A long-distance sending quantity prediction and optimization method based on departure schedule for multi-railway passenger transport hub

Abstract

The present application relates to a kind of based on the sending quantity prediction and optimization method of long-distance of multiple railway passenger hub based on departure frequency, including the sending quantity prediction and optimization of long-distance of multiple railway passenger hub, wherein the sending quantity prediction method of long-distance of multiple railway passenger hub is as follows: S1) travel demand estimation;S2) mode division;S3) long-distance sending quantity decomposition;S4) hub selection;The optimization method of the sending quantity of long-distance of multiple railway passenger hub is as follows: G1) feasible solution construction and initial scheme generation;G2) optimization model construction;G3) heuristic algorithm solution, which can be directly applied to the saturation prediction and departure frequency optimization of hub in the process of railway passenger hub planning, obtain the predicted sending quantity and optimized departure frequency of different railway passenger hub, and the calculation speed is fast, suitable for the sending quantity prediction of multiple railway passenger hub in city.

Description

Technical Field

[0001] This invention belongs to the field of railway transportation planning and operation management technology, and in particular relates to a method for predicting and optimizing long-distance passenger volume at multiple railway passenger hubs based on train departure schedules. Background Technology

[0002] 1. Overview of Railway Long-Distance Passenger Volume Forecast

[0003] Unlike intra-city rail transit (such as subways and light rail) and inter-city rail transit (such as intercity subways and intercity railways), inter-city or inter-provincial rail transit (i.e., long-distance rail travel) has significantly different characteristics. For the first two types of rail travel, passengers' departure and destination are usually close to rail stations, and the differences in travel time and economic costs between different modes of transportation are small, resulting in fierce competition, and some passengers will switch to other modes of transportation. However, in long-distance rail travel, regardless of the origin and destination of the passenger's journey, it is necessary to choose a railway passenger hub with train services to the destination city to complete the journey. In contrast, the number of railway passenger hubs is far less than that of urban rail transit stations, and passengers have relatively limited choices in departure hubs. On the other hand, air travel is difficult to compete with rail due to higher ticket prices and fewer hubs; road travel differs significantly from rail travel in terms of time costs, and air travel differs significantly from rail travel in terms of economic costs. Therefore, passengers who choose rail for long-distance travel have relatively stable travel preferences, and their travel characteristics are significantly different from short-distance rail passenger flow. The prediction method for long-distance rail passenger volume also needs to be different from the rail passenger flow prediction model for intra-city and inter-city rail travel.

[0004] 2. Overview of Railway Passenger Hub Construction Planning

[0005] Many large and mega-cities typically have one or more large railway passenger hubs. Different hubs differ in terms of departure capacity, train type, departure destination, and construction location. These factors collectively influence travelers' choices of long-distance travel modes and departure hubs within the city, thereby affecting the city's overall long-distance railway passenger volume.

[0006] Planned and newly built railway passenger hubs will compete with existing hubs, thereby diverting the city's total railway passenger volume. If the diversion is too large, the transport capacity of the newly built hubs may quickly reach saturation or even exceed its capacity; if the diversion is too small, it will result in idle hub capacity, making it difficult to effectively share the transport pressure of existing hubs.

[0007] To enhance the scientific rigor and rationality of railway passenger hub planning, it is necessary to not only predict the total passenger volume from departure cities to destination cities but also to reasonably estimate the distribution pattern of this volume among different hubs. This prediction relies not only on the hub's own characteristics (such as departure capacity, train type, and departure / departure points) but also on city-level factors, such as the hub's spatial location, surrounding transportation capacity, and service population size. Therefore, accurately predicting the passenger volume of each railway passenger hub by comprehensively considering these two types of factors is one of the core aspects of railway passenger hub construction planning.

[0008] After obtaining the predicted passenger volume for each hub, optimization is needed based on the results: appropriately increasing the capacity of hubs that may be saturated, and appropriately reducing the size of hubs with low predicted passenger flow. Since the scale of hub construction and transportation capacity depends on the train schedules to various destinations, and the schedule optimization problem is complex and subject to numerous constraints, a specialized mathematical optimization model needs to be constructed to optimize the train schedules based on changes in hub saturation, so as to achieve a reasonable match between transportation capacity and demand, and determine the appropriate construction scale for each hub.

[0009] 2. A Brief Introduction to Theoretical Research and Practical Methods for Forecasting Long-Distance Passenger Volume at Existing Railway Passenger Hubs

[0010] Current theoretical research on long-distance passenger volume forecasting at railway passenger hubs, both domestically and internationally, mainly falls into two categories: demand forecasting for railway passenger hubs and passenger travel choice behavior forecasting. Figure 1 The existing methods for demand forecasting at railway passenger hubs mainly include the following three categories:

[0011] (1) Single-site prediction method: This method uses the characteristics of the research site itself or similar existing sites as a reference to analyze the main influencing factors and historical change patterns of transmission volume. The prediction method has gradually evolved from the traditional "four-stage method" to various time series models and deep learning methods.

[0012] (2) Railway network traffic prediction method: Taking the complete railway line or part of the railway network as the research object and the goal of meeting the long-distance travel needs of passengers, we construct models such as bipartite graph maximum weight matching, bi-level programming, and multi-objective programming to solve the optimal passenger flow allocation and train operation scheme.

[0013] (3) Prediction method based on train schedule: Based on the constraints of train schedule, predict the long-distance travel demand of passengers and further derive the optimal operation plan.

[0014] Existing methods for predicting passenger travel choices on railways mainly include:

[0015] (1) Competition analysis between railways and other long-distance transportation modes: Given the known demand for long-distance travel, quantitative modeling is performed based on factors such as travel cost, time value, and comfort to calculate the probability of passengers choosing between various long-distance transportation modes.

[0016] (2) Competition Analysis among Railway Passenger Hubs: Under the premise of clear demand for long-distance travel, a probability model is established for passengers to choose different railway passenger hubs within the city, taking residence location, travel mode and departure time as the main factors. At present, research on railway passenger hubs themselves is still relatively limited, and related studies are mostly focused on general directions such as departure hub selection prediction and transportation mode selection to hub.

[0017] 3. Problems with existing theoretical research and practical methods

[0018] The specific problems with the existing methods mentioned above are as follows:

[0019] (1) It is difficult to obtain basic data for prediction

[0020] Forecasting methods that focus on railway lines or networks typically rely on precise train operation plans or timetables. However, accurate operation plans or timetables are often difficult to obtain during the hub planning phase. Even if relevant departments provide operational plans for the forecast period, the results may still deviate significantly from actual operations, leading to forecasting errors. Therefore, the basic input data usually needs to be appropriately simplified and subject to assumptions.

[0021] (2) Lack of systematic prediction methods for multiple railway passenger hubs

[0022] The process of forecasting and optimizing long-distance travel demand between cities, railway mode selection, railway passenger hub selection, and railway passenger hub travel demand constitutes a complete multi-hub long-distance passenger volume forecasting and optimization process. However, existing research mostly focuses on a single link, lacks systematic methodological support, and has not yet formed a complete forecasting and optimization framework and model system that connects all levels.

[0023] (3) Lack of optimization methods

[0024] After obtaining the travel demand forecast results of railway passenger hubs, existing studies generally lack analytical methods to infer key influencing factors (such as departure frequency and operation plan) from the demand results, and also lack research on optimization models and algorithms with the saturation of multi-hub facilities as the target, making it difficult to achieve the linkage optimization of forecasting and planning decisions.

[0025] To address the aforementioned problems in traditional long-distance railway passenger volume forecasting and passenger hub construction planning, the following technical challenges exist:

[0026] 1) Modeling passenger hub selection at the regional level is challenging: Travel time and cost to hubs are key factors influencing long-distance travelers' hub choices. Accurately characterizing this impact requires regional division of cities and calculation of the probability of passengers in different regions choosing different hubs. However, existing long-distance passenger volume forecasting methods generally use cities as the smallest unit of analysis, making it difficult to refine city-level railway passenger volume to even smaller spatial units.

[0027] 2) Lack of comprehensive modeling methods for the impact of hub operation plans: In addition to the travel cost to the hub, the operation plan of railway passenger hubs (including frequency, train type, and reach range) also significantly affects passengers' hub choices. However, existing research lacks an effective method to comprehensively model operation plan factors with travel cost factors such as travel time and cost to the hub and jointly calculate the probability of choice.

[0028] 3) High complexity in optimizing hub capacity and train operation plans: After obtaining the predicted results of railway passenger hubs, it is necessary to further evaluate whether the planned hub's dispatch capacity is reasonable and optimize the train operation plan based on the set objectives. Since the number of train services is determined by the product of the number of departure city hubs and the number of destination cities or provinces, the problem is huge and the optimization is difficult. Therefore, it is necessary to construct a specialized optimization model and algorithm to achieve reasonable adjustment and optimization of the train operation plan. Summary of the Invention

[0029] To address the aforementioned problems, this invention proposes a method for predicting and optimizing long-distance passenger traffic volume at multiple railway passenger hubs based on departure schedules. The traffic volume prediction part includes four main steps: travel demand estimation, mode classification, traffic volume decomposition, and hub selection.

