City region rail and city region urban rail train timetable collaborative optimization method

Abstract

The invention relates to a transfer demand-based city region rail and urban urban rail train timetable collaborative optimization method, which comprises the following steps of: constructing a dynamic transfer demand-based city region rail and urban urban rail train timetable collaborative optimization model, and solving the city region rail and urban urban rail train timetable collaborative optimization model; and obtaining a collaborative optimization result of the urban rail and urban rail train timetable. The method is suitable for a multi-system rail transit network with a transfer connection relation, and the arrival and departure time of the train can be optimized according to the dynamic transfer requirements of passengers, so that the train connection efficiency is improved, the transfer waiting time is shortened, and the overall operation efficiency and service level of a rail transit system are improved.

Description

Technical Field

[0001] This invention relates to the field of urban rail transit technology, and in particular to a method for collaborative optimization of train timetables for urban rail transit and suburban rail transit based on transfer demand. Background Technology

[0002] As urban rail transit systems become increasingly complex, with multiple modes of rail transit networks coexisting, such as suburban railways, urban subways, and light rail, passenger transfer efficiency has become a crucial indicator for measuring overall service quality. Train timetables, as a core element of the dispatching system, directly impact operational efficiency and passenger satisfaction through their optimization.

[0003] In existing technologies, research on train timetable optimization mainly focuses on the following three directions:

[0004] One approach addresses timetable optimization methods for single-mode rail transit. The literature (Coordination and Optimization of Urban Rail Train Timetables Considering Passenger Transfers, Ning Liqiao, 2019) proposes a timetable optimization model based on flexible departure intervals, which can improve transfer efficiency within the metro system. However, this type of model has a relatively simplified structure and is difficult to adapt to the complex coordination problems under multi-line, multi-mode rail systems.

[0005] Second, research is being conducted on timetable coordination and scheduling among multiple rail systems. References ("A Method for Determining Departure Times Based on Reasonable Passenger Train Connection Conditions. Chen Lingling & Wang Ciguang. Journal of Southwest Jiaotong University, 2007, 42(2): 234-7.") propose a method for optimizing train departure times based on reasonable connection conditions. References ("Evaluation of Connection Modes between Urban Express Lines and Intercity Rail Transit Based on Rough Set Theory. Zong Chuanling & Yang Chongming & Yang Deming. Transportation Systems Engineering and Information, 2011, 11(2): 130-5.") use rough set theory to evaluate the connection modes between urban express lines and intercity rail transit. These methods have some effectiveness in improving system connection efficiency, but due to complex modeling and numerous variables, their solution efficiency and practical deployment capabilities are limited. Similarly, CN110533219A proposes a method for optimizing the last train times of urban rail transit, which is applicable to specific scenarios, but still has limitations in the coordinated optimization of multiple rail systems.

[0006] Thirdly, dynamic timetable optimization methods based on passenger flow data. The literature (A Bi-Objective Timetable Optimization Model for Urban Rail Transit Based on the Time-Dependent Passenger Volume. SUN H, WU J, MA H, et al. IEEE Transactions on Intelligent Transportation Systems, 2019, 20(2): 604-15.) constructs a bi-objective optimization model based on time-dependent passenger flow. The literature (Train timetabling in rail transit network under uncertain and dynamic demand using Advanced and Adaptive NSGA-II. HAN Z, HAN B, LI D, et al. Transportation Research Part B: Methodological, 2021, 154: 65-99.) introduces the adaptive NSGA-II algorithm to achieve train timetable optimization under dynamic passenger demand. These methods improve the responsiveness of timetables, but generally do not model transfer route selection, station spatial structure, and facility bottlenecks. Correspondingly, patent CN116542404B discloses a method for predicting transfer time based on an index model, but does not cover the passage and stairwell traffic status; patent CN104866925B focuses on timetable optimization for energy consumption control, but also does not consider the differences in transfer behavior and station distribution.

[0007] In summary, existing literature and patent solutions have made some progress in terms of timetable optimization, transfer connection modeling and dynamic scheduling, but they generally have the following shortcomings: (1) No correlation model between passenger transfer behavior and station familiarity differences has been established; (2) Lack of description of the passage status of spatial facilities such as passages and stairs; (3) Lack of a train timetable collaborative optimization mechanism for multi-system lines; (4) Insufficient integration depth of intelligent optimization algorithms in scheduling modeling. Summary of the Invention

[0008] To address the problems existing in the prior art, the present invention aims to provide a method for the coordinated optimization of train timetables between urban rail transit and suburban rail transit based on transfer demand. This method addresses the passenger flow characteristics and train scheduling coordination requirements at transfer stations in multi-mode rail systems. Through behavioral-level passenger flow modeling, dynamic arrival prediction, and a multi-objective optimization algorithm guided by reinforcement learning, it achieves synchronous adjustment of multi-mode train schedules and improves service efficiency. This method can realize the coordinated optimization of train timetables between urban rail transit and suburban rail transit in transfer modes, reducing waiting time for transfer passengers at transfer stations.

