Method and system for ticket amount allocation optimization under mixed ticket system of urban area and suburban railway

Abstract

This invention provides a method and system for optimizing ticket allocation under a hybrid fare system for urban and suburban railways, belonging to the field of transportation operation management technology. This invention breaks through the limitations of a single fare system, achieving online and offline dual-system collaboration through a dynamic ticket conversion mechanism, effectively solving the problem of commuter passenger flow being squeezed and significantly improving passenger flow satisfaction; it solves the difficult problem of high-dimensional optimization of ticket allocation by designing an improved particle swarm optimization algorithm (integrating dynamic parameter adjustment and diverse restart mechanisms), greatly improving computational efficiency and supporting minute-level optimization of a network of hundreds of stations; it accurately matches passenger flow characteristics, constructing a dual-system demand coupling model based on OD passenger flow distribution, significantly improving seat utilization and transportation revenue, and directly supporting the "four-network integration" fare system interoperability project.

Description

Technical Field

[0001] This invention relates to the field of transportation operation management technology, specifically to a method and system for optimizing ticket allocation under a mixed ticketing system for urban and suburban railways. Background Technology

[0002] With the vigorous development of urban agglomerations and metropolitan areas, the flow of people between regions is becoming increasingly frequent, and passengers have an increasingly urgent need for the "four-network integration" of rail transit, especially the interconnection and integrated development of subways, intercity railways, and suburban railways. This integration is not only a physical connection of transportation infrastructure, but also a deep collaboration in service models, ticketing systems, and other aspects, providing passengers with a more convenient and efficient travel experience.

[0003] As a rapid rail transit component of the urban integrated transportation system, suburban railways provide commuter-oriented, high-speed, and high-capacity transportation services between urban centers and surrounding towns, playing a vital role in serving residents' travel needs and alleviating urban traffic congestion. With the continued advancement of the "four-network integration" strategy for metropolitan area rail transit, the coordination of ticketing systems between suburban railways and trunk railways, intercity railways, and urban rail transit has become a key challenge. Traditional single-ticket systems for suburban railways, such as a flat fare for the entire journey or fare based on distance, are ill-suited to the complex scenarios of high-frequency, mixed commuter and long-distance passenger flows. To improve operational efficiency and passenger convenience, suburban railways are actively exploring public transport-like operations, leading to the emergence of new hybrid ticketing systems. Under this model, passengers can purchase fixed-seat tickets in advance through online ticketing systems (such as 12306) or directly enter the station through offline AFC systems (such as swiping transportation cards or using QR codes). This hybrid ticketing system is an innovative model that combines traditional railway ticketing with the convenience of urban rail transit. Its core lies in how to rationally allocate the number of online and offline tickets sold in each section, ensuring that train seats are fully utilized, maximizing operational revenue while meeting the needs of different passenger flows as much as possible, and thus promoting the development of the "four-network integration" of rail transit towards a higher quality and higher efficiency.

[0004] Ticket allocation is a plan for distributing railway transport capacity. By understanding and effectively predicting the distribution of passenger demand, tickets are rationally allocated to stations along the train route. This scientifically improves and enhances the quality of transport planning, balances the distribution of passenger demand among trains, fully meets passenger travel needs, and increases the utilization rate of train seating capacity. Currently, optimization strategies for railway ticket allocation mainly focus on ticket allocation under the traditional ticketing system. The research focuses on ticketing models that do not consider offline entry via AFC (Automatic Fare Collection) systems, specifically optimizing ticket allocation for passenger trains on trunk lines and intercity railways. The algorithms for solving related models are also based on algorithms designed under the traditional ticketing model. Therefore, constructing an optimization model and algorithm for ticket allocation on urban (suburban) railways under a hybrid ticketing model is of great significance for promoting the ticketing system interoperability project of "four-network integration" in rail transit.

[0005] While existing railway ticket allocation technologies have achieved some success in trunk and intercity railways, their core flaw lies in their inability to adapt to mixed ticketing systems in urban (suburban) railways. Specifically, current solutions optimize only a single online booking system, neglecting the real-time passenger flow demand of offline AFC (card / QR code entry) systems. This leads to online reserved tickets squeezing offline capacity resources for short-distance commuters, and offline demand is not included in the revenue function, resulting in an overall underestimation of revenue. Existing models and algorithms do not model the demand coupling relationship between the "online + offline" dual ticketing systems, nor do they consider the overlapping use of tickets in both systems, or the competition and complementarity of passenger flow between them. Especially in complex OD networks, there is still no suitable solution for constructing and designing models and algorithms for coordinated ticket allocation optimization for multiple trains and ticket types. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for optimizing ticket allocation under a mixed ticketing system for urban and suburban railways, so as to solve at least one of the technical problems existing in the background art.

[0007] To achieve the above objectives, the present invention adopts the following technical solution:

[0008] In a first aspect, the present invention provides a method for optimizing ticket allocation under a mixed fare system for urban and suburban railways, comprising:

[0009] OD Passenger Flow Data Collection and Distribution Parameter Fitting: Extract historical passenger flow data for each OD section, including passenger boarding and alighting stations, ticket sales, and corresponding train stopping plans; based on historical data, perform probability distribution fitting on passenger flow demand for each OD section;

[0010] Based on the fitting results, a railway hybrid ticketing system ticket allocation model is constructed: it is assumed that different passenger trains have the same single ticket price on the same origin and destination (OD), and the passenger flow demand on each OD is described by a known normal distribution function; all trains only provide seated tickets and over-selling is not allowed. With the goal of maximizing the passenger ticket revenue of the entire railway and the seat capacity of each train and each section as constraints, the ticket allocation scheme of all passenger trains is optimized.

