Subway train working diagram and demand management collaborative optimization method in reserved travel mode

Abstract

The invention provides a subway train working diagram and demand management collaborative optimization method in an appointment trip mode, which comprises the following steps: acquiring subway line data and passenger flow data, and establishing decision variables; according to the coupling relation between the reserved passengers and the non-reserved passengers in the subway system, the fairness between the number of the passengers served by the train in each station and the number of the waiting passengers, and the coupling relation between the transport capacity and the transport volume, constructing constraint conditions; constructing an initial subway train working diagram and demand management collaborative optimization nonlinear programming model by combining subway line data, passenger flow data, decision variables and constraint conditions; equivalently converting the nonlinear programming model into a linear form according to a large M constraint to obtain a demand management collaborative optimization linear programming model; and according to mathematical characteristics of the linear programming model, designing a solving algorithm for solving until a standard subway train working diagram, a reservation quota allocation scheme and a passenger flow control scheme are obtained. According to the method, the service efficiency is improved, and the operation cost is reduced.

Description

Technical Field

[0001] The present invention relates to the technical field of urban public transportation operation management, and in particular to a method for collaboratively optimizing a subway train operation diagram and demand management in a reservation travel mode. Background Art

[0002] With the rapid development of scientific and technological innovation and new technologies, the traditional transportation system is in a stage of accelerated transformation and upgrading. For a long time, how to effectively deal with the highly concentrated commuter passenger flow in time and space has been a major challenge faced by the operation and management of urban rail transit. The initial solution was to add new lines or shorten the departure interval to increase the supply of transportation capacity. In recent years, as the utilization of urban physical space has tended to be saturated and the minimum train departure interval has entered the "2-minute era", passenger flow control strategies have become a widely adopted demand management measure in China's super-large-scale urban rail transit systems (such as Beijing, Shanghai, Guangzhou, etc.). This strategy controls the number of people waiting on the platform to avoid overcrowding, thereby reducing the risk of stampede accidents or train delays. It is worth noting that in March 2020, Beijing Metro innovatively launched a travel reservation practice. During the one-year pilot implementation period, the model served a total of 1.17 million passengers, achieving an average daily saving of 3.5 minutes per person, and was recognized by up to 88% of passengers. This move has significantly improved operational efficiency and service quality, and provided a new solution for the operation and management of future smart urban rail.

[0003] Although the reservation travel mode can provide high-quality travel services, it also increases the complexity of the operation organization of the urban rail transit system. On the one hand, reserved passengers and unreserved passengers share station space and train capacity resources, and there is a close coupling relationship. The unreasonable allocation of reservation quotas will inevitably have a negative impact on the travel experience of unreserved passengers, thereby reducing the fairness of service between reserved and unreserved 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 this problem be fundamentally alleviated. Existing research mostly focuses on a single aspect, usually optimizing the train operation diagram and passenger flow control strategy separately. There is no literature that systematically explores the problem of coordinated optimization of demand management and train operation diagram that takes into account service fairness under the reservation travel mode. Therefore, the service efficiency of the subway system in the existing technology is low and the operating cost is high. Summary of the invention

[0004] In view of this, the present invention provides a method for collaborative optimization of subway train operation diagram and demand management under a reservation travel mode to solve the above problems.

[0005] The present invention provides a method for collaborative optimization of subway train operation diagram and demand management under a reservation travel mode, comprising: obtaining subway line data and passenger flow data, 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 passenger flow scene set and a dynamic passenger flow demand; establishing decision variables based on the line data and the passenger flow data; constructing constraint conditions according to the coupling relationship between reserved passengers and unreserved passengers in the subway system, the fairness relationship between the number of passengers served by the train at each station and the number of waiting passengers, and the coupling relationship between capacity and volume; combining the subway line data, The passenger flow data, the decision variables and the constraints are used to construct an initial subway train operation diagram and a demand management collaborative optimization nonlinear programming model under the reservation travel mode with minimizing the weighted sum of the total waiting time of passengers and the line congestion as the optimization goal; the demand management collaborative optimization nonlinear programming model is equivalently converted into a linear form according to the large M constraint, and the large M value is derived to obtain a demand management collaborative optimization linear programming model with a tighter upper bound; according to the mathematical characteristics of the demand management collaborative optimization linear programming model, a solution algorithm is designed to solve it until a standard subway train operation diagram, a reservation quota allocation plan and a passenger flow control plan are obtained.