[0009] The technical solution to achieve the purpose of this invention is as follows:

[0010] A method for coordinating the optimization of timetables for urban rail transit and urban rail transit based on transfer demand is proposed. This method involves constructing a coordinating optimization model for the timetables of urban rail transit and urban rail transit based on dynamic transfer demand, and solving the coordinating optimization model to obtain the coordinating optimization results of the timetables of urban rail transit and urban rail transit.

[0011] The objective function of the coordinated optimization model for the timetables of urban rail transit and suburban rail transit is:

[0012] ,

[0013] ,

[0014] ,

[0015] The constraints are:

[0016] ,

[0017] ,

[0018] ,

[0019] ,

[0020] In the formula, This represents the transfer passenger weight at station i. Indicates time t at station The number of passengers waiting to transfer; Indicates site ,time The number of non-transfer waiting passengers, This represents the operating cost of the train at station i at time t. Indicates the service balance weight; and Let $\mathbf$ and $\mathbf$ represent the departure times of the $k$-th train before and after optimization, respectively. Indicates the line ,direction Upper The optimized departure times for this train. Indicates the line ,direction Upper The departure time of this train. and These represent the minimum safe interval and the maximum tolerable interval for the departure times of any two adjacent trains traveling in the same direction, respectively. Indicates the line ,direction The actual number of passengers on the k-th train when it departs from station i. Indicates the train's maximum rated capacity; Indicates the line ,direction Upper After the train departs, the station The number of stranded passengers, Indicates the line ,direction Upper After the train departs, the station The number of stranded passengers, Indicates the line ,direction The number of passengers arriving at the station at time t. Indicates the line ,direction Upper The valid transfer deadline for train i; Indicates the line ,direction Upper The train is at the station The duration of the stop, and These represent the minimum boarding / alighting operation time and the maximum permitted stop time for operational scheduling, respectively. , where n=1 represents the train going up and n=2 represents the train going down.

[0021] As a further optimization of the present invention, the circuit ,direction Upper The valid transfer deadline for train i at station i is:

[0022]

[0023] In the formula, Indicates the starting point of the valid transfer time window; Indicates the line ,direction Upper The upper limit of the effective transfer time window for a train. To serve the reaction time constant, Indicates the line ,direction Upper The train is at the station The maximum number of passengers allowed. Indicates the line ,direction The k-1th train is at the station The number of stranded passengers.

[0024] As a further optimization of the present invention, based on dynamic transfer demand, the transfer area is divided into passageways and stairs, and a passenger flow distribution model for passageways and a passenger flow distribution model for stairs system are constructed to obtain the number of passengers arriving at different stations at different times.

[0025] As a further optimization of the present invention, based on the different passenger flow densities within the passageway, the passageway walking state is divided into free walking state and following walking state, and passageway passenger flow movement distribution models are established for each of the different states:

[0026] (1) In free walking mode:

[0027] ,

[0028] in, Indicates time t. Passenger count is output at the end of the passageway; For from the first Average walking time from the beginning to the end of a passageway; For a moment No. Passenger flow entering the passageway; The probability distribution function of step speed The time mapping function, v is the pedestrian walking speed that follows a normal distribution in the free state, and μ and σ are the mean and standard deviation, respectively;

[0029] (2) In the following walking state:

[0030] ,

[0031] in, For time t Passenger flow entering the passageway For statistical time intervals.

[0032] As a further optimization of the present invention, the criteria for dividing the passenger walking state within the passage are as follows: if time t is... Passenger numbers passing through the passage If the density of passengers allowed to move freely per unit width exceeds the threshold threshold, the passage is considered to be in a free-moving state; otherwise, it is in a following-moving state. , This represents the maximum throughput coefficient per unit width of the passageway under free-walking conditions. To ensure lateral safety spacing between passengers This represents the channel width.

[0033] As a further optimization of the present invention, considering passenger dwell time within the passageway, the passageway passenger flow distribution model is as follows:

[0034] ,

[0035] in, Entering the dwell point at time t And the passenger flow that stops or stays, ; , For a moment Enter the stop point Total passenger flow For the point of stay The percentage of stays; , To ensure lateral safety spacing between passengers For channel width, This refers to the effective longitudinal occupancy length for passengers. The effective length of the dwell point p; For a moment At the stop Passenger flow that did not stop .

