Passenger flow distribution-based high-speed rail out-of-advance-sale-period dynamic pricing method

Abstract

The invention relates to the technical field of traffic, and discloses a passenger flow distribution-based high-speed rail out-of-advance-sale-period dynamic pricing method, which comprises the following steps of: optimizing dynamic pricing and passenger flow distribution under the same framework for a ticket price floating scene out of the pre-sale period, and designing a four-dimensional supply and demand space-time service network considering passenger classification, a bidirectional parallel breadth-first path search method and a passenger travel generalized cost formula are put forward, a differential dual-target pricing model outside a pre-sale period is constructed and converted into a single-target problem, and a passenger flow distribution method based on reality guidance and multi-term Logit is adopted for solving. Meanwhile, a ticket price rate dynamic optimization method based on simulated annealing is adopted to adjust the current ticket price rate of the train so as to output the optimal ticket price rate and the optimal solution; according to the method, the multi-target ticket price optimization problem of traffic flow matching is considered from reality, and the feasibility and scientificity of dynamic pricing outside the pre-sale period of the high-speed rail are improved.

Description

Technical Field

[0001] The present invention relates to the technical field of transportation, and particularly to a dynamic pricing method for high-speed trains outside the advance booking period based on passenger flow distribution. Background Art

[0002] Currently, there are complex problems with the fare floating mechanism of high-speed trains, specifically: (1) there are many restrictions in aspects such as the types of lines, the range of trains, and the price floating range applicable to fare floating; (2) the current fare floating mechanism does not fully conduct differential pricing according to market segmentation, resulting in slow improvement in overall revenue; (3) the diversity of management tools and the complexity of decision-making processes in the process of price work practice make the idealized price floating models produced by existing research unable to fully adapt to actual pricing work, and it is difficult to ensure the achievement of expected revenue; (4) there are many factors related to railway transportation management in the existing fixed fare scheme, resulting in the current fare floating mechanism mostly being a small-range floating strategy based on subjective experience, lacking scientific classification criteria and theoretical support, and lacking an overall idea and adjustment strategy for optimizing fare floating for large-scale complex railway networks. Summary of the Invention

[0003] In view of the above deficiencies in the prior art, the present invention provides a dynamic pricing method for high-speed trains outside the advance booking period based on passenger flow distribution. For the fare floating scenario outside the advance booking period, dynamic pricing and passenger flow allocation are optimized in the same framework. A four-dimensional supply-demand spatio-temporal service network considering passenger classification is designed, a bidirectional parallel breadth-first path search method and a generalized cost formula for passenger travel are proposed, a differential dual-objective pricing model outside the advance booking period is constructed and converted into a single-objective problem, and a passenger flow allocation method based on reality orientation and multinomial Logit is used for solution. At the same time, a dynamic optimization method for fare rates based on simulated annealing is used to adjust the current fare rates of trains, effectively alleviating problems such as low revenue and unscientific fare floating mechanisms existing in the existing fare schemes.

[0004] In order to achieve the above object of the invention, the technical solution adopted by the present invention is:

[0005] A dynamic pricing method for high-speed trains outside the advance booking period based on passenger flow distribution, comprising the following steps:

[0006] S1. Divide OD levels and train levels respectively, and set different fare rate adjustment ranges for trains of different levels;

[0007] S2. Obtain the initial fare rates of trains, and update the initial fare rates of trains according to the fare rate adjustment ranges;

[0008] S3. Based on the updated train fare rates, establish a price-demand function to correct the OD passenger flow;

[0009] S4. Based on the corrected OD passenger flow volume, construct a four-dimensional supply-demand spatio-temporal service network considering passenger classification, and use the bidirectional parallel breadth-first path search method to screen reasonable service paths to generate a set of reasonable service paths;

[0010] S5. By obtaining the ticket price, travel time, departure time, arrival time, and comfort level, calculate the generalized travel cost of passengers under each reasonable service path;

[0011] S6. Based on the train timetable data, and combining the generalized travel cost of passengers and the corrected OD passenger flow volume under each reasonable service path, construct a bi-objective function of maximizing enterprise revenue and minimizing passenger travel cost and convert it into a single-objective problem, and at the same time set constraint conditions;

[0012] S7. Based on the single-objective problem and constraint conditions, use the passenger flow allocation method based on reality orientation and multinomial Logit to perform passenger flow allocation, and output the current optimal solution and the current ticket price rate of the train;

[0013] S8. Use the dynamic optimization method of ticket price rate based on simulated annealing to adjust the current ticket price rate of the train to generate an updated train ticket price rate and the current iteration solution. After calculating the objective difference between the current iteration solution and the current optimal solution, judge whether the iteration condition is satisfied to output the optimal ticket price rate and the optimal solution under the optimal ticket price rate.

[0014] The present invention has the following beneficial effects:

[0015] 1. A dynamic pricing method for high-speed rail outside the pre-sale period based on passenger flow allocation proposed by the present invention conducts a coupled correlation analysis of passengers and enterprises based on ticket price floating, optimizes dynamic pricing and passenger flow allocation in a unified framework, and at the same time, based on the traditional two-dimensional spatio-temporal service network, incorporates seat attributes and passenger classification to construct three-dimensional and four-dimensional supply-demand spatio-temporal service networks, improving the accurate description ability of passenger selection behavior and optimizing the matching degree of the supply-demand market;

[0016] 2. A bi-objective pricing model for enterprises and passengers facing the outside of the pre-sale period is established from the perspective of game theory, reducing the idealization deviation of the existing mathematical model; at the same time, a bidirectional parallel breadth-first path search method and a passenger flow allocation method based on reality orientation and multinomial Logit are designed, enhancing the feasibility of the ticket price optimization method from theoretical feasibility to practical application in large-scale networks in China. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 is a schematic flow chart of a dynamic pricing method for high-speed rail outside the pre-sale period based on passenger flow allocation proposed by the present invention;

[0018] Figure 2 is a schematic diagram of a three-dimensional supply-demand spatio-temporal service network of a time segment in the embodiment;

[0019] Figure 3 Schematic diagram of a four - dimensional supply - demand spatio - temporal service network considering passenger classification in the embodiment

[0020] Figure 4 Schematic diagram of a one - transfer path search in the embodiment Specific implementation manners

[0021] The following describes the specific implementation manners of the present invention to facilitate those skilled in the art of this technology to understand the present invention. However, it should be clear that the present invention is not limited to the scope of the specific implementation manners. For those of ordinary skill in the art of this technology, as long as various changes are within the spirit and scope of the present invention defined and determined by the appended claims, these changes are obvious, and all inventions and creations using the concept of the present invention are within the scope of protection.

