A modular bus operation scheduling optimization method and device and a storage medium

Abstract

The application discloses a kind of modularization public transport operation scheduling optimization method, device and storage medium, wherein method includes: determining the bus line of providing modularization public transport service and the range of site involved, the passenger flow demand data of gathering between different sites;According to the operation characteristics of bus line and geographical environment factor, determine model parameter value, and build model;According to passenger flow demand data and public transport operation characteristics, solve model, obtain the operation scheduling scheme under the condition of the lowest total cost of system;The operation scheduling scheme of modularization public transport system is optimized, and optimal balance in economic, energy and environmental benefits is realized.The present application considers the uncertainty of passenger flow arrival and random delay, and is more in line with the actual situation of passengers when taking bus, can provide a more practical scheme for the scheduling of modularization public transport, improve the service efficiency and social benefit of public transport system.The present application can be widely applied in the field of public transport operation scheduling.

Description

Technical Field

[0001] This invention relates to the field of public transportation operation scheduling, and in particular to a modular method, apparatus and storage medium for optimizing public transportation operation scheduling. Background Technology

[0002] In the public transportation systems of megacities, a persistent conflict exists between uncertain passenger demand and fixed transport capacity, leading to significant passenger waiting time costs and wasted vehicle capacity. Modular buses offer a potential solution, dynamically adjusting vehicle capacity by disassembling and reassembling identical carriages at stops. Currently, however, a suitable scheduling scheme for modular buses is lacking. Summary of the Invention

[0003] In order to at least partially solve one of the technical problems existing in the prior art, the purpose of this invention is to provide a modular bus operation scheduling optimization method, device and storage medium.

[0004] The technical solution adopted in this invention is:

[0005] A modular public transport operation scheduling optimization method includes the following steps:

[0006] S1. Determine the bus routes and station areas that provide modular bus services, and collect passenger flow demand data between different stations;

[0007] S2. Based on the operational characteristics of the bus route and geographical environmental factors, determine the model parameter values ​​and build the model;

[0008] S3. Based on passenger flow demand data and public transport operation characteristics, solve the model to obtain the operation scheduling scheme with the lowest total system cost; where the total system cost includes operating cost and passenger waiting cost;

[0009] S4. Optimize the operation and scheduling scheme of the modular public transport system to achieve the best balance in terms of economic, energy and environmental benefits.

[0010] Further, step S1 specifically includes:

[0011] The bus routes and stops covered by the modular bus service in the scheduling scheme are determined, including the number of stops, the number of carriages at each stop, and the distance between stops. Passenger flow demand data between different stops is collected, including the number of passengers departing from and arriving at each stop and the time.

[0012] Further, determining the model parameter values ​​includes:

[0013] Based on the operating characteristics of modular buses, determine the number of passengers per carriage, the average operating cost per carriage, the average waiting time cost for passengers, the average driving speed of the vehicle, and the minimum design headway.

[0014] The average operating cost per carriage includes depreciation costs, energy consumption costs to overcome air resistance, and environmental pollution costs caused by carbon dioxide emissions.

[0015] Furthermore, the model is constructed in the following manner:

[0016] A1. Based on passenger demand and the characteristics of modular bus operation, determine the assumptions that the model must meet;

[0017] A2. Determine the constraints that the model must satisfy, including vehicle operation constraints, minimum headway constraints, and constraints that meet passenger demand.

[0018] A3. The objective function of the model is to minimize the total system cost. The total system cost includes operating costs and passenger waiting costs. Operating costs include vehicle operating costs, energy costs for overcoming wind resistance, and environmental costs caused by greenhouse gas emissions.

[0019] A4. Linearize the established nonlinear programming model using equivalent mathematical transformations.

[0020] Furthermore, the assumptions in step A1 include:

[0021] ① Each station is not allowed to be overcrowded. Passengers will board the first carriage that arrives at the station.

[0022] ②The time each carriage spends at a station is constant, and the speed at which it travels between stations is also constant;

[0023] ③ All stations have enough carriages, and there is no limit to the overall capacity of the system.

[0024] Furthermore, the expression for the vehicle operation constraint is:

[0025]

[0026] Where, x tis This is a binary variable; its value is 1 when the system dispatches s carriages from station i at time t, and 0 otherwise. Represents a set of subway stations. A set representing points in time. This represents the set of the number of carriages at each station.

