A method for optimizing bus schedule with maximum synchronous transfer considering passenger flow constraints

Abstract

The present invention discloses a method for optimizing a bus schedule with maximum synchronous transfers considering passenger flow constraints. The arrival and departure times of each train at the subway station studied during peak hours, the operation information of bus lines around the subway station, subway automatic ticket vending and checking system data, bus card swiping data, mobile phone signaling data, and bus operation GPS data are obtained, the geometric layout of bus lines around the subway station is analyzed, effective transfer lines are screened, and the number of effective transfer passengers is counted; the study period is divided by clustering, and the vehicle arrival rules, transfer passenger travel time, bus station capacity, and bus vehicle full load rate are comprehensively considered to establish a bus line schedule optimization model based on the maximum number of transfers; the improved gray wolf algorithm is used to solve the model to obtain the bus line schedule optimization plan. The present invention can optimize the efficiency of bus operation, effectively reduce the waiting time for passenger transfers, and improve the passenger bus travel experience.

Description

Technical Field

[0001] The invention relates to the technical field of urban public transportation operation management, in particular to a method for optimizing a maximum synchronous transfer bus schedule considering passenger flow constraints. Background Art

[0002] Subway and bus schedules are often set independently, resulting in an inefficient connection between the two modes of transportation, which seriously affects the smoothness and satisfaction of passengers. Therefore, when optimizing bus schedules, the operation of subways along the lines should be considered and integrated to form an efficient and coordinated operation model, and by building a cooperative and complementary urban public transportation system, the optimal allocation and efficient use of public transportation resources can be achieved.

[0003] On the other hand, given the significant differences between subways and buses in terms of vehicle capacity, line layout, functional positioning, and the pulsed characteristics of passenger flow in time and space, in actual operation, it is easy to lead to inefficient transfer systems and even cause traffic congestion. Summary of the invention

[0004] In view of this, the purpose of the present invention is to provide a maximum synchronous transfer bus schedule optimization method considering passenger flow constraints, which is conducive to optimizing bus operation efficiency, effectively reducing passenger transfer waiting time, and improving passengers' bus travel experience.

[0005] To achieve the above object, the present invention adopts the following technical solution: a method for optimizing a maximum synchronous transfer bus schedule considering passenger flow constraints, comprising the following steps:

[0006] Step S1: Obtain the subway station train departure timetable, subway station surrounding bus line operation information, subway automatic ticket vending system data, bus card swiping data, mobile phone signaling data, bus operation GPS data;

[0007] Step S2: Analyze the geometric layout of bus routes around the subway station under study, and filter out bus routes whose downstream are parallel to the subway line;

[0008] Step S3: Divide the research period by clustering;

[0009] Step S4: Analyze the passenger transfer walking pattern, bus line bus full load rate, passenger flow arrival pattern, vehicle arrival pattern, match passenger data, and calculate the number of transfer passengers on the effective transfer line;

[0010] Step S5: Based on the transfer mode of passengers transferring from subway to bus, bus to subway, and bus to bus, a maximum synchronous transfer bus schedule optimization model is established;

[0011] Step S6: Optimizing the traditional gray wolf algorithm, solving the maximum synchronous transfer bus schedule optimization model, and taking the approximate optimal solution of the model decision variables as the bus departure schedule of the maximum synchronous transfer solution, thereby completing the maximum synchronous transfer bus schedule optimization method considering passenger flow constraints;

[0012] In a preferred embodiment, the step S5 specifically includes the following steps:

[0013] Step S51: for the studied subway station, define it and surrounding bus transfer stations and lines as a topological structure;

[0014] Step S52: Construct a set of subway train numbers within the research period M ={1,2,3,…, m}, m Indicates subway train number and bus stop collection R ={1,2,3,…, r}, r Represents a collection of bus stops and bus routes L ={1,2,3,…, l}, l Indicates bus routes; passing through bus stops R Any bus stop r Line collection L r ={1,2,…, l r}, l r Indicates passing by bus stop R Any bus stop r The route, all bus schedules of all routes are set U = ( A l , B b ,…, L i , S j ), bus routes l Bus schedule collection L i =(1,2,…, f l ), f l The bus routes during the study period l The last shift, l i For Line l Flights i The index of other bus routes can be expressed in the same way;

