CN112529288A - Multi-train differential pricing strategy optimization method and system - Google Patents

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

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CN112529288A
CN112529288A CN202011438109.5A CN202011438109A CN112529288A CN 112529288 A CN112529288 A CN 112529288A CN 202011438109 A CN202011438109 A CN 202011438109A CN 112529288 A CN112529288 A CN 112529288A
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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 multi-train differential pricing strategy optimization method and a multi-train differential pricing strategy optimization system, wherein the method comprises the following steps: step S1, analyzing the time-varying characteristics of the travel demand of the passenger by using the historical ticketing data; step S2, describing the selection behavior of passengers in different departure time periods among the differently priced multiple trains by adopting multiple Logit models to obtain a time-period trip selection model; step S3, considering that the trip selection of passengers is limited by the transportation capacity of the train, designing a passenger flow distribution method considering capacity constraint, combining the Logit model, distributing the passenger time-varying requirements to the trains with capacity constraint, and obtaining the passenger requirements on each train; and S4, constructing a differential pricing optimization model of double-layer multi-row trains of the intercity high-speed railway, aiming at maximizing passenger ticket income, evaluating the multi-row ticket price scheme by adopting the passenger flow distribution method of the step S3, calculating an optimization target, and optimizing and adjusting the multi-row ticket price scheme according to the optimization target.

Description

Multi-train differential pricing strategy optimization method and system
Technical Field
The invention relates to a method and a system for differential pricing optimization of multiple trains of intercity high-speed railways, in particular to a method and a system for differential pricing strategy optimization of multiple trains of passengers considering passenger selection behaviors under time-varying requirements and capacity constraints.
Background
In recent years, with the rapid development of high-speed railways, more and more students begin to pay attention to the research on the revenue management problem of the railway transportation industry. However, most scholars only study the fare optimization problem of one train in view of the complexity and the solving difficulty of the practical problem. A discrete selection model is typically used to analyze the passenger's selection behavior.
Zhang and Ma, and the like, research the pricing problem of the group tickets of the high-speed railway train, but only consider the passenger demand between the starting station and the final station of one train, and limit the application range of the model. Riss and
Figure BDA0002829149700000011
the important role of passenger selection behavior modeling in railway revenue management is explained by the people, and experimental analysis is carried out on a single train aiming at the revenue management problem of a French high-speed railway. The 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-trip train in a pre-sale period is designed, an optimization model is designed to be convex planning, and the model is solved by adopting Lagrange multipliers and KKT conditions. Hetrakul and Cirillo research the comprehensive optimization problem of fare floating and seat allocation of railway trains, the method separately calculates the profit maximization problem of each train, adopts a hidden hierarchy model to describe the travel selection behavior of passengers on ticket buying time, and uses LINGO 12.0 software to solve.
There are also some scholars who study the fare optimization problem for multiple trains. Qin and Zeng and the like research a comprehensive optimization method of multi-train fare floating and seat allocation of a high-speed railway in a pre-sale period, a plurality of logit models are adopted to describe the selection behavior of passengers among a plurality of trains, the 4 trains are optimized and calculated by adopting an artificial bee colony algorithm, but the model parameters are directly given, the influence of the fare on the selection of passenger ticket buying time is not considered, and reasonable basis is lacked; hu and Shi et al studied similar problems and designed a large-scale example for analysis, but the solution quality was highly dependent on the initial solution and the global convergence of the algorithm could not be determined.
None of these studies above has considered the time varying needs of passengers. The passenger demand is a basic link in the revenue management, and researchers can predict and know the distribution of the travel demand of the passengers about relevant influence factors such as ticket prices, ticket buying time and the like based on historical ticket selling data, and assume that the travel demand of the passengers has randomness and accords with Poisson distribution and the like. In fact, some scholars have considered the time-varying needs of passengers in the problems of train schedule optimization, optimization of train operation schemes, and design of passenger flow distribution methods. But the time-varying requirements have not been fully studied in the train fare optimization problem.
In summary, the current status of fare optimization for railway trains is summarized as follows: (1) more scholars concentrate on researching the fare optimization problem of a single train, and lack research on the differential pricing optimization problem of multiple trains; (2) passenger demand is generally expressed as elastic demand on fares, random demand in a pre-sale period and the like, and the fluctuation characteristics of passenger demand in different departure periods are lack of research; (3) by aiming at the large-scale multi-trip train fare optimization problem, the convergence stability and the calculation efficiency of the solving algorithm are still to be improved.
