CN112529288B - Multi-train differentiated pricing strategy optimization method and system - Google Patents

Multi-train differentiated pricing strategy optimization method and system Download PDF

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CN112529288B
CN112529288B CN202011438109.5A CN202011438109A CN112529288B CN 112529288 B CN112529288 B CN 112529288B CN 202011438109 A CN202011438109 A CN 202011438109A CN 112529288 B CN112529288 B CN 112529288B
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苏焕银
彭舒婷
陶文聪
代慧子
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Wuyi University
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Abstract

The invention discloses a method and a system for optimizing a differentiated pricing strategy of a plurality of trains, wherein the method comprises the following steps: step S1, analyzing time-varying characteristics of travel demands of passengers by using historical ticketing data; step S2, describing the selection behaviors of passengers in different departure time periods among differentially priced multi-trip trains by adopting a plurality of Logit models, and obtaining a time-period travel selection model; step S3, considering that the travel selection of passengers is limited by the transportation capacity of the trains, designing a passenger flow distribution method considering capacity constraint, combining the Logit model, distributing the time-varying demands of the passengers to the trains with the capacity constraint, and obtaining the demands of the passengers on each train; and S4, constructing a double-layer multi-train differentiated pricing optimization model of the inter-city high-speed railway, taking the maximum income of tickets as a target, evaluating the multi-train fare scheme by adopting the passenger flow distribution method of the step S3, calculating an optimization target, and optimizing and adjusting the multi-train fare scheme according to the optimization target.

Description

Multi-train differentiated pricing strategy optimization method and system
Technical Field
The invention relates to a multi-train differentiated pricing optimization method and system for an inter-city high-speed railway, in particular to a multi-train differentiated pricing strategy optimization method and system for passenger selection behaviors under consideration of time-varying requirements and capacity constraints.
Background
In recent years, with the rapid development of high-speed railways, more and more students are beginning to pay attention to the study of the income management problems of the railway transportation industry. However, in view of the complexity and solving difficulty of the practical problem, most students only study the fare optimization problem of one train. Discrete selection models are typically employed to analyze the selection behavior of passengers.
Zhang and Ma et al have studied the pricing problem of group tickets for high speed rail trains, but only consider the passenger demand between the originating and terminating stops of a trip, limiting the application scope of the model. Riss (r.s.)The important role of passenger selection behavior modeling in railway revenue management is described by the et al, and experimental analysis is performed on a single train aiming at the revenue management problem of the French high-speed railway. Zheng and Liu are researched aiming at the fare optimization problem of the Chinese high-speed railway train, a fare optimization method of a single train in a pre-selling period is designed, an optimization model is designed into convex planning, and Lagrange multiplier and KKT conditions are adopted to solve the model. Hetrakul and Cirillo research comprehensive optimization problems of fare floating and seat allocation of railway trains, the method separately calculates the income maximization problem of each train, adopts a latent hierarchical model to describe travel selection behaviors of passengers on ticket purchasing time, and solves by application software LINGO 12.0.
There are also some students studying the fare optimization problem of multiple trains. Qin and Zeng et al research comprehensive optimization methods of multi-train fare floating and seat allocation of a high-speed railway in a pre-selling period, adopt a plurality of logic models to describe the selection behavior of passengers among trains, perform optimization calculation on 4 trains by an example, and solve the problems by adopting an artificial bee colony algorithm, wherein model parameters are directly given, the influence of fare on the selection of ticket purchasing time of the passengers is not considered, and reasonable basis is lacked; hu and Shi et al have studied similar problems and devised a large scale example for analysis, but the solution quality is highly dependent on the initial solution and the global convergence of the algorithm cannot be determined.
None of these studies above consider the time-varying needs of passengers. The passenger demand is a basic link in the income management, and researchers can predict and learn the distribution of the travel demand of the passenger about relevant influencing factors, such as fare, ticket buying time and the like, based on historical ticket selling data, and assume that the travel demand of the passenger has randomness and accords with poisson distribution and the like. In fact, some scholars have considered the time-varying demands of passengers in the optimization of train schedules, optimization of train operation schemes, design of passenger flow distribution methods, and the like. However, in the train fare optimization problem, the time-varying demands have not been fully studied.
In summary, the present situation of fare optimization for railway trains is summarized as follows: (1) More students concentrate on researching fare optimization problems of single trains, and research on differentiated pricing optimization problems of multiple trains is lacking; (2) Passenger demand is typically expressed as elastic demand regarding fare, random demand during pre-sales, etc., whereas passenger demand fluctuation features for different departure periods lack investigation; (3) The convergence stability and the calculation efficiency of the solving algorithm are still to be improved through the problem of optimizing the fare of the large-scale multi-trip train.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide a multi-train differentiated pricing strategy optimization method and system, and the aim of inter-city high-speed railway multi-train differentiated pricing optimization is fulfilled by taking time-varying requirements and passenger selection behaviors under capacity constraint into consideration.
To achieve the above and other objects, the present invention provides a method for optimizing a differential pricing strategy of a plurality of trains, comprising the steps of:
step S1, analyzing time-varying characteristics of travel demands of passengers by using historical ticketing data;
step S2, describing the selection behaviors of passengers in different departure time periods among differentially priced multi-trip trains by adopting a plurality of Logit models, and obtaining a time-period travel selection model;
Step S3, designing a passenger flow distribution method considering capability constraint in consideration of the limitation of the travel selection of passengers on the transportation capability of the trains, and combining the plurality of Logit models to distribute the time-varying demands of the passengers to the trains with the capability constraint to obtain the demands of the passengers on each train;
and S4, constructing a double-layer multi-train differentiated pricing optimization model of the inter-city high-speed railway, taking the income maximization of the tickets as a target, evaluating the multi-train fare scheme by adopting the passenger flow distribution method considering the capacity constraint in the step S3, calculating an optimization target, and optimizing and adjusting the multi-train fare scheme according to the optimization target.
Preferably, in step S1, a statistical regression method is used to obtain the departure time period probability distribution of the passenger demand according to the historical ticketing data.
Preferably, the passenger travel OD pair is denoted as (r, s), r is the upper station, s is the lower station, and the passenger demand in the day of the OD pair (r, s) is denoted as q rs The probability that the passenger demand is in the kth departure period is noted asThe passenger's demand during departure period k is noted +.>Then->
Preferably, in step S2, the set of trains coming at the OD pair (r, S) and proceeding from station r in the kth period is noted asThe running time of train j between OD pairs (r, s) is noted as t rs (j) The fare is marked as c rs (j) The utility of passenger selection train j is expressed as
wherein ,θ1 and θ2 As a parameter, ε j As a random term of the number of items,
according to the principle of multiple Logit models, the time-varying demand of the passengers of the OD pair (r, s) is realizedThe probability of selecting train j is；
Preferably, in step S2, a questionnaire is designed, and the time-lapse selection model parameters are estimated using the questionnaire data.