[0011] Solving the hybrid ticket allocation system based on an improved particle swarm optimization algorithm: The complex ticket allocation scheme is encoded as a particle position vector, where each particle represents a complete allocation scheme with dimensions 2×K×N. OD Odd-numbered online ticket amounts Even-numbered digits store offline ticket amounts The core parameters are adaptively adjusted according to the iteration process to avoid premature convergence.

[0012] As a further limitation of the first aspect of this invention, the adaptive adjustment of core parameters according to the iterative process to avoid premature convergence includes: nonlinear decay of the inertia weight ω, adaptive decrease of the cognitive coefficient c1 to gradually reduce the influence of individual memory, adaptive increase of the social coefficient c2 to gradually enhance the group's collaborative ability; real-time monitoring and dynamic intervention of the particle swarm state, and when particles aggregate or stagnate for a long time, the system injects diversity to escape local optima and ensure global search capability. A multi-round selection mechanism is adopted to overcome the influence of algorithm randomness.

[0013] As a further limitation of the first aspect of the invention, in order to accurately calculate the expected sales volume and To improve solution speed, Gauss-Hermitian orthogonal approximation is used instead of numerical integration when calculating the demand probability density function, thus efficiently calculating the integral term; the remaining ticket quota e reserved online is utilized. ij Real-time updates on the fulfillment of offline demand distribution; for model-specific constraints: an adaptive exponential penalty is applied to the overcapacity portion in the seat capacity constraint to ensure the mandatory nature of the constraint; in the stop matching constraint, a service identifier u is introduced. kij Automatically mask invalid OD pairs.

[0014] As a further limitation of the first aspect of the present invention, the OD passenger flow data collection and distribution parameter fitting includes: assuming that n passenger trains operate on a suburban railway consisting of L+1 stops and L sections, and there are multiple stopping schemes; the passenger flow demand of each OD can be regarded as following an independent normal distribution, and the probability density function f of the passenger flow demand in the OD interval (i,j) is... ij (x) can be represented as:

[0015]

[0016] Where i,j are the origin and destination station numbers of the OD, x is the potential passenger demand in the OD interval (i,j), and μ ij Let σ be the average of the historical passenger flow demand of OD(i,j). ij The standard deviation of historical passenger flow demand is given; the historical passenger flow demand value for each OD is the actual passenger flow of that OD section on that day, which is the sum of the online booking demand and the offline swipe / card entry demand for all trains running on that OD on that day.

[0017] As a further limitation of the first aspect of the present invention, when only one train is operating, if the probability density function of the system's pre-booked passenger flow demand on the line in interval (i,j) is... If we can calculate the expected number of online ticket sales for this train in the interval (i,j), then the expected sales volume is:

[0018]

[0019] in, The number of tickets allocated to the train in the online system within the OD interval (i,j) is the online ticketing limit. The expected sales volume under the uncertainty of demand is calculated mathematically using the probability density function. When the actual demand for online tickets is less than the allocated ticket limit, the sales volume is the actual demand. When the actual demand is greater than the allocated ticket limit, the sales volume is always the allocated ticket limit.

[0020] As a further limitation of the first aspect of the present invention, when k trains are running on the line, and the probability density function of online ticket booking passenger flow demand for each OD is... and the probability density function of passenger flow demand in the offline AFC system. Given that a multi-train mixed ticketing system ticket allocation model is obtained with the objective of maximizing passenger ticket revenue for urban (suburban) railways and the constraint of the maximum seat capacity of each section of the train, considering capacity constraints, is obtained.

[0021] Secondly, the present invention provides a ticket allocation optimization system under a mixed ticketing system for urban and suburban railways, comprising:

[0022] The fitting module is used for OD passenger flow data collection and distribution parameter fitting: extracting historical passenger flow data for each OD section, including passenger boarding and alighting stations, ticket sales, and corresponding train stopping plans; and fitting the probability distribution of passenger flow demand for each OD based on historical data.

[0023] The module is used to build a railway hybrid ticketing system ticket allocation model based on the fitting results: it assumes that different passenger trains have the same single ticket price on the same origin and destination (OD), and the passenger flow demand on each OD is described by a known normal distribution function; all trains only provide seated tickets and overselling is not allowed. With the goal of maximizing the passenger ticket revenue of the entire railway and the seat capacity of each train and each section as constraints, the ticket allocation scheme of all passenger trains is optimized.

[0024] The solution module is used to solve the hybrid ticket allocation optimization model based on the improved particle swarm optimization algorithm: it encodes the complex ticket allocation scheme as particle position vectors, where each particle represents a complete allocation scheme with dimensions 2×K×N. OD Odd-numbered online ticket amounts Even-numbered digits store offline ticket amounts The core parameters are adaptively adjusted according to the iteration process to avoid premature convergence.

[0025] Thirdly, the present invention provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the fare allocation optimization method under the mixed fare system for urban and suburban railways as described in the first aspect.

[0026] Fourthly, the present invention provides a computer device including a memory and a processor, wherein the processor and the memory communicate with each other, the memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the fare allocation optimization method under the mixed fare system of urban and suburban railways as described in the first aspect.

[0027] Fifthly, the present invention provides an electronic device, comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the fare allocation optimization method under the mixed fare system for urban and suburban railways as described in the first aspect.

[0028] Terminology Explanation:

[0029] Suburban railways: Suburban railways are rail transit systems that connect the central urban areas of metropolitan areas with surrounding towns and provide high-capacity, public transport services for commuters. Lines using urban rail transit systems are also known as suburban express lines (suburban rapid rail transit).

[0030] Hybrid ticketing: an innovative model that combines traditional railway ticketing with the convenience of urban rail transit. Passengers can either purchase fixed-seat tickets in advance through online platforms (such as the China Railway system (12306 platform)) or directly enter the station by swiping their transportation card / boarding code on-site.