[0036] As a further optimization of the present invention, the passenger flow distribution model of the staircase system is as follows:

[0037] ,

[0038] in, For a moment Passenger flow output from the pedestrian staircase , For a moment Passenger flow entering the pedestrian staircase For a moment The number of people stranded on the staircases. The maximum number of people who can pass through the staircase per unit of time; For a moment Passenger flow output of escalators , For a moment Passenger flow entering escalators For a moment The number of people stuck on the escalator This represents the maximum number of people that can pass through the escalator per unit of time.

[0039] As a further optimization of the present invention, the collaborative optimization model of the timetable of urban rail transit and urban rail transit is solved by the fast non-dominated sorting genetic algorithm RNSGA-II guided by reinforcement learning.

[0040] In addition, the present invention provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the above-described method for collaborative optimization of timetables for urban rail transit and urban rail transit based on transfer demand.

[0041] The present invention also provides an electronic device, comprising:

[0042] Memory, used to store computer programs;

[0043] A processor is used to implement the steps of the above-described method for collaborative optimization of train timetables between urban rail transit and suburban rail based on transfer demand when executing the computer program.

[0044] The significant advantages of this invention compared to existing technologies are:

[0045] (1) The passenger flow distribution model of the transfer station based on passenger route familiarity constructed in this invention can dynamically simulate the differences in path selection and movement behavior of different types of passengers in the passage and stair system. It comprehensively considers free walking, following state and staying phenomenon, takes into account passenger heterogeneity and transfer space structure, realizes fine modeling of complex transfer behavior, and improves the adaptability and prediction accuracy of the model in multi-mode rail transit hubs.

[0046] (2) The timetable optimization method for urban rail and urban rail trains proposed in this invention innovatively introduces a transfer direction weight setting mechanism and combines the dynamic target station passenger flow estimation results to construct a multi-objective optimization model, realizing the synchronous adjustment and coordinated control of the two types of line operation diagrams, effectively improving transfer efficiency, balancing the service level of non-transfer directions, and enhancing the overall system operation efficiency and passenger experience.

[0047] (3) The present invention uses the reinforcement learning-guided fast non-dominated sorting genetic algorithm (RNSGA-II) as the solution engine. While improving the diversity of solution sets and convergence performance, it enhances the adaptability of the algorithm in high-dimensional complex optimization space, avoids getting trapped in local optima, and is suitable for large-scale train timetable optimization scenarios. It provides a highly operable and stable intelligent optimization method for actual scheduling systems. Attached Figure Description

[0048] Figure 1 This is a flowchart of the passenger movement distribution model.

[0049] Figure 2 This is a flowchart showing the changes in passenger flow at fixed service facilities.

[0050] Figure 3 It is used to determine the arrival status of passengers boarding the train.

[0051] Figure 4 This is the flowchart of the RNSGA-II algorithm. Detailed Implementation

[0052] The embodiments of the present invention will be described in detail below with reference to the accompanying drawings.

[0053] This invention addresses the passenger flow characteristics and train scheduling coordination requirements at transfer stations in multi-mode rail systems. It proposes a collaborative optimization method for train timetables of urban rail and suburban rail based on transfer demand. Through behavioral-level passenger flow modeling, dynamic arrival prediction, and a multi-objective optimization algorithm guided by reinforcement learning, the method achieves synchronous adjustment of multi-mode operation schedules and improves service efficiency.

[0054] The technical solution adopted in this invention is a method for collaborative optimization of timetables for urban rail transit and suburban rail transit based on transfer demand, which includes the following two steps:

[0055] Step A: Collect and model transfer demand, and construct a passenger flow movement model based on passenger route selection and arrival time distribution to simulate the passenger gathering behavior at different stations at different times;

[0056] Step B: Using the transfer demand model constructed in Step A as input, embed the objective function and constraints of the train departure timetable optimization problem, and combine it with a multi-objective evolutionary algorithm to generate a coordinated optimization timetable scheme for urban rail and suburban rail trains that balances transfer efficiency and service level.

[0057] In step A, the model is constructed by expanding on the transfer area, which may include passageways and stair systems. Therefore, the constructed model includes a passageway passenger flow distribution model and a stair system passenger flow distribution model, such as... Figure 1 As shown.