Preferably, in step S3, the passenger flow distribution method considering the capacity constraint determines the probability of selecting a train by the passenger time-varying demand according to the above-mentioned multiple logic model, and then determines the ratio of the passenger time-varying demand of each outgoing OD pair to be able to be distributed according to the transportation capacity of the train, that is, the ratio of the acceptable passenger time-varying demand of each OD pair to the total passenger time-varying demand of the OD pair, thereby determining the passenger demand F (j, x), 1.ltoreq.x.ltoreq.h (j) -1, j.epsilon.w distributed on each train, and satisfying the following capacity constraint conditions:
F(j,x)≤CA j 。
preferably, in step S3, the mth passenger flow distribution stage is specifically as follows:
step 1, for time-varying demand(r, s) ∈rs, k=7, 8, …,22, constructing an optional train set, denoted +.>
Step 2, for time-varying demand(r, s) ∈rs, k=7, 8, …,22, calculated in the set +_using the multiple Logit model >The probability of selecting the train j is denoted as P (j|r, s, k, m);
step 3, on the premise of meeting the capacity constraint, distributing the unallocated passenger demands to the trains as much as possible and setting each O-D pair to be availableThe distributed demand is equal to the ratio of the O-D to the total demand and is marked as eta m Until a train section is full or passenger demands are fully distributed;
step 4: the number of passengers allocated on each train is calculated. For the passenger demand of the O-D pair (r, s) in the kth departure period, the number of passengers assigned to train j during this period is
Step 5, if eta m >And 0, ending the stage and transferring to the (m+1) th stage, otherwise ending the whole passenger flow distribution process.
Preferably, in step S4, the double-deck multi-train differentiated pricing optimization model is:
upper layer model:
s.t.
(r,s)∈RS
(r,s)∈LEG j ,j∈W
and (3) a lower layer model: the passenger flow distribution method considering capacity constraint.
Preferably, in step S4, for the double-deck multi-train differentiated pricing optimization model, the improved direct search simulated annealing algorithm is used to solve the optimization model.
In order to achieve the above object, the present invention further provides a multi-train differentiated pricing strategy optimization system, comprising:
The time-varying demand analysis unit is used for analyzing time-varying characteristics of the travel demands of the passengers by utilizing historical ticketing data;
the time-interval travel selection model building unit is used for describing the selection behaviors of passengers in different departure time intervals among different priced trains by adopting a plurality of Logit models to obtain a time-interval travel selection model;
the passenger demand distribution unit considers the limitation of the travel selection of passengers by the transportation capacity of the trains, designs a passenger flow distribution method considering capacity constraint, combines the multiple Logit models, distributes the passenger time-varying demands to the trains with the capacity constraint, and obtains the passenger demands on each train;
and the fare optimization adjusting unit is used for constructing a double-layer multi-train differentiated pricing optimization model of the inter-city high-speed railway, taking the income maximization of the passenger tickets as a target, evaluating the multi-train fare scheme by adopting a passenger flow distribution method of the passenger demand distribution unit considering the capacity constraint, calculating an optimization target, and optimizing and adjusting the multi-train fare scheme according to the optimization target.
Compared with the prior art, the multi-train differential pricing strategy optimization method and system analyze the time-varying demand characteristics of the passengers according to historical ticketing data to determine the time-varying demand expression form of the passengers, adopt a plurality of Logit models to describe the selection behavior of the time-varying demands of the passengers among the differentially priced multi-trains, simultaneously evaluate the pricing scheme by a passenger flow distribution method with constraint of design consideration capability, construct an inter-city high-speed railway multi-train differential pricing optimization model based on the pricing scheme, aim at maximizing the income of the passengers, optimally design the fare of the multi-trip trains on each train operation section, and finally solve the optimization model through an improved direct search simulated annealing algorithm, thereby achieving the aim of the inter-city high-speed railway multi-train differential pricing optimization.
Drawings
FIG. 1 is a flow chart of steps of a method for optimizing a differential pricing strategy for multiple trains according to the present invention;
FIG. 2 is a system architecture diagram of a multi-train differentiated pricing strategy optimization system of the present invention.
Detailed Description
Other advantages and effects of the present invention will become readily apparent to those skilled in the art from the following disclosure, when considered in light of the accompanying drawings, by describing embodiments of the present invention with specific embodiments thereof. The invention may be practiced or carried out in other embodiments and details within the scope and range of equivalents of the various features and advantages of the invention.
FIG. 1 is a flow chart of steps of a method for optimizing a differential pricing strategy for multiple trains according to the present invention. The invention discloses a multi-train differentiated pricing strategy optimization method, which comprises the following steps of:
and S1, analyzing time-varying characteristics of the travel demands of the passengers by utilizing historical ticketing data.
In the step, the time-varying characteristics of the inter-city high-speed railway passenger demand are analyzed, and the expression form of the passenger time-varying demand is determined. In order to facilitate description of time-varying characteristics of passenger demand and acquisition of time-varying demands of passengers, a statistical regression method may be employed to obtain departure period probability distribution of passenger demand based on historical ticketing data.
Specifically, it is assumed that the passenger demand is small before 7 and after 23 according to the historical ticketing data, and thus, the passenger demand between 7 and 23 is studied. For convenience of presentation, the time of day of operation is divided into time periods at hourly intervals, such as time periods [7:00,7:59 ]]Referred to as period 7, time period [8:00,8:59]Called period 8, and so on, the time of day is divided into 16 periods, i.e., period 7 through period 22. The passenger travel OD (Origin Destination, boarding station and alighting station) pair is marked as (r, s), r is boarding station, s is alighting station, and the passenger demand of the OD pair (r, s) in one day is marked as q rs Passenger demand is located in the kth departure periodThe probability is recorded asThe passenger's demand during departure period k is noted +.>Then
And S2, describing the selection behaviors of passengers in different departure time periods among differentially priced multi-trip trains by adopting a plurality of Logit models, obtaining a time-period travel selection model, and estimating model parameters by utilizing questionnaire survey data.
In step S2, a plurality of Logit models are adopted to analyze how the time-varying demands of passengers select trains among the trains with differential pricing, so as to realize travel utility maximization.
For convenience of description, the following symbols are designed. The set of all station compositions is denoted as SN, and the set of all OD pair compositions is denoted as RS. The set of all train compositions is denoted w= { j }. For train j e W, h (j) is the stop number of train j, For train j's along-trip sequence set +.>Train j is stopping->To stop->Is called the train section, noted +.>The operating sections of train j form a set, denoted LEG j . For x is less than or equal toX 'and y' are not more than y, called run section->Covering the operating section->Marked as->The transport capacity of train j is denoted CA j Train in the operating section->The passenger flow is expressed as F (j, x), and x is more than or equal to 1 and less than or equal to h (j) -1.