[0022] As Figure 1 shown, a dynamic pricing method for high - speed rail outside the advance sale period based on passenger flow distribution includes the following steps S1 - S8:

[0023] S1. Divide the OD levels and train levels respectively, and set different fare rate adjustment ranges for trains of different levels.

[0024] Specifically, step S1 specifically includes S11 - S14:

[0025] S11. Based on the arrival and departure passenger flows, the number of arrival and departure trains, the GDP and population of the urban nodes to which the stations belong, determine the levels of each station along the line, and divide them into large stations, medium - sized stations, and small stations.

[0026] S12. According to the station levels, determine the OD levels, and divide them into large - station OD, medium - sized - station OD, and small - station OD.

[0027] S13. According to the types, quantities, and proportions of stations served by the trains, determine the train levels and OD levels, and divide them into large - station trains, medium - sized - station trains, and small - station trains respectively.

[0028] S14. Based on historical fare rates, actual operation conditions, and passenger willingness, set the fare rate adjustment ranges for trains of different levels.

[0029] In this embodiment, it is for setting the train fare rate adjustment strategy based on pedigree. That is, according to the station level, the level and quantity of the stopping stations, the train level and OD level are respectively divided, so as to set different fare rate adjustment ranges [r1, r2] for trains of different levels. The principle is as follows: The serialization of high-speed trains refers to forming a series of train products with different technical parameters, functions and service characteristics for different demands and application scenarios to meet the multi-level and diversified travel needs of passengers and realize the standardization, modularization and serialization of train products. Among them, the classification criteria for train serialization include multiple dimensions such as travel speed, stop pattern, operating distance, departure frequency, etc.; The train fare adjustment strategy considering serialization classifies trains based on the stop pattern and the number of stops. Trains of different levels have different fare rate adjustment ranges, and the fare rate adjustment ranges of trains of the same level can be further subdivided by combining elements such as historical passenger flow and historical turnover. That is: First, based on factors such as the arrival and departure passenger flow of stations, the number of arrival and departure trains, the GDP and population of the urban nodes to which they belong, determine the level of each station along the line, generally divided into large stations, medium stations, and small stations; Second, according to the type, quantity, and proportion of stations served by trains, determine the train level, generally divided into large station trains, medium station trains, and small station trains. Similarly, OD is generally divided into large station OD, medium station OD, and small station OD. The operating conditions of different lines are different, and the train serialization classification criteria are different; Finally, combine historical fare information (historical fare rate, actual operating conditions, and passenger willingness in questionnaire surveys) to set the fare rate adjustment ranges for different types of trains. Among them, OD (Origin-Destination) is the starting and ending points of transportation trips.

[0030] S2. Obtain the initial train fare rate and update the initial train fare rate according to the fare rate adjustment range.

[0031] Specifically, step S2 specifically includes:

[0032] Obtain the initial train fare rate, and judge whether the initial train fare rate is within the fare rate adjustment range. If so, update the train fare rate to the initial train fare rate; otherwise, judge whether the initial train fare rate is less than the lower bound of the fare rate adjustment range. If so, update the train fare rate to the lower bound of the fare rate adjustment range; otherwise, update the train fare rate to the upper bound of the fare rate adjustment range, and finally obtain the updated train fare rate.

[0033] In this embodiment, the initial train fare rate is r0. If it is the first iteration, first judge whether r0 is within [r1, r2]. If r0 ∈ [r1, r2], then update the train fare rate r to the initial train fare rate, that is, r = r0; If and r0 > r2, then r = r2; If and r0 < r1, then r = r1. Among them, the units of r0, r, r1, and r2 are yuan / km.

[0034] S3. Based on the updated train fare rate, establish a price-demand function to correct the OD passenger flow volume.

[0035] Specifically, the price-demand function in step S3 is:

[0036]

[0037] where p represents the fare, and f w (p) represents the passenger flow volume of ODw (corrected OD passenger flow volume) when the fare is p, η represents the passenger fare sensitivity coefficient, which is related to the seat class, and p w,z,0 represents the initial average fare of seat z of ODw, and q w,z,0 represents the initial passenger flow volume of seat z of ODw.

[0038] In this embodiment, the principle of establishing the price-demand function is as follows: the floating of the high-speed rail fare has a direct impact on the passenger flow demand. When the fare decreases, it will attract potential passengers to choose high-speed rail for travel; when the fare increases, it may cause some existing passengers to switch to other transportation modes, resulting in the loss of passenger flow. Therefore, quantitatively describing the relationship between the fare and the passenger flow demand is of great significance for the operation decision-making, revenue management, and service quality improvement of high-speed rail transportation enterprises.

[0039] In the high-speed rail passenger transport market, an elastic demand function is commonly used to describe the sensitivity of passengers to fares. The meaning of elastic demand is the percentage change in the market demand volume caused by a 1% change in the commodity price, or the reaction degree of the change in the commodity demand volume to the price change. The elastic demand function can flexibly show the reaction degree of passengers to fares in different market environments, thus providing a scientific basis for high-speed rail transportation enterprises to formulate reasonable fare strategies; therefore, the established high-speed rail price-demand function is

[0040] S4. Based on the corrected OD passenger flow volume, construct a four-dimensional supply-demand spatio-temporal service network considering passenger classification, and use the bidirectional parallel breadth-first path search method to screen reasonable service paths to generate a set of reasonable service paths.

[0041] Specifically, step S4 specifically includes S41 - S43:

[0042] S41. Construct a three-dimensional supply-demand spatio-temporal service network including time, space, and seats.

[0043] S42. Based on the three-dimensional supply-demand spatio-temporal service network, classify passengers, and classify the passenger categories and seat categories according to different colors to construct a four-dimensional supply-demand spatio-temporal service network considering passenger classification.

[0044] In this embodiment, the design principles of steps S41 - S42 are as follows: It is known that the spatio - temporal service network is a travel service network with time - window constraints based on the train timetable for passengers to choose from. The train timetable is strictly constrained by time (such as arrival time, departure time, transfer time, etc.) and space (such as departure station, arrival station, transfer station, etc.). The traditional two - dimensional train service network formed based on the train timetable includes time attributes (such as departure time, arrival time, in - transit time, transfer time, etc.) and space attributes (such as departure station, arrival station, transfer station, etc.). From the perspective of passengers, different seat classes correspond to different service qualities for the same OD and the same train; from the perspective of the enterprise, different seat classes correspond to different travel costs and different fare revenues for the same OD and the same train.