[0015] Step S53: Set the bus departure time and the synchronization variable as two decision variables, and maximize the number of synchronous transfers as the objective function maxZ. The calculation formula is as follows:

[0016]

[0017] In the formula, is the simultaneous decision variable for transferring from subway to bus; is the synchronous decision variable for transfers between different bus lines; The simultaneous decision variables for bus transfer to subway; and is the proportionality coefficient, which is used to quantify the difference between subway and bus transfers. The larger the proportionality coefficient, the greater the weight of synchronization, indicating that the value of synchronization between the line and the subway is higher;

[0018] Step S54: Set the departure interval constraint, the calculation formula is as follows:

[0019]

[0020] In the formula, and For bus routes l Two adjacent flights i and i -1 departure time; The departure time of the first bus of each regular bus route during the study period; and Bus routes l The maximum and minimum departure intervals; T For the research period, Indicates the bus routes during the study period l The last bus departure time of

[0021] Step S55: Set the synchronization determination constraint, the calculation formula is as follows:

[0022]

[0023] In the formula, For bus routes l of vehicles from the station to the bus stop r Average travel time; For subway trains m The arrival time of It is the walking time for passengers from the subway station hall to the bus stop; is an arbitrarily large but not infinite positive number; The length of the time window for transferring from subway to bus; For bus routes s Flights j The departure time of ,and ; For bus routes s of vehicles from the station to the bus stop r Average travel time; For bus routes l of vehicles from the station to the bus stop r With bus lines s of vehicles from the station to the bus stop r time difference; At the same bus stop r The length of the time window for transferring from one bus line to another; It is the walking time for passengers from the bus stop to the subway station hall; The length of the time window for transferring from bus to subway;

[0024] Step S56: Set the value range of the synchronization determination variable, and the calculation formula is as follows:

[0025]

[0026] Step S57: The number of transfer passengers is constrained, and the calculation formula is as follows:

[0027]

[0028] In the formula, is the reduction factor of the alternative bus routes; For bus stops r the maximum number of passengers that can be accommodated; Get off at subway station m and you will be at the bus stop r The number of passengers waiting to transfer to another bus; The revised bus stop r The maximum number of passengers that can be accommodated;

[0029] Step S58: Set the passenger load factor constraint, the calculation formula is as follows:

[0030]

[0031] In the formula, To reach the bus stop r The passenger load factor of public transport vehicles at the time of is the bus load factor.

[0032] In a preferred embodiment, the step 3 specifically includes the following steps:

[0033] Step S31: Eliminate time periods with a small number of bus routes based on the operation information of bus routes around the subway station;

[0034] Step S32: Divide the operation data of each line into two groups: working days and rest days;

[0035] Step S33: Based on the travel time characteristics, a K-center point clustering algorithm is used to perform clustering to obtain clustering results for working days and rest days;

[0036] Step S34: Fit the line clustering results with a distribution function, and use the KS test to evaluate the fitting effect, so as to obtain the distribution function of the average one-way running time of the line.

[0037] In a preferred embodiment, the step S4 specifically includes the following steps:

[0038] Step S41: analyzing the walking characteristics of passengers from four aspects: walking speed, static space, dynamic space, and psychological buffer space;

[0039] Step S42: Analyze the arrival pattern of bus-to-subway passenger flow to obtain the transfer travel time;

[0040] Step S43: Analyze the arrival pattern of subway-to-bus passenger flow to obtain transfer travel time;

[0041] Step S44: Analyze the arrival pattern of public buses and, in combination with GPS data, obtain the average arrival time of public buses at each station;

[0042] Step S45: Calculate the number of transfer passengers based on the valid bus routes.