[0030] First, in the travel demand estimation stage, based on the regional GDP, resident population, comprehensive time costs of highways, railways and air travel of the departure and destination cities, as well as the current long-distance passenger volume data, the gravity model is used to fit the parameters; then, combined with the expected regional GDP, resident population and comprehensive time costs of each mode of transport during the planning period, the long-distance travel demand between cities during the planning period is predicted.

[0031] Second, in the mode-of-use (MOU) segmentation stage, long-distance travel demand is allocated based on the comprehensive time cost of different modes of transportation (road, rail, and air), yielding the long-distance passenger volume for rail. Similar to the gravity model, the parameters of the discrete choice model are also fitted using current data.

[0032] Third, in the volume decomposition stage, the long-distance railway volume between cities is further decomposed into various regions within the departure city to obtain the volume distribution of "region-destination city", which provides a basis for subsequent hub selection.

[0033] Fourth, in the hub selection stage, considering factors such as travel time and cost from various regions to different railway passenger hubs, as well as travel time, ticket price, and number of departures from the hub to the destination city, the internal accessibility utility value and the external service level utility value are calculated separately. Based on the discrete choice model, parameters are fitted using current data to predict the probability of passengers choosing each railway passenger hub, ultimately obtaining the long-distance passenger volume prediction results under the multi-hub system.

[0034] After forecasting long-distance passenger volume, it is necessary to combine the upper limits of the existing and planned railway passenger hubs' transport capacity with the forecast results to calculate the saturation level of each hub, and optimize and adjust the train operation plan based on the set saturation target. The train operation plan typically includes elements such as operating sections, train types, operating routes, and the number of train pairs. Among these, the most significant factors affecting long-distance passenger volume are travel time and the number of train pairs. Since travel time remains relatively stable under the condition that the departure and destination cities are fixed, this method simplifies the modeling of the operation plan, using the number of train pairs as the main independent variable and hub saturation as the optimization objective. This simplification not only effectively reduces the complexity of long-distance passenger volume calculation but also significantly improves the operability and computational efficiency of operation plan optimization.

[0035] The technical solution of the present invention is as follows:

[0036] A method for predicting and optimizing long-distance passenger volume at multiple railway passenger hubs based on departure schedules is characterized by including prediction and optimization of long-distance passenger volume at multiple railway passenger hubs. The prediction method for long-distance passenger volume at multiple railway passenger hubs is as follows: S1) travel demand estimation; S2) mode classification; S3) long-distance passenger volume decomposition; S4) hub selection. The optimization method for long-distance passenger volume at multiple railway passenger hubs is as follows: G1) feasible solution construction and initial scheme generation; G2) optimization model construction; G3) heuristic algorithm solution.

[0037] Preferably, a method for predicting and optimizing long-distance passenger transport volume at multiple railway passenger hubs based on departure schedules is characterized by: S1) Estimating travel demand: Based on the current resident population, GDP, combined time costs of highways, railways, and air travel between departure and destination cities, and the total long-distance passenger transport volume between cities, a gravity model is constructed and fitted; then, combined with the resident population, GDP, and combined time costs of each mode of transportation during the planning period, the future total long-distance passenger transport volume between cities is predicted; the specific steps are as follows:

[0038] S11) Calculate the city quality G of city i according to the following formula. i :

[0039]

[0040] In the formula, Ai and R i Let represent the regional GDP and the number of permanent residents of city i, respectively.

[0041] S12) Calculate the comprehensive time cost d from departure city i to destination city j using the following formula. ij :

[0042]

[0043] In the formula, b represents the number of the long-distance travel mode of transportation, and x 1ij x 2ij x 3ij and x 4ij Let represent the average time cost of traveling from city i to city j by high-speed rail, conventional rail, highway, and air transport, respectively.

[0044] S13)T ij Let represent the estimated total long-distance transmission volume from city i to any city j. For the total long-distance transmission volume from origin city i to non-adjacent destination city j within the province, the following gravity formula is used for calculation:

[0045]

[0046] In the formula, Let be the gravitational adjustment coefficient for the journey from departure city i to non-adjacent destination city j within the province. and Let be the urban quality adjustment coefficients for city i and city j, respectively. This is a time cost adjustment factor. and These are all adjustment coefficients for additional terms in the gravitational formula; these parameters need to be obtained by fitting current data.

[0047] S14) The total long-distance transmission volume from departure city i to destination city j outside the province is calculated using the following gravity formula:

[0048]

[0049] In the formula, γ Outside This is the gravitational adjustment coefficient for the distance from the departure city to the destination city outside the province. Let be the combined urban quality adjustment coefficient for city i and city j. This is a time cost adjustment factor. and These are all adjustment coefficients for additional terms in the gravitational formula; these parameters need to be obtained by fitting current data.

[0050] S15) The above two formulas are fitted using the trust region reflection algorithm. The objective function E1 for minimizing the loss during fitting is:

[0051]

[0052] In the formula, N represents the actual total long-distance transmission volume. O and N D These represent the number of departure cities and the number of destination cities that need to be jointly studied and considered;

[0053] S16) Prediction:

[0054] 1. Calculate city quality G using the current resident population and GDP data of each city. i Then, calculate the comprehensive time cost d based on the average time cost of different modes of transportation from the departure city to the destination city. ij ;

[0055] 2. Using the current urban quality G i and comprehensive time cost d ij Data, and the actual total long-distance transmission volume. Based on whether the destination city and the departure city are located in the same province, the gravitational formulas in S13) and S14) are fitted according to the loss objective function E1 in S15) to solve for the gravitational formula parameters.

[0056] 3. Urban quality G during the planning period, calculated based on data of planned permanent resident population and regional GDP. i and comprehensive time cost d ij Based on whether the destination city and the departure city are located in the same province, the total long-distance transmission volume is predicted using the already fitted gravity formulas (S13) and (S14).

[0057] Preferably, a method for predicting and optimizing long-distance passenger volume at multiple railway passenger hubs based on departure schedules is characterized by the following steps: S2) Method division: A discrete choice model is fitted using the current time costs, ticket costs, and long-distance passenger volumes of highways, railways, and airlines; and the future long-distance railway passenger volume from the departure city to the destination city is predicted based on the time and ticket price levels of each mode of transportation during the planning period. Specific steps are as follows:

[0058] S21) The probability that a passenger chooses rail transportation when traveling from departure city i to destination city j is calculated using the following Logit formula:

[0059]

[0060] In the formula, b is the mode of transportation number, β1 and β2 are the parameters of average time cost and average fare cost, respectively, and p bijy represents the probability that a passenger chooses mode b to complete a trip from city i to city j. 1ij y 2ij y 3ij and y 4ij Let $\frac{1}{2}$ represent the average ticket cost for high-speed rail, conventional rail, highway, and air transportation from city $i$ to city $j$, respectively.

[0061] The parameters of the Logit formula above are solved using the trust region reflection algorithm, and the objective function E2 for minimizing the loss during fitting is:

[0062]

[0063] In the formula, This represents the current status of long-distance travel when choosing mode b, among which...

[0064] S22) Prediction, the steps are as follows:

[0065] 1. Average time cost of using different modes of transportation currently bij and average ticket cost y bij And the current status of different modes of transportation, total long-distance passenger volume Fit the loss objective function E2 and solve for the Logit formula parameters;

[0066] 2. The average time cost x for different modes of transportation based on planning or forecasting. bij and average ticket cost y bij The probability of choosing mode b in the future is predicted using the already fitted Logit formula. Further forecasts for long-distance railway passenger volume are as follows:

[0067] Preferably, a method for predicting and optimizing long-distance passenger volume at multiple railway passenger hubs based on departure schedules is characterized by: S3) Long-distance passenger volume decomposition: decomposing the city-level railway long-distance passenger volume into various regions within the city to obtain the railway long-distance passenger volume from the region to the destination city. The decomposition is based on the current situation of travelers choosing hubs for long-distance travel from different regions within the city, obtained from mobile phone signaling data. The specific steps are as follows:

[0068] The long-distance rail passenger volume of the departure city is broken down into regions within the departure city. The specific steps for this breakdown are as follows:

[0069] S31) Mobile signaling tracing: Let Z be the number of regions within the originating city i. i The number of hubs is H iBased on mobile signaling data, determine the mobile signaling trajectories whose starting point is within the departure city i, whose destination is far from the departure city, and which pass through the area surrounding the railway passenger hub, and count them to obtain the mobile signaling feature matrix. Its dimension is Z i ×H i , where element p izh This indicates the probability of region z within departure city i selecting hub h for external travel.

[0070] The rate is calculated using the following formula:

[0071]

[0072] In the formula, k is the number of the railway passenger hub, v izh and v izk This indicates the passenger selection hub within region z of departure city i.