Disclosure of Invention
In order to overcome the defects in the prior art, the invention aims to provide a method and a system for optimizing a multi-train differential pricing strategy, which aim to realize the inter-city high-speed railway multi-train differential pricing optimization by considering passenger selection behaviors under time-varying requirements and capacity constraints.
In order to achieve the above and other objects, the present invention provides a multi-row vehicle differentiated pricing strategy optimization method, which includes the following steps:
step S1, analyzing the time-varying characteristics of the travel demand of the passenger by using the historical ticketing data;
step S2, describing the selection behavior of passengers in different departure time periods among the differently priced multiple trains by adopting multiple Logit models to obtain a time-period trip selection model;
step S3, considering that the trip selection of passengers is limited by the transportation capacity of the train, designing a passenger flow distribution method considering capacity constraint, and combining the plurality of Logit models to distribute the passenger time-varying requirements to the trains with capacity constraint to obtain the passenger requirements on each train;
and S4, constructing a differential pricing optimization model of double-layer multi-row trains of the intercity high-speed railway, aiming at maximizing passenger ticket income, evaluating the multi-row ticket price scheme by adopting the passenger flow distribution method considering capacity constraint in the step S3, calculating an optimization target, and optimizing and adjusting the multi-row ticket price scheme according to the optimization target.
Preferably, in step S1, a statistical regression method is used to obtain the probability distribution of departure time interval required by the passenger according to the historical ticketing data.
Preferably, the OD for passenger travel is recorded as (r, s), r is the upper station, s is the lower station, and the OD records the passenger demand within one day for (r, s) as qrsThe probability that the passenger demand is in the kth departure time period is recorded
Figure BDA0002829149700000031
The passenger's demand in departure time k is recorded as
Figure BDA0002829149700000032
Then
Figure BDA0002829149700000033
Preferably, in step S2, the set of trains that stop at OD pair (r, S) and depart from station r in the kth time period is recorded as
Figure BDA0002829149700000034
The running time of the train j between OD pairs (r, s) is denoted as trs(j) And the fare is recorded as crs(j) Then the passenger's utility of selecting train j is expressed as
Figure BDA0002829149700000035
wherein ,θ1 and θ2Is a parameter, epsilonjIn the case of the random term,
according to the principle of a plurality of Logit models, OD is used for the passenger time-varying requirement of (r, s)
Figure BDA0002829149700000036
Selecting the probability of the train j as;
Figure BDA0002829149700000037
preferably, in step S2, a questionnaire is designed, and the time-interval travel selection model parameters are estimated using questionnaire data.
Preferably, in step S3, the passenger flow allocation method considering capacity constraint determines the probability of selecting trains by passenger time-varying demands according to the multiple logit models by designing allocation rules, and then determines the assignable proportion of the passenger time-varying demands of each travel OD pair according to the transportation capacity of the trains, that is, the ratio of the acceptable passenger time-varying demands of each OD pair to the total passenger time-varying demands of the OD pair, so as to determine the passenger demand F (j, x) allocated to each train, where 1 is greater than or equal to x is less than or equal to h (j) -1, j belongs to W, and meets the following capacity constraint condition:
F(j,x)≤CAj。
preferably, in step S3, the details of the mth passenger flow distribution stage are as follows:
step 1, for time-varying requirements
Figure BDA0002829149700000041
(r, s) e RS, k 7,8, …,22, constructing a set of optional trains, and recording the set as
Figure BDA0002829149700000042
Step 2, for time-varying requirements
Figure BDA0002829149700000043
(r, s) belongs to RS, k is 7,8, … and 22, and a multinomial Logit model is adopted to calculate in the set
Figure BDA0002829149700000044
The probability of selecting train j is marked as P (j | r, s, k, m);
and 3, distributing the unallocated passenger demands to the train as much as possible on the premise of meeting the capacity constraint, setting the proportion of the distributable demands of each O-D pair to the total demands of the O-D pairs to be the same, and recording as etamUntil a certain train section is full or passenger demands are completely distributed;
and 4, step 4: the number of passengers allocated per train trip is calculated. For the passenger demand of the O-D pair (r, s) in the kth departure period, the number of passengers assigned to the train j in this stage is
Figure BDA0002829149700000045
Step 5, if etam>0, the stage is finished and the (m +1) th stage is carried out, otherwise, the passenger flow distribution process is finished integrally.
