Method for coordinated optimization of metro train diagram and demand management under reservation travel mode

Abstract

The application provides a pre-booking mode subway train diagram and demand management collaborative optimization method, comprising: obtaining subway line data and passenger flow data, and establishing decision variables; according to the coupling relationship between pre-booking passengers and non-booking passengers in the subway system, the fairness between the number of passengers served by the train at each station and the number of passengers waiting, and the coupling relationship between the transport capacity and the transport volume, constraint conditions are constructed; combining the subway line data, the passenger flow data, the decision variables and the constraint conditions, an initial subway train diagram and demand management collaborative optimization nonlinear programming model is constructed; according to the big M constraint, the nonlinear programming model is equivalent to a linear form, and a demand management collaborative optimization linear programming model is obtained; according to the mathematical characteristics of the linear programming model, a solving algorithm is designed for solving until a standard subway train diagram, a pre-booking quota allocation scheme and a passenger flow control scheme are obtained. The method improves the service efficiency and reduces the operation cost.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of urban public transport operation management, and particularly relates to a subway train diagram and demand management collaborative optimization method under a reservation travel mode. BACKGROUND

[0002] With the rapid development of scientific and technological innovation and new technologies, the traditional transportation system is in the stage of accelerating transformation and upgrading. For a long time, how to effectively deal with the highly concentrated commuter flow in space and time has been a major challenge faced by urban rail transit operation management. The initial solution is to open new lines or shorten the train interval to improve the supply of transportation capacity. In recent years, with the utilization of urban physical space tending to saturation and the minimum train interval entering the "2-minute era", passenger flow control strategy has become a widely used demand management measure in China's super-large urban rail transit systems (such as Beijing, Shanghai, Guangzhou, etc.). This strategy controls the number of waiting passengers on the platform to avoid excessive congestion, thereby reducing the risk of stampede accidents or train delays, significantly improving operational efficiency and service quality, and providing a new solution for the future operation management of smart urban rail transit.

[0003] Although the reservation travel mode can provide high-quality travel services, it also increases the complexity of urban rail transit system operation organization. On the one hand, reservation passengers and non-reservation passengers share station space and train capacity resources, and there is a close coupling relationship. Unreasonable reservation quota allocation will inevitably have a negative impact on the travel experience of non-reservation passengers, thereby reducing the service fairness between reservation and non-reservation passengers. On the other hand, the essential reason for passenger flow oversaturation is the mismatch between supply and demand. Only by optimizing the precise allocation of supply-side resources while managing the demand side can the problem be fundamentally alleviated. Existing researches are mostly focused on a single aspect, usually optimizing train diagram and passenger flow control strategy respectively, and there is no literature systematically discussing the collaborative optimization problem of demand management and train diagram under the reservation travel mode, taking into account the service fairness. Therefore, the subway system in the prior art has low service efficiency and high operation cost. SUMMARY

[0004] Therefore, the present application provides a subway train diagram and demand management collaborative optimization method under a reservation travel mode to solve the above problems.

[0005] The application provides a subway train diagram and demand management collaborative optimization method in a reservation travel mode, comprising: obtaining subway line data and passenger flow data, wherein the subway line data comprises a station set, a train set and a discrete time period set in the line, and the passenger flow data comprises a set of passenger flow scenarios and dynamic passenger flow demand; based on the line data and the passenger flow data, decision variables are established; according to the coupling relationship between reservation passengers and non-reservation passengers in the subway system, the fairness relationship between the number of passengers served by the train at each station and the number of passengers waiting, and the coupling relationship between the transport capacity and the transport volume, constraint conditions are constructed; in combination with the subway line data, the passenger flow data, the decision variables and the constraint conditions, an initial subway train diagram and demand management collaborative optimization nonlinear programming model in the reservation travel mode is constructed, with the weighted sum of the total passenger waiting time and the line congestion degree as the optimization objective; according to the big M constraint, the demand management collaborative optimization nonlinear programming model is equivalently converted into a linear form, and the big M value is derived, to obtain a demand management collaborative optimization linear programming model with a more compact upper bound; according to the mathematical properties of the demand management collaborative optimization linear programming model, a solving algorithm is designed to solve, until a standard subway train diagram, a reservation quota allocation scheme and a passenger flow control scheme are obtained.