[0006] In another implementation of the present invention, the decision variables include decision variables related to train arrival time, decision variables related to train departure time, train departure indicator variables, reservation quota allocation decision variables and passenger flow control decision variables.

[0007] In another implementation of the present invention, the constraint conditions include train operation diagram constraints, passenger flow dynamic evolution process constraints, and coupling constraints between reserved and unreserved passengers.

[0008] In another implementation of the present invention, the train operation diagram constraint is expressed as:

[0009]

[0010] in, h and Indicates the 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 Indicates whether time t is within the departure interval window of trains i and i+1 at station s; a is Represents decisions related to train arrival times

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

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

[0013]

[0014]

[0015] Among them, κ isv Indicates the minimum service ratio; Indicates the number of passengers who have made reservations and are boarding the bus; w isv represents the number of passengers waiting without reservations, r isv Indicates the number of stranded people; represents the decision variable for allocating reservation quotas, b isv Represents the passenger flow control decision variable; t represents the discrete time period, t∈T, i represents the train number, i∈I, s, v represent the station, s, v∈S.

[0016] In another implementation of the present invention, the coupling constraint between the reserved and unreserved passengers is expressed as:

[0017]

[0018] in, and is Respectively represent the number of passengers with reservations and the number of passengers without reservations in the car; l is Indicates the number of people getting off the bus; z i Indicates the maximum number of waiting passengers, including reserved and unreserved passengers.

[0019] In another implementation of the present invention, the objective function of the optimization target is expressed as:

[0020] minλ1F e +λ2F c

[0021]

[0022] Among them, F e represents the passenger waiting time, F c Indicates the passenger line congestion.

[0023] The method for collaborative optimization of subway train operation diagram and demand management under the reservation travel mode of the present invention considers providing convenience for reserved passengers to directly enter the station and take the train, and at the same time effectively serves non-reserved passengers according to the passenger flow control strategy, takes minimizing waiting time and line congestion as the goal, combines constraints such as service fairness, train capacity, and train operation safety, considers two types of demand management methods, reservation travel and passenger flow control, and proposes a collaborative optimization model of subway train operation diagram and demand management for time-varying passenger flow; according to the characteristics of the model, a hybrid algorithm efficient solution model combining adaptive large neighborhood search and commercial optimization solver is designed, and the emerging reservation travel method is combined with the traditional passenger flow control method. By balancing the needs of reserved and non-reserved passengers while ensuring the best match between capacity and demand as much as possible, the coordinated optimization of the train operation diagram and the demand management strategy is achieved, the matching of capacity and volume is improved, and theoretical support is provided for the efficient operation of the actual subway system. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following briefly introduces the drawings required for use in the embodiments or the prior art descriptions. By reading the detailed description of the following implementations, the advantages and benefits of the solutions become clear to those skilled in the art. The drawings are only used to illustrate the preferred implementations and are not to be considered as limiting the present invention.

[0025] In the attached picture:

[0026] Figure 1 It is a flowchart of a method for collaborative optimization of subway train operation diagram and demand management in a reservation travel mode according to an embodiment of the present invention.

[0027] Figure 2 A schematic diagram of demand management according to an embodiment of the present invention.

[0028] Figure 3 The figure is a schematic diagram of a solution algorithm according to an embodiment of the present invention.

[0029] Figure 4 FIG. 1 is a schematic diagram of a fixed line according to an embodiment of the present invention.