[0045] Based on the traditional train service network, a three - dimensional supply - demand spatio - temporal service network is constructed, incorporating the seat service supply resources of passenger tickets (such as business class, first - class, second - class, moving sleeper, etc.). The three - dimensional extended service network is a dynamic weighted directed graph composed of a set of spaces, a set of times, a set of trains, a set of seat classes, a set of service arcs, a set of service nodes, a set of service - arc impedances, etc. Specifically, as Figure 2 shown Figure 2 shows the service supply situation of an intercepted time segment, that is: the time attribute consists of the seat sale time, the train departure time, and the train arrival time; the space attribute consists of the physical station nodes providing seat services; the service - level attribute consists of the train seat classes; Figure 2 The three - dimensional directions of

[0046] represent time, space, and seat supply respectively. With the increasing diversification and personalization of passengers' travel demands, there are significant differences among different passengers in terms of travel time, seat selection, price sensitivity, and service requirements. Business passengers focus on time efficiency and comfort, leisure passengers focus on cost - performance and experience, and commuter passengers focus on punctuality and convenience. Facing the diverse passenger - flow demands of large - scale complex operation networks, in order to accurately identify the types and demand characteristics of passengers, based on Figure 2 , passengers are classified, and a four - dimensional supply - demand spatio - temporal service network considering passenger classification is constructed. The four - dimensional supply - demand spatio - temporal service network can comprehensively reflect the complexity of the high - speed rail transportation system, has better dynamic adjustment capabilities, realizes the transformation from general service to personalized service, and the upgrade from static planning to dynamic adjustment, thus better meeting the supply - demand fit of the high - speed rail transportation market and enhancing the overall performance and service quality of the high - speed rail transportation system. Specifically, as Figure 3As shown, to highlight the supply-demand elements, the passenger categories and seat categories are classified and drawn in different colors. Among them, the passenger categories are divided into three categories: i1, i2, and i3, which are drawn in green, purple, and yellow respectively; the seat categories are divided into two categories: S1 and S2, which are drawn in blue and gray respectively; T1, T2, and T3 represent time attributes, that is, the departure time and arrival time; A, B, C, and D all represent spatial attributes, that is, the stations.

[0047] In addition, since the search scale of the spatio-temporal service network grows exponentially with the increase in the number of stations and trains, to reduce the number of redundant routes in the search process and improve the efficiency of the route search algorithm, this embodiment proposes a bidirectional parallel breadth-first search method in step S43. Its search principle is to first search for direct routes and then search for transfer routes. In each search process, the arc sets are expanded in parallel from the departure station and the arrival station. When the two expanded arc sets overlap, the single-path search process ends. The bidirectional parallel breadth-first path search taking the direct path search and the one-transfer path search as examples is specifically as follows:

[0048] S43. Based on the four-dimensional supply-demand spatio-temporal service network considering passenger classification, use the bidirectional parallel breadth-first path search method to screen reasonable service paths and generate a set of reasonable service paths, specifically S431 - S437:

[0049] S431. Take the line information, the corrected OD passenger flow, and the train timetable as inputs.

[0050] S432. Randomly select an OD from all ODs, use it as the current OD, and for the current OD, traverse all trains to search for trains t that serve both the departure station s o and the arrival station s d , and satisfy the stop order: index(t, s o ) < index(t, s d ). Take all the direct arc segments between the departure stations and arrival stations that meet the stop order as direct paths to generate a set of direct paths, that is:

[0051] Z1 = (o, d, l1)

[0052] where index(t, s o ) represents the stop order of the departure station s o in train t, its originating station is 1, and it increments by one each time after that. index(t, s d ) represents the stop order of the arrival station s d in train t. Z1 represents the set of direct paths, o represents the departure station, d represents the arrival station, and l1 represents the direct path.

[0053] In this embodiment, a direct path search is performed, that is, for the current OD, all trains are traversed to search for direct arcs between the departure station and the terminal station, so as to add the direct arcs that meet the travel needs of passengers to the direct path set.

[0054] S433: Determine whether to perform a transfer route search. If so, execute step S434; otherwise, execute step S435.

[0055] In this embodiment, if only a direct path is searched, step S435 may be directly executed.

[0056] S434, for the current OD, traverse the transfer intermediate station s i , search for departure stations serving both Transfer station Train t1, and traverses the intermediate stations for transfer at the same time Arrival Station Train t2 is selected, and according to the transfer standard, the arcs from the departure station to the transfer intermediate station and from the transfer intermediate station to the arrival station are merged as transfer paths to generate a transfer path set, namely:

[0057] Z2=(o,d,l2)

[0058] Among them, Z2 represents the transfer path set, and l2 represents the transfer path.

[0059] The transfer standards are:

[0060] Train t1 service departure station Transfer station And the docking sequence is:

[0061] And train t2 serves transfers to intermediate stations Arrival Station And the docking sequence is:

[0062] And train t1 is at the transfer station Arrival time Earlier than train t2 at the transfer station Departure time Right now:

[0063] And train t1 is at the transfer station Arrival time Subtract train t2 at the transfer station Departure time Greater than or equal to the minimum passenger transfer time interval at the transfer station.

[0064] In this embodiment, for the one-time transfer path search, that is, for the current OD, the loop is traversed and superimposed to search for the transfer arcs between the departure station and the arrival station, so as to add the transfer arcs that meet the travel needs of passengers to the transfer path set. Specifically, as Figure 4 shown, Figure 4 in the transfer station set is (TA, TB, TC, TE, TF), and the transfer train set is (t1 - t7).

[0065] S435. Screen the direct path set or the transfer path set respectively, delete the service paths that do not meet the reasonable path determination criteria, and at the same time eliminate the service paths with a transport capacity of 0; among them, the reasonable path determination criteria are transfer times constraint, transfer time constraint, non-repeated section constraint of the path, transfer station capacity constraint, non-repeated transfer nodes, and non-repeated transfer trains.

[0066] In this embodiment, considering the rationality of the path itself and the transport organization rules, the direct path set and the transfer path set are screened. Since illogical situations such as repeated transfer stations, transfer trains, and sections will not occur in reality, the screening criteria include non-repeated transfer nodes, non-repeated transfer trains, transfer times constraint, transfer time constraint, non-repeated section constraint of the path, transfer station capacity constraint, etc., and at the same time, unreasonable and service paths with a transport capacity of 0 are removed.

[0067] S436. Merge the screened direct path set and the transfer path set to generate a reasonable service path set, and add it to the current OD attribute.

[0068] S437. Determine whether all ODs have completed the service path search. If so, end the search; otherwise, execute step S431.

[0069] S5. Calculate the generalized travel cost of passengers under each reasonable service path by obtaining the fare, travel time, departure time, arrival time, and comfort level.