[0006] In another implementation manner of the application, the decision variables comprise train arrival time related decision variables, train departure time related decision variables, train departure indication variables, reservation quota allocation decision variables and passenger flow control decision variables.

[0007] In another implementation manner of the application, the constraint conditions comprise train diagram constraints, passenger flow dynamic evolution process constraints and coupling constraints between reservation passengers and non-reservation passengers.

[0008] In another implementation manner of the application, the train diagram constraints are expressed as:

[0009]

[0010] wherein, h and represent minimum and maximum departure interval limits; ε is represents the stop time of train i at station s; η is represents the running time of train i between station s and station s+1; y ist represents whether t time is within the departure interval time window of train i and i+1 at station s; a is represents train arrival time related decision

[0011] variable, d is represents train departure time related decision variable, x istdenotes the train departure indicator variable; t denotes the discrete time period, t∈T, i denotes the train number, i∈I, s, v denotes the station, s, v∈S.

[0012] In another implementation of the present application, the passenger flow dynamic evolution process constraint is represented as:

[0013]

[0014]

[0015] wherein κ isv denotes the minimum service ratio; denotes the number of boarding passengers of the reservation passengers; w isv denotes the number of waiting passengers of the non-reservation passengers, r isv denotes the number of stranded passengers; denotes the reservation quota allocation decision variable, b isv denotes the passenger flow control decision variable; t denotes the discrete time period, t∈T, i denotes the train number, i∈I, s, v denotes the station, s, v∈S.

[0016] In another implementation of the present application, the coupling constraint between the reservation and non-reservation passengers is represented as:

[0017]

[0018] wherein, and o is denote the number of reservation passengers and non-reservation passengers among the passengers on the train respectively; l is denotes the number of passengers getting off; z i denotes the maximum number of waiting passengers including the reservation passengers and non-reservation passengers.

[0019] In another implementation of the present application, the objective function of the optimization objective is represented as:

[0020] minλ1F e +λ2F c

[0021]

[0022] wherein F e denotes the passenger waiting time, F c denotes the passenger line congestion degree.

[0023] The subway train diagram and demand management collaborative optimization method in the pre-booking travel mode of the application considers providing convenience for pre-booking passengers to directly enter a station and take a train, and effectively serving non-pre-booking passengers according to a passenger flow control strategy, with the minimum waiting time and line congestion degree as the target, combining with the service fairness, train capacity, train operation safety and other constraints, considering the pre-booking travel and passenger flow control two types of demand management methods, the subway train diagram and demand management collaborative optimization model for time-varying passenger flow is proposed; according to the characteristics of the model, a hybrid algorithm combining adaptive large neighborhood search and commercial optimization solver is designed to efficiently solve the model, the emerging pre-booking travel method is combined with the traditional passenger flow control method, by balancing the demand of pre-booking and non-pre-booking passengers and as far as possible ensuring the best matching of transport capacity and demand, the collaborative optimization of train diagram and demand management strategy is realized, the matching of transport capacity and transport volume is improved, and theoretical support is provided for efficient operation of the actual subway system. BRIEF DESCRIPTION OF DRAWINGS

[0024] In order to more clearly illustrate the technical solutions in the embodiments of the application or the prior art, below the drawings needed to be used in the embodiment or prior art description will be briefly introduced, through reading the following detailed description of the embodiment, the advantages and benefits in the scheme become clear and obvious to those skilled in the art. The drawings are only for the purpose of showing the preferred embodiments, and are not considered as a limitation of the application.

[0025] In the drawings:

[0026] Figure 1 The flowchart of the subway train diagram and demand management collaborative optimization method in the pre-booking travel mode of an embodiment of the application.

[0027] Figure 2 The demand management schematic diagram of an embodiment of the application.

[0028] Figure 3 The solving algorithm schematic diagram of an embodiment of the application.

[0029] Figure 4 The fixed line schematic diagram of an embodiment of the application.