[0027] The expression for the minimum headway constraint is:

[0028]

[0029] Among them, y t The variable is a binary variable; its value is 1 when a carriage departs from a station at time t, and 0 otherwise; h represents the minimum design headway between carriages; t ′ This indicates the departure time of the previous carriage at this station;

[0030] The expression for the constraint that satisfies passenger demand is:

[0031]

[0032]

[0033]

[0034]

[0035]

[0036] Among them, u ijt′t Let z be an integer variable representing the number of passengers who arrive at station i within the time interval [t′-1, t′], disembark, and proceed to station j to wait for the vehicle departing at time t; ijt′t Let v be an integer variable representing the number of passengers who boarded at station i within the time interval [t′-1, t′] and want to get off at station j, waiting to catch the vehicle departing at time t; ti P represents the number of passengers leaving station i on the vehicle departing at time t; ijt′ Let i represent the number of passengers who arrive at station i and proceed to station σ within any given time [t′-1, t′], satisfying the following condition: It is a random variable that follows a Poisson distribution.

[0037] Furthermore, the expression for the objective function is:

[0038]

[0039] Where C represents the average operating cost per carriage. s_wind C represents the energy cost C incurred by each carriage in overcoming wind resistance. s_GHG This represents the environmental cost of greenhouse gas emissions per train car, d. i，i+1 C represents the distance between station i and station i+1. time Δt represents the passenger waiting time cost. i δ represents the time from the first station to station i, and δ represents the time interval.

[0040] Furthermore, the linearization of the established nonlinear programming model using equivalent mathematical transformations includes:

[0041] The service requirement constraint (1) that the model needs to satisfy is transformed into the following linear constraint:

[0042]

[0043]

[0044]

[0045] Where M represents a given large positive number;

[0046] Introducing auxiliary variable w tis =x tis y t The service requirement constraint (5) that the model needs to satisfy is transformed into the following linear constraint:

[0047]

[0048] w tis Linearization is achieved using the following formula:

[0049] w tis ≤x tis t∈T, i∈I, s∈S

[0050] w tis ≤y t t∈T, i∈I, s∈S

[0051] w tis ≥x tis +y t -1t∈T, i∈I, s∈S

[0052] p ijt′ In the demand service constraints (2) and (3), the random variables that follow a Poisson distribution are represented by the following formula:

[0053]

[0054] in, This represents the average number of passengers who board station i within time [t-1, t] and want to go to station j, waiting to catch a vehicle departing at time t.

[0055] Introduce auxiliary variables that satisfy the chance constraint To linearize the demand service constraints (2) and (3):

[0056]

[0057] Where ε represents the acceptable error, when p ijt′ When ε is known, the following formula can be used to obtain ε. Minimum value:

[0058]

[0059] when When the value is given, The value is also fixed, therefore When solving the objective function, it can be regarded as a constant, and the service requirements (2) and (3) are transformed into:

[0060]

[0061]

[0062] The objective function is now transformed into the following linear problem:

[0063]

[0064] Another technical solution adopted in this invention is:

[0065] A modular bus operation scheduling optimization device includes:

[0066] At least one processor;

[0067] At least one memory for storing at least one program;

[0068] When the at least one program is executed by the at least one processor, the at least one processor implements the method described above.

[0069] Another technical solution adopted in this invention is:

[0070] A computer-readable storage medium storing a processor-executable program, which, when executed by a processor, performs the method described above.

[0071] The beneficial effects of this invention are: it takes into account the uncertainty and random delays of passenger arrival, which is more in line with the actual situation of passengers taking public transportation. It can provide a more practical, low-carbon and environmentally friendly solution for the scheduling of modular buses, improve the service efficiency and social benefits of the public transportation system, and has practical promotion value. Attached Figure Description

[0072] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following description is provided with accompanying drawings of the relevant technical solutions in the embodiments of the present invention or the prior art. It should be understood that the accompanying drawings described below are only for the purpose of clearly illustrating some embodiments of the technical solutions of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0073] Figure 1 This is a flowchart illustrating the operation of a modular bus operation scheduling optimization method that considers the randomness of passenger arrivals in an embodiment of the present invention.