[0058] A.1 Passenger Flow Distribution Model

[0059] In this invention, to depict the movement process of transfer passengers in station passageways, a passageway passenger flow distribution model based on walking states is established. According to the different passenger flow densities within the passageway, the passenger movement states are divided into free walking states and following walking states, and corresponding passenger flow output modeling methods are established for each.

[0060] A.1.1 Determination of Channel Travel Status

[0061] Let the channel width be , time t Passenger numbers passing through the passage If the following conditions are met:

[0062]

[0063] If the channel segment is in a free-moving state, it is considered to be in a following state; otherwise, it is considered to be in a following state. The parameters are defined as follows:

[0064] The maximum passage capacity coefficient (persons / meter) under free walking conditions per unit passage width can be obtained by considering the lateral safety distance and the longitudinal effective occupancy length.

[0065] The lateral safety distance between passengers (meters) can be determined by the aisle width and the maximum number of passengers that can pass side by side.

[0066] : Channel width (meters).

[0067] This criterion reflects the density threshold of the maximum number of freely moving passengers that can be accommodated per unit width of the passage. When the number of people passing through at any given time exceeds this threshold, the system enters the "follow-walking state".

[0068] A.1.2 Passenger Flow Distribution Model Based on Different Walking States

[0069] Let the first Segment channel at time The input passenger flow is Based on density levels, passenger traffic patterns can be categorized into three types:

[0070] (1) Modeling of free walking state

[0071] When the crowd density in the passageway is low, passengers move independently at their own pace. Follows a normal distribution:

[0072]

[0073] Where v is the pedestrian's walking speed (m / s), which follows a normal distribution in the free state; μ and σ are the mean and standard deviation of the normal distribution.

[0074] Then the passage time The relationship with walking speed is:

[0075]

[0076] in, The distance traveled by the passenger (m).

[0077] After converting the walking speed distribution to a time distribution, convolving the input passenger flow, we obtain the output passenger flow for that segment:

[0078]

[0079] in, Indicates time t. Passenger count is output at the end of the passageway; Indicates the channel output status, used to distinguish it from other stages or variables; For from the first Average walking time from the beginning to the end of a passageway; For a moment No. Passenger flow entering the passageway; The probability distribution function of step speed The time mapping function is derived from It is obtained through variable transformation.

[0080] (2) Following state modeling

[0081] When crowd density is high, passengers cannot freely adjust their speed, forming a constant-speed following flow. Let the uniform walking speed in this following state be denoted as . Then at time t The passenger flow entering the passageway is:

[0082]

[0083] Where ρ is the passenger flow density (people / ).

[0084] (3) State switching and output rules

[0085] Treat the transition of walking state as a condition-triggered process:

[0086] If in free movement mode: ;

[0087] If in follow mode: ;

[0088] in, The statistical time interval is (s).

[0089] Note: To maintain consistency in modeling, time is assumed to be divided into uniform discrete time intervals, denoted as _____. That is, each moment represents the final state of the statistical period. Unless otherwise specified, the terms appearing in various chapters of this article are not part of the statistical timeframe. Both refer to the time step, which applies to all input, output, and dwell update processes.

[0090] A.1.3 Modeling Considering the Influence of Route Familiarity

[0091] In transfer corridors, some passengers, unfamiliar with the layout, need to rely on signage to determine their direction, sometimes resulting in brief pauses at specific locations. This causes a temporary decrease in the corridor's width at those points, creating a "cognitive bottleneck" and ultimately impacting the overall corridor's throughput efficiency.

[0092] Let the number of this stop be At any moment Enter the stop point Total passenger flow is At the stop The proportion of stays is The dwell input flow at that point is:

[0093] .

[0094] Because the stopping behavior is arranged longitudinally, each passenger occupies a certain length. The maximum number of people that can stay at the same time in this section of the passage (maximum throughput capacity) can be expressed as:

[0095]

[0096] in, The effective longitudinal occupancy length for passengers can be determined by the distance traveled by pedestrians. Time interval Number of people and pace It can be concluded that; Let p be the effective length of the dwell point.

[0097] Considering that some passengers may briefly stop at the stop due to unfamiliarity with the route, the passage capacity at this location is limited, meaning that only a certain number of passengers can resume their journey per unit of time. Let time t be the time when passengers enter the stop. And the number of passengers who stopped to linger was ,but:

[0098]

[0099] in, This represents the average dwell time per person. The formula indicates that if the number of people currently in the queue does not exceed the maximum release capacity of that segment, all travel can resume; otherwise, only passengers within the upper limit are allowed to pass, while the rest continue to wait.