[0030] Figure 5 The service proportion thermal map of each train in each station after optimization under different minimum service proportion settings of an embodiment of the application. DETAILED DESCRIPTION

[0031] In order to make the personnel in the art better understand the technical solutions in the embodiments of the present application, the technical solutions in the embodiments of the present application will be described clearly and in detail below in combination with the drawings in the embodiments of the present application. Obviously, the described embodiments are only some of the embodiments of the present application, not all the embodiments. Based on the embodiments in the embodiments of the present application, all other embodiments obtained by those of ordinary skill in the art should belong to the scope of protection of the embodiments of the present application.

[0032] Figure 1 A pre-trip mode subway train diagram and demand management collaborative optimization method flowchart provided by the embodiments of the present application is shown in FIG. 1, which mainly includes: Figure 1

[0033] S101, subway line data and passenger flow data are obtained, wherein the subway line data includes a station set, a train set and a discrete time period set in the line, and the passenger flow data includes a set of passenger flow scenarios and dynamic passenger flow demand.

[0034] For example, the following necessary parameters and data are determined in advance: the station distribution in the subway line; the basic parameters of train operation, including the inter-station running time, the maximum and minimum departure interval, the station stop time, etc.; the maximum passenger capacity of the train; the passenger flow demand of each station in each period, etc.

[0035] S102, decision variables are established based on the line data and the passenger flow data.

[0036] S103, according to the coupling relationship between pre-trip passengers and non-pre-trip passengers in the subway system, the fairness relationship between the number of passengers served by the train at each station and the number of passengers waiting, and the coupling relationship between the transport capacity and the transport volume, constraint conditions are constructed.

[0037] S104, combined with the subway line data, the passenger flow data, the decision variables and the constraint conditions, an initial subway train diagram and demand management collaborative optimization nonlinear programming model in the pre-trip mode is constructed, with the weighted sum of the minimum total waiting time of passengers and the line congestion degree as the optimization objective.

[0038] S105, according to the large M constraint, the demand management collaborative optimization nonlinear programming model is equivalent to a linear form, and the large M value is derived to obtain a demand management collaborative optimization linear programming model with a more compact upper bound.

[0039] S106, according to the mathematical properties of the demand management collaborative optimization linear programming model, a solving algorithm is designed to solve until the standard subway train diagram, the pre-trip quota allocation scheme and the passenger flow control scheme are obtained.

[0040] ​The pre-booking travel mode subway train diagram and demand management collaborative optimization method of the application considers providing convenience of direct entry and boarding for pre-booking passengers, effectively serving non-pre-booking passengers according to passenger flow control strategies, taking minimum waiting time and line congestion as targets, combining service fairness, train capacity, train operation safety and other constraints, considering pre-booking travel and passenger flow control two types of demand management methods, and proposing a subway train diagram and demand management collaborative optimization model for time-varying passenger flow; according to the model characteristics, a hybrid algorithm combining adaptive large neighborhood search and commercial optimization solver is designed to efficiently solve the model, the emerging pre-booking travel method is combined with the traditional passenger flow control method, the best matching of capacity and demand is ensured as much as possible while balancing the demand of pre-booking and non-pre-booking passengers, the train diagram and demand management strategy collaborative optimization is realized, the matching of capacity and traffic is improved, and theoretical support is provided for efficient operation of the actual subway system.

[0041] In another implementation manner of the application, the decision variables include train arrival time related decision variables, train departure time related decision variables, train departure indication variables, pre-booking quota allocation decision variables and passenger flow control decision variables.

[0042] In another implementation manner of the application, the constraint conditions include train diagram constraints, passenger flow dynamic evolution process constraints and coupling constraints between pre-booking and non-pre-booking passengers.

[0043] In another implementation manner of the application, the train diagram constraints are expressed as:

[0044]

[0045]

[0046] wherein, h and denote minimum and maximum departure interval limits; ε is denotes the stop time of train i at station s; η is denotes the running time of train i between station s and station s+1; y ist denotes whether t time is within the departure interval time window of trains i and i+1 at station s; a is denotes the train arrival time related decision variable, d is denotes the train departure time related decision variable, x ist denotes the train departure indication variable; t denotes a discrete time period, t∈T, i denotes a train number, i∈I, s and v denote stations, s,v∈S.