[0030] Figure 5 This is a heat map of the optimized service ratios of each train at each station under different minimum service ratio settings according to an embodiment of the present invention. DETAILED DESCRIPTION

[0031] In order to enable those skilled in the art to better understand the technical solutions in the embodiments of the present invention, the technical solutions in the embodiments of the present invention will be described clearly and in detail below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. All other embodiments obtained by ordinary technicians in the field based on the embodiments in the embodiments of the present invention should fall within the scope of protection of the embodiments of the present invention.

[0032] Figure 1 A schematic flow chart of a method for collaboratively optimizing a subway train operation diagram and demand management in a reservation travel mode provided by an embodiment of the present invention is shown in FIG. Figure 1 As shown, this embodiment mainly includes:

[0033] S101. Obtain subway line data and passenger flow data, 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] Exemplarily, the following necessary parameters and data are predetermined: station distribution in the subway line; basic train operation parameters, including inter-station running time, maximum and minimum departure intervals, station stop time, etc.; maximum passenger capacity of the train; passenger flow demand at each station in each time period, etc.

[0035] S102: Establish decision variables based on route data and passenger flow data.

[0036] S103. Constraints are constructed based on the coupling relationship between reserved passengers and unreserved passengers in the subway system, the fairness relationship between the number of passengers served by the train at each station and the number of waiting passengers, and the coupling relationship between capacity and volume.

[0037] S104. Combining subway line data, passenger flow data, decision variables and constraints, construct an initial subway train operation diagram and demand management collaborative optimization nonlinear programming model under the reservation travel mode with the optimization goal of minimizing the weighted sum of total passenger waiting time and line congestion.

[0038] S105. 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 the demand management collaborative optimization linear programming model with a tighter upper bound.

[0039] S106. According to the mathematical characteristics of the demand management collaborative optimization linear programming model, a solution algorithm is designed to solve the problem until a standard subway train operation diagram, a reservation quota allocation plan and a passenger flow control plan are obtained.

[0040] The method for collaborative optimization of subway train operation diagram and demand management under the reservation travel mode of the present invention considers providing convenience for reserved passengers to directly enter the station and take the train, and at the same time effectively serves non-reserved passengers according to the passenger flow control strategy, takes minimizing waiting time and line congestion as the goal, combines constraints such as service fairness, train capacity, and train operation safety, considers two types of demand management methods, reservation travel and passenger flow control, and proposes a collaborative optimization model of subway train operation diagram and demand management for time-varying passenger flow; according to the characteristics of the model, a hybrid algorithm efficient solution model combining adaptive large neighborhood search and commercial optimization solver is designed, and the emerging reservation travel method is combined with the traditional passenger flow control method. By balancing the needs of reserved and non-reserved passengers while ensuring the best match between capacity and demand as much as possible, the coordinated optimization of the train operation diagram and the demand management strategy is achieved, the matching of capacity and volume is improved, and theoretical support is provided for the efficient operation of the actual subway system.

[0041] In another implementation of the present invention, the decision variables include decision variables related to train arrival time, decision variables related to train departure time, train departure indicator variables, reservation quota allocation decision variables and passenger flow control decision variables.

[0042] In another implementation of the present invention, the constraint conditions include train operation diagram constraints, passenger flow dynamic evolution process constraints, and coupling constraints between reserved and unreserved passengers.

[0043] In another implementation of the present invention, the train operation diagram constraint is expressed as:

[0044]

[0045]

[0046] in, h and Indicates the 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 Indicates whether time t is within the departure interval window of trains i and i+1 at station s; a is represents the decision variables related to train arrival time, d is represents the decision variables related to the train departure time, x ist Represents the train departure indicator variable; t represents the discrete time period, t∈T, i represents the train number, i∈I, s, v represent the station, s, v∈S.

[0047] In another implementation of the present invention, the passenger flow dynamic evolution process constraint is expressed as:

[0048]

[0049] Among them, κ isv Indicates the minimum service ratio; Indicates the number of passengers who have made reservations and are boarding the bus; w isv represents the number of passengers waiting without reservations, r isv Indicates the number of stranded people; represents the decision variable for allocating reservation quotas, b isv Represents the passenger flow control decision variable; t represents the discrete time period, t∈T, i represents the train number, i∈I, s, v represent the station, s, v∈S.