Preferably, in step S4, the two-layer multi-row differential pricing optimization model is:
an upper layer model:
Figure BDA0002829149700000046
s.t.
Figure BDA0002829149700000047
Figure BDA0002829149700000048
Figure BDA0002829149700000049
(r,s)∈RS
Figure BDA00028291497000000410
(r,s)∈LEGj,j∈W
the lower layer model: the passenger flow distribution method considering the capacity constraint.
Preferably, in step S4, for the double-layer multi-row differential pricing optimization model, the optimization model is solved by using an improved direct search simulated annealing algorithm.
In order to achieve the above object, the present invention further provides a multi-row vehicle differentiated pricing strategy optimization system, including:
the time-varying demand analysis unit is used for analyzing time-varying characteristics of the travel demands of the passengers by using historical ticketing data;
the time-interval trip selection model construction unit is used for describing the selection behavior of passengers in different starting time intervals among the differently priced multiple trains by adopting multiple Logit models to obtain a time-interval trip selection model;
the passenger demand distribution unit is used for designing a passenger flow distribution method considering capacity constraint in consideration of the limitation of train transportation capacity on trip selection of passengers, and distributing passenger time-varying demands to trains with capacity constraint by combining the plurality of Logit models to obtain the passenger demand on each train;
and the ticket price optimization adjusting unit is used for constructing a differential pricing optimization model of double-layer multi-row cars of the intercity high-speed railway, evaluating a multi-row ticket price scheme by adopting a passenger flow distribution method considering capacity constraint of the passenger demand distribution unit with the goal of maximizing passenger ticket income, calculating an optimization goal, and optimizing and adjusting the multi-row ticket price scheme according to the optimization goal.
Compared with the prior art, the multi-train differential pricing strategy optimization method and system provided by the invention analyze passenger time-varying demand characteristics according to historical ticketing data to determine a passenger time-varying demand expression form, describe the selection behavior of the passenger time-varying demand among differentially-priced multi-train by adopting a plurality of Logit models, design a passenger flow distribution method considering capacity constraint to evaluate a pricing scheme, construct an intercity high-speed railway multi-train differential pricing optimization model based on the pricing scheme, optimally design the fare of the multi-train in each train operation section by taking the passenger ticket income maximization as a target, and finally solve the optimization model by an improved direct search simulated annealing algorithm, so that the purpose of intercity high-speed railway multi-train differential pricing optimization is realized.
Drawings
FIG. 1 is a flowchart illustrating steps of a multi-row differential pricing strategy optimization method according to the present invention;
fig. 2 is a system architecture diagram of a multi-row vehicle differential pricing strategy optimization system according to the present invention.
Detailed Description
Other advantages and capabilities of the present invention will be readily apparent to those skilled in the art from the present disclosure by describing the embodiments of the present invention with specific embodiments thereof in conjunction with the accompanying drawings. The invention is capable of other and different embodiments and its several details are capable of modification in various other respects, all without departing from the spirit and scope of the present invention.
Fig. 1 is a flowchart illustrating steps of a multi-row differential pricing strategy optimization method according to the present invention. The invention discloses a multi-train differential pricing strategy optimization method, which comprises the following steps:
and step S1, analyzing the time-varying characteristics of the travel demand of the passenger by using the historical ticketing data.
In the step, time-varying characteristics of passenger demands of the intercity high-speed railway are analyzed, and expression forms of the passenger time-varying demands are determined. In order to conveniently describe the time-varying characteristics of the passenger demands and obtain the time-varying demands of the passengers, the probability distribution of the departure time period of the passenger demands can be obtained by adopting a statistical regression method according to historical ticketing data.