[0070] In this embodiment, the generalized travel cost of passengers is affected by multiple factors such as fare economy, time rapidity, transfer convenience, and seat comfort. Therefore, factors such as fare, travel time, departure time, arrival time, and comfort level are uniformly converted into price costs for calculation to calculate the generalized travel cost of passengers, as follows:

[0071] Specifically, the formula for calculating the generalized travel cost of passengers under each reasonable service path in step S5 is:

[0072]

[0073] Among them, C i,rDenotes the generalized travel cost for passenger i to choose route r, in yuan, c i,r,price Denotes the fare cost for passenger i to choose route r, in yuan, c i,r,traveltime Denotes the travel time cost for passenger i to choose route r, in yuan, c i,r,departtime Denotes the departure time cost for passenger i to choose route r, c i,r,arrivetime Denotes the arrival time cost for passenger i to choose route r, in yuan, c i,r,comfort Denotes the comfort cost for passenger i to choose route r, in yuan, α i,1 、α i,2 、α i,3 、α i,4 、α i,5 All denote the passenger choice parameters of passenger i, and their sum is 1, P i,r Denotes the fare cost for passenger i to choose route r, in yuan, d i,r Denotes the travel distance for passenger i to choose route i, in kilometers, τ r,rate Denotes the fare rate of route r, in yuan per kilometer, T i,r Denotes the total travel time for passenger i to choose route r, in hours, κ value Denotes the value of passenger time, in yuan per hour, T i,r,train Denotes the train operation time for passenger i to choose route r, in hours, T i,r,transfer Denotes the transfer time for passenger i to choose route r, in hours, k represents different departure time periods, such as k ∈ {1, 2, 3, 4, 5} for 6:00 - 8:00, 8:00 - 11:00, 11:00 - 14:00, 14:00 - 16:00, 16:00 - 19:00, ω d,k Denotes the travel time period preference parameter, P d,k Denotes the expected fare for the travel time period, in yuan, k′ represents different arrival time periods, such as k′ ∈ {1, 2, 3, 4, 5} for 8:00 - 11:00, 11:00 - 14:00, 14:00 - 16:00, 16:00 - 19:00, 19:00 - 20:00, ω a,k′ Denotes the arrival time period preference parameter, P a,k′ Denotes the expected fare for the arrival time period, in yuan, H recovery Denotes the passenger fatigue recovery function, H i,value Denotes the unit - time fare function for passenger i to choose route r, M represents the maximum passenger fatigue recovery time, in hours, ζ represents a dimensionless parameter, e represents the exponential function, δ represents the fatigue recovery time intensity coefficient, in per hour h -1 。

[0074] S6. Based on the train timetable data, combined with the generalized travel cost of passengers under each reasonable service path and the corrected OD passenger flow, construct a bi-objective function that maximizes the enterprise revenue and minimizes the passenger travel cost, and convert it into a single-objective problem, while setting the constraint conditions.

[0075] Specifically, step S6 specifically includes S601 - S613:

[0076] S601. Based on the generalized travel cost of passengers under each reasonable service path, the corrected OD passenger flow, and the train timetable data, construct a bi-objective function that maximizes the enterprise revenue and minimizes the passenger travel cost, that is:

[0077]

[0078] Among them, F represents the enterprise revenue, E represents the passenger travel cost, maax represents taking the maximum value, min represents taking the minimum value, p w,r represents the fare for passengers of ODw choosing path r, in yuan, f w,r represents the passenger flow of ODw choosing path r, in people, C w,r represents the generalized travel cost of passengers of ODw choosing path r, in yuan.

[0079] In this embodiment, the floating of high-speed rail train fares is affected by many factors. When modeling, it is assumed that the research object only includes high-speed rail trains, without involving the game competition between other transportation modes, and the overbooking situation is not considered. Therefore, for the enterprise, the optimization goal of the model is to maximize the enterprise revenue, and F represents the optimization goal related to the enterprise income. Therefore, for passengers, the optimization goal of the model is to minimize the passenger travel cost, and E represents the optimization goal related to the passenger benefit.

[0080] S602. Convert the bi-objective function into a single-objective problem and construct the total objective function, that is:

[0081]

[0082] Among them, G represents the total objective function, that is, the total railway revenue, respectively represent the passenger ideal goal and the enterprise ideal goal, and the passenger ideal goal is calculated from the generalized travel cost formula and the travel cost-benefit expectation, and the enterprise ideal goal is calculated from the historical revenue of the line and the fare floating benefit expectation.

[0083] In this embodiment, due to the conflict and uncertainty between the above-mentioned dual-objective functions of maximizing enterprise revenue and minimizing passenger travel costs, the multi-objective problem is converted into a single-objective problem, and the total objective function is denoted as G. Different from the multi-objective Pareto optimization idea, the single-objective problem is directly solved instead of obtaining a set of non-dominated solutions. On the one hand, it can reduce the problem complexity and avoid problems such as slow convergence and easy entrapment in local optima that may occur in multi-objective algorithms; on the other hand, it enhances the adaptability and flexibility of the model. The composition of the total objective function G can be flexibly adjusted according to different scenario requirements, and it is also more robust in dealing with uncertainties (such as sensitivity analysis).

[0084] S603. Establish a fare floating constraint, that is:

[0085]

[0086] wherein, represents the initial fare for passengers on ODw choosing path r, with the unit of yuan, n represents the maximum fare reduction ratio, m represents the maximum fare increase ratio, and n and m are related to the train class and seat class.

[0087] In this embodiment, an overly high fare will hinder passengers' willingness to choose travel, and an overly low fare will weaken the enterprise's profitability; therefore, the upper and lower limits of fare floating for different train classes and different seat classes are different.

[0088] S604. Establish a non-inverted fare constraint, that is:

[0089]

[0090] wherein, v represents a station, belonging to path r, and the station v is located between the departure station o and the arrival station d, p (o,v),r represents the fare for passengers on OD(o, v) choosing path r, with the unit of yuan, p (v,d),r represents the fare for passengers on OD(v, d) choosing path r, with the unit of yuan, p (o,d),r represents the fare for passengers on OD(o, d) choosing path r, with the unit of yuan.

[0091] In this embodiment, to ensure the fairness of passengers' travel and the rationality of railway operation, when the seat classes are the same, the fare for short-distance OD should be lower than that for long-distance OD; when the seat classes are the same and the total distance is equal, the sum of the fares for two short-distance OD should not be lower than the fare for one long-distance OD.

[0092] S605. Establish a fare grade constraint, that is:

[0093]

[0094] wherein, It represents the business class fare for passengers on ODw choosing route r, in yuan. It represents the premium first class fare for passengers on ODw choosing route r, which is an intermediate seat class between business class and first class, in yuan. It represents the first class fare for passengers on ODw choosing route r, in yuan. It represents the second class fare for passengers on ODw choosing route r, in yuan.