And limiting the passenger demand of each departure period to select the train which departs in the corresponding period according to the passenger time-varying demand. There are many factors that affect the passenger's selection of trains, only the time of operation and fare of the trains being considered here. The set of trains stopped at the OD pair (r, s) and starting from the station r in the kth period is recorded asThe running time of train j between OD pairs (r, s) is noted as t rs (j) The fare is marked as c rs (j) A. The invention relates to a method for producing a fibre-reinforced plastic composite Then the utility of passenger selection train j may be expressed as
wherein ,θ1 and θ2 As a parameter, ε j As a random term of the number of items,representing the random utility->Representing a portion of the determination in the stochastic utility.
Travel of OD pair (r, s) according to multiple Logit model principlesTime-varying demand for guestsThe probability of selecting train j is
The above is a time-division trip selection model.
The fare between the existing inter-city railway trains does not show differentiation. Therefore, the parameters of the model cannot be estimated according to the historical ticketing data, and therefore, in the invention, an SP questionnaire is designed to investigate passengers of the inter-city railway. The method is characterized in that the wide-bead inter-city railway train is used for investigation by passengers of the wide-bead inter-city railway, parameters of the model are estimated, the questionnaire designs 24 virtual ticket purchasing scenes altogether, each scene comprises 4 trains, and the information display of each train simulates ticket purchasing pages of the Chinese 12306 website, namely the departure time, arrival time, on-board time and ticket prices of the trains. The fare of the train is randomly floated up and down (the floating up is not more than 20% and the floating down is not more than 30%) on the basis of the existing fare, and the rest information is determined according to the current train schedule. According to personal information filled in by the passengers and trip habits, a virtual ticket purchasing scene is provided for the passengers, and the passengers select a train. The questionnaire was spread on the net 3 months in 2020, and 1967 valid questionnaires were retrieved altogether. The above model parameters were estimated based on the questionnaire data, and the results are shown in table 1.
TABLE 1 multiple Logit model parameter estimation
And step S3, designing a passenger flow distribution method considering capability constraint in consideration of the limitation of the travel selection of passengers on the transportation capability of the trains, and combining the plurality of Logit models to distribute the time-varying demands of the passengers to the trains with the capability constraint so as to obtain the demands of the passengers on each train.
In particular, the acceptable passenger demand for each train is limited by the transport capacity, and when demand is large, some passenger demands cannot be met. The passenger flow distribution method considering the capacity constraint determines the probability of selecting the train according to the time-varying demand of the passengers by designing a distribution rule and according to the plurality of logic models; and determining the ratio of the time-varying passenger demands of each traveling OD pair to the ratio of the time-varying passenger demands of each OD pair to the total time-varying passenger demands of the OD pair according to the transportation capacity of the train, so as to determine the time-varying passenger demands F (j, x) distributed on each train, wherein x is more than or equal to 1 and less than or equal to h (j) -1, j E W, and the following capacity constraint conditions are satisfied.
F(j,x)≤CA j (4)
CA j Indicating the transport capacity of train j.
The passenger selection train is determined in the process of purchasing the ticket, so that the passenger ticket purchasing process can be used as a passenger flow distribution process, and a passenger flow distribution method is designed by simulating the passenger ticket purchasing process. As the ticketing process progresses, portions of the train section are full and the optional trains for some passengers change. Therefore, the time points at which these changes occur are defined as dividing nodes, and the ticket purchasing process is divided into several stages. The optional trains of unassigned passengers do not change during each of the stages of demarcation. When all time-varying demand assignments are completed or no remaining train capacity meets unassigned passenger demands, the passenger flow assignment process ends. The m-th passenger flow distribution stage is specifically described as follows:
Step 1: for time-varying demands(r, s) ∈rs, k=7, 8, …,22, construct an optional train (with remaining capacity) set, denoted +.>
Step 2: for time-varying demands(r, s) ∈rs, k=7, 8, …,22, calculated in the set +_using the multiple Logit model>The probability of selecting train j is denoted as P (j|r, s, k, m).
Step 3: on the premise of meeting the capacity constraint, the unallocated passenger demands are allocated to the train as much as possible, and each O-D is set to have the same ratio of the allocable demands to the total demands and is marked as eta m Until a train section full or passenger demand is fully assigned.
Step 4: the number of passengers allocated on each train is calculated. For the passenger demand of the O-D pair (r, s) in the kth departure period, the number of passengers assigned to train j during this period is
Step 5: if eta m >And 0, ending the stage and transferring to the (m+1) th stage, otherwise ending the whole passenger flow distribution process.
For the train option sets in step 1 and step 2And a selection probability P (j|r, s, k, m) calculated according to the following formula
To calculate the assignable proportion eta of the mth stage m For each train operation sectionSetting a firstIntermediate variables, denoted as DeltaF m (j, x), the initial value is 0. In the mth phase, for each OD pair (r, s), each departure period k, each train +.>Each train operation section->The following accumulation calculation is performed:
wherein ,representing hypothesized time-varying demand +.>Passenger traffic allocated to train j without being limited by transportation capacity in the mth phase. Thus, after the above-described accumulation calculation is completed, η m ΔF m (j, x) means that all passengers' time-varying demands can be practically assigned to the train operation section in the mth phase +.>The passenger flow volume satisfies the following capacity constraint:
η m ΔF m (j,x)≤CA j -F(j,x) (8)
wherein CAj -F (j, x) represents a train operation sectionRemaining transport capacity at the beginning of the mth phase. And the ratio assigned per stage satisfies +.>
Thus, eta m Can be calculated from formula (9):
at the end of the mth phase, the train is running in sectionsThe passenger flow volume is updated by the formula (10):
F(j,x)＝F(j,x)+η m ΔF m (j,x) (10)
the above-mentioned method is characterized by that the passenger flow distribution of passenger time-varying requirement in mth stage is recorded as M total number of dividing stages, i.e. the passenger flow distribution method considering capability constraint is abbreviated as PACC. The results of the passenger flow allocation can be used to evaluate the train fare scheme.
And S4, constructing a double-layer multi-train differentiated pricing optimization model of the inter-city high-speed railway, taking the income maximization of the tickets as a target, evaluating the multi-train fare scheme by adopting the passenger flow distribution method considering the capacity constraint in the step S3, calculating an optimization target, and optimizing and adjusting the multi-train fare scheme according to the optimization target.
The optimizing method is used for cooperatively optimizing the fare of the multi-trip train on each running section, namely decision variables, and is marked as c rs (j),j∈W,(r,s)∈LEG j . Train fare affects not only the passenger's choice between trains, but also whether the passenger chooses to travel, i.e. the elastic demand. Increasing train fare may increase revenue but too high train fare may lead to loss of passenger flow, turning passengers to other alternative means of transportation, such as automobiles. Therefore, in the multi-train differentiated pricing optimization model, an exponential function is used to describe the impact of train fare on the total amount of passenger travel demand, as follows.
wherein ,average train fare for OD pair (r, s); average train fare when OD pair (r, s) is +.>When the corresponding passenger goes out, the demand is +.>The ticket can be obtained according to historical ticket selling data; the parameter phi can measure the demand elasticity corresponding to the change of the unit price, and the larger the value of phi is, the larger the price elasticity of the demand is.