[0073] The number of trips made at New H and hub K can be obtained through mobile phone signaling trajectory counting;

[0074] S32) Current Region to Destination City Matrix Estimation: Based on publicly available railway passenger hub traffic data, the number of trips s from any railway passenger hub h within city i to other cities j can be obtained under conventional or high-speed rail mode b (b=1,2). bihj Current number of trips This can form a matrix of current hub transmission volumes. Its dimension is H i ×N D Using transportation mode b (b=1,2), the matrix of current city i's internal area to the destination city. Its dimension is Z i ×N D Calculate using the following formula:

[0075]

[0076] in, elements This represents a trip from region z within city i to city j using mode b (b = 1, 2).

[0077] Passenger number;

[0078] S33) Estimation of the probability matrix from region to destination city: Based on We can obtain the probability of traveling from region z within departure city i to destination city j when using mode of transportation b (b = 1, 2).

[0079]

[0080] In the formula, m is the city number of the destination;

[0081] A probability matrix from region to destination city can be formed. Dimension Z i ×N D ;

[0082] S34) Future region-to-destination city matrix estimation: Total predicted long-distance traffic volume associated with departure city i Can form vectors When using transportation mode b (b=1,2), the matrix of future distances from the internal area of ​​city i to the destination city. Its dimension is Z i ×N D Estimate using the following formula:

[0083]

[0084] in, elements in This represents the number of passengers traveling from region z within city i to city j using mode of transportation b (b = 1, 2).

[0085] Preferably, a method for predicting and optimizing long-distance passenger traffic volume at multiple railway passenger hubs based on departure schedules is characterized by: S4) Hub selection: Based on the current travel time and cost from the urban area to each hub, the travel time from each hub to the destination city, train fares, and departure schedules, combined with the decomposed long-distance passenger traffic volume and the current passenger traffic volume of each hub, a discrete selection model is fitted; then, using the fitted model, the corresponding time and cost for the planning period, and the decomposed long-distance passenger traffic volume, the future long-distance passenger traffic volume of each railway passenger hub is predicted; the specific steps are as follows:

[0086] S41) Region-to-hub utility value: Within city i, the average travel time, average cost, and spatial distance from region z to hub h are respectively... and and The corresponding benefit value calculation parameters are set according to the mode of transportation b (b=1,2). and The utility value from region to hub is calculated using the following formula:

[0087]

[0088] S42) Hub-to-Destination Utility Values: In city i, using mode of transport b (b=1,2), the average travel time, average train fare, and number of train departures to destination city j via hub h are respectively... and The corresponding benefit value calculation parameters are as follows: and Before calculating the utility value, it is necessary to clarify that when there are 0 departures to the destination city j, the utility value of the hub is also 0. A variable representing the presence or absence of departures needs to be defined.

[0089]

[0090] The utility value from hub to destination is calculated using the following formula:

[0091]

[0092] S43) Hub Selection Probability: The probability q of a passenger choosing hub h when departing from region z within city i and using transportation mode b (b=1,2) to reach destination city j. bizhj Calculate using the following Logit formula:

[0093]

[0094] In the formula, γ = -∞, when hour,

[0095] The parameters of the Logit formula above are fitted using the trust region reflection algorithm, and the objective function for minimizing the loss during fitting is E. 3,bi for:

[0096]

[0097] S44) Predict long-haul passenger volume at the hub: based on the already fitted Logit formula and the predicted or planned data.

[0098] and Estimate the probability of hub selection when using mode of transportation b (b=1,2) in the future.

[0099] And predict the long-distance traffic volume from hub h within departure city i to destination city j.

[0100] Preferably, a method for predicting and optimizing long-distance passenger volume at multiple railway passenger hubs based on departure schedules is characterized by the following steps: G1) Construction of feasible solutions and generation of initial schemes: The feasible solution is represented by a departure schedule matrix with hubs as rows and destination cities as columns. Within the constraints, departure schedule matrices for high-speed railways and conventional railways are randomly generated as initial solutions, where matrix elements represent the specific number of departures for the corresponding train type. The specific steps are as follows:

[0101] G11) Let the optimized departure schedule matrix be x. bi =(x bihj ), its dimension is H i ×N D The structure of the feasible solution is X i =(x 1i ,x 2i (), composed of a departure schedule matrix for high-speed and conventional railways, x bihj There is also a certain range of variation. The current departure schedule, obtained from the train ticketing platform, is as follows: Let the lower limit coefficient and the upper limit coefficient be τ respectively. m (0<τ m <1) and τ M (τ M >1), x bihj The range of variation is constrained as follows:

[0102]

[0103] Randomly select an integer as x within the above range. bihj The initial feasible solution.

[0104] Preferably, a method for predicting and optimizing long-distance passenger volume at multiple railway passenger hubs based on departure schedules is characterized by the following optimization model construction: The departure schedules from each hub to each destination city are used as decision variables, the root mean square error between the actual saturation and reasonable saturation of each hub is used as the objective function, and constraints are set for the upper limit of the dispatch capacity of a single hub, the upper limit of the dispatch capacity of a combined hub, and the upper limit of the train dispatch capacity. The specific steps are as follows:

[0105] G21) Maintain and Unchanged, obtained through calculation Then, calculate the utility value from the hub to the destination. Further, following the Logit formula already fitted in the hub fitting step, calculate q. bizhj and Finally, calculate the objective function and make a judgment. Does the constraint satisfy?

[0106] Within departure city i, the reasonable saturation level for hub h is υ. h The corresponding maximum sending capacity is The objective function is calculated as follows:

[0107]

[0108] The main constraints of the G22 optimization model include the following three constraints:

[0109] 1) Maximum sending capacity of a single hub: The long-distance sending volume of each hub should not exceed the hub's own maximum number of passengers it can send.

[0110] Right now:

[0111]

[0112] 2) Maximum Train Capacity: High-speed and conventional railway trains have a certain maximum number of passengers they can carry. Therefore, the average passenger capacity per train pair, i.e., the ratio of the predicted long-distance passenger volume from hub h high-speed or conventional railway to each destination city to the number of train departures, should not exceed [a certain value]. Right now:

[0113]

[0114] 3) Upper limit constraint on the transmission capacity of the combined hub: The city is divided into multiple clusters and merged into a cluster set C. The predicted long-distance transmission volume of any cluster c (c∈C) should not be lower than the lower limit of the cluster's transmission capacity. and should not exceed the upper limit Right now:

[0115]

[0116] G23) to make X i In the optimization iteration process of heuristic algorithms, three constraints are satisfied, and a penalty function is introduced to improve the objective function:

[0117]

[0118] In the formula, ξ1, ξ2, and ξ3 are the penalty coefficients for the upper limit constraints of the single hub's dispatch capacity, train dispatch capacity, and combined hub dispatch capacity, respectively. When X i When some constraints are not satisfied, the portion that breaks the constraints will increase the objective function value, making X... i The quality of these components declines and they are gradually phased out during iterative optimization.

[0119] Preferably, a method for predicting and optimizing long-distance passenger volume at multiple railway passenger hubs based on departure schedules is characterized by the following steps: A heuristic algorithm (G3) is used to solve the problem. Based on the initial solution, a tabu search algorithm is employed to search for departure schedule matrices for high-speed and conventional railways that satisfy the constraints, thereby determining the optimal departure schedules from each hub to each destination city under different train systems. Furthermore, the optimized long-distance passenger volume for each hub within a city is calculated. The specific steps are as follows:

[0120] In the iterative optimization process using the tabu algorithm (G31), the following four neighborhoods are constructed sequentially at each step to increase the diversity of feasible solutions:

[0121] 1. Random neighborhood: directly based on x bihj The range of variation constraints randomly generate new feasible solutions X i The number of feasible solutions generated is n R The neighborhood is denoted as R;

[0122] 2. Perturbation neighborhood: for local optimal solutions To generate a new feasible solution, a random perturbation is performed, and the perturbation rate is ω. turb (0<ω turb <1), the number of feasible solutions generated is n T The specific method is as follows: Set X i Chinese x bi The number of elements is H i ×N D Randomly select ω turb ×H i ×N D Elements, according to range Replace the current value with a randomly selected integer, x. 1i and x 2i The same operation needs to be performed for all cases; repeat the above steps to obtain n. T There are 1 feasible solutions, and the resulting neighborhood representation is:

[0123] 3. Internal exchange neighborhood: Exchange any two elements of feasible solutions to generate two new feasible solutions. Let the exchange rate be ω. internal The number of generation times is n I The specific method is as follows: from the set Extract any two feasible solutions X from the middle i ′ and X i ", each randomly draws ω internal ×H i ×N D For each element, swap the elements x′ of two feasible solutions simultaneously using the following formula. bihj and x″ bihj :

[0124]

[0125] In the formula, For a temporarily feasible solution element, repeat the above steps n. I The second time, 2n was obtained. I There are 1 feasible solution, and the resulting neighborhood is represented as I(A);

[0126] 4. External Neighborhood Exchange: Exchange the departure matrix x of any two feasible solutions. 1i and x 2iTwo new feasible solutions are generated, and the number of generation times is n. E The specific method is as follows: extract any two feasible solutions X′ from set A. i and X″ i By exchanging the high-speed rail departure matrix, we obtain X′. i =(x″ 1i ,x′ 2i ), X″ i =(x′) 1i ,x″ 2i Repeat the above steps n. E The second time, 2n was obtained. E There are 1 feasible solution, and the resulting neighborhood is represented as E(A);

[0127] (G32) Before performing iterative optimization, a taboo list B is set. When a feasible solution in the neighborhood is selected as a local optimum, it is added to the taboo list. In the subsequent n iterations... tabu If the same feasible solution reappears in the next iteration, it cannot be selected as a local optimum. tabu Remove it from the taboo list after the next iteration;

[0128] The iterative optimization steps of the G33 tabu algorithm are as follows:

[0129] 1. Generate an initial feasible solution Set a local optimum and the global optimal solution

[0130] 2. Generate random neighborhood R and perturbation neighborhood And form a neighborhood set Generate the internal exchange neighborhood I(A) and the external exchange neighborhood E(A);

[0131] 3. Calculate the feasible solutions corresponding to the minimum objective function values ​​in the neighborhood A′=A∪I(A)∪E(A) that are not in the taboo list B, and set them as local optima.