[0095] In this embodiment, considering factors such as cost and service quality, the fares for different seat classes on the same OD and the same route are different; the fare values for business class, premium first class, first class, and second class decrease successively, with the business class fare being the highest and the second class fare being the lowest.

[0096] S606. Establish the OD passenger flow constraint, that is:

[0097]

[0098] Among them, PF represents the total passenger flow demand of all OD, in persons.

[0099] In this embodiment, the sum of the passenger flows allocated to each reasonable service route for a single OD should not be greater than the passenger flow demand of this OD, and the sum of the allocated passenger flows for all routes should not be greater than the passenger flow demands of all OD.

[0100] S607. Establish the non - negative constraint of route passenger flow, that is:

[0101] f w,r ≥0.

[0102] In this embodiment, according to common sense, the allocated passenger flow for each reasonable service route cannot be negative.

[0103] S608. Establish the train capacity constraint, that is:

[0104]

[0105] Among them, a r represents the passenger - carrying capacity of route r, in persons, a t represents the passenger - carrying capacity of train t, in persons, represents the passenger - carrying capacity of train t1, in persons, represents the passenger - carrying capacity of train t2, in persons.

[0106] In this embodiment, the capacity of the reasonable service route is restricted by the train capacity. The maximum capacity of the direct route is the train capacity, and the maximum capacity of the transfer route is the minimum value of the capacities of all trains.

[0107] S609. Establish the train connection time constraint, that is:

[0108] dep(t2, s) > arr(t1, s)

[0109] Among them, dep(t2, s) represents the departure time of train t2 at transfer station s, and arr(t1, s) represents the arrival time of train t1 at transfer station s.

[0110] In this embodiment, in the transfer path, when two trains are connected at the transfer station, the arrival time of the previous train should be earlier than that of the subsequent train.

[0111] S610. Establish the transfer times constraint, that is:

[0112] y ≤ U, y ∈ N +

[0113] Among them, u represents the number of transfers of passengers, U represents the maximum acceptable number of transfers of passengers, and N + represents positive integers.

[0114] In this embodiment, in the transfer path, the maximum acceptable number of transfers of passengers has an upper limit and is heterogeneous according to different regions, different lines, and different income levels.

[0115] S611. Establish the transfer time constraint, that is:

[0116] e s ≥ E s

[0117] Among them, e s represents the transfer time of passengers at transfer station s, in hours, and E s represents the minimum transfer time of transfer station s, in hours.

[0118] In this embodiment, in the transfer path, sufficient time needs to be reserved for passengers to perform transfer operations at the transfer station.

[0119] S612. Establish the transfer station capacity constraint, that is:

[0120]

[0121] Among them, y represents the y-th time period starting from 0 o'clock, with a duration of 30 minutes, and y = 1, 2,..., 48, represents the transfer passenger flow of passengers of ODw choosing path r within time period y, represents a 0-1 variable, which is 1 if the path r chosen by passengers of ODw includes transfer station s, otherwise 0, and TPF s represents the transfer passenger number threshold of transfer station s, which is determined by the transfer station level.

[0122] S613. Establish a non - repetitive section constraint for the path, that is:

[0123]

[0124] Among them, \(V\) represents the set of all station nodes of the path, and \(V\setminus(sta o , sta d ) represents the set of all station nodes of the path except the starting and ending points. \(sta i represents the \(i\) - th station node of the path, \(sta j represents the \(j\) - th station node of the path, \(sta k1 represents the \(k1\) - th station node of the path. All represent 0 - 1 variables. When it is 1, it means that the section corresponding to the subscript (\(sta i , sta k1 ), (\(sta k1 , sta j ) belongs to the current path; when it is 0, it means it does not belong.

[0125] S7. Based on the single - objective problem and constraint conditions, adopt a passenger flow distribution method based on reality - orientation and multinomial Logit to conduct passenger flow distribution, and output the current optimal solution and the current fare rate of the train.

[0126] In this embodiment, the travel choice behavior of high - speed railway passengers belongs to a discrete choice problem, which is usually described by the Logit model and its variants. Compared with the existing passenger flow distribution methods, the method based on reality - orientation and multinomial Logit adds considerations of actual ticket - selling strategies and common problems in passenger flow distribution in the solution steps, that is: Its advantages are to avoid the occupation of single - car capacity, avoid excessive occupation of transport capacity in a single distribution, and avoid excessive occupation of transport capacity by short - distance OD. The specific solution process is as follows:

[0127] Specifically, step S7 specifically includes S701 - S710:

[0128] S701. Take the corrected OD passenger flow volume and train timetable data as input.

[0129] In this embodiment, the number of OD levels depends on the number of station levels and the service passenger flow level.

[0130] S702. Adjust the OD level based on the actual supply - demand and operation conditions.

[0131] In this embodiment, if a certain OD matches a single - car, that is, only by taking a certain train can the travel needs of passengers be met, then appropriately increase the level of this OD to avoid the problem that passengers of this OD cannot board the train.

[0132] S703. Set the maximum passenger flow allocation volume f per time based on the adjusted OD level. max .

[0133] In this embodiment, due to the limited train capacity, sequential passenger flow allocation may result in a train serving only a single OD or a few ODs with large passenger flows. Therefore, the maximum passenger flow allocation volume f per time is set max to avoid the problem that a single passenger flow allocation occupies too much train capacity.

[0134] S704. Perform passenger flow allocation from high to low based on the adjusted OD level.

[0135] In this embodiment, generally speaking, the passenger flow of high-level ODs is greater than that of low-level ODs, and the coincidence degree of long-distance ODs and high-level ODs is relatively high. Prioritize the allocation of long-distance ODs to conform to the ticketing strategy of "long-distance passengers on long-distance trains" in the 12306 application in reality and avoid the problem that train capacity is occupied by a large number of short-distance ODs.

[0136] S705. Randomly select any OD in the current level as the current OD, and search for the reasonable service path under the current OD attribute based on the set of reasonable service paths.

[0137] In this embodiment, combined with the output result of the bidirectional parallel breadth-first search method, that is, the set of reasonable service paths, search for the reasonable service spatio-temporal path under the current OD attribute.

[0138] S706. Establish a passenger flow allocation formula for multinomial Logit, that is:

[0139]

[0140] Among them, μ represents the selection probability parameter of the multinomial Logit model;

[0141] Then, calculate the selection probability parameter of the multinomial Logit model and perform vehicle flow matching, specifically:

[0142] The theoretical passenger flow allocation volume f theory is the minimum value of the passenger travel demand of OD and the passenger capacity of the train, that is:

[0143] f theory = min{f(OD,demand), f(t,capcity)}

[0144] Among them, f(OD,demand) represents the passenger travel demand of OD, and f(t,capcity) represents the passenger capacity of train t.