Specifically, assume that the passenger is 7 o 'clock before and 23 o' clock according to the historical ticketing dataThe demands thereafter were all smaller, and therefore passenger demands between 7 and 23 points were investigated. For convenience of presentation, the operational time of day is divided into time periods, e.g., time periods [7:00,7:59 ], at hourly intervals]Referred to as period 7, time period [8:00,8:59 ]]Referred to as epoch 8 and so on, the time of day is divided into 16 epochs, epoch 7 through epoch 22. The OD (Origin Destination, getting on and getting off station) pair of the passenger trip is recorded as (r, s), r is the getting on station, s is the getting off station, and the passenger demand in one day of the OD pair (r, s) is recorded as qrsThe probability that the passenger demand is in the kth departure time period is recorded
Figure BDA0002829149700000061
The passenger's demand in departure time k is recorded as
Figure BDA0002829149700000062
Then
Figure BDA0002829149700000063
And step S2, describing the selection behaviors of passengers in different departure time periods among the differently priced multiple trains by adopting multiple Logit models to obtain a time period trip selection model, and estimating model parameters by using questionnaire survey data.
In step S2, a plurality of Logit models are used to analyze how the passenger time-varying demand selects a train among a plurality of trains with different pricing, so as to maximize the traveling utility.
For convenience of description, the following symbols are designed. The set formed by all stations is marked as SN, and the set formed by all OD pairs is marked as RS. The set of all trains is denoted as W ═ j }. For the train j epsilon W, let h (j) be the stop number of the train j,
Figure BDA0002829149700000064
order set for train j stopping along the way
Figure BDA0002829149700000065
Train j is at stop
Figure BDA0002829149700000066
To a stop station
Figure BDA0002829149700000067
Is called a train section and is marked as
Figure BDA0002829149700000068
The running sections of train j form a set, denoted as LEGj. For x ≦ x' and y ≦ y, the operating zone is called
Figure BDA0002829149700000071
Covering a run section
Figure BDA0002829149700000072
Is marked as
Figure BDA0002829149700000073
The transport capacity of train j is noted CAjIn the running section of the train
Figure BDA0002829149700000074
The passenger flow rate is marked as F (j, x), x is more than or equal to 1 and less than or equal to h (j) -1.
And limiting the passenger requirement of each departure time period to select the train which departs in the corresponding time period according to the passenger time-varying requirement. There are many factors that influence the selection of a train by passengers, and only the running time and fare of the train are considered here. Let the set of trains parked at OD pair (r, s) and departing from station r in the kth time period be denoted as
Figure BDA0002829149700000075
The running time of the train j between OD pairs (r, s) is denoted as trs(j) And the fare is recorded as crs(j) In that respect Then, the utility of the passenger selecting train j can be expressed as
Figure BDA0002829149700000076
wherein ,θ1 and θ2Is a parameter, epsilonjIn the case of the random term,
Figure BDA0002829149700000077
the effect of the randomness is represented as a random effect,
Figure BDA0002829149700000078
representing a determined portion of the random utility.
According to the principle of a plurality of Logit models, OD is used for the passenger time-varying requirement of (r, s)
Figure BDA0002829149700000079
Probability of selecting train j is
Figure BDA00028291497000000710
The above is a time-interval trip selection model.
Because the fare between the existing intercity railway trains does not show differentiation. Therefore, since the parameters of the model cannot be estimated from the historical ticketing data, in the present invention, an SP questionnaire is designed to investigate the passengers of the intercity railway. The method comprises the steps of surveying with Guangzhou interurban railway train stations and passengers of Guangzhou interurban railways, estimating parameters of a model and questionnaires, wherein 24 virtual ticket purchasing scenes are designed, each scene comprises 4 trains, and the information display of each train simulates ticket purchasing pages of a China 12306 website, namely the departure time, the arrival time, the on-board time and the ticket price of the train. The fare of the train is randomly floated up and down (floating up is not more than 20 percent and floating down is not more than 30 percent) on the basis of the existing fare, and the rest information is determined according to the current train schedule. According to the personal information filled by the passenger and the traveling habits, a virtual ticket purchasing scene is provided for the passenger, and the passenger can select one train. The questionnaire was unrolled onto the web in 3 months of 2020, and 1967 valid questionnaires were collected. The above model parameters were estimated from questionnaire survey data, and the results are shown in table 1.
TABLE 1 Multi-term Logit model parameter estimation
Figure BDA0002829149700000081
And step S3, considering that the trip selection of passengers is limited by the transportation capacity of the train, designing a passenger flow distribution method considering capacity constraint, and combining the plurality of Logit models to distribute the passenger time-varying requirements to the trains with capacity constraint to obtain the passenger requirements on each train.