For a given train fare scheme c rs (j) The average fare for the train during the kth departure period for the passenger demand of OD versus (r, s) can be simply expressed as
The probability of passenger demand in the kth departure period isThen the average train fare for OD pair (r, s) is expressed as
Then, the double-deck multi-train differentiated pricing optimization model can be expressed as follows,
upper layer model:
s.t.
formulae (11) - (13), (r, s) ∈RS
And (3) a lower layer model: PACC passenger flow distribution method
Wherein Z represents the income of the passenger ticket, and />Respectively representing the lower limit and the upper limit of the fare allowance value of the train on the running section (r, s). In the upper model, railway transportation enterprises optimize a train fare scheme; and in the lower model, evaluating the train fare scheme according to the passenger flow distribution method. And (4) calculating an optimization target type (14) according to the passenger flow distribution result by the railway transportation enterprises, and further evaluating and optimizing the train fare scheme.
Preferably, in a specific embodiment of the present invention, for the double-layer multi-train differentiated pricing optimization model, the improved direct search simulated annealing algorithm is adopted to solve the optimization model.
Specifically, decision variable c in the optimization model described above rs (j),(r,s)∈LEG j The number of j e W is large (e.g. when there are 50 trains with 4 running sections per train, the decision variable reaches 200), so a high-dimensional combinatorial optimization problem needs to be solved.
Simulated annealing (Simulated Annealing, SA) algorithms have global convergence and are widely used in engineering practice. Ali and Ali The et al designed a direct search simulated annealing (Direct Search Simulated Annealing, DSA) algorithm that improved the computational efficiency and accuracy of the algorithm. In order to improve convergence stability and convergence efficiency of an algorithm when solving a high-dimensional optimization problem, the invention improves a new solution generation method and an algorithm structure, and designs an improved direct search simulated annealing (Modified Direct Search Simulated Annealing, MDSA) algorithm.
The new solution generating method of the MDSA algorithm comprises the following 3 steps: (1) The method comprises the steps of randomly generating a new solution by adopting a variable-scale Cauchy distribution mode in a solution search space; (2) The method is to randomly select a certain number of solutions from a solution set and randomly combine the solution with the current optimal solution to generate a new solution. (3) The self-adaptive optimizing method generates a new solution by randomly perturbing the current optimal solution according to normal distribution.
For convenience of algorithm description, the total number of decision variables is recorded as cn, let C, C L and CU The vectors, and their lower and upper limits, of the decision variables are cn-dimensional column vectors, respectively, as follows
Then
C L ≤C≤C U (19)
The solution vector satisfying the expression (19) constitutes a search space, denoted as S. According to the constraint condition of the optimization model, the solution vectors C in the search space S are all feasible solutions. Let E (C) = -Z (C), then the optimization objective formula (14) is equivalent to min E (C), E (C) as an evaluation function in the MDSA algorithm.
Three new solution generating methods in the MDSA algorithm are described below, respectively.
(1) Variable-scale cauchy distribution random generation new solution
A new solution C is generated in the search space S in a variable-scale cauchy distribution. The cauchy distribution probability density function centered on the origin is:
in the formula As the scale parameter, the number of iterations based on the algorithm is calculated as the following formula (21) to achieve a large-scale search in the initial period of optimization and a small-scale fine search in the later period of optimization.
Wherein a is the cooling iteration times.
The calculation formula of the new solution C is as follows:
wherein the symbols areRepresenting the Hadamard product, AY is a cn-dimensional column vector randomly generated according to equations (20) and (21), y is a cn-dimensional unit column vector, abs is an absolute value function, and w is a random number generated in (0, 1) in a uniform distribution.
(2) Combining with the optimal solution to generate a new solution
Firstly, RN solutions are randomly selected from a solution set and recorded asThe RN solutions and the optimal solution C Best The random combination is performed to generate a new solution C, each component of which is determined according to equation (24).
wherein ,wi Is [0,1]Random numbers generated in a uniform distribution. The RN is determined from the solution set, taking about 8% of the solution set size. The method can improve the searching efficiency of the optimal solution and the convergence stability of the algorithm.
(3) Adaptive method for generating new solution
The new solution C in the adaptive method is the best solution C in the search space S Best Random disturbance is generated in the adjacent area according to normal distribution, so that the algorithm can be prevented from being sunk into a local extremum too early.
Wherein the symbols areRepresenting the Hadamard product, b is the search radius adjustment factor, I is the adaptation factor, y is the cn-dimensional unit column vector, determined according to equations (26) - (28), respectively:
wherein Ta For the current temperature, m a Is random number distributed uniformly in interval (0, 5), gamma i Is interval [0,1 ]]The random number uniformly distributed in the matrix is beta, and the self-adaptive probability is generally 0.1.SY is a cn-dimensional column vector randomly derived from a standard normal distribution.
After calculation according to equation (25), the new solution C generated may exceed the search space S, and the components in the new solution C are modified according to the following equation:
the following describes the structural design of the MDSA algorithm in the present invention
In the MDSA algorithm of the present invention, the initial temperature T 0 The probability of receipt of a new solution that needs to satisfy the initial stage is greater than a predetermined value (typically between values 0.8 and 0.9). March chain length L a Calculated according to the following formula (30):
probability P of new solution being accepted acc Calculated according to the following formula (31):
coefficient of cooling theta a The value interval of (2) is [ theta ] min ＝0.80,θ max ＝0.9]Initial value theta 0 ＝0.85，θ a Update method reference [24 ] ]. After a certain number of cooling, if the temperature is continuously lowered several times (marked by delta a), the optimal point evaluation function value E min Unchanged or no significant change (i.eδ is a given positive real number) is used as a criterion for the algorithm to fall into a local extremum. When delta a<When τ (τ is a given positive integer), randomly generating a new solution from the variable-scale cauchy distribution with probability scp or generating a new solution by combining probability 1-scp with the optimal point; when delta a is more than or equal to tau, a self-adaptive method is adopted to generate a new solution.
Specifically, the structure of the MDSA algorithm is as follows.