[0132] 4. If satisfied set up

[0133] 5. Add to taboo list B, check B, and add the existing n tabu Remove feasible solutions from B in the next iteration, and repeat the steps.

[0134] 2-5, until the number of iterations of the algorithm exceeds the maximum number of iterations M. Iter , This will be output as the optimal departure schedule.

[0135] get Then, q is calculated according to the fitted Logit formula obtained in the hub selection step of long-distance traffic forecasting. bizhj and To further obtain the long-distance transmission volume and saturation of each hub in the future.

[0136] Compared with the prior art, the present invention, employing the above technical solution, has the following beneficial effects:

[0137] This method for predicting and optimizing long-distance passenger volume at multiple railway passenger hubs based on departure schedules can be directly applied to the planning process of railway passenger hubs, including hub saturation prediction and departure schedule optimization. It can obtain predicted passenger volume and optimized departure schedules for different railway passenger hubs, and has a fast calculation speed, making it suitable for predicting passenger volume at multiple railway passenger hubs within a city. Attached Figure Description

[0138] Figure 1 This is a schematic diagram illustrating the theoretical research and practical methods for predicting long-distance passenger volume at existing railway passenger hubs.

[0139] Figure 2 This is a flowchart of a method for predicting and optimizing long-distance passenger traffic at multiple railway passenger hubs.

[0140] Figure 3 This is a flowchart of the travel demand estimation method.

[0141] Figure 4 This is a flowchart of the method of dividing the process.

[0142] Figure 5 This is a flowchart of the data transmission volume breakdown.

[0143] Figure 6 This is a schematic diagram illustrating the main principles of hub selection.

[0144] Figure 7 This is a flowchart of the hub selection method.

[0145] Figure 8 This is a schematic diagram of the feasible solution structure.

[0146] Figure 9 This is a schematic diagram of the neighborhood structure.

[0147] Figure 10 This is a flowchart of the iterative optimization process of the tabu algorithm.

[0148] Figure 11 This is a diagram illustrating the error in the total long-distance transmission volume from the sending city to the destination city.

[0149] Figure 12 This is a diagram illustrating the projected future total long-distance traffic volume from the sending city to the destination city.

[0150] Figure 13This is a schematic diagram illustrating the error in long-distance railway freight volume from the sending city to various destination cities.

[0151] Figure 14 This is a diagram illustrating the projected future long-distance rail traffic volume from the sending city to various destination cities.

[0152] Figure 15 This is a schematic diagram illustrating the absolute error of high-speed rail long-distance passenger volume from urban hubs to various destination cities.

[0153] Figure 16 This is a schematic diagram illustrating the absolute error of long-distance conventional rail traffic volume from urban hubs to various destination cities.

[0154] Figure 17 This is a diagram showing the comparison of optimized saturation error.

[0155] Figure 18 This is a diagram illustrating the optimization of long-distance passenger volume and departure frequency.

[0156] Figure 19 This is a schematic diagram of the iterative optimization process of a heuristic algorithm. Detailed Implementation

[0157] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0158] This invention presents a method for predicting and optimizing long-distance passenger traffic volume at multiple railway passenger hubs based on departure schedules. It fits a gravity model and a discrete choice model to data on current intercity long-distance passenger traffic volume, railway long-distance passenger traffic volume, passenger traffic volume at different railway passenger hubs within a city, and other influencing factors. It calculates the probability of hub selection in different areas within the city and the passenger traffic volume at different hubs during the prediction period. Furthermore, using the fitted discrete choice model, with departure schedules as the decision variable and saturation as the objective, it optimizes the predicted passenger traffic volume of each railway passenger hub, providing a reference for the planning of new railway passenger hubs within a city.

[0159] Forecast of long-distance passenger traffic at multiple railway passenger hubs

[0160] Overall Approach

[0161] This invention discloses a method for predicting and optimizing long-distance passenger traffic at multiple railway passenger hubs based on departure schedules. It mainly consists of two methods: prediction and optimization. This section describes the prediction method, which comprises four main steps, as follows: Figure 2 As shown, the details are as follows:

[0162] 1) Travel demand estimation: Based on the current resident population, regional GDP, comprehensive time cost of highway, railway and air transportation in the departure and destination cities, as well as the total long-distance traffic volume between cities, a gravity model is constructed and fitted; then, combined with the resident population, regional GDP and comprehensive time cost of each mode of transportation in the planning period, the total long-distance traffic volume between cities in the future is predicted.

[0163] 2) Mode Classification: Using the time cost, ticket cost, and long-distance passenger volume of existing highways, railways, and air transport, a discrete choice model is fitted; and based on the time and ticket price levels of each mode of transport during the planning period, the future long-distance railway passenger volume from the departure city to the destination city is predicted.

[0164] 3) Due to the varying attractiveness of different railway passenger hubs within a city to different regions, meaning passengers have different hub selection preferences at the regional level, it is necessary to decompose the city-level long-distance railway passenger volume into different regions within the city before hub selection, thus obtaining the long-distance railway passenger volume from the region to the destination city. The decomposition is based on the current situation of travelers choosing hubs for long-distance travel from different regions within the city, obtained from mobile signaling data.

[0165] 4) Hub selection: Based on the current travel time and cost from the urban area to each hub, the travel time from each hub to the destination city, train ticket prices and departure times, etc., combined with the decomposed long-distance railway passenger volume and the current passenger volume of each hub, a discrete selection model is fitted; then, using the fitted model and the time, cost and other parameters corresponding to the planning period, as well as the decomposed long-distance railway passenger volume, the future long-distance passenger volume of each railway passenger hub is predicted.

[0166] The goal of this method is to quickly fit a mathematical model using current data, and then use forecast or planning data to estimate the total long-distance passenger volume, railway long-distance passenger volume, and long-distance passenger volume of each hub.

[0167] The following is a detailed description of the method for predicting long-distance passenger traffic at multiple railway passenger hubs.

[0168] Travel demand estimates

[0169] Calculate the city quality G of city i using the following formula. i :

[0170]

[0171] In the formula, A i and R i Let represent the regional GDP and the number of permanent residents of city i, respectively.

[0172] Because of the significant differences in travel time, train fares, and departure frequencies between high-speed rail (high-speed trains, bullet trains, and intercity bullet trains) and conventional rail (express trains, special express trains, and direct trains), among the three long-distance transportation modes of rail, road, and air, rail is further divided into high-speed rail and conventional rail.

[0173] Calculate the combined time cost d from departure city i to destination city j using the following formula. ij :

[0174]

[0175] In the formula, b represents the number of the long-distance travel mode of transportation, and x 1ij x 2ij x 3ij and x 4ij Let $\mathbf$ and $\mathbf$ represent the average time cost of traveling from city $i$ to city $j$ using high-speed rail, conventional rail, highway, and air transport, respectively.

[0176] T ij Let represent the estimated total long-distance transmission volume from city i to any city j. The total long-distance transmission volume from origin city i to non-adjacent destination city j within the same province is calculated using the following gravity formula:

[0177]

[0178] In the formula, The gravitational adjustment coefficient is the distance from the departure city i to the non-adjacent destination city j within the province. and Let be the urban quality adjustment coefficients for city i and city j, respectively. This is a time cost adjustment factor. and These are all adjustment coefficients for additional terms in the gravitational formula; these parameters need to be obtained by fitting current data.

[0179] The total long-distance shipments from departure city i to destination city j outside the province are calculated using the following gravity formula:

[0180]

[0181] In the formula, γ Outside This is the gravity adjustment coefficient from the departure city to the destination city outside the province. Let be the combined urban quality adjustment coefficient for city i and city j. This is a time cost adjustment factor. and These are all adjustment coefficients for additional terms in the gravitational formula; these parameters need to be obtained by fitting current data.

[0182] The above two formulas are fitted using the trust region reflection algorithm. The objective function E1 for minimizing the loss during fitting is:

[0183]

[0184] In the formula, N represents the actual total long-distance transmission volume. O and N D These represent the number of departure cities and the number of destination cities that need to be jointly studied and considered.