[0074] Figure 2 This is a diagram showing the passenger arrival status at each station in an embodiment of the present invention;

[0075] Figure 3 This is a flowchart illustrating the steps of a modular bus operation scheduling optimization method in an embodiment of the present invention. Detailed Implementation

[0076] The embodiments of the present invention are described in detail below. Examples of these embodiments are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention. The step numbers in the following embodiments are set only for ease of explanation, and there is no limitation on the order between the steps. The execution order of each step in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0077] In the description of this invention, it should be understood that the orientation descriptions, such as up, down, front, back, left, right, etc., are based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0078] In the description of this invention, "several" means one or more, "more than" means two or more, "greater than," "less than," and "exceeding" are understood to exclude the stated number, while "above," "below," and "within" are understood to include the stated number. The use of "first" and "second" in the description is merely for distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0079] In the description of this invention, unless otherwise explicitly defined, terms such as "set up," "install," and "connect" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this invention in conjunction with the specific content of the technical solution.

[0080] Based on modular public transport facilities, this invention considers the uncertainty and random delays in passenger arrivals, and comprehensively analyzes the operating costs, passenger waiting costs, energy consumption, and environmental costs of the public transport system to seek the optimal solution under different scheduling schemes. This invention provides a more practical, low-carbon, and environmentally friendly solution for the scheduling of modular public transport, improving the service efficiency and social benefits of the public transport system, and has practical application value.

[0081] like Figure 1 and Figure 3 This embodiment provides a modular bus operation scheduling optimization method. This method, considering passenger flow uncertainty and random delays, establishes a nonlinear programming model by dynamically disassembling and reassembling identical buses at stops within a bus fleet, thereby achieving the lowest economic, energy, and environmental costs for the bus system. The method specifically includes the following steps:

[0082] S101. Determine the bus routes and station areas that provide modular bus services, and collect passenger flow demand data between different stations.

[0083] Determine the modular bus routes and stations covered by the scheduling plan, determine the number of stations, the number of carriages at each station, and the distance between stations, and collect passenger flow demand data between different stations, including the number of passengers departing from and arriving at each station and the time.

[0084] S102. Based on the operational characteristics of the bus route and geographical environmental factors, determine the model parameter values ​​and build the model.

[0085] In this embodiment, based on the operating characteristics of modular buses, the passenger capacity of each carriage, the average operating cost per carriage, the average passenger waiting time cost, the average vehicle speed, and the minimum design headway are determined. The average operating cost per carriage includes depreciation costs, energy consumption costs to overcome air resistance, and environmental pollution costs caused by carbon dioxide emissions.

[0086] S103. Based on passenger flow demand data and public transport operation characteristics, solve the model to obtain the operation scheduling scheme with the lowest total system cost; where the total system cost includes operating cost and passenger waiting cost.

[0087] The model is constructed in the following way:

[0088] B1. Based on passenger demand and the characteristics of modular bus operation, determine the assumptions that the model must meet.

[0089] The model assumptions in step B1 are as follows:

[0090] ① Each station is not allowed to be overcrowded. Passengers will board the first carriage that arrives at the station.

[0091] ②The time each carriage spends at a station is constant, and the speed at which it travels between stations is also constant.

[0092] ③ All stations have enough carriages, and there is no limit to the overall capacity of the system.

[0093] B2. Determine the various constraints that the model must meet, including vehicle operation constraints, minimum headway constraints, and constraints for meeting passenger demand.

[0094] The vehicle operation constraints in step B2 are as follows:

[0095]

[0096] Where x tis This is a binary variable; its value is 1 when the system dispatches s carriages from station i at time t, and 0 otherwise. Represents a set of subway stations. A set representing points in time; Each point in time has an equal time interval δ; This represents the set of the number of carriages at each station.

[0097] The minimum headway constraint that the model must satisfy is:

[0098]

[0099] Where y t This is a binary variable; its value is 1 when a carriage departs from a station at time t, and 0 otherwise; h represents the minimum design headway between carriages.