[0047] In another implementation manner of the application, the passenger flow dynamic evolution process constraints are expressed as:

[0048]

[0049] wherein, κ isv represents the minimum service ratio; represents the number of boarding passengers of the reserved passengers; w isv represents the number of waiting passengers of the non-reserved passengers, r isv represents the number of stranded passengers; represents the reserved quota allocation decision variable, b isv represents the passenger flow control decision variable; t represents a discrete time period, t∈T, i represents a train, i∈I, s, v represents a station, s, v∈S.

[0050] In another implementation manner of the present application, the coupling constraint between the reserved and non-reserved passengers is represented as:

[0051]

[0052] wherein, and o is respectively represent the number of reserved passengers and the number of non-reserved passengers among the passengers; l is represents the number of alighting passengers; z i represents the maximum number of waiting passengers including the reserved passengers and the non-reserved passengers.

[0053] Exemplarily, as Figure 2 shown, from the supply and demand sides, by improving the supply of transport capacity and optimizing the reserved quota allocation scheme and the passenger flow control strategy, the matching degree of transport capacity and transport volume is improved, the congestion degree of stations along the line is reduced, and the operation efficiency is improved.

[0054] On the demand side, the reserved passengers can directly enter the platform after arriving at the station by using the dedicated reserved access gate, and wait on the platform for the train to arrive. In addition, the non-reserved passengers need to queue in the station hall to obtain access permission, and then enter the platform through the regular gate.

[0055] On the supply side, by adjusting the train diagram, the best matching between the transport capacity and the dynamic passenger flow demand is realized. In addition, considering that excessive reserved quota allocation will inevitably weaken the service level of non-reserved passengers, under the premise of ensuring the service fairness between the reserved and non-reserved passengers, the problem of how to cooperatively optimize the train diagram, the reserved quota fine-grained dynamic allocation plan and the passenger flow control strategy to minimize the line congestion degree during peak hours is solved.

[0056] In another implementation manner of the present application, the objective function of the optimization objective is represented as:

[0057] minλ1F e +λ2F c (21)

[0058]

[0059] wherein F e denotes the passenger waiting time, F c denotes the passenger line congestion degree.

[0060] In another implementation form of the present application, the demand management collaborative optimization nonlinear programming model in step S104 comprises:

[0061]

[0062] On the basis of the above scheme, the model linearization method and the derivation method of the large M value in step S105 specifically comprise:

[0063] Constraints (9) and (12) are typical nonlinear constraints in the form of integer variables multiplied by 0-1 variables, and auxiliary variables can be introduced for linearization processing.

[0064] Specifically, define auxiliary variables Constraint (9) can be equivalently converted into:

[0065]

[0066] wherein,

[0067] Similarly, define auxiliary variables Constraint (12) can be restructured as:

[0068]

[0069] wherein, β isvt in formula (25) is equivalent to:

[0070]

[0071] wherein,

[0072] Constraint (22) contains the form of 2 0-1 variables multiplied by 1 integer variable. In linearization processing, first define Its equivalent linear form is:

[0073]

[0074] In addition, define auxiliary variables γ ist = y ist ∑ v∈S,v>s r isv , and its linear equivalent form is:

[0075]

[0076] wherein,

[0077] In view of this, the constraint (22) can be equivalently transformed as:

[0078]

[0079] In summary, the above integer nonlinear programming model can be equivalently reconstructed as the following integer linear programming model:

[0080] min λ1F e + λ2F c

[0081] s.t. (1)-(8), (10)-(11), (13)-(20), (22)-(29). (30)

[0082] On the basis of the above scheme, the solving algorithm described in step S106, as shown in Figure 3 specifically includes:

[0083] Step 1: Considering that the interval running time, station stopping time and the first train departure time are fixed values, when the departure interval is determined, the entire train diagram can be obtained. A coding method based on the departure interval is designed, denoted as H={h1,…,h |I|-1}, wherein and an initial feasible solution is generated according to the constraint (4).

[0084] Step 2: An adaptive large neighborhood search (ALNS) algorithm is used to perform neighborhood transformation on the current solution through destruction operators and repair operators, thereby generating a new feasible solution. At each iteration, the destruction operator and the repair operator are randomly selected according to the weight of each operator, and the weight of each operator is updated according to the performance of each operator. To avoid falling into local optimum, the initial solution of the next iteration is selected according to the simulated annealing rule after each iteration.