[0050] In another implementation of the present invention, the coupling constraint between the reserved and unreserved passengers is expressed as:

[0051]

[0052] in, and is Respectively represent the number of passengers with reservations and the number of passengers without reservations in the car; l is Indicates the number of people getting off the bus; z i Indicates the maximum number of waiting passengers, including reserved and unreserved passengers.

[0053] For example, Figure 2 As shown, starting from both the supply and demand sides, by increasing capacity supply and optimizing reservation quota allocation plans and passenger flow control strategies, the matching degree of capacity and volume can be improved, the congestion of stations along the line can be reduced and operational efficiency can be improved.

[0054] On the demand side, passengers with reservations can use special reservation entry gates to enter the platform directly after arriving at the station, and wait on the platform for the upcoming train. In addition, passengers without reservations need to queue in the station hall and wait for entry permission. Once permission is obtained according to the passenger flow control strategy, they can enter the platform through regular gates.

[0055] On the supply side, by adjusting the train schedule, we strive to achieve the best match between capacity and dynamic passenger flow demand. In addition, considering that too many reservation quotas will inevitably weaken the service level for passengers without reservations, under the premise of ensuring service fairness between reserved and non-reserved passengers, we have solved the problem of how to coordinately optimize the train schedule, refine the dynamic allocation plan of reservation quotas and passenger flow control strategy to minimize line congestion during peak hours.

[0056] In another implementation of the present invention, the objective function of the optimization target is expressed as:

[0057] minλ1F e +λ2F c (twenty one)

[0058]

[0059] Among them, F e represents the passenger waiting time, F c Indicates the passenger line congestion.

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

[0061]

[0062] Based on the above solution, the model linearization method and the derivation method of the large M value in step S105 specifically include:

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

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

[0065]

[0066] in,

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

[0068]

[0069] Among them, β in formula (25) isvt The equivalent form of the part is:

[0070]

[0071] in,

[0072] Constraint (22) consists of two 0-1 variables multiplied by one integer variable. When linearizing, we first define Its equivalent linear form is:

[0073]

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

[0075]

[0076] in,

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

[0078]

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

[0080] minλ1F e +λ2F c

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

[0082] Based on the above solution, the solution algorithm described in step S106 is as follows: Figure 3 As shown, specifically including:

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

[0084] Step 2: Use the Adaptive Large Neighborhood Search (ALNS) algorithm to transform the neighborhood of the current solution through the destruction operator and the repair operator to generate a new feasible solution. In 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 its performance. To avoid falling into the local optimum, after each iteration, the initial solution for the next iteration is selected according to the simulated annealing rule.

[0085] Step 3: Fix the train operation diagram obtained by the ALNS algorithm and solve the model using branch and bound to evaluate the pros and cons of the train operation diagram. A better demand management solution and train operation diagram are obtained through step-by-step iteration.

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

[0087] The following is a detailed description based on Example 1:

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

[0089] Table 1 Basic data of the example

[0090]

[0091] According to the given input data above, code is written in Java to construct the model and solution algorithm framework of the present invention, and the problem is solved to obtain a better subway train operation diagram, passenger flow control plan and reservation quota allocation plan.

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

[0093]

[0094] As can be seen from Table 2, the GUROBI calculation time is relatively long, and no feasible solution is found when solving examples Q3, Q4, and Q5. In comparison, the ALNS+GUROBI algorithm exhibits superior performance: when solving smaller examples Q1 and Q2, the algorithm not only saves approximately 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 scale of the example increases, the solution time of the algorithm continues to increase, but an approximate optimal solution can be found within 3600 seconds. The above results show that the ALNS+GUROBI algorithm proposed in the present invention has the ability to converge quickly and solve efficiently, and can meet the solution needs of actual operation scenarios.

