determine the first arrival time of the transfer passengers who disembark when the j-th train arrives at the current transfer station and the transfer time required to transfer from the current transfer station to the adjacent transfer station, based on the arrival time of the j-th train arriving at the current transfer station and the transfer time required to transfer from the current transfer station to the adjacent transfer station. The train determination module is used to determine, based on the first arrival time, the kth train that leaves the adjacent transfer station before the first arrival time and the k+1th train that leaves the adjacent transfer station after the first arrival time in any direction of operation of the adjacent metro line, where 1≤k≤K and K is the total number of trains in any direction of operation on the adjacent metro line. The arrival time determination module is used to determine, based on the target departure interval between every two trains on the adjacent metro line, the inter-station running time of trains on the adjacent metro line between two adjacent stations and the station dwell time of trains at stations, and the transfer time required to transfer from the adjacent transfer station to the current transfer station, the second arrival time of transfer passengers who disembark at the adjacent transfer station and arrive at the current transfer station before the departure time of the j-th train from the current transfer station; and the third arrival time of transfer passengers who arrive at the current transfer station after the departure time of the j-th train from the current transfer station. The target departure interval optimization module is used to optimize the target departure intervals corresponding to train j and train j+1 based on the departure time of train k and train k+1 from the adjacent transfer station, the first arrival time, the second arrival time, the third arrival time, and the preset boundary threshold for departure intervals, to obtain the optimized departure intervals corresponding to train j and train j+1. The optimized departure intervals corresponding to each train in any direction of operation on any metro line are used to formulate the scheduling timetable for each train in any direction of operation on any metro line.

11. An electronic device, characterized in that, include: processor; Memory used to store processor-executable instructions; The processor is configured to implement the method of any one of claims 1 to 9 when executing instructions stored in the memory.

12. A non-volatile computer-readable storage medium storing computer program instructions thereon, characterized in that, When the computer program instructions are executed by the processor, they implement the method described in any one of claims 1 to 9.

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