[0031] Ticket allocation: In transportation systems (such as railways and airlines), operators divide the available seats / capacity of a single mode of transport (such as a train or an airplane) into different shares according to a pre-set strategy, and allocate them to different sales channels, ticket types, or passenger groups. Its core objective is to optimize resource utilization, balance supply and demand, and maximize revenue or ensure fairness in public services.

[0032] The "Four-Network Integration" of Rail Transit: Through planning coordination, standard collaboration, and management optimization, the integration of trunk railways, intercity railways, suburban railways, and urban rail transit will be promoted to form a multi-level rail transit network with complementary functions and shared resources.

[0033] The beneficial effects of this invention are as follows: It breaks through the limitations of a single ticketing system, and achieves online and offline dual-system collaboration through a dynamic ticketing conversion mechanism, effectively solving the problem of commuter passenger flow being squeezed and significantly improving passenger flow satisfaction rate; it solves the difficult problem of high-dimensional optimization of ticketing allocation by designing an improved particle swarm algorithm (integrating dynamic parameter adjustment and diverse restart mechanisms), which greatly improves computational efficiency and can support minute-level optimization of road networks at the level of hundreds of stations; it accurately matches passenger flow characteristics, and constructs a dual-system demand coupling model based on OD passenger flow distribution, which significantly improves seat utilization and transportation revenue, and directly supports the "four-network integration" ticketing system interoperability project.

[0034] The advantages of additional aspects of the invention will be set forth more clearly in the following description or will be learned by practice of the invention. Attached Figure Description

[0035] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the following description of the embodiments will be briefly introduced. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is a flowchart of the improved adaptive particle swarm optimization algorithm described in an embodiment of the present invention.

[0037] Figure 2 This is a schematic diagram of the three-train stopping scheme according to an embodiment of the present invention.

[0038] Figure 3 This is a graph showing the change in expected return with the number of iterations as described in an embodiment of the present invention.

[0039] Figure 4 This is a schematic diagram of the train ticket allocation optimization scheme according to an embodiment of the present invention.

[0040] Figure 5 This is a schematic diagram of the train ticket allocation optimization scheme according to an embodiment of the present invention.

[0041] Figure 6 This is a schematic diagram of the train ticket allocation optimization scheme according to an embodiment of the present invention.

[0042] Figure 7 This is a schematic diagram illustrating the expected sales volume of each OD as described in an embodiment of the present invention. Detailed Implementation

[0043] Embodiments of the present invention are described in detail below, examples of which 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.

[0044] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0045] It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as here.

[0046] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, and / or groups thereof.

[0047] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0048] To facilitate understanding of the present invention, the present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. However, the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0049] Those skilled in the art should understand that the accompanying drawings are merely schematic diagrams of embodiments, and the components in the drawings are not necessarily essential for implementing the present invention.

[0050] This invention belongs to the field of urban (suburban) railway operation and management technology under the background of four-network convergence. Specifically, it involves an optimization method for the allocation of urban (suburban) railway tickets in a mixed ticketing scenario (online platform reservation and ticket booking and offline AFC system card swiping / scanning QR code entry in parallel). By constructing a passenger flow prediction model and ticket allocation control mechanism, it solves the resource competition contradiction between online and offline seats for multiple trains and multiple origins / departments, and achieves synergistic optimization of maximizing capacity utilization and passenger fairness.

[0051] Existing urban (suburban) railways implementing a hybrid fare system rely primarily on fixed rules or manual experience to determine the ratio of online to offline ticket allocations. This lack of quantitative analysis of the competition between online and offline ticket purchases leads to high seat vacancy rates and passenger congestion. This invention constructs a hybrid fare allocation optimization model, combining historical passenger flow data and trends to predict passenger demand across different ticketing channels. It optimizes the calculation of online and offline ticket allocations for different trains in different origin-destination (OD) sections, effectively reducing vacancy rates, improving passenger satisfaction, and ensuring efficient resource utilization.

[0052] The computational complexity of multi-train, multi-OD collaborative optimization models is excessively high. Traditional algorithms for solving multi-train, multi-OD ticket allocation models exhibit exponentially increasing computational complexity, resulting in poor accuracy, slow speed, susceptibility to local optima, and poor stability. This invention designs an improved particle swarm optimization algorithm for solving hybrid ticket allocation optimization models. This ensures the stability of the model solution in multi-train, multi-OD scenarios while significantly improving accuracy and speed, enabling the finding of a ticket allocation scheme closer to the global optimum in a shorter time.

[0053] Example 1

[0054] In this embodiment 1, a ticket allocation optimization system under a mixed ticketing system for urban and suburban railways is first provided, including:

[0055] The fitting module is used for OD passenger flow data collection and distribution parameter fitting: extracting historical passenger flow data for each OD section, including passenger boarding and alighting stations, ticket sales, and corresponding train stopping plans; and fitting the probability distribution of passenger flow demand for each OD based on historical data.

[0056] The module is used to build a railway hybrid ticketing system ticket allocation model based on the fitting results: it assumes that different passenger trains have the same single ticket price on the same origin and destination (OD), and the passenger flow demand on each OD is described by a known normal distribution function; all trains only provide seated tickets and overselling is not allowed. With the goal of maximizing the passenger ticket revenue of the entire railway and the seat capacity of each train and each section as constraints, the ticket allocation scheme of all passenger trains is optimized.

[0057] The solution module is used to solve the hybrid ticket allocation optimization model based on the improved particle swarm optimization algorithm: it encodes the complex ticket allocation scheme as particle position vectors, where each particle represents a complete allocation scheme with dimensions 2×K×N. OD Odd-numbered online ticket amounts Even-numbered digits store offline ticket amounts The core parameters are adaptively adjusted according to the iteration process to avoid premature convergence.