[0100] The passenger demand service constraints that the model needs to satisfy are:

[0101] ①

[0102] ②

[0103] ③

[0104] ④

[0105] ⑤

[0106] Where: u ijt′t Let z be an integer variable representing the number of passengers who arrive at station i within the time interval [t′-1,t′], disembark, and proceed to station j to wait for the vehicle departing at time t; ijt′t Let v be an integer variable representing the number of passengers who boarded at station i within the time interval [t′-1, t′] and want to get off at station j, waiting to catch the vehicle departing at time t; ti p represents the number of passengers leaving station i on the vehicle departing at time t; ijt′ Let i represent passengers who arrive at station i and proceed to station j within any given time [t′-1,t′], satisfying the following condition: It is a random variable that follows a Poisson distribution.

[0107] B3. Determine the template function of this model to minimize the total system cost, including vehicle operating costs, energy consumption costs for overcoming wind resistance, environmental costs caused by greenhouse gas emissions, and passenger waiting time costs.

[0108] The objective function of the model in step B3 is:

[0109]

[0110] B4. Linearize the established nonlinear programming model using equivalent mathematical transformations.

[0111] The model linearization process in step B4 is as follows:

[0112] The service requirement constraint ① that the model needs to satisfy is transformed into the following linear constraint:

[0113]

[0114]

[0115]

[0116] Where M represents a given large positive number.

[0117] Introducing auxiliary variable w tis =x tis y t The service requirement constraint ⑤ that the model needs to satisfy is transformed into the following linear constraint:

[0118]

[0119] w tis Linearization can be achieved using the following formula:

[0120] w tis ≤xtis t∈T, i∈I, s∈S

[0121] w tis ≤y t t∈T, i∈I, s∈S

[0122] w tis ≥x tis +y t -1t∈T,i∈I,s∈S

[0123] p ijt′ In the demand service constraints ② and ③, the random variables that follow a Poisson distribution can be expressed by the following formula:

[0124]

[0125] in This represents the average number of passengers who board station i within time [t-1,t] and want to go to station j, waiting to catch a vehicle departing at time t. This number can be obtained from historical data.

[0126] We introduce auxiliary variables that satisfy the chance constraint. To linearize the demand service constraints ② and ③.

[0127]

[0128] Where ε represents the acceptable error, when p ijt′ When ε is known, the following formula can be used to obtain ε. The minimum value.

[0129]

[0130] when When the value is given, The value is also fixed, therefore These can be treated as constants when solving the objective function. Demand service constraints ② and ③ are transformed into:

[0131]

[0132]

[0133] The objective function is now transformed into the following linear problem:

[0134]

[0135] S104. Optimize the operation and scheduling scheme of the modular public transport system to achieve the best balance in terms of economic, energy and environmental benefits.

[0136] By using the above method, a vehicle scheduling scheme with the minimum total system cost is obtained, and the operation scheduling scheme of the existing modular public transport system is optimized to achieve the optimal balance in terms of economic, energy and environmental benefits.

[0137] The following combination Figure 1 , Figure 2 The above method will be explained in detail with specific embodiments.

[0138] like Figure 1 As shown, this embodiment provides a modular bus operation scheduling optimization method that considers the randomness of passenger arrivals. On a bus route with a total length of 31.3 kilometers, there are 15 bus stops, each equipped with 6 carriages, each carriage carrying 350-700 passengers, and the designed operating speed of the buses is 1.33 kilometers per minute; among which, Figure 2 This is a graph showing passenger arrivals at each station. Passenger arrival and departure demand data were collected for each station. The calculation parameters are shown in Table 1.

[0139] Table 1 Calculation Parameters for Examples

[0140]

[0141]

[0142] Using the above data and parameters as input, the minimum cost of the modular bus system and its scheduling scheme under the minimum cost are obtained. The scheme is compared with existing system scheduling schemes, and the results are shown in Table 2. Except for operating costs, this scheme can significantly reduce various system costs, resulting in a substantial reduction in total cost.

[0143] Table 2 Comparison of Results between Example Scheme and Baseline Scheme

[0144]

[0145] In summary, this invention has at least the following advantages and beneficial effects: Compared with other scheduling methods for modular transportation systems, this invention considers the uncertainty and random delays of passenger arrivals, which is more in line with the actual situation of passengers taking public transportation. Furthermore, while considering the operating costs of the public transportation system and passenger waiting costs, it introduces energy consumption and environmental costs, seeking the optimal solution under different scheduling schemes. This invention can provide a more practical, low-carbon, and environmentally friendly solution for the scheduling of modular public transportation, improving the service efficiency and social benefits of the public transportation system, and has practical application value.