[0185] like Figure 3 The specific prediction steps are as follows:

[0186] 4. Calculate city quality G using the current resident population and GDP data of each city. i Then, calculate the comprehensive time cost d based on the average time cost of different modes of transportation from the departure city to the destination city. ij ;

[0187] 5. Use city quality G i and comprehensive time cost d ij and actual long-distance transmission volume data. Depending on whether the destination city and the departure city are located in the same province, the above two gravity formulas are selected respectively, and the parameters of the gravity formula are solved by fitting the loss objective function E1.

[0188] 6. Urban quality G calculated based on planned permanent resident population and regional GDP data. i and comprehensive time cost d ij Based on whether the destination city and the departure city are located in the same province, the total long-distance transmission volume is predicted using a pre-fitted gravity formula.

[0189] Method of division

[0190] The probability that a passenger chooses rail transportation when traveling from departure city i to destination city j is calculated using the following Logit formula:

[0191]

[0192] In the formula, b is the mode of transportation number, β1 and β2 are the parameters of average time cost and average fare cost, respectively, and p bij y represents the probability that a passenger chooses mode b to complete a trip from city i to city j. 1ij y 2ij y 3ij and y 4ijLet $\mathbf$ and $\mathbf$ represent the average ticket cost for high-speed rail, conventional rail, highway, and air transportation from city $i$ to city $j$.

[0193] The parameters of the Logit formula above are also solved using the trust region reflection algorithm, and the objective function E2 for minimizing the loss during fitting is:

[0194]

[0195] In the formula, This represents the current status of long-distance travel when choosing mode b, among which...

[0196] like Figure 4 The specific prediction steps are as follows:

[0197] 3. Average time cost of using different modes of transportation currently available x bij and average ticket cost y bij And the current status of different modes of transportation, total long-distance passenger volume Fit the loss objective function E2 and solve for the Logit formula parameters;

[0198] 4. Average time cost x for different modes of transportation based on planning or forecasting. bij and average ticket cost y bij The probability of choosing mode b in the future is predicted using the already fitted Logit formula. Further forecasts for long-distance railway passenger volume are as follows:

[0199] Decompose the sending volume

[0200] Before considering the impact of regional location on passenger choice of railway hubs, it is necessary to break down the long-distance rail traffic volume of the departure city into regions within the departure city. For example... Figure 5 The specific decomposition steps are as follows:

[0201] 1. Mobile signaling tracing: Let Z be the number of regions within the originating city i. i The number of hubs is H i Based on mobile signaling data, determine the mobile signaling trajectories whose starting point is within the departure city i, whose destination is far from the departure city, and which pass through the area surrounding railway passenger hubs. Count these trajectories to obtain the mobile signaling feature matrix. (dimension Z) i ×H i ). Among them, element p izh Let z be the region within the departure city i that chooses hub h for external travel, calculated using the following formula:

[0202]

[0203] In the formula, k is the number of the railway passenger hub, v izh and v izk The number of passengers departing from area z within departure city i who choose to travel through hub h and hub k can be obtained through mobile phone signaling trajectory counting.

[0204] 2. Current Region-to-Destination City Matrix Estimation: Based on publicly available railway passenger hub traffic data, the number of trips s from any city i to other cities j via railway passenger hub h within the city i can be obtained under conventional or high-speed rail mode b (b=1,2). bihj Current number of trips This can form a matrix of current hub transmission volumes. (dimension H) i ×N D Using transportation mode b (b=1,2), the matrix of current city i's internal area to the destination city. (dimension Z) i ×N D Calculate using the following formula:

[0205]

[0206] in, elements This represents the number of passengers traveling from region z within city i to city j using mode b (b = 1, 2).

[0207] 3. Estimation of the probability matrix from region to destination city: Based on We can obtain the probability of traveling from region z within departure city i to destination city j when using mode of transportation b (b = 1, 2).

[0208]

[0209] In the formula, m is the city number of the destination.

[0210] A probability matrix from region to destination city can be formed. (dimension Z) i ×N D ).

[0211] 4. Future region-to-destination city matrix estimation: Total predicted long-distance passenger volume associated with departure city i Can form vectors When using transportation mode b (b=1,2), the matrix of future distances from the internal area of ​​city i to the destination city. (dimension Z) i×N D Estimate using the following formula:

[0212]

[0213] in, elements in This represents the number of passengers traveling from region z within city i to city j using mode of transportation b (b = 1, 2).

[0214] Hub Selection

[0215] The main factors considered in hub selection fall into two categories: when choosing a railway passenger hub for long-distance travel, passengers consider two main factors: internal accessibility and external service level. Internal accessibility factors include travel time, cost, and spatial distance, while external service level factors include travel time, train ticket prices, and the number of trains departing.

[0216] like Figure 6 The main principle of hub selection is as follows: Within city i, calculate the utility value from region z to hub h, and the utility value from hub h to destination city j. These represent the passenger's preference for the hub, considering internal accessibility and external service level, respectively. Using these two utility values, the probability values ​​for passengers choosing different hubs when traveling from city i to city j can be calculated. The probabilities of multiple hubs are then correlated with the matrix. Multiplying these matrices yields a travel demand matrix for passengers traveling from city i to city j, originating from different regions and passing through different hubs to reach their destination city. This matrix can then be used to obtain the predicted long-distance passenger volume for each hub. For example... Figure 7 The specific steps are as follows:

[0217] 1. Region-to-hub utility value: Within city i, the average travel time, average cost, and spatial distance from region z to hub h are respectively... and Because the characteristics of passengers on high-speed trains and regular trains are significantly different, and The corresponding benefit value calculation parameters should be set according to the mode of transportation b (b=1,2). and The utility value from region to hub is calculated using the following formula:

[0218]

[0219] 2. Hub-to-Destination Utility: In city i, using mode of transportation b (b=1,2), the average travel time, average train fare, and number of departures to destination city j via hub h are as follows: and The corresponding benefit value calculation parameters are as follows: and Before calculating the utility value, it is necessary to clarify that when there are 0 departures to the destination city j, the utility value of the hub is also 0. A variable representing the presence or absence of departures needs to be defined.

[0220]

[0221] The utility value from hub to destination is calculated using the following formula:

[0222]

[0223] 3. Hub Selection Probability: The probability q of a passenger choosing hub h when departing from region z within city i and using transportation mode b (b=1,2) to reach destination city j. bizhj Calculate using the following Logit formula:

[0224]

[0225] In the formula, γ = -∞, when hour,

[0226] 4. The parameters of the Logit formula above are also fitted using the trust region reflection algorithm, and the objective function for minimizing the loss during fitting is E. 3,bi for:

[0227]

[0228] 5. Predict long-distance passenger volume at hubs: Based on the fitted Logit formula and the predicted or planned data.

[0229] and The probability of hub selection when using transportation mode b (b=1,2) in the future can be estimated. And predict the long-distance traffic volume from hub h within departure city i to destination city j.

[0230] Optimization of long-distance passenger volume at multiple railway passenger hubs

[0231] Overall Approach

[0232] This invention discloses a method for predicting and optimizing long-distance passenger transport volume at multiple railway passenger hubs based on departure schedules. It mainly consists of two methods: prediction and optimization. The optimization method is described here, as follows:

[0233] 1) Feasible solution construction and initial scheme generation: The feasible solution is represented by a departure matrix with hubs as rows and destination cities as columns, as the decision variables. Within the constraints, departure matrices for high-speed railways and conventional railways are randomly generated as the initial solution, where the matrix elements represent the specific number of departures for the corresponding train type.

[0234] 2) Optimization Model Construction: The number of train departures from each hub to each destination city is used as the decision variable, and the root mean square error between the actual saturation and the reasonable saturation of each hub is used as the objective function. Constraints such as the upper limit of the dispatch capacity of a single hub, the upper limit of the dispatch capacity of a combined hub, and the upper limit of the train dispatch capacity are set to construct an optimization model.

[0235] 3) Heuristic algorithm solution: Based on the initial solution, the tabu search algorithm is used to search for the departure matrix of high-speed railway and conventional railway that meet the constraints, so as to determine the optimal departure schedule from each hub to each destination city under different train systems, and further calculate the optimized long-distance passenger volume of each hub within the city.

[0236] To determine the optimal long-distance passenger volume for hubs within multiple departure cities, steps 1-3 can be performed independently for each departure city to obtain the optimal long-distance passenger volume and best departure schedule for hubs within different departure cities. The following is a detailed description of the method for optimizing long-distance passenger volume across multiple railway passenger hubs.

[0237] Construction of feasible solutions and generation of initial schemes

[0238] like Figure 8 Let the optimized departure schedule matrix be x. bi =(x bihj (Dimension H) i ×N D The structure of the feasible solution is X. i =(x 1i ,x 2i (This is a matrix consisting of departure times for high-speed and conventional railways.) bihj There is also a certain range of variation; the current departure schedule obtained from China 12306 is as follows: Let the lower limit coefficient and the upper limit coefficient be τ respectively. m (0<τ m <1) and τ M (τ M >1), x bihj The range of variation is constrained as follows:

[0239]

[0240] Randomly select an integer as x within the above range. bihj The initial feasible solution.