[0043] In a preferred embodiment, the implementation steps of step S6 are as follows:

[0044] Step S61: Introducing a cosine law-based variation convergence factor a , the calculation formula is:

[0045]

[0046] Where: a min and a max are the upper and lower limits of the convergence factor, respectively, the gray wolf algorithm a min Take 0, a max Take 2, d and d max They are the current number of iterations and the maximum number of iterations of the algorithm respectively;

[0047] Step S62: Update the optimized position, the calculation formula is:

[0048]

[0049] Where: w 1. w 2. w 3 are α , β and δ The dynamic weight coefficient of the wolf in updating the next generation of wolf pack positions, f α , f β , f δ They are α , β and δ Wolf fitness; They represent the best fitness in the traditional grey wolf algorithm. α The wolf is the potential optimal solution. β Wolf, δ The wolf's position vector; t Represents algebra; Indicates the location of the next generation of gray wolf individuals;

[0050] The dynamic update formula of its position is transformed into:

[0051]

[0052] Step S63: Add simulated annealing operation, the calculation formula is:

[0053]

[0054] Where: is the fitness of the newly generated solution to the model, represents the fitness of the current solution, T p is the current temperature.

[0055] Compared with the prior art, the present invention has the following beneficial effects:

[0056] The present invention realizes the maximum synchronous transfer between buses and subways, which not only fully considers the bus running time, station capacity and passenger load factor, but also takes into account the transfer and travel patterns of passengers within the study period, thereby realizing efficient coordination within the public transportation system, maximizing the overall efficiency of public transportation, and improving passengers' travel experience and satisfaction.

[0057] The bus timetable optimization scheme calculated by the present invention provides a kind of efficient and economical resource allocation idea for public transportation operation management departments, helps to improve the operation efficiency of the public transportation system, promotes the fairness and sustainable development of public transportation, and has practical significance for building a more harmonious and livable urban transportation environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 A flowchart of a method implementation of an embodiment of the present invention;

[0059] Figure 2 It is a flow chart of fitting the distribution function of the average one-way running time of a line in an embodiment of the present invention;

[0060] Figure 3 A flowchart for calculating the number of valid transfer passengers in an embodiment of the present invention;

[0061] Figure 4 A flowchart of constructing a schedule optimization model in an embodiment of the present invention;

[0062] Figure 5 The flowchart of the improved grey wolf algorithm is constructed in the embodiment of the present invention. DETAILED DESCRIPTION

[0063] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0064] It should be noted that the following detailed descriptions are illustrative and are intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present application belongs.

[0065] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application; as used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or their combinations.

[0066] A method for optimizing the maximum synchronous transfer bus schedule considering passenger flow constraints. Obtain the arrival and departure times of each train at the subway station studied during peak hours, the operation information of bus lines around the subway station, subway automatic ticket vending and checking system data, regular bus card swiping data, mobile phone signaling data, and regular bus operation GPS data. Analyze the geometric layout of bus lines around the subway station, screen effective transfer lines and count the number of effective transfer passengers; divide the study period by clustering, comprehensively consider the vehicle arrival pattern, transfer passenger travel time, regular bus station capacity and regular bus vehicle full load rate, and establish a bus line schedule optimization model based on the maximum number of transfers; use the improved gray wolf algorithm to solve the model and obtain the optimization plan for the regular bus line schedule. Figure 1 As shown, the specific implementation steps of this method are as follows:

[0067] A method for optimizing bus schedules with maximum synchronous transfers considering passenger flow constraints, Figure 1-5 , including the following steps:

[0068] Step S1: Obtain the subway station train departure timetable, subway station surrounding bus line operation information, subway automatic ticket vending system data, bus card swiping data, mobile phone signaling data, bus operation GPS data;

[0069] Step S2: Analyze the geometric layout of bus routes around the subway station under study, and filter out bus routes whose downstream are parallel to the subway line;

[0070] Step S3: Divide the research period by clustering;

[0071] Step S4: Analyze the passenger transfer walking pattern, bus line bus full load rate, passenger flow arrival pattern, vehicle arrival pattern, match passenger data, and calculate the number of transfer passengers on the effective transfer line;

[0072] Step S5: Based on the transfer mode of passengers transferring from subway to bus, bus to subway, and bus to bus, a maximum synchronous transfer bus schedule optimization model is established;

[0073] Step S6: Optimize the traditional gray wolf algorithm to solve the maximum synchronous transfer bus schedule optimization model, and use the approximate optimal solution of the model decision variables as the bus departure schedule of the maximum synchronous transfer solution, thereby completing the maximum synchronous transfer bus schedule optimization method considering passenger flow constraints.