Specifically, the passenger demand that can be accepted by each train is limited by transportation capacity, and when the demand is large, part of the passenger demand cannot be met. The passenger flow distribution method considering capacity constraint determines the probability of selecting trains according to the time-varying demands of passengers by designing a distribution rule according to the multiple logit models; and then determining the proportion of the passenger time-varying demands of each travel OD pair which can be allocated according to the transport capacity of the train, namely determining the ratio of the passenger time-varying demand which can be accepted by each OD pair to the total passenger time-varying demand of the OD pair, so as to determine the passenger demand F (j, x) allocated on each train, wherein x is more than or equal to 1 and less than or equal to h (j) -1, and j belongs to W, and the following capacity constraint conditions are met.
F(j,x)≤CAj (4)
CAjRepresenting the transport capacity of train j.
Considering that the passenger selects the train and is determined in the ticket purchasing process, 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, some train segments become full and the alternative trains for some passengers change. Therefore, the time points of the change are divided into dividing nodes, and the ticket purchasing process is divided into a plurality of stages. Within each classification phase, the alternative trains to which passengers are not assigned do not change. When all the time-varying demand allocations are complete or there is no remaining train capacity to meet the demand for unallocated passengers, the passenger flow allocation process ends. The details of the mth passenger flow distribution phase are as follows:
step 1: for time varying demands
Figure BDA0002829149700000082
(r, s) ∈ RS, k ═ 7,8, …,22, and a set of alternative trains (with remaining capacity) is constructed and recorded as
Figure BDA0002829149700000091
Step 2: for time varying demands
Figure BDA0002829149700000092
(r, s) belongs to RS, k is 7,8, … and 22, and a multinomial Logit model is adopted to calculate in the set
Figure BDA0002829149700000093
The probability of selecting train j is denoted as P (j | r, s, k, m).
And 3, step 3: on the premise of meeting capacity constraint, unallocated passenger demands are allocated to the train as much as possible, the proportion of allocable demands of each O-D pair to the total demands of the O-D pairs is set to be the same, and the proportion is recorded as etamUntil either a certain train section is full or passenger demand is fully allocated.
And 4, step 4: the number of passengers allocated per train trip is calculated. For the passenger demand of the O-D pair (r, s) in the kth departure period, the number of passengers assigned to the train j in this stage is
Figure BDA0002829149700000094
And 5, step 5: if etam>0, the stage is finished and the (m +1) th stage is carried out, otherwise, the passenger flow distribution process is finished integrally.
For train option sets in step 1 and step 2
Figure BDA0002829149700000095
And a selection probability P (j | r, s, k, m) calculated according to the following formula
Figure BDA0002829149700000096
Figure BDA0002829149700000097
For calculating the assignable proportion eta of the mth stagemFor each train operating section
Figure BDA0002829149700000098
An intermediate variable is set, denoted as Δ Fm(j, x) and the initial value is 0. In the mth phase, for each OD pair (r, s), each departure period k, each train trip
Figure BDA0002829149700000099
Each train operating section
Figure BDA00028291497000000910
The following cumulative calculation is performed:
Figure BDA00028291497000000911
wherein ,
Figure BDA00028291497000000912
representing hypothetical time-varying requirements
Figure BDA00028291497000000913
The amount of passenger traffic assigned to train j is not limited by the transport capacity in the mth stage. Thus, after the above-mentioned cumulative calculation is completed, ηmΔFm(j, x) indicates that all passenger time varying demands can be actually allocated to the train operation section in the mth stage
Figure BDA00028291497000000914
The following capacity constraints are satisfied:
ηmΔFm(j,x)≤CAj-F(j,x) (8)
wherein CAj-F (j, x) represents a train operating section
Figure BDA00028291497000000915
Remaining transport capacity at the beginning of the mth stage. And the proportion of each stage distribution satisfies
Figure BDA0002829149700000101
Thus ηmCan be calculated by equation (9):
Figure BDA0002829149700000102
at the end of the mth phase, the train operating section
Figure BDA0002829149700000103
The amount of passenger flow above is updated by equation (10):
F(j,x)＝F(j,x)+ηmΔFm(j,x) (10)
the passenger flow distribution method for the time-varying passenger demand in the mth stage is abbreviated as PACC, where the total number of the divided stages is M, that is, the passenger flow distribution method considering capacity constraint. The results of the passenger flow assignment can be used to evaluate a train fare scheme.