[0145] The actual passenger flow allocation volume f actual is the theoretical passenger flow allocation volume f theoryWith the minimum value of the single - maximum passenger flow allocation volume f max , that is:

[0146] f actual = min{f theory , f max}}.

[0147] S707. Update the passenger travel demand of OD and the passenger - carrying capacity of the train, that is:

[0148]

[0149] S708. Retain the OD with the remaining passenger flow greater than 0 and sort them randomly.

[0150] In this embodiment, the purpose of retaining the OD with the remaining passenger flow greater than 0 and sorting them randomly is to avoid the problem that some OD cannot be allocated because they are at the end of the passenger flow allocation queue.

[0151] S709. Judge whether all OD have been traversed at the current OD level. If so, execute step S710; otherwise, execute step S705.

[0152] S710. Judge whether all OD levels have been traversed. If so, output the current optimal solution and the current fare rate of the train; otherwise, execute step S704.

[0153] S8. Use the dynamic optimization method of fare rate based on simulated annealing to adjust the current fare rate of the train, generate the updated train fare rate and the current iteration solution. After calculating the objective difference between the current iteration solution and the current optimal solution, judge whether the iteration condition is satisfied to output the optimal fare rate and the optimal solution under the optimal fare rate.

[0154] In this embodiment, the simulated annealing method is to introduce randomness in the search process, allow accepting inferior solutions with a certain probability, so as to avoid falling into local optima and enhance the global search ability. The overall method starts from a relatively high initial temperature, gradually reduces the temperature, and finally converges to the global optimal solution at the low - temperature stage. Therefore, the dynamic optimization method of fare rate based on simulated annealing is used to adjust the current fare rate of the train, and its specific process is as follows:

[0155] Specifically, step S8 specifically includes S81 - S86:

[0156] S81. Set the minimum temperature T min , the maximum number of iterations L, the convergence threshold Δc, the attenuation factor H. Through pre - heating, calculate the initial temperature T, that is:

[0157]

[0158] Among them, Δx maxdenotes the maximum objective difference in the neighborhood solution, ln denotes the logarithmic function, and Prob denotes the initial acceptance probability;

[0159] S82. Within the fare rate adjustment range and at the initial temperature, randomly perturb the current fare rate of the train to update the current fare rate of the train and generate an updated train fare rate.

[0160] In this embodiment, the lowest temperature T min , the maximum number of iterations L, the convergence threshold Δc, and the attenuation factor H can be adjusted manually, and H is generally 0.95. Among them, preheating is to randomly generate an initial solution and several neighborhood solutions, calculate the objective difference between the neighborhood solution and the initial solution, and based on the initial acceptance probability Prob (usually taking values of 0.8 or 0.9) and the maximum objective difference Δx in the neighborhood solution max , to solve the process of the initial temperature T.

[0161] S83. Based on the updated train fare rate, calculate the total railway revenue and use it as the current iterative solution x2;

[0162] S84. Calculate the objective difference Δx between the current optimal solution x1 and the current iterative solution x2, and determine whether the objective difference Δ is greater than or equal to 0. If so, update the current optimal solution to the current iterative solution, that is: x1 = x2, and execute step S86. Otherwise, execute step S85.

[0163] S85. Calculate the acceptance probability of the inferior solution and determine whether the acceptance probability of the inferior solution is greater than or equal to the convergence threshold. If so, update the current optimal solution to the current iterative solution, that is: x1 = x2, and execute step S86. Otherwise, execute step S82.

[0164] In this embodiment, the acceptance probability of the inferior solution is Exp(-Δx / T), and Exp is the probability.

[0165] S86. Determine whether the lowest temperature T min or the maximum number of iterations L is reached. If so, end the iteration, use the updated train fare rate as the optimal fare rate, and output the optimal fare rate and the optimal solution under the optimal fare rate. Otherwise, after updating the initial temperature to H*T, execute step S82

[0166] In this embodiment, the optimal solution is the total railway revenue, and also includes the passenger flow distribution result (train flow-carrying information and OD boarding information).

[0167] In summary, a dynamic pricing method for high-speed trains outside the pre-sale period based on passenger flow allocation proposed by the present invention conducts a coupled correlation analysis of passengers and enterprises based on fare fluctuations, optimizes dynamic pricing and passenger flow allocation within a unified framework, and at the same time, based on the traditional two-dimensional spatio-temporal service network, incorporates seat attributes and passenger classification to construct three-dimensional and four-dimensional supply-demand spatio-temporal service networks, improving the accurate description ability of passenger choice behavior and optimizing the matching degree of the supply-demand market; from the perspective of game theory, a dual-objective pricing model for enterprises and passengers outside the pre-sale period is established, reducing the idealized deviation of existing mathematical models; at the same time, a two-way parallel breadth-first path search method and a passenger flow allocation method based on reality orientation and multinomial Logit are designed, enhancing the feasibility of the fare optimization method from theoretical feasibility to practical application in China's large-scale network.

[0168] Specific embodiments are applied in the present invention to elaborate on the principles and implementation manners of the present invention. The descriptions of the above embodiments are only used to help understand the method and its core idea of the present invention; at the same time, for those of ordinary skill in the art, according to the idea of the present invention, there will be changes in the specific implementation manners and application scopes. In summary, the content of this specification should not be construed as a limitation to the present invention.

[0169] Those of ordinary skill in the art will realize that the embodiments described herein are for helping readers understand the principles of the present invention, and it should be understood that the protection scope of the present invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific deformations and combinations that do not depart from the essence of the present invention based on the technical revelations disclosed in the present invention, and these deformations and combinations are still within the protection scope of the present invention.

Claims

1. A dynamic pricing method outside the advance booking period of high-speed rail based on passenger flow distribution, characterized in that, The following steps are involved: S1. Divide OD grades and train grades respectively, and set different fare rate adjustment ranges for trains of different grades; S2. Obtain the initial train fare rate, and update the initial train fare rate according to the fare rate adjustment range; S3, based on the updated train fare rate, establish a price demand function to correct the OD passenger flow; S4. Based on the modified OD passenger flow, a four-dimensional supply-demand spatiotemporal service network considering passenger classification is constructed, and a bidirectional parallel breadth-first path search method is used to screen reasonable service paths and generate a set of reasonable service paths; S5. Calculate the generalized cost of passenger travel under each reasonable service path by obtaining the ticket price, travel time, departure time, arrival time and comfort level; S6. Based on the train schedule data, combined with the generalized cost of passenger travel under each reasonable service path and the modified OD passenger flow, a dual objective function of maximizing enterprise revenue and minimizing passenger travel cost is constructed and converted into a single objective problem, and constraints are set at the same time; S7. Based on the single-objective problem and constraints, a passenger flow allocation method based on reality orientation and multi-logit is used to allocate passenger flow, and the current optimal solution and the current fare rate of the train are output; S8. Use the fare rate dynamic optimization method based on simulated annealing to adjust the current fare rate of the train, generate an updated train fare rate and the current iterative solution, calculate the target difference between the current iterative solution and the current optimal solution, and then determine whether the iteration conditions are met to output the optimal fare rate and the optimal solution under the optimal fare rate.