Start to
Randomly generating n=7 (cn+1) solutions to form an initial solution set a;
for each solution in set a, the execution,
from formulas (11) - (13), the elastic requirement q of each OD pair is calculated rs ；
Calculating the time-varying demand of each OD pair from equation (1)
Distributing the time-varying demands of passengers to the trains by adopting a PACC method;
calculating an evaluation function value E (C) of the solution according to the passenger flow distribution result;
determining the best and worst solutions in A and the corresponding evaluation function value E min and Emax ；
Initializing parameters, determining an initial temperature T according to a rule of thumb 0 The cooling iteration number a=0;
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preferably, the invention extends to the problem of differential floating optimization of multiple train fare within a pre-sale period. The problem expands the selection behavior of passengers by one dimension, the passengers need to select among multiple trains, the problem of selecting the early ticket purchasing period is also related, the problem is solved by collecting related data, and the influence of differential floating of ticket prices of the multiple trains on the selection behavior of the passengers in the pre-selling period is analyzed.
FIG. 2 is a system architecture diagram of a multi-train differentiated pricing strategy optimization system of the present invention. The invention discloses a multi-train differentiated pricing strategy optimization system, which comprises the following steps:
the time-varying demand analysis unit 201 is configured to analyze time-varying characteristics of the travel demand of the passenger using the historical ticketing data.
In this step, the time-varying demand analysis unit 201 analyzes the time-varying characteristics of the inter-city high-speed railway passenger demand, and determines the expression form of the passenger time-varying demand. In order to facilitate description of time-varying characteristics of passenger demand and acquisition of time-varying demands of passengers, a statistical regression method may be employed to obtain departure period probability distribution of passenger demand based on historical ticketing data.
Specifically, it is assumed that the passenger demand is small before 7 and after 23 according to the historical ticketing data, and thus, the passenger demand between 7 and 23 is studied. For convenience of presentation, the time of day of operation is divided into time periods at hourly intervals, such as time periods [7:00,7:59 ]]Referred to as period 7, time period [8:00,8:59]Called period 8, and so on, the time of day is divided into 16 periods, i.e., period 7 through period 22. The OD pair of the passengers going out is marked as (r, s), r is the upper station, s is the lower station, and the passenger demand of the OD pair (r, s) in one day is marked as q rs The probability that the passenger demand is in the kth departure period is noted asThe passenger's demand during departure period k is noted +.>Then
The time-interval travel selection model construction unit 202 is configured to describe the selection behavior of passengers in different departure time intervals between differentially priced trains by using multiple logic models, obtain a time-interval travel selection model, and estimate model parameters by using questionnaire survey data.
In the time-division travel selection model building unit 202, a plurality of Logit models are adopted to analyze how the passenger time-varying demands select trains among the trains with differential pricing, so as to realize travel utility maximization.
For convenience of description, the following notations are designed: the set of all station components is denoted as SN, and the set of all OD pair components is denoted asAnd RS. The set of all train compositions is denoted w= { j }. For train j e W, h (j) is the stop number of train j,for train j's along-trip sequence set +.>Train j is stopping->To stop->Is called the train section, noted +.>The operating sections of train j form a set, denoted LEG j . For x.ltoreq.x ′ And y is ′ Y is less than or equal to y, called run zone->Covering the operating section->Marked as->The transport capacity of train j is denoted CA j Train in the operating section- >The passenger flow is expressed as F (j, x), and x is more than or equal to 1 and less than or equal to h (j) -1.
And limiting the passenger demand of each departure period to select the train which departs in the corresponding period according to the passenger time-varying demand. There are many factors that affect the passenger's selection of trains, only the time of operation and fare of the trains being considered here. The set of trains stopped at the OD pair (r, s) and starting from the station r in the kth period is recorded asThe running time of train j between OD pairs (r, s) is noted as t rs (j) The fare is marked as c rs (j) A. The invention relates to a method for producing a fibre-reinforced plastic composite Then the utility of passenger selection train j may be expressed as
wherein ,θ1 and θ2 As a parameter, ε j Is a random term.
According to the principle of multiple Logit models, the time-varying demand of the passengers of the OD pair (r, s) is realizedThe probability of selecting train j is
The above is a time-division trip selection model.
The fare between the existing inter-city railway trains does not show differentiation. Therefore, the parameters of the model cannot be estimated according to the historical ticketing data, and therefore, in the invention, an SP questionnaire is designed to investigate passengers of the inter-city railway. The method is characterized in that the wide-bead inter-city railway train is used for investigation by passengers of the wide-bead inter-city railway, parameters of the model are estimated, the questionnaire designs 24 virtual ticket purchasing scenes altogether, each scene comprises 4 trains, and the information display of each train simulates ticket purchasing pages of the Chinese 12306 website, namely the departure time, arrival time, on-board time and ticket prices of the trains. The fare of the train is randomly floated up and down (the floating up is not more than 20% and the floating down is not more than 30%) on the basis of the existing fare, and the rest information is determined according to the current train schedule. According to personal information filled in by the passengers and trip habits, a virtual ticket purchasing scene is provided for the passengers, and the passengers select a train. The questionnaire was spread on the net 3 months in 2020, and 1967 valid questionnaires were retrieved altogether. And estimating the model parameters according to the questionnaire data.
The passenger demand distribution unit 203 designs a passenger flow distribution method considering capacity constraint in consideration of the limitation of the travel selection of passengers by the transportation capacity of the trains, combines the multiple logic models, distributes the passenger time-varying demands to the trains with the capacity constraint, and obtains the passenger demands on each train.
In particular, the acceptable passenger demand for each train is limited by the transport capacity, and when demand is large, some passenger demands cannot be met. The passenger flow distribution method considering the capacity constraint determines the probability of selecting the train according to the time-varying demand of the passengers by designing a distribution rule and according to the plurality of logic models; and determining the ratio of the time-varying passenger demands of each traveling OD pair to the ratio of the time-varying passenger demands of each OD pair to the total time-varying passenger demands of the OD pair according to the transportation capacity of the train, so as to determine the time-varying passenger demands F (j, x) distributed on each train, wherein x is more than or equal to 1 and less than or equal to h (j) -1, j E W, and the following capacity constraint conditions are satisfied.
F(j,x)≤CA j (4)
The passenger selection train is determined in the process of purchasing the ticket, so that the passenger ticket purchasing process can be used as a passenger flow distribution process, and a passenger flow distribution method is designed by simulating the passenger ticket purchasing process. As the ticketing process progresses, portions of the train section are full and the optional trains for some passengers change. Therefore, the time points at which these changes occur are defined as dividing nodes, and the ticket purchasing process is divided into several stages. The optional trains of unassigned passengers do not change during each of the stages of demarcation. When all time-varying demand assignments are completed or no remaining train capacity meets unassigned passenger demands, the passenger flow assignment process ends. The m-th passenger flow distribution stage is specifically described as follows:
Step 1: for time-varying demands(r, s) ∈rs, k=7, 8, …,22, build an optional columnVehicle (with remaining capacity) set, denoted +.>
Step 2: for time-varying demands(r, s) ∈rs, k=7, 8, …,22, calculated in the set +_using the multiple Logit model>The probability of selecting train j is denoted as P (j|r, s, k, m).