[0241] Optimize model building

[0242] Keep and Unchanged, obtained through calculation Then, calculate the utility value from the hub to the destination. Therefore, q is calculated further according to the Logit formula already fitted in the hub fitting step. bizhj and Finally, calculate the objective function and make a judgment. Does it satisfy the constraints?

[0243] Within departure city i, the reasonable saturation level for hub h is υ. h The corresponding maximum sending capacity is The objective function is calculated as follows:

[0244]

[0245] The main constraints of the optimization model include the following three types:

[0246] 1. Maximum sending capacity of a single hub: The long-distance sending volume of each hub should not exceed the hub's own maximum number of passengers it can send. Right now:

[0247]

[0248] 2. Maximum Train Capacity: Both high-speed and conventional railway trains have a certain maximum passenger capacity. Therefore, the average passenger capacity per train pair, i.e., the ratio of the predicted long-distance passenger volume from hub h high-speed or conventional railway to each destination city to the number of train departures, should not exceed [a certain value]. Right now:

[0249]

[0250] 3. Constraints on the Upper Limit of Combined Hub Sending Capacity: Different stations within a city have different functions and need to serve different population groups in different areas of the city. For example, railway passenger hubs in the suburbs have limited passenger sending capacity and mainly serve the suburban population, not undertaking most of the functions of railway passenger hubs in the city center, and vice versa. Only within clusters with similar functions and service scopes can long-distance sending volume be adjusted between hubs by adjusting departure schedules to minimize the objective function value. Multiple clusters within the city are merged into a cluster set C, where the predicted long-distance sending volume of any cluster c (c∈C) should not be lower than the lower limit of the cluster's sending capacity. and should not exceed the upper limit Right now:

[0251]

[0252] To make X i In the optimization iteration process of heuristic algorithms, three constraints are satisfied, and a penalty function is introduced to improve the objective function:

[0253]

[0254] In the formula, ξ1, ξ2, and ξ3 are the penalty coefficients for the upper limit constraints of the single hub's dispatch capacity, train dispatch capacity, and combined hub dispatch capacity, respectively. When X i When some constraints are not satisfied, the portion that breaks the constraints will increase the objective function value, making X... i The quality of these components declines and they are gradually phased out during iterative optimization.

[0255] Heuristic algorithm solution

[0256] During the iterative optimization process using the tabu algorithm, each step requires constructing the following four types of neighborhoods in sequence to increase the diversity of feasible solutions:

[0257] 5. Random neighborhood: directly based on x bihj The range of variation constraints randomly generate new feasible solutions X i The number of feasible solutions generated is n R The neighborhood is denoted as R;

[0258] 6. Disturb the neighborhood: such as Figure 9 For local optimal solutions A random perturbation is applied to generate a new feasible solution. Let the perturbation rate be ω. turb (0<ω turb <1), the number of feasible solutions generated is n T The specific method is as follows: Set X i Chinese x bi The number of elements is H i ×N D Randomly select ω turb ×H i ×N D Elements, according to range Replace the current value with a randomly selected integer. 1i and x 2i The same operation needs to be performed for all cases; repeat the above steps to obtain n. T There are 1 feasible solutions, and the resulting neighborhood representation is:

[0259] 7. Internal exchange neighborhood: such as Figure 9 Swap elements of any two feasible solutions to generate two new feasible solutions. Let the swap rate be ω. internal The number of generation times is n IThe specific method is as follows: from the set Extract any two feasible solutions X from the middle i ′ and X i ", each randomly draws ω internal ×H i ×N D For each element, swap the elements x of two feasible solutions simultaneously using the following formula. b ′ ihj and x b " ihj :

[0260]

[0261] In the formula, This is a temporarily feasible solution element. Repeat the above steps n. I The second time, 2n was obtained. I There are 1 feasible solution, and the resulting neighborhood is represented as I(A);

[0262] 8. External exchange neighborhood: such as Figure 9 Swap the departure schedule matrix x of any two feasible solutions 1i and x 2i This generates two new feasible solutions. Let the number of generation times be n. E The specific method is as follows: extract any two feasible solutions X′ from set A. i and X″ i By exchanging the high-speed rail departure matrix, we obtain X′. i =(x″ 1i ,x′ 2i ), X″ i =(x′) 1i ,x″ 2i Repeat the above steps n. E The second time, 2n was obtained. E There are 1 feasible solution, and the resulting neighborhood is represented as E(A);

[0263] Before performing iterative optimization, a tabu list B needs to be set up. The purpose is to reduce computation and prevent repeated searches during the iteration process. When a feasible solution in the neighborhood is selected as a local optimum, it is added to the tabu list. tabu If the same feasible solution reappears in the next iteration, it cannot be selected as a local optimum. tabu Remove it from the taboo list after the next iteration.

[0264] After determining the method for generating neighborhoods and the form of the taboo list, such as Figure 10 As shown, the iterative optimization steps of the tabu algorithm are as follows:

[0265] 6. Generate an initial feasible solution Set a local optimum and the global optimal solution

[0266] 7. Generate random neighborhood R and perturbation neighborhood And form a neighborhood set Generate the internal exchange neighborhood I(A) and the external exchange neighborhood E(A);

[0267] 8. Calculate the feasible solutions corresponding to the minimum objective function values ​​in the neighborhood A′=A∪I(A)∪E(A) that are not in the taboo list B, and set them as local optima.

[0268] 9. If satisfied set up

[0269] 10. Add to taboo list B, check B, and add the existing n tabu Remove feasible solutions from B in the next iteration, and repeat steps 2-5 until the number of iterations exceeds the maximum number of iterations M. Iter , This will be output as the optimal departure schedule.

[0270] get Then, q is calculated according to the fitted Logit formula obtained in the hub selection step of long-distance traffic forecasting. bizhj and To further obtain the long-distance transmission volume and saturation of each hub in the future.

[0272] The present invention will be further described in detail below with reference to a specific embodiment:

[0273] Example:

[0274] Considering that GZ City currently has 8 operational railway hubs: GZQ, IZQ, GBQ, GGQ, QSQ, XWQ, ZCA, and GBA, and plans to build 5 more railway hubs: BDA, CH, ZSC, NS, and HP.

[0275] The research scope includes GZ city as the departure city and the provincial capitals of 31 provinces (excluding GD, HK, and MC) as destination cities. Long-distance rail travel includes both high-speed and conventional rail. A gravity model and two discrete choice models are fitted using current data. The long-distance rail traffic volume from the departure city to the 31 destination cities and the long-distance traffic volume at each hub are then predicted. Based on a predetermined saturation optimization objective, the planned train schedules are inferred and optimized. There are N... O =1, N D =31, current status H1 is 8, future status is 13.

[0276] Fitting error and prediction results:

[0277] (1) Travel demand estimation: The root mean square error of the gravity model fitting is 6525.5. For the specific error in the total long-distance travel volume from the sending city to each destination city, please refer to [link / reference]. Figure 11 For the projected total future long-distance traffic volume from the sending city to each destination city, please see [link / reference]. Figure 12 .

[0278] (2) Method Classification: The mean square error of the discrete selection model after fitting is 470.34. For specific errors in long-distance railway freight volume from the sending city to each destination city, please refer to... Figure 13 For forecasts of future long-distance rail passenger volume from sending cities to various destination cities, please see [link / reference]. Figure 14 .

[0279] (3) Hub Selection: The root mean square error of the discrete selection model is 589.75. The absolute errors of high-speed rail and conventional long-distance rail traffic from intra-city hubs to various destination cities are shown below. Figure 15 and Figure 16 .

[0280] Fitting parameter results:

[0281] (1) Travel demand estimation: γ Outside =1448.4,

[0282] (2) Method of division: β1 = -0.001416, β2 = -0.008587;

[0283] (3) Hub selection:

[0284] Before optimizing long-distance freight volume, it is necessary to determine the following parameters: the upper limit of long-distance freight capacity for these 13 railway hubs: GZQ, GGQ, IZQ, QSQ, GBQ, BDA, XWQ, ZCA, GBA, HP, NS, ZSC, and CH. The following capacity limits were set at 121,000, 98,000, 135,000, 101,000, 132,000, 28,000, 48,000, 44,000, 114,000, 120,000, 119,000, 29,000, and 19,000 passengers per day respectively, representing the reasonable saturation level of the hub. h The upper limit of the average passenger capacity per train pair is set at 40%, 60%, 60%, 20%, 25%, 60%, 60%, 30%, 85%, 35%, 10%, 10%, and 35% respectively. The numbers were set to 772, 649, 1106, 366, 332, 332, 426, 326, 772, 435, 366, 332, and 554 per person / pair, respectively.

[0285] The groups are divided into 5 major groups, with corresponding minimum sending capacities for individual stations and combined stations. and upper limit They are respectively:

[0286] (1) Central station cluster: GZQ, GBA, GGQ, IZQ, with a minimum of 143,000 passengers / day and a maximum of 428,000 passengers / day;

[0287] (2) Northern Gateway Cluster: GBQ, BDA, with a minimum of 24,000 visitors / day and a maximum of 71,000 visitors / day;

[0288] (3) Eastern Gateway Cluster: XWQ, HP, with a minimum of 36,000 visitors / day and a maximum of 108,000 visitors / day;

[0289] (4) Southern Gateway Cluster: QSQ, NS, with a minimum of 16,000 visitors / day and a maximum of 49,000 visitors / day;

[0290] (5) Node station clusters: ZCA, ZSC, CH, with a minimum of 13,000 passengers / day and a maximum of 39,000 passengers / day;

[0291] x bihj The lower and upper limits of the range of variation are set to τ. m =0.5 and τ M =1.5, and the coefficients of the penalty terms in the objective function are set to ξ1=0.1, ξ2=0.1 and ξ3=0.1 respectively.