[0100] Ultimately, the number of people output at the end of this channel is:

[0101]

[0102] in, This indicates the passenger flow that did not involve any stops.

[0103] A.2 Passenger Flow Distribution Model for Staircase System

[0104] The staircase system described in this invention includes two types of vertical transportation facilities: pedestrian stairs and escalators. When passengers arrive at the staircase entrance, they can choose to use either the pedestrian stairs or the escalator based on their own behavioral preferences or the real-time crowd situation.

[0105] (1) Initial flow splitting modeling

[0106] Set at time At any given time, the passenger flow is Among them are A certain percentage of passengers choose the stairs, and the rest choose the escalators. Therefore, the initial input flow for the stairs and escalators is:

[0107] ,

[0108] ,

[0109] in, , These represent pedestrian stairs and escalators, respectively.

[0110] (2) Modeling of escalator queuing guidance behavior

[0111] If queues form on the escalators, some passengers will switch to the stairs. Let the transfer rate be . The maximum unit throughput of the escalator is The portion exceeding the passage capacity is:

[0112] .

[0113] The corrected inputs for pedestrian stairs and escalators are:

[0114] ,

[0115] .

[0116] (3) Output modeling under traffic capacity constraints

[0117] Let the maximum number of people that can pass through the staircase and escalator per unit time be respectively. and The time interval is To handle backlogs across different time periods, a time-based approach is introduced. Number of people stranded on staircases and escalators , Then at time The outputs of the stairs and escalators are:

[0118] ,

[0119] ,

[0120] The corresponding delay update is:

[0121] ,

[0122] ,

[0123] Ultimately, the staircase system in The total output flow at time t is:

[0124] .

[0125] The detailed flowchart is as follows: Figure 2 As shown.

[0126] The modeling results described above will be used in the subsequent timetable collaborative optimization model to build the foundation for calculating the number of passengers arriving at different stations at different times. Based on the passenger flow movement distribution model, the transfer area is first divided. Then, based on the walking status within each passage and the selection results of stairs or escalators, the output of each passage and the output of the stair system are obtained, further yielding the number of passengers arriving at different stations at different times. For example, a transfer area can be divided into passage + stairs + passage. First, based on the walking status within the first passage, the output passenger flow of that passage is obtained based on the passage passenger flow movement distribution model. Then, using the output passenger flow of the first passage as the input of the stair system, the output passenger flow of the stair system is obtained based on the stair system passenger flow movement distribution model. Finally, using the output passenger flow of the stair system as the input of the second passage, the output passenger flow of that passage is obtained based on the walking status within the second passage and the passage passenger flow movement distribution model. Since entering the station occurs after passing through the second passage, the output passenger flow of the second passage at this point represents the number of passengers arriving at the station.

[0127] Step B consists of two parts: constructing a timetable collaborative optimization model and designing a solution algorithm based on RNSGA-II.

[0128] B.1 Construction of Timetable Collaborative Optimization Model

[0129] B.1.1 Model Construction

[0130] To facilitate model construction and method implementation, and improve algorithm solution efficiency, the following settings are made for train operation and passenger behavior. The following is a preferred embodiment of the present invention, but the invention is not limited thereto:

[0131] (1) Line structure: The research object is a two-way independent operation of a double-track system. The trains are modeled separately in the up and down directions, do not interfere with each other, the running path is known, and the station structure is stable.

[0132] (2) Regarding transfer behavior: No transfer behavior occurs between the up and down lines of the same line. All transfer behaviors occur between different lines, and the transfer path is unique. The transfer intention has been determined by the prior model.

[0133] (3) Passenger flow input data: The number of passengers arriving at each station in the study area within a discrete time period can be obtained through historical passenger flow data (such as AFC system records) or existing prediction models, and is regarded as known input.

[0134] (4) Regarding train operation rules: Trains follow the "first-in, first-out" rule, meaning that trains are not allowed to overtake within a section or station. The departure order of each train at each station is strictly controlled by its arrival time.

[0135] (5) Queuing rules and capacity constraints: Passengers board the train in order of arrival and service. If the train is full when it arrives, the remaining passengers will be held up on the next train.

[0136] (6) Research boundary treatment: A virtual train mechanism is introduced at the boundary of the research period to ensure that each passenger in the model has a corresponding opportunity to ride, so as not to affect the integrity of the optimization solution.

[0137] B.1.2 Ride-taking behavior modeling and capacity constraint logic

[0138] When the train arrives at the station, passengers make their travel decisions based on the remaining capacity of the train, and there are two possible scenarios:

[0139] 1. Passengers are considered to have successfully boarded the train if there is sufficient remaining capacity and their arrival time falls within the permitted boarding time range.