2. The dynamic pricing method outside the advance sale period of high-speed rail based on passenger flow distribution according to claim 1, wherein Step S1 specifically includes: S11. Based on the passenger flow of stations, the number of trains arriving and departing, and the GDP and population of the city nodes to which they belong, the level of each station along the line is determined and divided into large stations, medium stations, and small stations; S12. Determine the OD level according to the station level, and divide it into large station OD, medium station OD, and small station OD; S13. Determine the train grade and OD grade according to the type, quantity and proportion of each type of station served by the train, and divide them into large-station train, medium-station train and small-station train respectively; S14. Based on historical fare rates, actual operating conditions and passenger wishes, set fare rate adjustment ranges for different grades of trains.

3. The dynamic pricing method based on passenger flow distribution outside the advance booking period according to claim 2, wherein Step S2 specifically includes: Get the initial train fare rate, and determine whether the initial train fare rate is within the fare rate adjustment range. If so, update the train fare rate to the initial train fare rate. Otherwise, determine whether the initial train fare rate is less than the lower limit of the fare rate adjustment range. If so, update the train fare rate to the lower limit of the fare rate adjustment range. Otherwise, update the train fare rate to the upper limit of the fare rate adjustment range, and finally obtain the updated train fare rate.

4. The dynamic pricing method outside the advance sale period of high-speed rail based on passenger flow distribution according to claim 3, wherein The price demand function in step S3 is: Among them, p represents the ticket price, and f w (p) represents the passenger flow of ODw when the ticket price is p, η represents the passenger ticket price sensitivity coefficient, and p w,z,0 represents the initial average ticket price of seat z of ODw, and q w,z,0 represents the initial passenger flow of seat z of ODw.

5. The dynamic pricing method based on passenger flow distribution outside the advance booking period according to claim 4, characterized in that Step S4 specifically includes: S41. Construct a three-dimensional supply-demand spatiotemporal service network including time, space and seats; S42. Based on the three-dimensional supply-demand spatiotemporal service network, passengers are classified, and passenger categories and seat categories are classified according to different colors to construct a four-dimensional supply-demand spatiotemporal service network that takes passenger classification into consideration; S43. Based on the four-dimensional supply-demand spatio-temporal service network considering passenger classification, the bidirectional parallel breadth-first path search method is used to screen reasonable service paths and generate a set of reasonable service paths.

6. The dynamic pricing method outside the advance sale period of high-speed rail based on passenger flow distribution according to claim 5, wherein Step S43 specifically includes: S431. Take the line information, the corrected OD passenger flow volume, and the train timetable as inputs; S432. Randomly select an OD from all ODs, use it as the current OD, and for the current OD, traverse all trains to search for trains t that serve both the departure station s o and the arrival station s d , and satisfy the stop order: index(t, s o ) < index(t, s d ). Take all the direct arc segments between the departure stations and arrival stations that satisfy the stop order as direct paths, and generate a direct path set, that is: Z1 = (o, d, l1) Among them, index(t, s o ) represents the stop order of the departure station s o in train t, and index(t, s d ) represents the stop order of the arrival station s d in train t. Z1 represents the set of direct paths, o represents the departure station, d represents the arrival station, and l1 represents the direct path; S433. Determine whether to search for transfer paths. If so, execute step S434; otherwise, execute step S435; S434. For the current OD, traverse the transfer intermediate station s i , search for the train t1 that serves both the departure station and the transfer intermediate station , and traverse the train t2 that serves both the transfer intermediate station and the arrival station . According to the transfer standard, merge the arcs between the departure station and the transfer intermediate station, and between the transfer intermediate station and the arrival station as the transfer path, and generate a set of transfer paths, that is: Z2 = (o, d, l2) Among them, Z2 represents the set of transfer paths, and l2 represents the transfer path; Among them, the transfer criteria are: Departure station of train t1 service And the transfer intermediate station And meet the stopping order as follows: and the train t2 serves the intermediate transfer station and the arrival station and satisfies the stopping order as follows: and the arrival time of train t1 at the transfer intermediate station is earlier than the departure time of train t2 at the transfer intermediate station That is: ​ And the arrival time of train t1 at the transfer intermediate station minus the departure time of train t2 at the transfer intermediate station is greater than or equal to the minimum passenger transfer time interval of the transfer station; ​​ S435. Screen the direct path set or the transfer path set respectively, delete the service paths that do not meet the reasonable path determination criteria, and at the same time eliminate the service paths with a transport capacity of 0; Among them, the reasonable path determination criteria are transfer times constraint, transfer time constraint, non-repetitive section constraint of the path, transfer station capacity constraint, non-repetitive transfer nodes, non-repetitive transfer trains; S436. Merge the screened direct path set and the transfer path set to generate a set of reasonable service paths and add it under the current OD attribute; S437. Determine whether all OD have completed the service path search. If so, end the search; otherwise, execute step S431.

7. The dynamic pricing method outside the advance sale period of high-speed rail based on passenger flow distribution according to claim 6, characterized in that, The formula for calculating the generalized cost of passenger travel under each reasonable service path in step S5 is: Among them, C i,r represents the generalized travel cost for passenger i to choose route r, c i,r,price represents the fare cost for passenger i to choose route r, c i,r,traveltime represents the travel time cost for passenger i to choose route r, c i,r,departtime represents the departure time cost for passenger i to choose route r, c i,r,arrivetime represents the arrival time cost for passenger i to choose route r, c i,r,comfort represents the comfort cost for passenger i to choose route r, α i,1 , α i,2 , α i,3 , α i,4 , α i,5 all represent the passenger selection parameters of passenger i, P i,r represents the fare cost for passenger i to choose route r, d i,r represents the travel distance for passenger i to choose route i, τ r,rate represents the fare rate of route r, T i,r represents the total travel time for passenger i to choose route r, κ value represents the value of passenger time, T i,r,train represents the train operation time for passenger i to choose route r, T i,r,transfer represents the transfer time for passenger i to choose route r, k represents different departure time periods, ω d,k represents the travel time period preference parameter, P d,k represents the expected fare of passengers during the travel time period, k′ represents different arrival time periods, ω a,k′ represents the arrival time period preference parameter, P a,k′ represents the expected fare of passengers during the arrival time period, H recovery represents the passenger fatigue recovery function, H i,value represents the unit time fare function for passenger i to choose route r, M represents the maximum fatigue recovery time of passengers, ζ represents the dimensionless parameter, e represents the exponential function, and δ represents the fatigue recovery time intensity coefficient.