[0058] In this embodiment, the above-described system is used to implement a method for optimizing ticket allocation under a mixed fare system for urban and suburban railways, including:

[0059] OD Passenger Flow Data Collection and Distribution Parameter Fitting: Extract historical passenger flow data for each OD section, including passenger boarding and alighting stations, ticket sales, and corresponding train stopping plans; based on historical data, perform probability distribution fitting on passenger flow demand for each OD section;

[0060] Based on the fitting results, a railway hybrid ticketing system ticket allocation model is constructed: it is assumed that different passenger trains have the same single ticket price on the same origin and destination (OD), and the passenger flow demand on each OD is described by a known normal distribution function; all trains only provide seated tickets and over-selling is not allowed. With the goal of maximizing the passenger ticket revenue of the entire railway and the seat capacity of each train and each section as constraints, the ticket allocation scheme of all passenger trains is optimized.

[0061] Solving the hybrid ticket allocation system based on an improved particle swarm optimization algorithm: The complex ticket allocation scheme is encoded as a particle position vector, where each particle represents a complete allocation scheme with dimensions 2×K×N. OD Odd-numbered online ticket amounts Even-numbered digits store offline ticket amounts The core parameters are adaptively adjusted according to the iteration process to avoid premature convergence.

[0062] The system adaptively adjusts core parameters according to the iteration process to avoid premature convergence, including: nonlinear decay of the inertia weight ω, adaptive decrease of the cognitive coefficient c1 to gradually reduce the influence of individual memory, and adaptive increase of the social coefficient c2 to gradually enhance group collaboration. The system monitors the particle swarm state in real time and intervenes dynamically; when particles aggregate or stagnate for a long period, diversity injection helps them escape local optima, ensuring global search capability. A multi-round selection mechanism is employed to overcome the influence of algorithm randomness.

[0063] To accurately calculate expected sales volume and To improve solution speed, Gauss-Hermitian orthogonal approximation is used instead of numerical integration when calculating the demand probability density function, thus efficiently calculating the integral term; the remaining ticket quota e reserved online is utilized. ij Real-time updates on the fulfillment of offline demand distribution; for model-specific constraints: an adaptive exponential penalty is applied to the overcapacity portion in the seat capacity constraint to ensure the mandatory nature of the constraint; in the stop matching constraint, a service identifier u is introduced. kij Automatically mask invalid OD pairs.

[0064] The OD passenger flow data collection and distribution parameter fitting includes: assuming a suburban railway consisting of L+1 stops and L sections, with n passenger trains operating and multiple stopping options. Based on existing research, the passenger flow demand of each OD can be considered to follow an independent normal distribution, and the probability density function f of the passenger flow demand in the OD interval (i,j) is... ij (x) can be represented as:

[0065]

[0066] Where i,j are the origin and destination station numbers of the OD, x is the potential passenger demand in the OD interval (i,j), and μ ij Let σ be the average of the historical passenger flow demand of OD(i,j). ij The standard deviation of historical passenger flow demand is given; the historical passenger flow demand value for each OD is the actual passenger flow of that OD section on that day, which is the sum of the online booking demand and the offline swipe / card entry demand for all trains running on that OD on that day.

[0067] When only one train is running, if the probability density function of the system's booked passenger flow demand on the line in interval (i,j) is... If we can calculate the expected number of online ticket sales for this train in the interval (i,j), then the expected sales volume is:

[0068]

[0069] in, The number of tickets allocated to the train in the online system within the OD interval (i,j) is the online ticketing limit. The expected sales volume under the uncertainty of demand is calculated mathematically using the probability density function. When the actual demand for online tickets is less than the allocated ticket limit, the sales volume is the actual demand. When the actual demand is greater than the allocated ticket limit, the sales volume is always the allocated ticket limit.

[0070] When k trains are running on the line, and the probability density function of online ticket booking passenger flow demand for each OD is... and the probability density function of passenger flow demand in the offline AFC system. Given that a multi-train mixed ticketing system ticket allocation model is obtained with the objective of maximizing passenger ticket revenue for urban (suburban) railways and the constraint of the maximum seat capacity of each section of the train, considering capacity constraints, is obtained.

[0071] Example 2

[0072] This embodiment provides a method for optimizing the allocation of tickets under a hybrid fare system to meet the operational needs of urban (suburban) railways. Based on actual train operation plans, this method constructs a hybrid fare allocation optimization model, calibrates parameters using historical ticketing data, and utilizes passenger flow demand forecasts to achieve online and offline pre-allocation optimization calculations for multiple trains in complex station-stop scenarios. This provides a scientific basis and theoretical support for the formulation of passenger ticketing plans.

[0073] The hybrid fare allocation optimization method for urban (suburban) railway operations proposed in this embodiment includes the following steps:

[0074] Step 1: Od Flow Data Collection and Distribution Parameter Fitting

[0075] The passenger flow data used were historical passenger flow data for each OD (Original Departure / Outlet) section extracted from the AFC (Automatic Fare Collection) system of urban (suburban) railways and online ticketing systems (such as 12306), including passenger boarding and alighting stations, ticket sales, and corresponding train stopping plans. Based on the historical data, a probability distribution was fitted to the passenger flow demand of each OD.

[0076] Suppose a suburban railway consisting of L+1 stops and L sections operates n passenger trains with multiple stopping options. Based on existing research, the passenger demand at each origin-destination (OD) can be considered to follow an independent normal distribution. The probability density function f of the passenger demand in the OD interval (i,j) is... ij (x) can be represented as:

[0077]

[0078] Where i,j are the origin and destination station numbers of the OD, x is the potential passenger demand in the OD interval (i,j), and μ ijLet σ be the average of the historical passenger flow demand of OD(i,j). ij This represents the standard deviation of historical passenger flow demand. The historical passenger flow demand value for each OD is the actual passenger flow in that OD section on that day, which is the sum of the online booking demand and the offline QR code / card entry demand for all trains operating in that OD on that day.