[0140] 2. Due to insufficient train capacity, some passengers are stranded at stations, waiting for the next train. Figure 3 As shown.

[0141] To accurately reflect the dynamic relationship between train departure time and passenger boarding behavior, this invention coordinates passenger arrival time with train running time, calculates the effective carrying time of the train, and determines whether passengers can board the train on time.

[0142] Let the number of passengers waiting for train k in direction n on line m at station i be:

[0143] ,

[0144] in: Indicates the starting point of the valid transfer time window; Indicates the first The upper limit of the effective transfer time window for a train; Represents the number of passengers left behind at station i by the previous train k−1 (res stands for residual).

[0145] If the first The remaining capacity of the train is The remaining capacity of the previous train is The actual number of passengers that can be carried is:

[0146] ;

[0147] The valid transfer deadline for trains is recorded as follows:

[0148]

[0149] in, This is the minimum reaction time for the train, used to ensure the shortest possible stopping time for the train and the shortest possible waiting time for passengers. Indicates the first The train is at the station The maximum number of passengers allowed; This indicates the number of passengers who did not board the previous train; Indicates the first The upper limit of the effective transfer time window for a train; This represents the effective transfer deadline for the k-th train on line m, in direction n, at station i. The above modeling results will be used in the subsequent objective function to form the basis for calculating the waiting time cost for transfer passengers and the efficiency of train services.

[0150] B.1.3 Objective Function Design

[0151] To achieve the synergistic goal of optimizing passenger experience and improving operational efficiency, this invention constructs a multi-objective optimization model for train timetables, with the objective function comprising the following three sub-objectives:

[0152] (1) Minimize transfer passenger waiting time

[0153] To reduce passenger waiting time at transfer stations, transfer directions are set. The weight is , Indicates time t at station Based on the number of passengers waiting to transfer, the target transfer waiting time is:

[0154] ,

[0155] Among them, the waiting time for transfers Can be determined by the travel time window model The derivation yields a measure of passenger waiting intensity at key transfer points per unit of time.

[0156] (2) Minimize the service cost for non-transfer passengers

[0157] To balance the waiting experience for non-transfer passengers with train load distribution, stations are set up ,time The number of non-transfer waiting passengers is The train operating cost function is: This can be used to measure the service burden on non-transfer passengers by comprehensively considering indicators such as train running time, carriage occupancy rate, and crowding; let the service balance weight be... Then the objective function is:

[0158] ,

[0159] in, It can be calculated by combining factors such as train travel time and carriage occupancy.

[0160] (3) Minimize the adjustment range of train timetables

[0161] To maintain the stability of the train operation plan, let the original and optimized departure times of the k-th train be respectively... and The target adjustment range is:

[0162] .

[0163] This objective is used to measure the overall deviation of the optimized train timetable from the original scheduling plan, and to control operational stability.

[0164] The three objectives described above constitute a multi-objective optimization problem, which is solved using a reinforcement learning-guided fast non-dominated sorting genetic algorithm (RNSGA-II). This algorithm retains the ability to produce multiple solutions while enhancing the distribution and convergence of the solutions, supporting the output of multiple Pareto optimal solutions for operators to flexibly choose according to actual needs.

[0165] B.1.4 Constraint Modeling

[0166] To ensure the optimized train timetable is both engineering feasible and practically executable, this invention introduces the following four types of key constraints into the multi-objective optimization model:

[0167] (1) Train departure interval constraints

[0168] To ensure the safety and continuity of train operations, the departure time interval between any two adjacent trains traveling in the same direction should not be less than the minimum safe interval. And must not exceed the maximum tolerance interval. Its constraints are expressed as: ,

[0169] in, Indicates the line ,direction Upper The actual departure time of the train.

[0170] (2) Train capacity constraints

[0171] The number of passengers on a train must not exceed the maximum rated capacity of the vehicle. ,Right now:

[0172] ,

[0173] in, This represents the actual number of passengers carried when the k-th train departs from station i.

[0174] (3) Constraints on handling passenger delays

[0175] Passengers unable to board their current train will be automatically placed in the queue for the next train, following a first-come, first-served principle, thus creating a mechanism for accumulating passenger congestion across different time periods. The update formula is as follows:

[0176] ,

[0177] in, Indicates the first After the train departs, the station The number of stranded passengers; For the first The set of valid travel time windows for each train.

[0178] (4) Station dwell time constraints

[0179] Train stopping time at each station It must be greater than the minimum boarding and alighting operation time. And must not exceed the upper limit allowed by operational scheduling. :

[0180] ,

[0181] in, Indicates train On the site The actual stop time.