[0085] Step 3: The train diagram obtained by the ALNS algorithm is fixed, and the model is solved by using branch and bound to evaluate the advantages and disadvantages of the train diagram, and through step-by-step iteration to obtain a better demand management scheme and train diagram.

[0086] Based on the above basic data, the model and solving algorithm program proposed in the present application are programmed in Java to obtain the corresponding subway train diagram, passenger flow control scheme and reservation quota allocation plan.

[0087] The following will be described in detail according to Example 1:

[0088] The contents of the present application are verified by taking Beijing Metro Bantong Line as an example, as shown in the figure, the line contains 13 stations, which are named A, B, C, D, E, F, G, H, I, J, K, L, M in turn. The station stop time of the line is set to 1 minute, the minimum and maximum departure interval are 2 minutes and 6 minutes respectively, and the train capacity is 1800 people. Discretize the research period with 1 minute as the discrete time granularity. As shown in Table 1, five cases are considered, which have different research periods and train numbers. Figure 4

[0089] Table 1 Basic data of examples

[0090]

[0091] According to the above given input data, the code is written in Java to build the model and solve the algorithm framework described in the present application, and the problem is solved, that is, the optimal subway train diagram, passenger flow control scheme and reservation quota allocation plan can be obtained.

[0092] Firstly, GUROBI is called and the algorithm (denoted as ALNS+GUROBI algorithm) is used to solve the optimization model described in the present application. In this group of experiments, the upper limit of the solving time of GUROBI is 7200 seconds. This group of experiments uses the input data of Q1-Q5 examples, and sets the minimum service ratio of non-reserved passengers to 20%, and the weight coefficients in the objective function are 1 and 10 respectively to balance the difference in order of magnitude. Table 2 shows the comparison results of the above two solving methods, wherein the third column represents the objective function value; the fourth column gives the Optimility gap (unit: percentage), which represents the difference between the result obtained by GUROBI under the given solving time limit and the true optimal solution; the fifth column is the difference (unit: percentage) between the solution obtained by ALNS+GUROBI algorithm and the solution obtained by GUROBI, which is calculated by the following formula:

[0093]

[0094] ​As can be seen from Table 2, the GUROBI has a long calculation time, and no feasible solution is found when solving instances Q3, Q4 and Q5. In contrast, the ALNS+GUROBI algorithm exhibits superior performance: when solving instances Q1 and Q2 of smaller size, the algorithm not only saves about 88% and 77% of the calculation time, respectively, but also finds the optimal solution and a high-quality solution with a Gap of 2.44%; as the size of the instance increases, the algorithm's solution time continues to increase, but it can find an approximate optimal solution within 3600 seconds. The above results show that the ALNS+GUROBI algorithm proposed by the present application has the ability of fast convergence and efficient solution, and can meet the solution needs of actual operation scenarios.

[0095] Table 2 ALNS+GUROBI and GUROBI solution results comparison

[0096]

[0097] Based on instance Q3, the results of operation efficiency and line congestion degree under different minimum service ratios are compared and analyzed. Specifically, three experiments are considered, in which the minimum service ratio κ is set to 0, 10% and 20%, respectively. The ALNS+GUROBI algorithm is used for solving. Table 3 shows the optimization results of operation efficiency, line congestion degree, service ratio and reservation ratio under different minimum service ratios. The service ratio is calculated by the number of boarding passengers of non-reserved passengers divided by the waiting passengers, and if the waiting passengers are 0, the value is NAN, which is not included in the statistical results. The fourth column is the number of trains at each station whose service ratio is less than 10% or 20% after optimization, and the fifth column is the reservation ratio (unit: percentage), which is calculated by the number of reservations divided by the total number of passengers.