And S4, constructing a differential pricing optimization model of double-layer multi-row trains of the intercity high-speed railway, aiming at maximizing passenger ticket income, evaluating the multi-row ticket price scheme by adopting the passenger flow distribution method considering capacity constraint in the step S3, calculating an optimization target, and optimizing and adjusting the multi-row ticket price scheme according to the optimization target.
The optimization method synergistically optimizes the fare of the multiple trains in each running section, namely a decision variable, which is recorded as crs(j),j∈W,(r,s)∈LEGj. The train fare not only influences the selection of passengers among multiple trains, but also influences whether the passengers select trains to go out, namely the elasticity requirement. Increasing the train fare may increase revenue, but an excessive train fare may result in loss of passenger flow, diverting passengers to other alternative vehicles, such as automobiles. Therefore, the multi-row vehicle differential pricing optimization modelIn the model, an exponential function is used to describe the influence of the train fare on the total amount of passenger travel demand, as shown below.
Figure BDA0002829149700000104
wherein ,
Figure BDA0002829149700000105
represents the mean train fare of the OD pair (r, s); when OD is equal to (r, s) the average train fare is
Figure BDA0002829149700000106
The corresponding travel demand of the passengers is
Figure BDA0002829149700000107
Can be obtained according to historical ticket selling data; the parameter phi can measure the demand elasticity corresponding to the change of unit price, and the larger the value of phi is, the larger the price elasticity of the demand is.
Fare scheme c for a given trainrs(j) OD passenger demand for (r, s) in the kth departure period can be simply expressed as the train average fare
Figure BDA0002829149700000111
The probability of passenger demand in the kth departure time period is
Figure BDA0002829149700000112
Then the average train fare of the OD pair (r, s) is expressed as
Figure BDA0002829149700000113
Then, the two-tier multi-train differential pricing optimization model can be expressed as follows,
an upper layer model:
Figure BDA0002829149700000114
s.t.
the formulae (11) to (13), (r, s) ∈ RS
Figure BDA0002829149700000115
The lower layer model: PACC passenger flow distribution method
Wherein Z represents the income of the passenger ticket,
Figure BDA0002829149700000116
and
Figure BDA0002829149700000117
respectively representing the lower limit and the upper limit of the fare allowable value of the train in the running section (r, s). In the upper model, the railway transportation enterprise optimizes a train fare scheme; and in the lower-layer model, the train fare scheme is evaluated according to a passenger flow distribution method. And (3) calculating an optimization target formula (14) by the railway transportation enterprise according to the passenger flow distribution result, and further evaluating and optimizing the train fare scheme.
Preferably, in the embodiment of the present invention, for the double-layer multi-row differential pricing optimization model, an improved direct search simulated annealing algorithm is adopted to solve the optimization model.
In particular, the decision variable c in the optimization model described abovers(j),(r,s)∈LEGjThe number of j ∈ W is large (e.g. when the number of trains is 50, and there are 4 travel zones per train, the decision variables reach 200), so a high-dimensional combinatorial optimization problem needs to be solved.
The Simulated Annealing (SA) algorithm has global convergence and is widely used in engineering practice. Ai and
Figure BDA0002829149700000118
the DSA algorithm is designed by the people, and the algorithm is improvedThe calculation efficiency and the calculation accuracy. In order to improve the convergence stability and the convergence efficiency of the algorithm in solving the high-dimensional optimization problem, the invention improves the new solution generation method and the algorithm structure, and designs an improved Direct Search Simulated Annealing (MDSA) algorithm.
The new solution generation method of the MDSA algorithm comprises the following 3 steps: (1) randomly generating a new solution by variable-scale Cauchy distribution, wherein the method randomly generates the new solution by adopting a variable-scale Cauchy distribution mode in a solution search space; (2) and combining the solution with the optimal solution to generate a new solution, wherein the method randomly selects a certain number of solutions in a solution set to be randomly combined with the current optimal solution to generate the new solution. (3) Self-adaptive optimization generates a new solution, and the method generates the new solution by random disturbance in normal distribution near the current optimal solution.