[0079] Step 2: Construct a fare allocation model for the mixed fare system of urban (suburban) railways.

[0080] For the public transport-like operation of suburban railways, which supports direct entry via transportation cards or QR codes (similar to subways), no advance ticket purchase is required. This has led to the development of a hybrid fare system, where passengers can book tickets in advance through online platforms like 12306 or enter the station by scanning a QR code on-site. Currently, suburban railways allocate different fixed ticket quotas to electronic tickets and on-site QR code tickets. During holidays, in addition to increasing train services, strategies are employed to fine-tune the different ticket quotas for online and offline bookings. However, in actual operation, passenger flow changes are often complex and uncertain, making simple adjustments to ticket quotas insufficient for precise responses. This embodiment constructs a ticket quota allocation optimization model that considers both online booking and on-site card / QR code ticketing for complex multi-train origin-destination (OD) scenarios (hereinafter referred to as the "hybrid fare quota optimization model").

[0081] In this embodiment, optimization decisions are made only for the ticket allocation scheme. Therefore, it is assumed that different passenger trains have the same single ticket price on the same origin-destination (OD), and the passenger flow demand on each OD is described by a known normal distribution function. All trains only provide seated tickets and overselling is not allowed. The goal is to maximize the passenger ticket revenue of the entire urban (suburban) railway, and the seat capacity of each train in each section is used as a constraint to optimize the ticket allocation scheme for all passenger trains.

[0082] (1) Optimization model of ticket amount for single-train hybrid ticketing system

[0083] When only one train is running, if the probability density function of the system's booked passenger flow demand on the line in interval (i,j) is... If we can calculate the expected number of online ticket sales for this train in the interval (i,j), then the expected sales volume is:

[0084]

[0085] in, The number of tickets allocated to the train in the online system within the OD interval (i,j) is the online ticketing limit. Equation (2) uses the probability density function to calculate the expected sales volume under demand uncertainty. When the actual demand for online tickets is less than the allocated ticket amount, the sales volume is the actual demand. When the actual demand is greater than the allocated ticket amount, the sales volume is always the allocated ticket amount.

[0086] If the probability density function of passenger flow demand in the offline AFC system of the train in the interval (i,j) is... If we can calculate the expected sales volume of offline AFC tickets for this train in the interval (i,j), then the expected sales volume is:

[0087]

[0088] in, Allocate the number of tickets for this train in the offline AFC system within the OD section (i,j), i.e., the offline card / code ticket limit. ij To reserve the remaining ticket quota in the online system within the OD interval (i,j), in practical scenarios, the ticket quota allocated online but not sold can be converted into available resources in the offline AFC system in real time, thereby avoiding idle capacity. Similarly, Equation (3) uses the probability density function to calculate the expected sales volume under demand uncertainty. When the actual demand of the offline AFC system is less than the sum of the allocated ticket quota and the remaining online ticket quota, the sales volume is the actual demand volume. When the actual demand is greater than the sum of the allocated ticket quota and the remaining online ticket quota, the sales volume is always the sum of the allocated ticket quota and the remaining online ticket quota.

[0089] The expected revenue of this train can be expressed as:

[0090]

[0091] Where, p ij Let be the ticket price for the train in the OD interval (i,j), which is a constant.

[0092] Therefore, based on passenger flow demand forecasts for each OD section, and with the objective of maximizing ticket revenue for urban (suburban) railways, and constrained by the maximum seat capacity of each train segment, a single-train hybrid ticketing system ticket allocation model considering capacity constraints is proposed.

[0093]

[0094] Among them, C m u represents the maximum capacity of the train on section m. ij Let u be a 0-1 variable indicating whether the train serves the OD interval (i,j). If the train stops at both station i and station j, then u ij =1, otherwise u ij =0. Equation (6) is the objective function of the single-train mixed ticketing system ticket allocation model, and the optimization objective is to maximize the revenue of the ticket allocation scheme. Equation (8) is the seating capacity constraint, which means that the total number of online reservation tickets and offline AFC system entry tickets sold by the train should not exceed the train's capacity. Constraints (9) and (10) ensure that the final ticket allocation scheme matches the train's stopping scheme.

[0095] (2) Multi-train mixed ticketing system ticket amount optimization model

[0096] In real-world scenarios, multiple trains often run on a single line throughout the day, and each train may have different stopping plans. These stopping plans directly impact the ticket allocation strategy. Due to the diversity and complexity of train stopping plans in the actual railway network, it is essential to comprehensively consider various stopping plans for different trains in order to design a more scientific ticket allocation strategy, thereby effectively improving occupancy rates and railway revenue.

[0097] When k trains are running on the line, and the probability density function of online ticket booking passenger flow demand for each OD is... and the probability density function of passenger flow demand in the offline AFC system. Given that, based on the derivation process of the single-train mixed ticketing system fare allocation model above, a multi-train mixed ticketing system fare allocation model can be obtained, which aims to maximize passenger ticket revenue for urban (suburban) railways and is constrained by the maximum seat capacity of each section of the train, considering capacity constraints.

[0098]

[0099] in, Allocate the number of tickets for train k in the online system reservation for the OD section (i,j). Assign the number of tickets to train k in the offline AFC system within the OD section (i,j), e ij To reserve the remaining number of tickets in the online system within the OD interval (i,j). ij Let C be the fare for each train in the OD section (i,j). km u is the upper limit of the capacity of train k on section m. kij Let u be a 0-1 variable indicating whether train k serves the OD interval (i,j). If the train stops at both station i and station j, then u kij =1, otherwise u kij =0. Equation (12) is the objective function of the multi-train mixed ticketing system ticket allocation model. The optimization objective is to maximize the passenger ticket revenue of the ticket allocation scheme. Since there are many factors affecting the demand of each train, it is difficult to directly predict the demand corresponding to each train. Therefore, in Equation (12), the ticket amount of all trains is summed to directly calculate the total expected sales volume of the k train interval (i,j).