[0098] Table 3 Comparison of operation efficiency, line congestion degree, service fairness and reservation ratio results for non-reserved passengers under different minimum service ratios

[0099]

[0100] From the results of Table 3, when the minimum service ratio is increased from 0 to 10%, the passenger waiting time increases slightly from 103887 to 103898 (about 0.01% growth), while the line congestion increases from 6605 to 6635 (about 0.45% growth). Notably, the number of service ratios less than 10% decreases from 22 to 0. Further, when the minimum service ratio is increased to 20%, compared to the minimum service ratio of 0, the passenger waiting time and line congestion increase by 3.51% and 0.51%, respectively; in addition, the number of service ratios less than 10% and 20% is reduced to 0. This indicates that the extreme unfairness between the reserved passengers (whose service ratio is 100%) and the non-reserved passengers has been effectively addressed by increasing the minimum service ratio. The detailed service ratio results of the trains at each station are shown in Table 4, where the white squares represent the waiting number of non-reserved passengers being 0 or the service ratio being 0. Figure 5

[0101] In summary, the reservation travel mode subway train diagram and demand management collaborative optimization model constructed by the present application and the efficient solving algorithm combining adaptive large neighborhood search and branch and bound method can effectively improve the operation efficiency and service quality, and can provide long-term, stable and effective demand management measures for subway system operation practice.

[0102] The method of the present application can be applied in industrial control systems in manufacturing, energy and transportation industries, and can enhance the attack resistance of the system by providing customized security services.

[0103] In another aspect of the present application, the electronic device includes a processor, a memory, and a communication bus, a communication interface.

[0104] In another aspect of the present application, the electronic device includes a processor, a memory, and a communication bus, a communication interface.

[0105] The processor, the memory and the communication interface communicate with each other through the communication bus.

[0106] The communication interface is used for communication with other electronic devices or servers.

[0107] The processor is used for executing a program, and specifically can execute the steps of any one of the above-mentioned reservation travel mode subway train diagram and demand management collaborative optimization methods.

[0108] Specifically, the program can include program code, which includes computer operation instructions.

[0109] ​The processor can be a central processing unit (CPU), or an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement one or more embodiments of the application. The one or more processors included in the smart device can be of the same type, such as one or more CPUs, or can be of different types, such as one or more CPUs and one or more ASICs.

[0110] The memory is configured to store a program. The memory can include a high-speed RAM memory, and can further include a non-volatile memory, such as at least one disk memory.

[0111] The program can be specifically configured to cause the processor to perform the steps of any of the methods for optimizing a metro train diagram and demand management in a reservation travel mode described in the embodiments. The specific implementation of each step in the program can refer to the corresponding description of the steps and units performed by the method for optimizing a metro train diagram and demand management in a reservation travel mode described above, and will not be described here. It can be clearly understood by those skilled in the art that, for the convenience and brevity of description, the specific working processes of the devices and modules described above can refer to the corresponding process descriptions in the foregoing method embodiments.

[0112] The exemplary embodiments of the present application also provide a non-transitory computer-readable storage medium having computer instructions stored therein, wherein the computer instructions are configured to cause a computer to execute the method of the embodiments of the present application.

[0113] The method according to the embodiments of the present application described above can be implemented in hardware, firmware, or as software or computer code that can be stored in a recording medium such as a CD ROM, a RAM, a floppy disk, a hard disk, or an optical disk, or downloaded through a network and stored in a remote recording medium or a non-transitory machine-readable medium and then stored in a local recording medium, so that the method described herein can be processed by such software using a general-purpose computer, a special-purpose processor, or programmable or special-purpose hardware such as an ASIC or an FPGA. It can be understood that the computer, the processor, the microprocessor controller, or the programmable hardware includes a storage component (for example, a RAM, a ROM, a flash memory, etc.) that can store or receive software or computer code, when the software or computer code is accessed and executed by the computer, the processor, or the hardware, the method described herein is implemented. In addition, when a general-purpose computer accesses the code for implementing the method shown herein, the execution of the code will convert the general-purpose computer into a special-purpose computer for executing the method shown herein.

[0114] To this end, particular embodiments of the application have been described. Other embodiments are within the scope of the following claims. In some cases, the actions recited in the claims can be performed in a different order and still achieve desirable results. Additionally, the processes depicted in the accompanying figures do not necessarily require the particular order shown, or sequential order, to achieve the desired results. In certain implementations, multitasking and parallel processing can be advantageous.

[0115] It should be noted that all directional indications, such as upper, lower, left, right, front, back, rear, etc., are merely used for convenience of description and are not intended to limit the application to a particular orientation.