[0074] The step 3 specifically includes the following steps:

[0075] Step S31: Eliminate time periods with a small number of bus routes based on the operation information of bus routes around the subway station;

[0076] Step S32: Divide the operation data of each line into two groups: working days and rest days;

[0077] Step S33: Based on the travel time characteristics, a K-center point clustering algorithm is used to perform clustering to obtain clustering results for working days and rest days;

[0078] Step S34: Fit the line clustering results with a distribution function, and use the KS test to evaluate the fitting effect, so as to obtain the distribution function of the average one-way running time of the line.

[0079] The step S4 specifically comprises the following steps:

[0080] Step S41: analyzing the walking characteristics of passengers from four aspects: walking speed, static space, dynamic space, and psychological buffer space;

[0081] Step S42: Analyze the arrival pattern of bus-to-subway passenger flow to obtain the transfer travel time;

[0082] Step S43: Analyze the arrival pattern of subway-to-bus passenger flow to obtain transfer travel time;

[0083] Step S44: Analyze the arrival pattern of public buses and, in combination with GPS data, obtain the average arrival time of public buses at each station;

[0084] Step S45: Calculate the number of transfer passengers based on the valid bus routes.

[0085] The step S5 specifically comprises the following steps:

[0086] Step S51: for the studied subway station, define it and surrounding bus transfer stations and lines as a topological structure;

[0087] Step S52: Construct a set of subway train numbers within the research period M ={1,2,3,…, m}, m Indicates subway train number and bus stop collection R ={1,2,3,…, r}, r Represents a collection of bus stops and bus routes L ={1,2,3,…, l}, l Indicates bus routes; passing through bus stops R Any bus stop r Line collection L r ={1,2,…, l r}, l r Indicates passing by bus stop R Any bus stopr The route, all bus schedules of all routes are set U = ( A l , B b ,…, L i , S j ), bus routes l Bus schedule collection L i =(1,2,…, f l ), f l The bus routes during the study period l The last shift, l i For Line l Flights i The index of other bus routes can be expressed in the same way;

[0088] Step S53: Set the bus departure time and the synchronization variable as two decision variables, and maximize the number of synchronous transfers as the objective function maxZ. The calculation formula is as follows:

[0089]

[0090] In the formula, is the simultaneous decision variable for transferring from subway to bus; is the synchronous decision variable for transfers between different bus lines; The simultaneous decision variables for bus transfer to subway; and is the proportionality coefficient, which is used to quantify the difference between subway and bus transfers. The larger the proportionality coefficient, the greater the weight of synchronization, indicating that the value of synchronization between the line and the subway is higher;

[0091] Step S54: Set the departure interval constraint, the calculation formula is as follows:

[0092]

[0093] In the formula, and For bus routes l Two adjacent flights i and i -1 departure time; The departure time of the first bus of each regular bus route during the study period; and Bus routes lThe maximum and minimum departure intervals; T For the research period, Indicates the bus routes during the study period l The last bus departure time of

[0094] Step S55: Set the synchronization determination constraint, the calculation formula is as follows:

[0095]

[0096] In the formula, For bus routes l of vehicles from the station to the bus stop r Average travel time; For subway trains m The arrival time of It is the walking time for passengers from the subway station hall to the bus stop; is an arbitrarily large but not infinite positive number; The length of the time window for transferring from subway to bus; For bus routes s Flights j The departure time of ,and ; For bus routes s of vehicles from the station to the bus stop r Average travel time; For bus routes l of vehicles from the station to the bus stop r With bus lines s of vehicles from the station to the bus stop r time difference; At the same bus stop r The length of the time window for transferring from one bus line to another; It is the walking time for passengers from the bus stop to the subway station hall; The length of the time window for transferring from bus to subway;

[0097] Step S56: Set the value range of the synchronization determination variable, and the calculation formula is as follows:

[0098]

[0099] Step S57: The number of transfer passengers is constrained, and the calculation formula is as follows:

[0100]

[0101] In the formula, is the reduction factor of the alternative bus routes; For bus stops r the maximum number of passengers that can be accommodated; Get off at subway station m and you will be at the bus stop r The number of passengers waiting to transfer to another bus; The revised bus stop r The maximum number of passengers that can be accommodated;

[0102] Step S58: Set the passenger load factor constraint, the calculation formula is as follows:

[0103]

[0104] In the formula, To reach the bus stop r The passenger load factor of public transport vehicles at the time of is the bus load factor.