[0100] Step 3: Solving the hybrid ticketing system's ticket amount optimization model based on the improved particle swarm optimization algorithm

[0101] The complex OD (origin-destination) ticket allocation problem for multiple trains is a high-dimensional, nonlinear problem with constraints. Particle Swarm Optimization (PSO) is often used as the primary algorithm for solving such problems due to its suitability for parallel search and ease of handling constraints. In this embodiment, an improved Adaptive Particle Swarm Optimization (APSO) algorithm is designed to solve the mixed ticket allocation model, taking into account the characteristics of the model. Its core innovation lies in:

[0102] (1) Adaptive design for high-dimensional decision space

[0103] As the number of trains K increases, the dimension of the decision variables becomes O(K×L). 2 With a growth rate of L (where L is the number of stations), traditional algorithms are prone to the curse of dimensionality, leading to slow convergence or even failure. This invention designs an algorithm that encodes the complex ticket allocation scheme as particle position vectors, where each particle represents a complete allocation scheme with dimensions of 2×K×N. OD Odd-numbered online ticket amounts Even-numbered digits store offline ticket amounts To avoid premature convergence, the core parameters are adaptively adjusted according to the iteration process: the inertia weight ω decays non-linearly, the cognitive coefficient c1 decreases adaptively to gradually reduce the influence of individual memory, and the social coefficient c2 increases adaptively to gradually enhance the group's collaborative ability. The particle swarm state is monitored in real time and dynamically intervened. When particles aggregate or stagnate for a long period, diversity injection is used to escape local optima and ensure global search capability. A multi-round selection mechanism is employed to overcome the influence of algorithm randomness.

[0104] (2) Stochastic demand response and mixed constraint handling

[0105] To accurately calculate expected sales volume and To improve solution speed, a Gaussian-Hermitian orthogonal approximation is used instead of numerical integration when calculating the demand probability density function, resulting in efficient computation of the integral term. This utilizes the remaining ticket quota for online booking. ij Real-time updates on the fulfillment of offline demand distribution. For model-specific constraints: In the seat capacity constraint, an adaptive exponential penalty is applied to the overcapacity portion (the penalty coefficient increases exponentially with iteration) to ensure the constraint's enforceability; in the stop matching constraint, a service identifier u is introduced. kij Automatically mask invalid OD pairs.

[0106] By combining historical passenger flow and operational data with the physical network characteristics of urban (suburban) railways, this embodiment utilizes the hybrid fare allocation model and solution algorithm to calculate and optimize the scheme, and evaluates its effect on improving the transportation revenue of urban (suburban) railways under the hybrid fare system.

[0107] In this embodiment, to verify the effectiveness of the proposed optimization model and algorithm for fare allocation under the mixed fare system for urban (suburban) railways, the Huairou-Miyun suburban railway line in Beijing is selected as the background. Three trains with different stopping schemes are used as the research objects. The stopping schemes for each train are shown in the attached figure. Figure 2 As shown: Train 1 stops at all stations, serving all 7 stations and 21 OD pairs; Train 2 skips stations, stopping at stations 1 / 3 / 5 / 7, serving 10 OD pairs; Train 3 stops at stations 1 / 4 / 7, serving 3 OD pairs. The fare parameters for each section are based on actual operating fares. The capacity of each train is assumed to be 400, and the parameters (mean, standard deviation) of the probability distribution function for online and offline passenger flow demand for each OD are reasonably set.

[0108] The relevant parameters in the algorithm were set (300 particles, 400 maximum iterations, and 5 iteration rounds), and the results were optimized using the case scenario. The curve showing the change in expected return with the number of iterations is attached. Figure 3 As shown, the expected return tends to stabilize and converge after approximately 250 iterations, eventually reaching 12258 yuan. (See attached image.) Figure 4 Appendix Figure 5 and appendix Figure 6 The document presents two ticket allocation schemes for three trains, derived after optimized calculations, for each of the two ticket types. (Attached) Figure 7 The expected sales volume for each OD after optimization is shown.

[0109] In traditional operating models, ticket allocation under the mixed fare system for suburban railways mainly relies on manual experience, using a fixed ratio to allocate online and offline tickets. To verify the effectiveness of the model and algorithm designed in this invention, the ticket revenue of this case was compared with that under the traditional ticket allocation method. The ratio of online to offline tickets was set to 3:1, 1:1, and 1:3, respectively, meaning the total online tickets were 300, 200, and 100, and the corresponding total offline tickets were 100, 200, and 300. Simulation calculations showed that, without overselling, the expected revenue under the three fixed-ratio ticket allocation schemes were 8455 yuan, 8684 yuan, and 7391 yuan, respectively. The optimized schemes improved revenue by approximately 45.0%, 41.2%, and 65.9%, respectively. Therefore, compared to the traditional ticket allocation scheme, the optimized ticket allocation method for the mixed fare system of suburban railways proposed in this invention can achieve a better revenue improvement effect.

[0110] Example 3

[0111] This embodiment 3 provides a non-transitory computer-readable storage medium for storing computer instructions. When executed by a processor, the computer instructions implement the fare allocation optimization method under the mixed fare system for urban and suburban railways as described above. The method includes:

[0112] OD Passenger Flow Data Collection and Distribution Parameter Fitting: Extract historical passenger flow data for each OD section, including passenger boarding and alighting stations, ticket sales, and corresponding train stopping plans; based on historical data, perform probability distribution fitting on passenger flow demand for each OD section;

[0113] Based on the fitting results, a railway hybrid ticketing system ticket allocation model is constructed: it is assumed that different passenger trains have the same single ticket price on the same origin and destination (OD), and the passenger flow demand on each OD is described by a known normal distribution function; all trains only provide seated tickets and over-selling is not allowed. With the goal of maximizing the passenger ticket revenue of the entire railway and the seat capacity of each train and each section as constraints, the ticket allocation scheme of all passenger trains is optimized.