[0292] The tabu algorithm is set with the following parameters: n R =5,n T =5, ω turb =0.10, n I =5, ω internal =0.25, n E =5,n tabu =10, M Iter =800.

[0293] Optimization results for long-distance transmission volume:

[0294] The optimized long-distance passenger volumes for the 13 railway hubs GZQ, GGQ, IZQ, QSQ, GBQ, BDA, XWQ, ZCA, GBA, HP, NS, ZSC, and CH are 48,900, 59,400, 81,100, 20,500, 30,700, 16,900, 29,500, 15,100, 97,000, 42,400, 11,900, 4,200, and 6,800 passenger trips per day, respectively. The optimized saturation rates are 40.4%, 60.4%, 60.0%, 20.4%, 23.2%, 61.4%, 61.0%, 34.3%, 85.2%, 35.3%, 10.0%, 14.2%, and 36.7%, respectively. The objective function value is 0.5197%, and the optimization results meet all constraints. A comparison of optimization saturation errors is shown below. Figure 17 Optimize long-distance passenger volume and departure frequency. Figure 18 .

[0295] The optimization iterative process of the tabu algorithm is shown in [link to documentation]. Figure 19 As can be seen, it only takes about 800 steps to complete the convergence and solution of the problem from 13 railway hubs to 31 destination cities, which takes about 544 seconds, and the solution speed is relatively fast.

Claims

1. A method for predicting and optimizing long-distance passenger volume at multiple railway passenger hubs based on departure schedules, characterized in that... This includes prediction and optimization of long-distance passenger volume at multiple railway passenger hubs. The prediction method for long-distance passenger volume at multiple railway passenger hubs is as follows: S1) travel demand estimation; S2) mode classification; S3) long-distance passenger volume decomposition; S4) hub selection. The optimization method for long-distance passenger volume at multiple railway passenger hubs is as follows: G1) feasible solution construction and initial scheme generation; G2) optimization model construction; G3) heuristic algorithm solution.

2. The method for predicting and optimizing long-distance passenger volume at multiple railway passenger hubs based on departure schedules, as described in claim 1, is characterized in that... S1) Travel Demand Estimation: Based on the current resident population, GDP, combined time costs of road, rail, and air transport in both departure and destination cities, and the total long-distance passenger volume between cities, a gravity model is constructed and fitted. Then, combined with the resident population, GDP, and combined time costs of each mode of transport during the planning period, the future total long-distance passenger volume between cities is predicted. The specific steps are as follows: S11) Calculate the city quality G of city i according to the following formula. i : In the formula, A i and R i Let represent the regional GDP and the number of permanent residents of city i, respectively. S12) Calculate the comprehensive time cost d from departure city i to destination city j using the following formula. ij : In the formula, b represents the number of the long-distance travel mode of transportation, and x 1ij x 2ij x 3ij and x 4ij Let represent the average time cost of traveling from city i to city j by high-speed rail, conventional rail, highway, and air transport, respectively. S13)T ij Let represent the estimated total long-distance transmission volume from city i to any city j. For the total long-distance transmission volume from origin city i to non-adjacent destination city j within the province, the following gravity formula is used for calculation: In the formula, Let be the gravitational adjustment coefficient for the journey from departure city i to non-adjacent destination city j within the province. and Let be the urban quality adjustment coefficients for city i and city j, respectively. This is a time cost adjustment factor. and These are all adjustment coefficients for additional terms in the gravitational formula; these parameters need to be obtained by fitting current data. S14) The total long-distance transmission volume from departure city i to destination city j outside the province is calculated using the following gravity formula: In the formula, γ Outside This is the gravitational adjustment coefficient from the departure city to the destination city outside the province. Let be the combined urban quality adjustment coefficient for city i and city j. This is a time cost adjustment factor. and These are all adjustment coefficients for additional terms in the gravitational formula; these parameters need to be obtained by fitting current data. S15) The above two formulas are fitted using the trust region reflection algorithm. The objective function E1 for minimizing the loss during fitting is: In the formula, N represents the actual total long-distance transmission volume. O and N D These represent the number of departure cities and the number of destination cities that need to be jointly studied and considered; S16) Prediction: 1) Calculate city quality G using the current resident population and regional GDP data of each city. i Then, calculate the comprehensive time cost d based on the average time cost of different modes of transportation from the departure city to the destination city. ij ; 2) Using the current urban quality G i and comprehensive time cost d ij Data, and the actual total long-distance transmission volume. Based on whether the destination city and the departure city are located in the same province, the gravitational formulas in S13) and S14) are fitted according to the loss objective function E1 in S15) to solve for the gravitational formula parameters. 3) Urban quality G during the planning period, calculated based on data on the planned permanent resident population and regional GDP. i and comprehensive time cost d ij Based on whether the destination city and the departure city are located in the same province, the total long-distance transmission volume is predicted using the already fitted gravity formulas (S13) and (S14).

3. A method for predicting and optimizing long-distance passenger volume at multiple railway passenger hubs based on departure schedules, as described in any one of claims 1-2, characterized in that... S2) Method Classification: A discrete choice model is fitted using the current time and fare costs of highways, railways, and air transport, as well as their respective long-distance passenger volumes. Based on the time and fare levels of each mode of transport during the planning period, the future long-distance railway passenger volume from the departure city to the destination city is predicted. The specific steps are as follows: S21) The probability that a passenger chooses rail transportation when traveling from departure city i to destination city j is calculated using the following Logit formula: In the formula, b is the mode of transportation number, β1 and β2 are the parameters of average time cost and average fare cost, respectively, and p bij y represents the probability that a passenger chooses mode b to complete a trip from city i to city j. 1ij y 2ij y 3ij and y 4ij Let $\frac{1}{2}$ represent the average ticket cost for high-speed rail, conventional rail, highway, and air transportation from city $i$ to city $j$, respectively. The parameters of the Logit formula above are solved using the trust region reflection algorithm, and the objective function E2 for minimizing the loss during fitting is: In the formula, This represents the current status of long-distance travel when choosing mode b, among which... S22) Prediction, the steps are as follows: 1) Average time cost using different modes of transportation currently available x bij and average ticket cost y bij And the current status of different modes of transportation, total long-distance passenger volume Fit the loss objective function E2 and solve for the Logit formula parameters; 2) The average time cost x for different modes of transportation based on planning or forecasting. bij and average ticket cost y bij The probability of choosing mode b in the future is predicted using the already fitted Logit formula. Further forecasts for long-distance railway passenger volume are as follows:

4. The method for predicting and optimizing long-distance passenger volume at multiple railway passenger hubs based on departure schedules, as described in claim 3, is characterized in that... S3) Long-distance passenger volume decomposition: The city-level railway long-distance passenger volume is decomposed into various areas within the city to obtain the railway long-distance passenger volume from the area to the destination city. The decomposition is based on the current situation of travelers choosing hubs from different areas within the city for long-distance travel, obtained from mobile phone signaling data. The specific steps are as follows: The long-distance rail passenger volume of the departure city is broken down into regions within the departure city. The specific steps for this breakdown are as follows: S31) Mobile signaling tracing: Let Z be the number of regions within the originating city i. i The number of hubs is H i Based on mobile signaling data, determine the mobile signaling trajectory where the starting point is within the departure city i, the destination is far from the departure city, and it passes through the area surrounding the railway passenger hub, and count the data to obtain the mobile signaling feature matrix. Its dimension is Z i ×H i , where element p izh Let z be the region within the departure city i that chooses hub h for external travel, calculated using the following formula: In the formula, k is the number of the railway passenger hub, v izh and v izk The number of passengers departing from area z within departure city i who choose hub h and hub k for their trips can be obtained through mobile phone signaling trajectory counting. S32) Current Region to Destination City Matrix Estimation: Based on publicly available railway passenger hub traffic data, the number of trips s from any railway passenger hub h within city i to other cities j can be obtained under conventional or high-speed rail mode b (b=1,2). bihj Current number of trips This can form a matrix of current hub transmission volumes. Its dimension is H i ×N D Using transportation mode b (b=1,2), the matrix of current city i's internal area to the destination city. Its dimension is Z i ×N D Calculate using the following formula: in, elements This represents the number of passengers traveling from region z within city i to city j using mode b (b = 1, 2). S33) Estimation of the probability matrix from region to destination city: Based on We can obtain the mode of transportation b (b = 1, 2). When, the probability of traveling from region z within the departure city i to the destination city j. In the formula, m is the city number of the destination; A probability matrix from region to destination city can be formed. Dimension Z i ×N D ; S34) Future region-to-destination city matrix estimation: Total predicted long-distance traffic volume associated with departure city i Can form vectors When using transportation mode b (b=1,2), the matrix of future distances from the internal area of ​​city i to the destination city. Its dimension is Z i ×N D Estimate using the following formula: in, elements in This represents the number of passengers traveling from region z within city i to city j using mode of transportation b (b = 1, 2).