[0105] The implementation steps of step S6 are as follows:

[0106] Step S61: Introducing a cosine law-based variation convergence factor a , the calculation formula is:

[0107]

[0108] Where: a min and a max are the upper and lower limits of the convergence factor, respectively, the gray wolf algorithm a min Take 0, a max Take 2, d and d max They are the current number of iterations and the maximum number of iterations of the algorithm respectively;

[0109] Step S62: Update the optimized position, the calculation formula is:

[0110]

[0111] Where: w 1. w 2. w 3 are α , β and δ The dynamic weight coefficient of the wolf in updating the next generation of wolf pack positions, f α , f β , f δ They are α ,β and δ Wolf fitness; They represent the best fitness in the traditional grey wolf algorithm. α The wolf is the potential optimal solution. β Wolf, δ The wolf's position vector; t Represents algebra; Indicates the location of the next generation of gray wolf individuals;

[0112] The dynamic update formula of its position is transformed into:

[0113]

[0114] Step S63: Add simulated annealing operation, the calculation formula is:

[0115]

[0116] Where: is the fitness of the newly generated solution to the model, represents the fitness of the current solution, T p is the current temperature.

[0117] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0118] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or block in the flowchart and / or block diagram, as well as the combination of the processes and / or blocks in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0119] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture including an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0120] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0121] The above is only a preferred embodiment of the present invention, and does not limit the present invention in other forms. Any technician familiar with the profession may use the above disclosed technical content to change or modify it into an equivalent embodiment with equivalent changes. However, any simple modification, equivalent change and modification made to the above embodiment according to the technical essence of the present invention without departing from the technical solution of the present invention still belongs to the protection scope of the technical solution of the present invention.