[0095] Table 2 Comparison of solution results between ALNS+GUROBI and GUROBI

[0096]

[0097] Based on example Q3, a comparative analysis is conducted on the results of operating efficiency and line congestion under different minimum service ratios. Specifically, three groups of 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 solution. Table 3 shows the optimization results of operating efficiency, line congestion, service ratio and reservation ratio under different minimum service ratios. The service ratio is calculated by dividing the number of passengers who board without reservations by the number of passengers waiting. If the number of waiting people is 0, the value is NAN and 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 dividing the number of reservations by the total number of passengers.

[0098] Table 3 Comparison of operating efficiency, route congestion, service fairness and reservation ratio under different minimum service ratios for passengers without reservation

[0099]

[0100] From the results in Table 3, we can see that when the minimum service ratio increases from 0 to 10%, the passenger waiting time increases slightly, from 103887 to 103898 (an increase of about 0.01%), while the line congestion increases from 6605 to 6635 (an increase of about 0.45%). It is worth noting that the number of service ratios below 10% dropped from 22 times to 0 times. Furthermore, when the minimum service ratio is increased to 20%, the passenger waiting time and line congestion increased by 3.51% and 0.51% respectively compared with the minimum service ratio of 0; in addition, the cases where the service ratio is less than 10% and 20% are both reduced to 0 times. This shows that after raising the minimum service ratio, the extreme unfairness that originally existed between reserved passengers (whose service ratio is 100%) and unreserved passengers has been effectively resolved. The detailed service ratio results of trains at each station are shown in the figure. Figure 5 As shown, the white squares represent that the number of waiting passengers without reservations is 0 or the service ratio is 0.

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

[0102] The method of the present invention can be applied in industrial control systems in industries such as manufacturing, energy, and transportation, and can enhance the system's anti-attack capability by providing customized security services.

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

[0104] in:

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

[0106] Communication interface, used to communicate with other electronic devices or servers.

[0107] The processor is used to execute the program, and specifically can execute the steps of the method for collaborative optimization of subway train operation diagram and demand management under the reservation travel mode in any of the above embodiments.

[0108] Specifically, the program may include program codes including computer operation instructions.

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

[0110] The memory is used to store programs. The memory may include a high-speed RAM memory, and may also include a non-volatile memory, such as at least one disk memory.

[0111] The program can be specifically used to enable the processor to execute the steps of any method for collaborative optimization of subway train operation diagram and demand management under the reservation travel mode described in the embodiment. The specific implementation of each step in the program can refer to the corresponding descriptions in the steps and units executed by the method for collaborative optimization of subway train operation diagram and demand management under any reservation travel mode in the above steps, which will not be repeated here. Those skilled in the art can clearly understand that for the convenience and simplicity of description, the specific working process of the above-described devices and modules can refer to the corresponding process description in the aforementioned method embodiment.

[0112] The exemplary embodiments of the present application also provide a non-transitory computer-readable storage medium storing computer instructions, wherein the computer instructions are used to enable a computer to execute the methods of the various embodiments of the present application.

[0113] The above-described method according to an embodiment of the present invention may be implemented in hardware, firmware, or as software or computer code that may be stored in a recording medium (such as a CD ROM, RAM, floppy disk, hard disk, or magneto-optical disk), or as computer code that is originally stored in a remote recording medium or a non-temporary machine-readable medium downloaded over a network and will be stored in a local recording medium, so that the method described herein may be stored in such software processing on a recording medium using a general-purpose computer, a dedicated processor, or programmable or dedicated hardware (such as an ASIC or FPGA). It is understood that a computer, processor, microprocessor controller, or programmable hardware includes a storage component (e.g., RAM, ROM, flash memory, etc.) that can store or receive software or computer code, and when the software or computer code is accessed and executed by a computer, processor, or 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 converts the general-purpose computer into a dedicated computer for executing the method shown herein.