Step 3: on the premise of meeting the capacity constraint, the unallocated passenger demands are allocated to the train as much as possible, and each O-D is set to have the same ratio of the allocable demands to the total demands and is marked as eta m Until a train section full or passenger demand is fully assigned.
Step 4: the number of passengers allocated on each train is calculated. For the passenger demand of the O-D pair (r, s) in the kth departure period, the number of passengers assigned to train j during this period is
Step 5: if eta m >And 0, ending the stage and transferring to the (m+1) th stage, otherwise ending the whole passenger flow distribution process.
For the train option sets in step 1 and step 2And a selection probability P (j|r, s, k, m) calculated according to the following formula
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To calculate the assignable proportion eta of the mth stage m For each train operation sectionAn intermediate variable is set and denoted as DeltaF m (j, x), the initial value is 0. In the mth phase, for each OD pair (r, s), each departure period k, each train +.>Each train operation section->The following accumulation calculation is performed:
wherein ,representing hypothesized time-varying demand +.>Passenger traffic allocated to train j without being limited by transportation capacity in the mth phase. Thus, after the above-described accumulation calculation is completed, η m ΔF m (j, x) means that all passengers' time-varying demands can be practically assigned to the train operation section in the mth phase +.>The passenger flow volume satisfies the following capacity constraint:
η m ΔF m (j,x)≤CA j -F(j,x) (8)
wherein CAj -F (j, x) represents a train operation sectionRemaining transport capacity at the beginning of the mth phase. And the ratio assigned per stage satisfies +.>
Thus, eta m Can be calculated from formula (9):
at the end of the mth phase, the train is running in sectionsThe passenger flow volume is updated by the formula (10):
F(j,x)＝F(j,x)+η m ΔF m (j,x) (10)
the above-mentioned method is characterized by that the passenger flow distribution of passenger time-varying requirement in mth stage is recorded as M total number of dividing stages, i.e. the passenger flow distribution method considering capability constraint is abbreviated as PACC. The results of the passenger flow allocation can be used to evaluate the train fare scheme.
The fare optimization adjustment unit 204 is configured to construct a city high-speed railway double-layer multi-train differentiated pricing optimization model, aim at maximizing the income of tickets, evaluate the multi-train fare scheme by adopting the passenger flow distribution method of the passenger demand distribution unit 203 considering the capacity constraint, calculate an optimization target, and perform optimization adjustment on the multi-train fare scheme according to the optimization target.
The optimizing method is used for cooperatively optimizing the fare of the multi-trip train on each running section, namely decision variables, and is marked as c rs (j),j∈W,(r,s)∈LEG j . Train fare affects not only the passenger's choice between trains, but also whether the passenger chooses to travel, i.e. the elastic demand. Increasing train fare may increase revenue but too high train fare may lead to loss of passenger flow, turning passengers to other alternative means of transportation, such as automobiles. Thus, in the multi-train differentiated pricing optimization model, we adoptThe impact of train fare on the total amount of travel demand of passengers is described by an exponential function, as follows.
wherein ,average train fare for OD pair (r, s); average train fare when OD pair (r, s) is +.>When the corresponding passenger goes out, the demand is +.>The ticket can be obtained according to historical ticket selling data; the parameter phi can measure the demand elasticity corresponding to the change of the unit price, and the larger the value of phi is, the larger the price elasticity of the demand is.
For a given train fare scheme c rs (j) The average fare for the train during the kth departure period for the passenger demand of OD versus (r, s) can be simply expressed as
The probability of passenger demand in the kth departure period isThen the average train fare for OD pair (r, s) is expressed as
Then, the double-deck multi-train differentiated pricing optimization model can be expressed as follows,
upper layer model:
s.t.
formulae (11) - (13), (r, s) ∈RS
And (3) a lower layer model: PACC passenger flow distribution method
Wherein Z represents the income of the passenger ticket, and />Respectively representing the lower limit and the upper limit of the fare allowance value of the train on the running section (r, s). In the upper model, railway transportation enterprises optimize a train fare scheme; and in the lower model, evaluating the train fare scheme according to the passenger flow distribution method. And (4) calculating an optimization target type (14) according to the passenger flow distribution result by the railway transportation enterprises, and further evaluating and optimizing the train fare scheme.
Preferably, in a specific embodiment of the present invention, for the double-layer multi-train differentiated pricing optimization model, the improved direct search simulated annealing algorithm is adopted to solve the optimization model.
Specifically, decision variable c in the optimization model described above rs (j),(r,s)∈LEG j The number of j e W is large (e.g. when there are 50 trains with 4 running sections per train, the decision variable reaches 200), so a high-dimensional combinatorial optimization problem needs to be solved.
Simulated annealing (Simulated Annealing, SA) algorithms have global convergence and are widely used in engineering practice. Ali and Ali The et al designed a direct search simulated annealing (Direct Search Simulated Annealing, DSA) algorithm to improveThe calculation efficiency and the calculation precision of the algorithm are improved. In order to improve convergence stability and convergence efficiency of an algorithm when solving a high-dimensional optimization problem, the invention improves a new solution generation method and an algorithm structure, and designs an improved direct search simulated annealing (Modified Direct Search Simulated Annealing, MDSA) algorithm.
The new solution generating method of the MDSA algorithm comprises the following 3 steps: (1) The method comprises the steps of randomly generating a new solution by adopting a variable-scale Cauchy distribution mode in a solution search space; (2) The method is to randomly select a certain number of solutions from a solution set and randomly combine the solution with the current optimal solution to generate a new solution. (3) The self-adaptive optimizing method generates a new solution by randomly perturbing the current optimal solution according to normal distribution.
For convenience of algorithm description, the total number of decision variables is recorded as cn, let C, C L and CU The vectors, and their lower and upper limits, of the decision variables are cn-dimensional column vectors, respectively, as follows
Then
C L ≤C≤C U (19)
The solution vector satisfying the expression (19) constitutes a search space, denoted as S. According to the constraint condition of the optimization model, the solution vectors C in the search space S are all feasible solutions. Let E (C) = -Z (C), then the optimization objective formula (14) is equivalent to min E (C), E (C) as an evaluation function in the MDSA algorithm.
Three new solution generating methods in the MDSA algorithm are described below, respectively.
(1) Variable-scale cauchy distribution random generation new solution
A new solution C is generated in the search space S in a variable-scale cauchy distribution. The cauchy distribution probability density function centered on the origin is:
in the formula As the scale parameter, the number of iterations based on the algorithm is calculated as the following formula (21) to achieve a large-scale search in the initial period of optimization and a small-scale fine search in the later period of optimization.
Wherein a is the cooling iteration times.