8. The dynamic pricing method outside the advance sale period of high-speed rail based on passenger flow distribution according to claim 7, wherein Step S6 specifically includes: S601. Based on the generalized cost of passenger travel, the corrected OD passenger flow volume, and the train timetable data under each reasonable service path, construct a bi-objective function for maximizing the enterprise revenue and minimizing the passenger travel cost, that is: Among them, F represents the enterprise revenue, E represents the travel cost of passengers, max represents taking the maximum value, min represents taking the minimum value, and p w,r represents the fare for passengers on ODw choosing route r, and f w,r represents the passenger flow of passengers on ODw choosing route r, and C w,r represents the generalized travel cost of passengers on ODw choosing route r; S602. Convert the bi-objective function into a single-objective problem and construct the total objective function, that is: where G represents the total objective function, i.e., the total railway revenue, represent the passenger ideal goal and the enterprise ideal goal respectively; S603. Establish a fare floating constraint, that is: Among them, represents the initial fare for passengers of ODw to choose route r, n represents the maximum fare reduction ratio, and m represents the maximum fare increase ratio; S604. Establish a fare non-inversion constraint, that is: Among them, v represents a station that belongs to path r and is located between the departure station o and the arrival station d, and p (o,v),r represents the fare for passengers choosing path r for OD(o, v), and p (v,d),r represents the fare for passengers choosing path r for OD(v, d), and p (o,d),r represents the fare for passengers choosing path r for OD(o, d); S605. Establish a fare class constraint, that is: Among them, represents the business class fare for passengers from ODw choosing route r, represents the premium first class fare for passengers from ODw choosing route r, represents the first class fare for passengers from ODw choosing route r, represents the second class fare for passengers from ODw choosing route r; S606. Establish an OD passenger flow volume constraint, that is: Among them, PF represents the total passenger flow demand of all OD; S607. Establish a non-negative path passenger flow volume constraint, that is: f w,r ≥0； S608. Establish a train capacity constraint, that is: Among them, a r represents the passenger capacity of path r, and a t represents the passenger capacity of train t, represents the passenger capacity of train t1, represents the passenger capacity of train t2; S609. Establish a train connection time constraint, that is: dep(t2, s) > arr(t1, s) Among them, dep(t2, s) represents the departure time of train t2 at the transfer station s, and arr(t1, s) represents the arrival time of train t1 at the transfer station s; S610. Establish a transfer times constraint, that is: u ≤ U, u ∈ N + Among them, u represents the number of passenger transfers, U represents the maximum number of transfers acceptable to passengers, and N + represents a positive integer; S611. Establish a transfer time constraint, that is: e s ≥E s Among them, e s represents the transfer time of passengers at the transfer station s, and E s represents the minimum transfer time of the transfer station s; S612. Establish a transfer station capacity constraint, that is: where y represents the y-th time period starting from 0 o'clock, represents the transfer passenger flow of passengers choosing route r of ODw within the time period y, represents a 0-1 variable, TPF s represents the transfer passenger number threshold of transfer station s; S613. Establish a non-repetitive section constraint of the path, that is: Among them, V represents the set of all station nodes on the path, and V\(sta o ,sta d ) represents the set of all station nodes on the path except the starting and ending points, and sta i represents the i-th station node on the path, and sta j represents the j-th station node on the path, and sta k1 represents the k1-th station node on the path, All represent 0-1 variables.

9. The dynamic pricing method outside the advance sale period of high-speed rail based on passenger flow distribution according to claim 8, wherein Step S7 specifically includes: S701. Take the corrected OD passenger flow volume and the train timetable data as inputs; S702. Adjust the OD level based on the actual supply-demand and operation conditions; S703. Set the maximum passenger flow allocation per single trip f based on the adjusted OD level max ; S704. Based on the adjusted OD level, perform passenger flow allocation from high to low; S705. Randomly select any OD in the current level as the current OD, and based on the set of reasonable service paths, search for the reasonable service paths under the current OD attribute; S706. Establish the passenger flow distribution formula for multinomial Logit, i.e.: Among them, μ represents the choice probability parameter of the multinomial Logit model; Then, calculate the choice probability parameter of the multinomial Logit model and perform vehicle flow matching, specifically: Theoretical passenger flow allocation volume f theory Is the minimum value of the passenger travel demand between OD and the passenger capacity of the train, that is: f theory = min{f(OD, demand), f(t, capcity)} Among them, f(OD,demand) represents the passenger travel demand of OD, and f(t,capcitu) represents the passenger capacity of train t; Actual passenger flow distribution volume f actual is the theoretical passenger flow distribution volume f theory and the minimum value of the single - maximum passenger flow distribution volume f max That is: f actual = min{f theory , f max}; S707. Update the passenger travel demand of OD and the passenger capacity of the train, i.e.: S708. Retain the OD with the remaining passenger flow greater than 0 and randomly sort them; S709. Determine whether all ODs have been traversed at the current OD level. If so, execute step S710; otherwise, execute step S705; S710. Determine whether all OD levels have been traversed. If so, output the current optimal solution and the current fare rate of the train; otherwise, execute step S704.

10. The dynamic pricing method based on passenger flow distribution outside the advanced booking period according to claim 9, wherein Step S8 specifically includes: S81. Set the minimum temperature T min , the maximum number of iterations L, the convergence threshold Δc, and the attenuation factor H. Through preheating, calculate the initial temperature T, that is: where, Δx max represents the maximum objective difference in the neighborhood solution, ln represents the logarithmic function, and Prob represents the initial acceptance probability; S82. Randomly perturb the current fare rate of the train within the fare rate adjustment range and at the initial temperature to update the current fare rate of the train and generate an updated train fare rate; S83. Calculate the total railway revenue based on the updated train fare rate and use it as the current iteration solution; S84. Calculate the target difference between the current optimal solution and the current iteration solution, and determine whether the target difference is greater than or equal to 0. If so, update the current optimal solution to the current iteration solution and execute step S86; otherwise, execute step S85; S85. Calculate the acceptance probability of the inferior solution, and determine whether the acceptance probability of the inferior solution is greater than or equal to the convergence threshold. If so, update the current optimal solution to the current iteration solution and execute step S86; otherwise, execute step S82; S86. Determine whether the lowest temperature T min or the maximum number of iterations L is reached. If so, end the iteration, take the updated train fare rate as the optimal fare rate, and output the optimal fare rate and the optimal solution under the optimal fare rate. Otherwise, after updating the initial temperature to H*T, execute step S82.

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