[0116] In the description of the present application, the terms "first", "second", etc., are used only for convenience and are not intended to imply or suggest a relative importance or a particular order of the technical features being described. Thus, features defined with "first", "second" can explicitly or implicitly include at least one of the features.

[0117] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application belongs. The terminology used in the description of the application herein is for the purpose of describing particular embodiments only and is not intended to be limiting of the application.

[0118] It should be noted that, although the specific embodiments of the present application are described in detail with reference to the accompanying drawings, it should not be understood as limiting the scope of protection of the present application. Various modifications and variations of the embodiments described in the claims are still within the scope of protection of the present application without creative labor.

[0119] The examples of the embodiments of the present application are intended to simply illustrate the technical features of the embodiments of the present application, so that those skilled in the art can intuitively understand the technical features of the embodiments of the present application, and are not improper limitations of the embodiments of the present application.

[0120] Finally, it should be noted that: the above embodiments are only used to illustrate the technical solutions of the present application, and not to limit it; although the present application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or make equivalent replacement for part of the technical features; and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the spirit and scope of the technical solutions of the embodiments of the present application.

Claims

1. A method for coordinated optimization of metro train diagram and demand management in a pre-booking travel mode, characterized in that, The method comprises the following steps: acquiring metro line data and passenger flow data, wherein the metro line data comprises a set of stations, a set of trains and a set of discrete time periods in the line, and the passenger flow data comprises a set of passenger flow scenarios and dynamic passenger flow demand; based on the line data and the passenger flow data, establishing decision variables; according to the coupling relationship between reserved passengers and non-reserved passengers in the metro system, the fairness relationship between the number of passengers served by a train at each station and the number of passengers waiting, and the coupling relationship between transport capacity and transport volume, constraint conditions are constructed; combining the metro line data, the passenger flow data, the decision variables and the constraint conditions, an initial metro train working diagram and demand management collaborative optimization nonlinear programming model under a reserved travel mode are constructed, with the optimization objective being to minimize the weighted sum of total passenger waiting time and line congestion degree; according to the large M constraint, the demand management collaborative optimization nonlinear programming model is equivalently converted into a linear form, and the large M value is derived, to obtain a demand management collaborative optimization linear programming model with a more compact upper bound; according to the mathematical properties of the demand management collaborative optimization linear programming model, a solving algorithm is designed to solve the model until a standard metro train working diagram, a reserved quota allocation scheme and a passenger flow control scheme are obtained; the constraint conditions comprise train working diagram constraints, passenger flow dynamic evolution process constraints and coupling constraints between reserved passengers and non-reserved passengers; the train working diagram constraints are represented as: wherein, and denote the minimum and maximum headway limits; denotes the dwell time of train i at station s; denotes the running time of train i between stations s and s+1; denotes whether the time t is within the headway time window of trains i and i+1 at station s; denotes the train arrival time related decision variable, denotes the train departure time related decision variable, denotes the train departure indicator variable; t denotes a discrete time period, i denotes a train service, , denotes a station, .

2. The method of claim 1, wherein, the decision variables comprise train arrival time related decision variables, train departure time related decision variables, train departure indicator variables, reserved quota allocation decision variables and passenger flow control decision variables.

3. The method of claim 1, wherein, the passenger flow dynamic evolution process constraints are represented as: wherein, denotes the minimum service ratio; denotes the number of boarding passengers of the reserved passengers; denotes the number of waiting passengers of the non-reserved passengers, denotes the number of stranded passengers; denotes the reserved quota allocation decision variable, denotes the passenger flow control decision variable; t denotes a discrete time period, , i denotes a train number, , denotes a station, .

4. The method of claim 3, wherein, the coupling constraints between reserved passengers and non-reserved passengers are represented as: wherein, and respectively represent the number of reserved passengers and the number of non-reserved passengers among the passengers in the vehicle; represents the number of passengers who get off the vehicle; represents the maximum number of waiting passengers including the reserved passengers and the non-reserved passengers.

5. The method of claim 4, wherein, the objective function of the optimization objective is represented as: wherein, represents the passenger waiting time, represents the passenger line congestion degree.

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