5. The method for predicting and optimizing long-distance passenger volume at multiple railway passenger hubs based on departure schedules, as described in claim 4, is characterized in that... S4) Hub Selection: Based on the current travel time and cost from the urban area to each hub, the travel time from each hub to the destination city, train fares and departure frequencies, and combined with the decomposed long-distance railway passenger volume and the current passenger volume of each hub, a discrete selection model is fitted; then, using the fitted model, the corresponding time and cost for the planning period, and the decomposed long-distance railway passenger volume, the future long-distance passenger volume of each railway passenger hub is predicted; the specific steps are as follows: S41) Region-to-hub utility value: Within city i, the average travel time, average cost, and spatial distance from region z to hub h are respectively... and and The corresponding benefit value calculation parameters are set according to the mode of transportation b (b=1,2). and The utility value from region to hub is calculated using the following formula: S42) Hub-to-Destination Utility Values: In city i, using mode of transport b (b=1,2), the average travel time, average train fare, and number of train departures to destination city j via hub h are respectively... and The corresponding benefit value calculation parameters are as follows: and Before calculating the utility value, it is necessary to clarify that when there are 0 departures to the destination city j, the utility value of the hub is also 0. A variable representing the presence or absence of departures needs to be defined. The utility value from hub to destination is calculated using the following formula: S43) Hub Selection Probability: The probability q of a passenger choosing hub h when departing from region z within city i and using transportation mode b (b=1,2) to reach destination city j. bizhj Calculate using the following Logit formula: In the formula, γ = -∞, when hour, The parameters of the Logit formula above are fitted using the trust region reflection algorithm, and the objective function for minimizing the loss during fitting is E. 3,bi for: S44) Predict long-haul passenger volume at the hub: based on the already fitted Logit formula and the predicted or planned data. and Estimate the probability of hub selection when using mode of transportation b (b=1,2) in the future. And predict the long-distance traffic volume from hub h within departure city i to destination city j.

6. The method for predicting and optimizing long-distance passenger volume at multiple railway passenger hubs based on departure schedules, as described in claim 5, is characterized in that... G1) Feasible Solution Construction and Initial Scheme Generation: Using a departure frequency matrix with hubs as rows and destination cities as columns as decision variables, a feasible solution is represented by the following steps. Within the constraints, departure frequency matrices for high-speed and conventional railways are randomly generated as initial solutions, where matrix elements represent the specific number of departures for the corresponding train type. G11) Let the optimized departure schedule matrix be x. bi =(x bihj ), its dimension is H i ×N D The structure of the feasible solution is X i =(x 1i ,x 2i (), composed of a departure schedule matrix for high-speed and conventional railways, x bihj There is also a certain range of variation. The current departure schedule, obtained from the train ticketing platform, is as follows: Let the lower limit coefficient and the upper limit coefficient be τ respectively. m (0<τ m <1) and τ M (τ M >1), x bihj The range of variation is constrained as follows: Randomly select an integer as x within the above range. bihj The initial feasible solution.

7. The method for predicting and optimizing long-distance passenger volume at multiple railway passenger hubs based on departure schedules, as described in claim 6, is characterized in that... G2) Optimization Model Construction: The number of train departures from each hub to each destination city is used as the decision variable. The root mean square error between the actual saturation and the reasonable saturation of each hub is used as the objective function. Simultaneously, constraints are set for the upper limits of individual hub dispatch capacity, combined hub dispatch capacity, and train dispatch capacity. The specific steps are as follows: G21) Maintain and Unchanged, obtained through calculation Then, calculate the utility value from the hub to the destination. Further, following the Logit formula already fitted in the hub fitting step, calculate q. bizhj and Finally, calculate the objective function and make a judgment. Does the constraint satisfy? Within departure city i, the reasonable saturation level for hub h is υ. h The corresponding maximum sending capacity is The objective function is calculated as follows: The main constraints of the G22 optimization model include the following three constraints: 1) Maximum sending capacity of a single hub: The long-distance sending volume of each hub should not exceed the hub's own maximum number of passengers it can send. Right now: 2) Maximum Train Capacity: High-speed and conventional railway trains have a certain maximum number of passengers they can carry. Therefore, the average passenger capacity per train pair, i.e., the ratio of the predicted long-distance passenger volume from hub h high-speed or conventional railway to each destination city to the number of train departures, should not exceed [a certain value]. Right now: 3) Upper limit constraint on the transmission capacity of the combined hub: The city is divided into multiple clusters and merged into a cluster set C. The predicted long-distance transmission volume of any cluster c (c∈C) should not be lower than the lower limit of the cluster's transmission capacity. and should not be higher than the top limit Right now: G23) to make X i In the optimization iteration process of heuristic algorithms, three constraints are satisfied, and a penalty function is introduced to improve the objective function: In the formula, ξ1, ξ2, and ξ3 are the penalty coefficients for the upper limit constraints of the single hub's dispatch capacity, train dispatch capacity, and combined hub dispatch capacity, respectively. When X i When some constraints are not satisfied, the portion that breaks the constraints will increase the objective function value, making X... i The quality of these components declines and they are gradually phased out during iterative optimization.

8. The method for predicting and optimizing long-distance passenger volume at multiple railway passenger hubs based on departure schedules, as described in claim 7, is characterized in that... G3) Heuristic Algorithm Solution: Based on the initial solution, the tabu search algorithm is used to search for the departure matrices of high-speed and conventional railways that satisfy the constraints, thereby determining the optimal departure schedules from each hub to each destination city under different train systems. Furthermore, the optimized long-distance passenger volume for each hub within a city is calculated. The specific steps are as follows: In the iterative optimization process using the tabu algorithm (G31), the following four neighborhoods are constructed sequentially at each step to increase the diversity of feasible solutions: 1) Random neighborhood: directly based on x bihj The range of variation constraints randomly generate new feasible solutions X i The number of feasible solutions generated is n R The neighborhood is denoted as R; 2) Perturbation neighborhood: for local optimal solutions To generate a new feasible solution, a random perturbation is performed, and the perturbation rate is ω. turb (0<ω turb <1), the number of feasible solutions generated is n T The specific method is as follows: Set X i Chinese x bi The number of elements is H i ×N D Randomly select ω turb ×H i ×N D Elements, according to range Replace the current value with a randomly selected integer, x. 1i and x 2i The same operation needs to be performed for all cases; repeat the above steps to obtain n. T There are 1 feasible solutions, and the resulting neighborhood representation is: 3) Internal exchange neighborhood: Exchange elements of any two feasible solutions to generate two new feasible solutions. Let the exchange rate be ω. internal The number of generation times is n I The specific method is as follows: from the set Extract any two feasible solutions X′ from the middle i and X″ i Each randomly selects ω internal ×H i ×N D For each element, swap the elements x′ of two feasible solutions simultaneously using the following formula. bihj and x′ bihj : In the formula, For a temporarily feasible solution element, repeat the above steps n. I The second time, 2n was obtained. I There are 1 feasible solution, and the resulting neighborhood is represented as I(A); 4) External Neighborhood Exchange: Exchange the departure matrix x of any two feasible solutions. 1i and x 2i Two new feasible solutions are generated, and the number of generation times is n. E The specific method is as follows: extract any two feasible solutions X′ from set A. i and X″ i By exchanging the high-speed rail departure matrix, we obtain X′. i =(x″ 1i ,x′ 2i ), X″ i =(x′) 1i ,x″ 2i Repeat the above steps n. E The second time, 2n was obtained. E There are 1 feasible solution, and the resulting neighborhood is represented as E(A); (G32) Before performing iterative optimization, a taboo list B is set. When a feasible solution in the neighborhood is selected as a local optimum, it is added to the taboo list. In the subsequent n iterations... tabu If the same feasible solution reappears in the next iteration, it cannot be selected as a local optimum. tabu Remove it from the taboo list after the next iteration; The iterative optimization steps of the G33 tabu algorithm are as follows: 1) Generate an initial feasible solution Set a local optimum and the global optimal solution 2) Generate random neighborhood R and perturbation neighborhood And form a neighborhood set Generate the internal exchange neighborhood I(A) and the external exchange neighborhood E(A); 3) Calculate the feasible solutions corresponding to the minimum objective function values ​​in the neighborhood A′=A∪I(A)∪E(A) that are not in the taboo list B, and set them as local optima. 4) If satisfied set up 5) Add to taboo list B, check B, and add the existing n tabu Remove feasible solutions from B in the next iteration, and repeat steps 2-5 until the number of iterations exceeds the maximum number of iterations M. Iter , This will be output as the optimal departure schedule. get Then, q is calculated according to the fitted Logit formula obtained in the hub selection step of long-distance traffic forecasting. bizhj and To further obtain the long-distance transmission volume and saturation of each hub in the future.

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