[0114] Thus far, specific embodiments of the present invention have been described. Other embodiments are within the scope of the appended claims. In some cases, the actions recited in the claims may be performed in a different order and still achieve the desired results. Additionally, the processes depicted in the accompanying drawings do not necessarily require the specific order or sequential order shown to achieve the desired results. In some embodiments, multitasking and parallel processing may be advantageous.

[0115] It should be noted that all directional indications in the embodiments of the present invention (such as up, down, left, right, back, etc.) are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.

[0116] In the description of the present invention, the terms "first" and "second" are only used to facilitate the description of different components or names, and cannot be understood as indicating or implying a sequential relationship, relative importance, or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may 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 those commonly understood by those skilled in the art of the present invention. The terms used in the specification of the present invention herein are only for the purpose of describing specific embodiments and are not intended to limit the present invention.

[0118] It should be noted that although the specific embodiments of the present invention are described in detail in conjunction with the accompanying drawings, it should not be understood as limiting the scope of protection of the present invention. Within the scope described in the claims, various modifications and variations that can be made by those skilled in the art without creative work still belong to the scope of protection of the present invention.

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

[0120] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for collaborative optimization of subway train operation diagram and demand management under reservation travel mode, characterized in that: include: Acquire subway line data and passenger flow data, wherein the subway line data includes a set of stations, a set of trains, and a set of discrete time periods in the line, and the passenger flow data includes a set of passenger flow scenarios and dynamic passenger flow demand; Establishing decision variables based on the route data and the passenger flow data; According to the coupling relationship between reserved passengers and unreserved passengers in the subway system, the fairness relationship between the number of passengers served by the train at each station and the number of waiting passengers, and the coupling relationship between capacity and volume, the constraints are constructed; Combining the subway line data, the passenger flow data, the decision variables and the constraints, constructing a nonlinear programming model for collaborative optimization of the initial subway train operation diagram and demand management under the reservation travel mode with minimization of the weighted sum of the total waiting time of passengers and the line congestion as the optimization goal; 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 tighter upper bound; According to the mathematical characteristics of the demand management collaborative optimization linear programming model, a solution algorithm is designed to solve the problem until a standard subway train operation diagram, a reservation quota allocation plan and a passenger flow control plan are obtained.

2. The method according to claim 1, characterized in that The decision variables include train arrival time-related decision variables, train departure time-related decision variables, train departure indicator variables, reservation quota allocation decision variables and passenger flow control decision variables.

3. The method according to claim 1, characterized in that The constraints include train operation diagram constraints, passenger flow dynamic evolution process constraints, and coupling constraints between reserved and unreserved passengers.

4. The method according to claim 3, characterized in that The train operation diagram constraint is expressed as: in, h and Indicates the 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 Indicates whether time t is within the departure interval window of trains i and i+1 at station s; a is represents the decision variables related to train arrival time, d is represents the decision variables related to the train departure time, x ist Represents the train departure indicator variable; t represents the discrete time period, t∈T, i represents the train number, i∈I, s, v represent the station, s, v∈S.

5. The method according to claim 4, characterized in that The constraints of the passenger flow dynamic evolution process are expressed as: Among them, κ isv Indicates the minimum service ratio; Indicates the number of passengers who have made reservations and are boarding the bus; w isv represents the number of passengers waiting without reservations, r isv Indicates the number of stranded people; represents the decision variable for allocating reservation quotas, b isv Represents the passenger flow control decision variable; t represents the discrete time period, t∈T, i represents the train number, i∈I, s, v represent the station, s, v∈S.

6. The method according to claim 5, characterized in that The coupling constraint between the reserved and unreserved passengers is expressed as: in, and is Respectively represent the number of passengers with reservations and the number of passengers without reservations in the car; l is Indicates the number of people getting off the bus; z i Indicates the maximum number of waiting passengers, including reserved and unreserved passengers.

7. The method according to claim 6, characterized in that The objective function of the optimization objective is expressed as: minλ1F e +λ2F c Among them, F e represents the passenger waiting time, F c Indicates the passenger line congestion.

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