[0146] This embodiment also provides a modular bus operation scheduling optimization device, including:

[0147] At least one processor;

[0148] At least one memory for storing at least one program;

[0149] When the at least one program is executed by the at least one processor, the at least one processor performs the following: Figure 3 The method shown.

[0150] This embodiment of a modular bus operation scheduling optimization device can execute a modular bus operation scheduling optimization method provided in the method embodiment of the present invention, and can execute any combination of implementation steps of the method embodiment, possessing the corresponding functions and beneficial effects of the method.

[0151] This application also discloses a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device can read the computer instructions from the computer-readable storage medium and execute the computer instructions, causing the computer device to perform... Figure 3 The method shown.

[0152] This embodiment also provides a storage medium storing instructions or programs that can execute the modular bus operation scheduling optimization method provided in the method embodiment of the present invention. When the instructions or programs are run, any combination of implementation steps of the method embodiment can be executed, and the method has the corresponding functions and beneficial effects.

[0153] In some alternative embodiments, the functions / operations mentioned in the block diagrams may not occur in the order shown in the operation diagrams. For example, depending on the functions / operations involved, two consecutively shown blocks may actually be executed substantially simultaneously, or the blocks may sometimes be executed in reverse order. Furthermore, the embodiments presented and described in the flowcharts of this invention are provided by way of example to provide a more comprehensive understanding of the technology. The disclosed methods are not limited to the operations and logic flows presented herein. Alternative embodiments are contemplated in which the order of various operations is altered and sub-operations described as part of a larger operation are executed independently.

[0154] Furthermore, although the invention has been described in the context of functional modules, it should be understood that, unless otherwise stated, one or more of the described functions and / or features may be integrated into a single physical device and / or software module, or one or more functions and / or features may be implemented in a separate physical device or software module. It is also understood that a detailed discussion of the actual implementation of each module is unnecessary for understanding the invention. Rather, given the properties, functions, and internal relationships of the various functional modules in the apparatus disclosed herein, the actual implementation of the module will be understood within the scope of conventional skill of an engineer. Therefore, those skilled in the art can implement the invention as set forth in the claims using ordinary techniques without excessive experimentation. It is also understood that the specific concepts disclosed are merely illustrative and not intended to limit the scope of the invention, which is determined by the full scope of the appended claims and their equivalents.

[0155] If the aforementioned functions are implemented as software functional units and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of this invention, essentially, or the part that contributes to the prior art, or a portion of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0156] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-included system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0157] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, since the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0158] It should be understood that various parts of the present invention can be implemented in hardware, software, firmware, or a combination thereof. In the above embodiments, multiple steps or methods can be implemented in software or firmware stored in memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one or a combination of the following techniques known in the art: discrete logic circuits having logic gates for implementing logical functions on data signals, application-specific integrated circuits (ASICs) having suitable combinational logic gates, programmable gate arrays (PGAs), field-programmable gate arrays (FPGAs), etc.

[0159] In the foregoing description of this specification, references to terms such as "one embodiment," "another embodiment," or "some embodiments" indicate that a specific feature, structure, material, or characteristic described in connection with an embodiment or example is included in at least one embodiment or example of the present invention. In this specification, illustrative expressions of the above terms do not necessarily refer to the same embodiment or example. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples.

[0160] Although embodiments of the invention have been shown and described, those skilled in the art will understand that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the claims and their equivalents.