[0114] Solving the hybrid ticket allocation system based on an improved particle swarm optimization algorithm: The complex ticket allocation scheme is encoded as a particle position vector, where each particle represents a complete allocation scheme with dimensions 2×K×N. OD Odd-numbered online ticket amounts Even-numbered digits store offline ticket amounts The core parameters are adaptively adjusted according to the iteration process to avoid premature convergence.

[0115] Example 4

[0116] This embodiment 4 provides a computer device, including a memory and a processor, wherein the processor and the memory communicate with each other, and the memory stores program instructions that can be executed by the processor. The processor calls the program instructions to execute the ticket allocation optimization method under the mixed ticketing system for urban and suburban railways as described above, the method including:

[0117] OD Passenger Flow Data Collection and Distribution Parameter Fitting: Extract historical passenger flow data for each OD section, including passenger boarding and alighting stations, ticket sales, and corresponding train stopping plans; based on historical data, perform probability distribution fitting on passenger flow demand for each OD section;

[0118] Based on the fitting results, a railway hybrid ticketing system ticket allocation model is constructed: it is assumed that different passenger trains have the same single ticket price on the same origin and destination (OD), and the passenger flow demand on each OD is described by a known normal distribution function; all trains only provide seated tickets and over-selling is not allowed. With the goal of maximizing the passenger ticket revenue of the entire railway and the seat capacity of each train and each section as constraints, the ticket allocation scheme of all passenger trains is optimized.

[0119] Solving the hybrid ticket allocation system based on an improved particle swarm optimization algorithm: The complex ticket allocation scheme is encoded as a particle position vector, where each particle represents a complete allocation scheme with dimensions 2×K×N. OD Odd-numbered online ticket amounts Even-numbered digits store offline ticket amounts The core parameters are adaptively adjusted according to the iteration process to avoid premature convergence.

[0120] Example 5

[0121] This embodiment 5 provides an electronic device, including: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the fare allocation optimization method under the mixed fare system for urban and suburban railways as described above. The method includes:

[0122] OD Passenger Flow Data Collection and Distribution Parameter Fitting: Extract historical passenger flow data for each OD section, including passenger boarding and alighting stations, ticket sales, and corresponding train stopping plans; based on historical data, perform probability distribution fitting on passenger flow demand for each OD section;

[0123] Based on the fitting results, a railway hybrid ticketing system ticket allocation model is constructed: it is assumed that different passenger trains have the same single ticket price on the same origin and destination (OD), and the passenger flow demand on each OD is described by a known normal distribution function; all trains only provide seated tickets and over-selling is not allowed. With the goal of maximizing the passenger ticket revenue of the entire railway and the seat capacity of each train and each section as constraints, the ticket allocation scheme of all passenger trains is optimized.

[0124] Solving the hybrid ticket allocation system based on an improved particle swarm optimization algorithm: The complex ticket allocation scheme is encoded as a particle position vector, where each particle represents a complete allocation scheme with dimensions 2×K×N. OD Odd-numbered online ticket amounts Even-numbered digits store offline ticket amounts The core parameters are adaptively adjusted according to the iteration process to avoid premature convergence.

[0125] In summary, the demand-foreseen-based hybrid fare allocation optimization model for urban (suburban) railways is one of the core components of this invention. This model establishes a dynamic fare conversion mechanism by simultaneously optimizing online pre-booked tickets and offline AFC (Automatic Fare Collection) tickets, providing a theoretical basis for the collaborative use of hybrid fare resources. The improved particle swarm optimization algorithm designed for the model is another core component of this invention. This algorithm employs cooperative coding techniques and dynamic parameter adjustment strategies, combined with a diverse restart mechanism, to efficiently solve the fare allocation problem in complex railway networks.

[0126] The core advantage of this invention lies in its pioneering hybrid ticketing system collaborative allocation framework and efficient solution algorithm, accurately responding to the mixed passenger flow demands of urban (suburban) railways. Specifically, it: 1) Breaks through the limitations of a single ticketing system, achieving online and offline dual-system collaboration through a dynamic ticketing conversion mechanism, effectively solving the problem of commuter passenger flow being squeezed and significantly improving passenger flow satisfaction; 2) Solves the difficult problem of high-dimensional optimization of ticketing allocation, designing an improved particle swarm optimization algorithm (integrating dynamic parameter adjustment and diverse restart mechanisms), greatly improving computational efficiency, and supporting minute-level optimization of a network of hundreds of stations; 3) Accurately matches passenger flow characteristics, constructing a dual-system demand coupling model based on OD passenger flow distribution, significantly improving seat utilization and transportation revenue, directly supporting the "four-network integration" ticketing system interoperability project.

[0127] This invention uses a normal distribution to describe OD passenger flow demand. While a Poisson distribution (suitable for low-frequency discrete demand) or a log-normal distribution (suitable for long-tail demand) can also be used to construct a demand function and optimize ticket allocation, the normal distribution more accurately characterizes the volatility of commuter passenger flow on urban (suburban) railways. This invention uses an improved particle swarm optimization (APSO) algorithm to solve the model. While genetic algorithms (based on chromosome crossover and mutation) or simulated annealing algorithms (based on temperature decay random search) can also solve the ticket allocation problem, APSO offers superior convergence speed and stability in high-dimensional decision spaces.