[0182] B.2 Design of Solving Algorithm Based on RNSGA-II

[0183] The aforementioned multi-objective train timetable optimization model is solved using the Reinforcement-guided Non-dominated Sorting Genetic Algorithm II (RNSGA-II).

[0184] like Figure 4 As shown, the RNSGA-II algorithm for solving the train timetable problem includes the following steps:

[0185] Step 1: Parameter Initialization

[0186] Set the algorithm-related parameters, including maximum number of iterations G, population size N, crossover probability Pc, mutation probability Pm, and learning rate. Discount Factor And initialize the Q value table.

[0187] Step 2: Chromosome Encoding

[0188] Train departure times within the study period are encoded as chromosomes, represented by integers, with units of discrete time interval numbers. Each individual contains two sets of chromosomes: one set corresponding to departure times at transfer stations; and one set corresponding to departure times at the originating station.

[0189] Step 3: Population Initialization

[0190] An initial population is randomly generated based on constraints to ensure that all individuals meet basic operational conditions such as departure intervals and capacity.

[0191] Step 4: Non-dominated sorting and crowding calculation

[0192] A rapid non-dominated ordination of the population is performed to assess the dominance of individuals in a multi-objective space, and crowding is calculated as an auxiliary indicator for ordination.

[0193] Step 5: Selection, Crossover, and Mutation Operations

[0194] The tournament selection strategy is used to select parent individuals from the current population, and then perform single-point crossover and uniform mutation to generate a new generation of offspring individuals.

[0195] Step 6: Determining "Transfer" in Reinforcement Learning-Driven Learning

[0196] In each iteration, the diversity and convergence of the current population are evaluated based on the migration judgment threshold Q to determine whether to perform the migration operation.

[0197] Step 7: Migration Parameter Update and Action Selection

[0198] according to The greedy strategy selects the current action (stay or migrate), performs the exchange of elite offspring between different populations, and updates the Q-value table.

[0199] Step 8: Elite Preservation and New Population Generation

[0200] The parent and offspring generations are merged, and a new generation of the population is selected based on rank and crowding, retaining non-inferior individuals.

[0201] Step 9: Termination Judgment

[0202] If the maximum number of iterations G is reached, output the Pareto optimal solution set; otherwise, return to Step 4 to continue iterating.

[0203] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

[0204] This application also provides an electronic device, including: a memory and a processor; the memory stores a computer program, and when the computer program is executed by the processor, it implements the above-described method for coordinated optimization of timetables for urban rail transit and urban rail transit.

[0205] This application also provides a computer-readable storage medium storing a computer program. When executed by a processor, the computer program implements the steps of the aforementioned method for coordinating and optimizing timetables for urban rail transit and suburban rail transit. The computer-readable storage medium may include various media capable of storing program code, such as a USB flash drive, external hard drive, read-only memory (ROM), random access memory (RAM), magnetic disk, or optical disk.

[0206] Those skilled in the art will understand that all or part of the processes in the methods of the above embodiments can be implemented by a computer program instructing related hardware. The computer program can be stored in a non-volatile computer-readable storage medium. When executed, the computer program can include the processes of the embodiments of the above methods. Any references to memory, storage, databases, or other media used in the embodiments provided in this application can include non-volatile and / or volatile memory. Non-volatile memory can include read-only memory (ROM), programmable ROM (PROM), electrically programmable ROM (EPROM), electrically erasable programmable ROM (EEPROM), or flash memory. Volatile memory can include random access memory (RAM) or external cache memory. By way of illustration and not limitation, RAM is available in various forms, such as static RAM (SRAM), dynamic RAM (DRAM), synchronous DRAM (SDRAM), dual data rate SDRAM (DDRSDRAM), enhanced SDRAM (ESDRAM), synchronous link DRAM (SLDRAM), Rambus direct RAM (RDRAM), direct memory bus dynamic RAM (DRDRAM), and memory bus dynamic RAM (RDRAM), etc.