Claims

1. A method for optimizing a bus schedule with maximum synchronous transfer considering passenger flow constraints, characterized in that: The following steps are involved: Step S1: Obtain the subway station train departure timetable, subway station surrounding bus line operation information, subway automatic ticket vending system data, bus card swiping data, mobile phone signaling data, bus operation GPS data; Step S2: Analyze the geometric layout of bus routes around the subway station under study, and filter out bus routes whose downstream are parallel to the subway line; Step S3: Divide the research period by clustering; Step S4: Analyze the passenger transfer walking pattern, bus line bus full load rate, passenger flow arrival pattern, vehicle arrival pattern, match passenger data, and calculate the number of transfer passengers on the effective transfer line; Step S5: Based on the transfer mode of passengers transferring from subway to bus, bus to subway, and bus to bus, a maximum synchronous transfer bus schedule optimization model is established; Step S6: Optimizing the traditional gray wolf algorithm, solving the maximum synchronous transfer bus schedule optimization model, and taking the approximate optimal solution of the model decision variables as the bus departure schedule of the maximum synchronous transfer scheme, thereby completing the maximum synchronous transfer bus schedule optimization method considering passenger flow constraints; The step S5 specifically comprises the following steps: Step S51: for the studied subway station, define it and surrounding bus transfer stations and lines as a topological structure; Step S52: Construct a set of subway train numbers within the research period M ={1,2,3,…, m }, m Indicates subway train numbers and bus stop collection R ={1,2,3,…, r }, r Represents a collection of bus stops and bus routes L ={1,2,3,…, l }, l Indicates bus routes; passing through bus stops R Any bus stop r Line collection L r ={1,2,…, l r }, l r Indicates passing by bus stop R Any bus stop r The route, all bus schedules of all routes are set U = ( A l , B b ,…, L i , S j ), bus routes l Bus schedule collection L i =(1,2,…, f l ), f l The bus routes during the study period l The last shift, l i For line l Flights i The index of other bus routes can be expressed in the same way; Step S53: Set the bus departure time and the synchronization variable as two decision variables, and maximize the number of synchronous transfers as the objective function maxZ. The calculation formula is as follows: In the formula, is the simultaneous decision variable for transferring from subway to bus; is the synchronous decision variable for transfers between different bus lines; The simultaneous decision variables for bus transfer to subway; and is the proportionality coefficient, which is used to quantify the difference between subway and bus transfers. The larger the proportionality coefficient, the greater the weight of synchronization, indicating that the value of synchronization between the line and the subway is higher; Step S54: Set the departure interval constraint, the calculation formula is as follows: In the formula, y li and l(i-1) For bus routes l Two adjacent flights i and i -1 departure time; The departure time of the first bus of each regular bus route during the study period; and Bus routes l The maximum and minimum departure intervals; T For the research period, Indicates the bus routes during the study period l The last bus departure time of Step S55: Set the synchronization determination constraint, the calculation formula is as follows: In the formula, For bus routes l of vehicles from the station to the bus stop r Average travel time; For subway trains m The arrival time of It is the walking time for passengers from the subway station hall to the bus stop; is an arbitrarily large but not infinite positive number; The length of the time window for transferring from subway to bus; For bus routes s Flights j The departure time of ,and ; For bus routes s of vehicles from the station to the bus stop r Average travel time; For bus routes l of vehicles from the station to the bus stop r With bus lines s of vehicles from the station to the bus stop r time difference; At the same bus stop r The length of the time window for transferring from one bus line to another; It is the walking time for passengers from the bus stop to the subway station hall; The length of the time window for transferring from bus to subway; Step S56: Set the value range of the synchronization determination variable, and the calculation formula is as follows: Step S57: The number of transfer passengers is constrained, and the calculation formula is as follows: In the formula, is the reduction factor of the alternative bus routes; For bus stops r the maximum number of passengers that can be accommodated; Get off at subway station m and you will be at the bus stop r The number of passengers waiting to transfer to another bus; The revised bus stop r The maximum number of passengers that can be accommodated; Step S58: Set the passenger load factor constraint, the calculation formula is as follows: In the formula, To reach the bus stop r The passenger load factor of public transport vehicles at the time of is the bus load factor; The implementation steps of step S6 are as follows: Step S61: Introducing a cosine law-based variation convergence factor a , the calculation formula is: Where: a min and a max are the upper and lower limits of the convergence factor, respectively, the gray wolf algorithm a min Take 0, a max Take 2, d and d max They are the current number of iterations and the maximum number of iterations of the algorithm respectively; Step S62: Update the optimized position, the calculation formula is: Where: w 1. w 2. w 3 are α , β and δ The dynamic weight coefficient of the wolf in updating the next generation of wolf pack positions, f α , f β , f δ They are α , β and δ Wolf fitness; They represent the best fitness in the traditional grey wolf algorithm. α The wolf is the potential optimal solution. β Wolf, δ The wolf's position vector; t Represents algebra; Indicates the location of the next generation of gray wolf individuals; The dynamic update formula of its position is transformed into: Step S63: Add simulated annealing operation, the calculation formula is: Where: is the fitness of the newly generated solution to the model, represents the fitness of the current solution, T p is the current temperature.

2. The method for optimizing a bus schedule with maximum synchronous transfer considering passenger flow constraints according to claim 1, characterized in that: The step 3 specifically comprises the following steps: Step S31: Eliminate time periods with a small number of bus routes based on the operation information of bus routes around the subway station; Step S32: Divide the operation data of each line into two groups: working days and rest days; Step S33: Based on the travel time characteristics, a K-center point clustering algorithm is used to perform clustering to obtain clustering results for working days and rest days; Step S34: Fit the line clustering results with a distribution function, and use the KS test to evaluate the fitting effect, so as to obtain the distribution function of the average one-way running time of the line.

3. The method for optimizing a bus schedule with maximum synchronous transfer considering passenger flow constraints according to claim 1, characterized in that: The step S4 specifically comprises the following steps: Step S41: analyzing the walking characteristics of passengers from four aspects: walking speed, static space, dynamic space, and psychological buffer space; Step S42: Analyze the arrival pattern of bus-to-subway passenger flow to obtain the transfer travel time; Step S43: Analyze the arrival pattern of subway-to-bus passenger flow to obtain transfer travel time; Step S44: Analyze the arrival pattern of public buses and, in combination with GPS data, obtain the average arrival time of public buses at each station; Step S45: Calculate the number of transfer passengers based on the valid bus routes.

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