The calculation formula of the new solution C is as follows:
wherein the symbols areRepresenting the Hadamard product, AY is a cn-dimensional column vector randomly generated according to equations (20) and (21), y is a cn-dimensional unit column vector, abs is an absolute value function, and w is a random number generated in (0, 1) in a uniform distribution.
(2) Combining with the optimal solution to generate a new solution
Firstly, RN solutions are randomly selected from a solution set and recorded asThe RN solutions and the optimal solution C Best The random combination is performed to generate a new solution C, each component of which is determined according to equation (24).
wherein ,wi Is [0,1]Random numbers generated in a uniform distribution. The RN is determined from the solution set, taking about 8% of the solution set size. The method can improve the searching efficiency of the optimal solution and the convergence stability of the algorithm.
(3) Adaptive method for generating new solution
The new solution C in the adaptive method is the best solution C in the search space S Best Random disturbance is generated in the adjacent area according to normal distribution, so that the algorithm can be prevented from being sunk into a local extremum too early.
Wherein the symbols areRepresenting the Hadamard product, b is the search radius adjustment factor, I is the adaptation factor, y is the cn-dimensional unit column vector, determined according to equations (26) - (28), respectively:
wherein Ta For the current temperature, m a Is random number distributed uniformly in interval (0, 5), gamma i Is interval [0,1 ]]The random number uniformly distributed in the matrix is beta, and the self-adaptive probability is generally 0.1.SY is a cn-dimensional column vector randomly derived from a standard normal distribution.
After calculation according to equation (25), the new solution C generated may exceed the search space S, and the components in the new solution C are modified according to the following equation:
the following describes the structural design of the MDSA algorithm in the present invention
In the MDSA algorithm of the present invention, the initial temperature T 0 The probability of receipt of a new solution that needs to satisfy the initial stage is greater than a predetermined value (typically between values 0.8 and 0.9). March chain length L a Calculated according to the following formula (30):
probability P of new solution being accepted acc Calculated according to the following formula (31):
coefficient of cooling theta a The value interval of (2) is [ theta ] min ＝0.80,θ max ＝0.9]Initial value theta 0 ＝0.85，θ a Update method reference [24 ] ]. After a certain number of cooling, if the temperature is continuously lowered several times (marked by delta a), the optimal point evaluation function value E min Unchanged or no significant change (i.eδ is a given positive real number) is used as a criterion for the algorithm to fall into a local extremum. When delta a<τ (τ is a given positive integer), the variable-scale Cauchy distribution is calculated with probability scpGenerating a new solution randomly or combining the probability 1-scp with the optimal point to generate the new solution; when delta a is more than or equal to tau, a self-adaptive method is adopted to generate a new solution.
Specifically, the structure of the MDSA algorithm is as follows.
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Examples
In the embodiment of the invention, numerical analysis is carried out by taking a wide-bead inter-city railway as an example, and ticket price optimization conditions of multiple trains with different departure time periods under different elastic demand coefficients are tested by using the invention. The calculation result shows that: the mean square error of the optimized values is within 100, and the average cooling times is within 200, which indicates that the optimized algorithm has better convergence stability and convergence efficiency; when phi is not equal to 1.0, the influence of the multi-train differentiated pricing optimization scheme on ticket income is larger; for phi=1.6, ticket revenue is increased by 10.25%.
In summary, the multi-train differential pricing strategy optimization method and system analyze the time-varying demand characteristics of the passengers according to the historical ticketing data to determine the time-varying demand expression form of the passengers, the selection behavior of the time-varying demands of the passengers among the differentially priced multi-trains is described by adopting a plurality of Logit models, meanwhile, the pricing scheme is evaluated by a passenger flow distribution method with the constraint of design consideration capability, an inter-city high-speed railway multi-train differential pricing optimization model is constructed based on the pricing scheme, the aim of maximizing the income of the passengers is achieved, the fare of the multi-trip trains on each train operation section is optimally designed, and finally, the optimization model is solved by an improved direct search simulated annealing algorithm, so that the aim of optimizing the inter-city high-speed railway multi-train differential pricing is achieved.
The above embodiments are merely illustrative of the principles of the present invention and its effectiveness, and are not intended to limit the invention. Modifications and variations may be made to the above-described embodiments by those skilled in the art without departing from the spirit and scope of the invention. Accordingly, the scope of the invention is to be indicated by the appended claims.

Claims (5)

1. A multi-train differentiated pricing strategy optimization method comprises the following steps:
step S1, analyzing time-varying characteristics of travel demands of passengers by using historical ticketing data;
step S2, describing the selection behaviors of passengers in different departure time periods among differentially priced multi-trip trains by adopting a plurality of Logit models, and obtaining a time-period travel selection model; describing the selection behaviors of passengers in different departure time periods among differentially priced multi-trip trains by adopting a plurality of Logit models to obtain a time-period travel selection model, wherein the method specifically comprises the following steps of: the OD pair of the passengers going out is marked as (r, s), r is the upper station, s is the lower station, and the passenger demand of the OD pair (r, s) in one day is marked as q rs The probability that the passenger demand is in the kth departure period is noted asThe passenger's demand during departure period k is noted +.>Then->The set of trains stopped at the OD pair (r, s) and starting from station r in the kth period is denoted +. >The running time of train j between OD pairs (r, s) is noted as t rs (j) The fare is marked as c rs (j) The passenger selects the utility of train jExpressed as: wherein ,θ1 and θ2 Is a coefficient, epsilon j Is a random item->Representing random utility->In (c) based on multiple Logit model principles, the time-varying demand of the OD pair (r, s) for passengersThe probability of selecting train j is: />
Step S3, considering that the travel selection of passengers is limited by the transportation capacity of the trains, designing a passenger flow distribution method considering capacity constraint, combining the multiple Logit models, distributing the time-varying demands of the passengers to the trains with the capacity constraint, and obtaining the demands of the passengers on each train; the passenger flow distribution method considering the capacity constraint specifically comprises the following steps: the probability of selecting a train by the time-varying demand of the passengers is determined according to the multiple logic models through designing the distribution rule, and then the ratio of the time-varying demand of the passengers of each travel OD pair to the time-varying demand of the total passengers of the OD pair, which is the ratio of the time-varying demand of the passengers which can be accepted by each OD pair, is determined according to the transportation capacity of the train, so that the distributed passenger demands F (j, x) on each train are determined, and x is not less than 1 and not more than h (j) -1, j E W, and the following capacity constraint conditions are satisfied: f (j, x) is less than or equal to CA j； wherein CAj Representing the transport capacity of train j;
the mth passenger flow distribution stage is specifically as follows: step 1, for time-varying demand(r, s) ∈rs, k=7, 8, …,22, constructing an optional train set, denoted +.>Step 2, for time-varying demand->(r, s) ∈rs, k=7, 8, …,22, calculated in the set +_using the multiple Logit model>The probability of selecting the train j is denoted as P (j|r, s, k, m); step 3, on the premise of meeting the capacity constraint, distributing as much of the unassigned passenger demands as possible to the train, setting the ratio of each O-D to the assignable demands to the total demands to be the same, and recording as eta m Until a train section is full or passenger demands are fully distributed; step 4: calculating the number of passengers allocated on each train; for the passenger demand of the O-D pair (r, s) in the kth departure period, the number of passengers assigned to train j during the departure period isStep 5, if eta m >0, ending the stage and transferring to the (m+1) th stage, otherwise ending the whole passenger flow distribution process;
wherein w= { j } is a set of all trains; x is the stop sequence number; h (j) is the stop number of the train j; m is the running stage serial number of passenger flow distribution; A set of train options; RS is the set of all OD pairs; η (eta) m The allocable proportion of the mth passenger flow allocation stage is calculated;
s4, constructing a double-layer multi-train differentiated pricing optimization model of the inter-city high-speed railway, taking the income maximization of tickets as a target, evaluating the multi-train fare schemes by adopting the passenger flow distribution method considering the capacity constraint in the step S3, calculating an optimization target, and optimizing and adjusting the multi-train fare schemes according to the optimization target; the double-layer multi-train differentiated pricing optimization model is as follows:
upper layer model:
s.t.