Claims

1. A method for collaborative optimization of timetables for urban rail transit and suburban rail transit based on transfer demand, characterized in that: This method constructs a collaborative optimization model of the timetables of urban rail transit and urban rail transit based on dynamic transfer demand, and solves the collaborative optimization model of the timetables of urban rail transit and urban rail transit to obtain the collaborative optimization results of the timetables of urban rail transit and urban rail transit. The objective function of the coordinated optimization model for the timetables of urban rail transit and suburban rail transit is: ， ， ， The constraints are: ， ， ， ， In the formula, This represents the transfer passenger weight at station i. Indicates time t at station The number of passengers waiting to transfer; Indicates site ,time The number of non-transfer waiting passengers, This represents the operating cost of the train at station i at time t. Indicates the service balance weight; and Let $\mathbf$ and $\mathbf$ represent the departure times of the $k$-th train before and after optimization, respectively. Indicates the line ,direction Upper The optimized departure times for this train. Indicates the line ,direction Upper The departure time of this train. and These represent the minimum safe interval and the maximum tolerable interval for the departure times of any two adjacent trains traveling in the same direction, respectively. Indicates the line ,direction The actual number of passengers on the k-th train when it departs from station i. Indicates the train's maximum rated capacity; Indicates the line ,direction Upper After the train departs, the station The number of stranded passengers, Indicates the line ,direction Upper After the train departs, the station The number of stranded passengers, Indicates the line ,direction The number of passengers arriving at the station at time t. Indicates the line ,direction Upper The valid transfer deadline for train i; Indicates the line ,direction Upper The train is at the station The duration of the stop, and These represent the minimum boarding / alighting operation time and the maximum permitted stop time for operational scheduling, respectively. , where n=1 represents the train going up and n=2 represents the train going down.

2. The method according to claim 1, characterized in that: line ,direction Upper The valid transfer deadline for train i at station i is: ， In the formula, Indicates the starting point of the valid transfer time window; Indicates the line ,direction Upper The upper limit of the effective transfer time window for a train. To serve the reaction time constant, Indicates the line ,direction Upper The train is at the station The maximum number of passengers allowed. Indicates the line ,direction The k-1th train is at the station The number of stranded passengers.

3. The method according to claim 1, characterized in that: Based on dynamic transfer demand, the transfer area is divided into passageways and stairs. Passenger flow distribution models for passageways and stairs are constructed to obtain the number of passengers arriving at different stations at different times.

4. The method according to claim 3, characterized in that: Based on the different passenger flow densities within the passageway, the passageway walking states are divided into free walking state and following walking state, and passenger flow movement distribution models are established for each state: (1) In free walking mode: ， in, Indicates time t. Passenger count is output at the end of the passageway; For from the first Average walking time from the beginning to the end of a passageway; For a moment No. Passenger flow entering the passageway; The probability distribution function of step speed The time mapping function, v is the pedestrian walking speed that follows a normal distribution in the free state, and μ and σ are the mean and standard deviation, respectively; (2) In the following walking state: ， in, For time t Passenger flow entering the passageway For statistical time intervals.

5. The method according to claim 4, characterized in that: The criteria for classifying passenger walking states within the passageway are as follows: if at time t... Passenger numbers passing through the passage If the density of passengers allowed to move freely per unit width exceeds the threshold threshold, the passage is considered to be in a free-moving state; otherwise, it is in a following-moving state. , This represents the maximum throughput coefficient per unit width of the passageway under free-walking conditions. To ensure lateral safety spacing between passengers This represents the channel width.

6. The method according to claim 4, characterized in that: Considering passenger dwell time within the passageway, the passenger flow distribution model for the passageway is as follows: ， in, Entering the dwell point at time t And the passenger flow that stops or stays, ; , For a moment Enter the stop point Total passenger flow For the point of stay The percentage of stays; , To ensure lateral safety spacing between passengers For channel width, This refers to the effective longitudinal occupancy length for passengers. The effective length of the dwell point p; For a moment At the stop Passenger flow that did not stop .

7. The method according to claim 3, characterized in that: The passenger flow distribution model for the staircase system is as follows: ， in, For a moment Passenger flow output from the pedestrian staircase , For a moment Passenger flow entering the pedestrian staircase For a moment The number of people stranded on the staircases. The maximum number of people who can pass through the staircase per unit of time; For a moment Passenger flow output of escalators , For a moment Passenger flow entering escalators For a moment The number of people stuck on the escalator This represents the maximum number of people that can pass through the escalator per unit of time.

8. The method according to claim 1, characterized in that: The RNSGA-II fast non-dominated sorting genetic algorithm guided by reinforcement learning was used to solve the collaborative optimization model of train timetables for urban rail transit and suburban rail transit.

9. An electronic device, characterized in that: include: Memory, used to store computer programs; A processor for executing the computer program to implement the steps of the method as described in any one of claims 1-8.

10. A computer-readable storage medium on which a computer program is stored, characterized in that: When the computer program is executed by a processor, it implements the steps of the method as described in any one of claims 1-8.

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