[0128] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0129] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0130] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0131] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0132] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solutions disclosed in the present invention, various modifications or variations that can be made by those skilled in the art without creative effort should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing ticket allocation under a mixed fare system for urban and suburban railways, characterized in that, include: OD passenger flow data collection and distribution parameter fitting: extract historical passenger flow data for each OD section, including passenger boarding and alighting stations, ticket sales and corresponding train stopping plans; Based on historical data, a probability distribution fit was performed on the passenger flow demand of each OD (Original Demand Site). Based on the fitting results, a railway hybrid ticketing system ticket allocation model is constructed: it is assumed that different passenger trains have the same single ticket price on the same origin-destination (OD), and the passenger flow demand on each OD is described by a known normal distribution function; all trains only provide seated tickets and overselling is not allowed. With the goal of maximizing the passenger ticket revenue of the entire railway and the seat capacity of each train and each section as constraints, the ticket allocation scheme of all passenger trains is optimized. Solving the hybrid ticket allocation system's ticket amount optimization model based on an improved particle swarm optimization algorithm: Complex ticket allocation schemes are encoded as particle position vectors, where each particle represents a complete allocation scheme with dimensions [missing information]. Odd-numbered online ticket amounts Even-numbered digits store offline ticket amounts ; To avoid premature convergence, the core parameters are adaptively adjusted according to the iteration process. This includes adjusting the inertia weight. Nonlinear decay, cognitive coefficient Adaptive diminishing returns, gradually reducing the influence of individual memory, social coefficient Adaptive incremental growth gradually enhances the group's collaborative capabilities; real-time monitoring of the particle swarm's state and dynamic intervention ensure global search capabilities by injecting diversity when particles aggregate or stagnate for extended periods; and a multi-round selection mechanism overcomes the influence of algorithm randomness. When only one train is running, if the probability density function of the system's booked passenger flow demand on the line in interval (i, j) is... If we can calculate the expected sales volume of online tickets for this train in the interval (i, j), then the expected sales volume is: ； in, The number of tickets allocated to the train in the online system within the OD interval (i, j) is the online ticketing limit. The expected sales volume under the uncertainty of demand is calculated mathematically using the probability density function. When the actual demand for online tickets is less than the allocated ticket amount, the sales volume is the actual demand. When the actual demand is greater than the allocated ticket amount, the sales volume is always the allocated ticket amount. When k trains are running on the line, and the probability density function of online ticket booking passenger flow demand for each OD is... and the probability density function of passenger flow demand in the offline AFC system. Given that a multi-train mixed ticketing system ticket allocation model is obtained with the objective of maximizing passenger ticket revenue for urban (suburban) railways and the constraint of the maximum seat capacity of each section of the train, considering capacity constraints, is obtained.

2. The method for optimizing ticket allocation under a mixed ticketing system for urban and suburban railways according to claim 1, characterized in that, To accurately calculate expected sales volume and To improve solution speed, Gauss-Hermitian orthogonal approximation is used instead of numerical integration when calculating the demand probability density function, thus efficiently calculating the integral term; and the remaining ticket quota is utilized for online booking. Real-time updates on the fulfillment of offline demand distribution; for model-specific constraints: an adaptive exponential penalty is applied to the overcapacity portion in the seat capacity constraint to ensure the constraint's enforceability; a service identifier is introduced in the stop matching constraint. Automatically mask invalid OD pairs.

3. The method for optimizing ticket allocation under a mixed ticketing system for urban and suburban railways according to claim 1, characterized in that, The OD passenger flow data collection and distribution parameter fitting includes: assuming a suburban railway consisting of L+1 stops and L sections, with n passenger trains operating and multiple stopping options; the passenger flow demand of each OD is considered to follow an independent normal distribution, and the probability density function of the passenger flow demand in the OD interval (i, j) is... Represented as: ； Where i and j are the origin and destination station numbers of the OD, and x is the potential passenger demand in the OD interval (i, j). Let OD(i, j) be the average of historical passenger flow demand. The standard deviation of historical passenger flow demand is given; the historical passenger flow demand value for each OD is the actual passenger flow of that OD section on that day, which is the sum of the online booking demand and the offline swipe / card entry demand for all trains running on that OD on that day.

4. A ticket allocation optimization system for urban and suburban railways under a mixed ticketing system based on the method described in any one of claims 1-3, characterized in that, include: The fitting module is used for OD passenger flow data collection and distribution parameter fitting: extracting historical passenger flow data for each OD section, including passenger boarding and alighting stations, ticket sales, and corresponding train stopping plans; and fitting the probability distribution of passenger flow demand for each OD based on historical data. The module is used to build a railway hybrid ticketing system ticket allocation model based on the fitting results: it assumes that different passenger trains have the same single ticket price on the same origin and destination (OD), and the passenger flow demand on each OD is described by a known normal distribution function; all trains only provide seated tickets and overselling is not allowed, with the goal of maximizing the passenger ticket revenue of the entire railway and the seat capacity of each section of each train as a constraint, to optimize the ticket allocation scheme of all passenger trains; The solution module is used to solve the hybrid ticket allocation optimization model based on the improved particle swarm optimization algorithm: it encodes the complex ticket allocation scheme as particle position vectors, where each particle represents a complete allocation scheme with dimensions of . Odd-numbered online ticket amounts Even-numbered digits store offline ticket amounts The core parameters are adaptively adjusted according to the iteration process to avoid premature convergence.

5. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium is used to store computer instructions, which, when executed by a processor, implement the fare allocation optimization method under the mixed fare system for urban and suburban railways as described in any one of claims 1-3.

6. A computer device, characterized in that, The system includes a memory and a processor, which communicate with each other. The memory stores program instructions that can be executed by the processor, and the processor calls the program instructions to execute the fare allocation optimization method under the mixed fare system for urban and suburban railways as described in any one of claims 1-3.

7. An electronic device, characterized in that, include: The electronic device includes a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the fare allocation optimization method under the mixed fare system for urban and suburban railways as described in any one of claims 1-3.

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