(r,s)∈RS；
wherein ,probability of being a passenger demand during the kth departure period;
average fare for the train during the kth departure period for the passenger demand of OD pair (r, s);
at the kth exit for passenger demandThe probability of the hair period is->Then the average train fare for OD pair (r, s);
a lower limit representing the permissible value of the fare of the train on the operating section (r, s);
an upper limit representing the permissible value of the fare of the train in the operating section (r, s);
LEG j representing the running section composition set of the train j;
and (3) a lower layer model: the passenger flow distribution method considering capacity constraint.
2. The multi-train differential pricing strategy optimization method as recited in claim 1, wherein: in step S1, a statistical regression method is adopted to obtain departure time interval probability distribution of passenger demands according to historical ticketing data.
3. The multi-train differential pricing strategy optimization method as recited in claim 1, wherein: in step S2, a questionnaire is designed, and the time-lapse selection model parameters are estimated using the questionnaire data.
4. The method for optimizing multi-train differentiated pricing strategy according to claim 1, wherein in step S4, for the double-layer multi-train differentiated pricing optimization model, an improved direct search simulated annealing algorithm is used to solve the optimization model.
5. A multi-train differentiated pricing strategy optimization system comprising:
the time-varying demand analysis unit is used for analyzing time-varying characteristics of the travel demands of the passengers by utilizing historical ticketing data;
the time-interval travel selection model building unit is used for describing the selection behaviors of passengers in different departure time intervals among different priced trains by adopting a plurality of Logit models to obtain a time-interval travel selection model;
describing the selection behaviors of passengers in different departure time periods among differentially priced multi-trip trains by adopting a plurality of Logit models to obtain a time-period travel selection model, wherein the method specifically comprises the following steps of: the OD pair of the passengers going out is marked as (r, s), r is the upper station, s is the lower station, and the passenger demand of the OD pair (r, s) in one day is marked as q rs The probability that the passenger demand is in the kth departure period is noted asThe passenger's demand during departure period k is noted +.>Then->The set of trains stopped at the OD pair (r, s) and starting from station r in the kth period is denoted +.>The running time of train j between OD pairs (r, s) is noted as t rs (j) The fare is marked as c rs (j) The utility of passenger selection train j is expressed as: wherein ,θ1 and θ2 Is a coefficient, epsilon j As a random term of the number of items,representing random utility->According to the principle of a multiple Logit model, the time-varying demand of the passengers of OD pair (r, s)>The probability of selecting train j is: />
The passenger demand distribution unit considers the limitation of the travel selection of passengers by the transportation capacity of the trains, designs a passenger flow distribution method considering capacity constraint, combines the multiple Logit models, distributes the passenger time-varying demands to the trains with the capacity constraint, and obtains the passenger demands on each train;
the passenger flow distribution method considering the capacity constraint specifically comprises the following steps: the probability of selecting a train by the time-varying demand of the passengers is determined according to the multiple logic models through designing the distribution rule, and then the ratio of the time-varying demand of the passengers of each travel OD pair to the time-varying demand of the total passengers of the OD pair, which is the ratio of the time-varying demand of the passengers which can be accepted by each OD pair, is determined according to the transportation capacity of the train, so that the distributed passenger demands F (j, x) on each train are determined, and x is not less than 1 and not more than h (j) -1, j E W, and the following capacity constraint conditions are satisfied: f (j, x) is less than or equal to CA j； wherein CAj Representing the transport capacity of train j;
the mth passenger flow distribution stage is specifically as follows: step 1, for time-varying demandk=7, 8, …,22, an alternative train set is constructed, denoted +.>Step 2, for time-varying demand->(r, s) ∈rs, k=7, 8, …,22, calculated in the set +_using the multiple Logit model>The probability of selecting the train j is denoted as P (j|r, s, k, m); step 3, on the premise of meeting the capacity constraint, distributing as much of the unassigned passenger demands as possible to the train, setting the ratio of each O-D to the assignable demands to the total demands to be the same, and recording as eta m Until a train section is full or passenger demands are fully distributed; step 4: calculating the number of passengers allocated on each train; for the passenger demand of the O-D pair (r, s) in the kth departure period, the number of passengers assigned to train j during the departure period isStep 5, if eta m >0, ending the stage and transferring to the (m+1) th stage, otherwise ending the whole passenger flow distribution process;
wherein w= { j } is a set of all trains; x is the stop sequence number; h (j) is the stop number of the train j; m is the running stage serial number of passenger flow distribution;a set of train options; RS is the set of all OD pairs; η (eta) m The allocable proportion of the mth passenger flow allocation stage is calculated;
the ticket price optimization adjusting unit is used for constructing a double-layer multi-train differentiated pricing optimization model of the inter-city high-speed railway, taking the income maximization of the passenger ticket as a target, adopting a passenger flow distribution method of the passenger demand distribution unit for considering the capacity constraint to evaluate a multi-train ticket price scheme, calculating an optimization target, and optimizing and adjusting the multi-train ticket price scheme according to the optimization target; the double-layer multi-train differentiated pricing optimization model is as follows:
upper layer model:
s.t.
(r,s)∈RS；
wherein ,probability of being a passenger demand during the kth departure period;
average fare for the train during the kth departure period for the passenger demand of OD pair (r, s);
the probability of being in the kth departure period for passenger demand is +.>Then the average train fare for OD pair (r, s);
indicating that the train is in the operating zoneThe lower limit of the fare on the segment (r, s) allowing a value;
an upper limit representing the permissible value of the fare of the train in the operating section (r, s);
LEG j representing the running section composition set of the train j;
and (3) a lower layer model: the passenger flow distribution method considering capacity constraint.
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