[0161] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the above embodiments. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A modular bus operation scheduling optimization method, characterized in that, Includes the following steps: S1. Determine the bus routes and station areas that provide modular bus services, and collect passenger flow demand data between different stations; S2. Based on the operational characteristics of the bus route and geographical environmental factors, determine the model parameter values ​​and build the model; S3. Based on passenger flow demand data and public transport operation characteristics, solve the model to obtain the operation scheduling scheme with the lowest total system cost; where the total system cost includes operating cost and passenger waiting cost; S4. Optimize the operation and scheduling scheme of the modular public transport system to achieve the best balance in terms of economic, energy and environmental benefits; The model is constructed in the following way: A1. Based on passenger demand and the characteristics of modular bus operation, determine the assumptions that the model must meet; A2. Determine the constraints that the model must satisfy, including vehicle operation constraints, minimum headway constraints, and constraints that meet passenger demand. A3. Determine the objective function of the model as minimizing the total system cost; A4. Linearize the established nonlinear programming model using equivalent mathematical transformations; The expression for the vehicle operation constraint is: in, It is a binary variable, when the system is... From the site Scheduling The value is 1 when there is a carriage; otherwise, it is 0. Represents a set of subway stations. ; A set representing points in time. ; This represents the set of the number of carriages at each station. ; The expression for the minimum headway constraint is: in, It is a binary variable, when a carriage is in The value is 1 when the time originates from a station, and 0 otherwise. Indicates the minimum design headway between carriages; This indicates the departure time of the previous carriage at this station; The expression for the constraint that satisfies passenger demand is: in, An integer variable, representing time. Internal arrival station and got off the bus to go to the station. Waiting to board The number of passengers in vehicles departing at any given time; An integer variable, representing time. Inside the station And wanted to get off the bus to go to the station. Waiting to board The number of passengers in vehicles departing at any given time; Indicates in Departure time on the vehicle leaving the station The number of passengers; Indicates at any given time Internal arrival stations And proceed to the station The number of passengers meets , is a random variable that follows a Poisson distribution; The expression for the objective function is: in, This indicates the average operating cost per carriage. This represents the energy cost of overcoming wind resistance in each carriage. The environmental cost of greenhouse gas emissions per train car Indicates site to station , This represents the cost of passenger waiting time. Indicates the distance from the first station to the next station. Time, Indicates a time interval; The linearization of the established nonlinear programming model using equivalent mathematical transformations includes: The service requirement constraint (1) that the model needs to satisfy is transformed into the following linear constraint: in Represents a given large positive number; Introducing auxiliary variables The service requirement constraint (5) that the model needs to satisfy is transformed into the following linear constraint: Linearization is achieved using the following formula: In the demand service constraints (2) and (3), the random variables that follow a Poisson distribution are represented by the following formula: in, Indicates time Inside the station And want to go to the station Waiting to board The average number of passengers per vehicle departing at any given time; Introduce auxiliary variables that satisfy the chance constraint To linearize the demand service constraints (2) and (3): in, Indicates an acceptable error, when and Given the given information, the following formula can be solved to obtain the result. Minimum value: when When the value is given, The value is also fixed, therefore When solving the objective function, it can be regarded as a constant, and the service requirements (2) and (3) are transformed into: The objective function is now transformed into the following linear problem: 。 2. The modular bus operation scheduling optimization method according to claim 1, characterized in that, Step S1 specifically includes: The bus routes and stops covered by the modular bus service in the scheduling scheme are determined, including the number of stops, the number of carriages at each stop, and the distance between stops. Passenger flow demand data between different stops is collected, including the number of passengers departing from and arriving at each stop and the time.

3. The modular bus operation scheduling optimization method according to claim 1, characterized in that, The determination of model parameter values ​​includes: Based on the operating characteristics of modular buses, determine the number of passengers per carriage, the average operating cost per carriage, the average waiting time cost for passengers, the average driving speed of the vehicle, and the minimum design headway. The average operating cost per carriage includes depreciation costs, energy consumption costs to overcome air resistance, and environmental pollution costs caused by carbon dioxide emissions.

4. The modular bus operation scheduling optimization method according to claim 1, characterized in that, The assumptions in step A1 include: a) Each station is not allowed to be overcrowded. Passengers will board the first carriage that arrives at the station. b) The time each carriage spends at a station is constant, and the speed at which it travels between stations is also constant; c) All stations have sufficient carriages, and there is no limit to the overall capacity of the system.

5. A modular bus operation scheduling optimization device, characterized in that, include: At least one processor; At least one memory for storing at least one program; When the at least one program is executed by the at least one processor, the at least one processor implements the method of any one of claims 1-4.

6. A computer-readable storage medium storing a processor-executable program, characterized in that, The processor-executable program, when executed by the processor, is used to perform the method as described in any one of claims 1-4.

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