For the convenience of algorithm description, let C, C remember the total number of decision variables as cnL and CUThe vectors, respectively the decision variables and their lower and upper limits, are cn-dimensional column vectors, as shown below
Figure BDA0002829149700000121
Figure BDA0002829149700000122
Figure BDA0002829149700000123
Then
CL≤C≤CU (19)
The solution vector satisfying equation (19) constitutes a search space, denoted as S. According to the constraint conditions of the optimization model, all solution vectors C in the search space S are feasible solutions. Let E (C) ═ z (C), then the optimization objective formula (14) is equivalent to min E (C), E (C) as the evaluation function in the MDSA algorithm.
Three new solution generation methods in the MDSA algorithm are described below.
(1) Random generation of new solution by variable-scale Cauchy distribution
A new solution C generated in a varying-scale cauchy distribution within the search space S. The Cauchy distribution probability density function centered at the origin is:
Figure BDA0002829149700000124
in the formula
Figure BDA0002829149700000125
The iteration number based on the algorithm is calculated according to the following formula (21) as a scale parameter so as to realize large-range search in the initial optimization stage and small-range fine search in the later optimization stage.
Figure BDA0002829149700000131
Wherein a is the number of cooling iterations.
The calculation formula for the new solution C is as follows:
Figure BDA0002829149700000132
Figure BDA0002829149700000133
wherein the symbols
Figure BDA0002829149700000139
Representing a 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 taking function, and w is a random number generated in (0,1) in a uniform distribution.
(2) Combining with the best solution to generate a new solution
Firstly, RN solutions are randomly selected from the solution set and are marked as
Figure BDA0002829149700000134
The RN solutions are compared with the optimal solution CBestRandom combinations are performed to generate a new solution C, each component of which is determined according to equation (24).
Figure BDA0002829149700000135
wherein ,wiIs [0,1 ]]Random numbers generated in a uniform distribution. RN is determined according to solution set, and the size of the solution set can be about 8%. The method can improve the search efficiency of the optimal solution and improve the convergence stability of the algorithm.
(3) Adaptive methods generate new solutions
The new solution C in the adaptive method is the best solution C in the search space SBestThe random disturbance is generated in the neighborhood according to normal distribution, so that the algorithm can be prevented from falling into local extreme values too early.
Figure BDA0002829149700000136
Wherein the symbols
Figure BDA0002829149700000137
Representing a Hadamard product, b a search radius adjustment coefficient, I an adaptation factor, and y a column vector of cn dimension, determined according to equations (26) to (28), respectively:
Figure BDA0002829149700000138
Figure BDA0002829149700000141
Figure BDA0002829149700000142
wherein TaAs the current temperature, the temperature of the battery is,mais a random number, gamma, uniformly distributed within the interval (0,5)iIs the interval [0,1]The random number is uniformly distributed, beta is the self-adaptive probability, and is generally 0.1. SY is a cn-dimensional column vector randomly obtained according to a standard normal distribution.
After calculation according to equation (25), the resulting new solution C may exceed the search space S, and the components in the new solution C are corrected according to the following equation:
Figure BDA0002829149700000143
the following describes the structural design of the MDSA algorithm of the present invention
In the MDSA algorithm of the present invention, the initial temperature T0The determination of (2) needs to satisfy that the reception probability of the new solution in the initial stage is greater than a predetermined value (generally between 0.8 and 0.9). Length of the Mahalanobis chain LaCalculated according to the following formula (30):
Figure BDA0002829149700000144
probability P of new solution being acceptedaccCalculated according to the following equation (31):
Figure BDA0002829149700000145
coefficient of temperature reduction thetaaHas a value range of [ theta ]min＝0.80,θmax＝0.9]Initial value of θ0＝0.85，θaReference [24 ]]. After a certain number of cooling cycles, the value of the function E is evaluated at the optimum point if several successive cooling cycles (marked with Delta a) are carried outminIs unchanged or has no obvious change (i.e. the product is not changed)
Figure BDA0002829149700000146
δ is a given positive real number) as a criterion for the algorithm to fall into a local extremum. When Δ a<τ (τ is a given positive integer), a new solution is randomly generated from a variable scale Cauchy distribution with probability scp or combined with the optimal point with probability 1-scpGenerating a new solution; when delta a is larger than or equal to tau, a new solution is generated by adopting a self-adaptive method.
Specifically, the structure of the MDSA algorithm is as follows.
Start of
Randomly generating N-7 (cn +1) solutions to form an initial solution set A;
for each solution in the set a, a determination is made, performed,
from equations (11) - (13), the elastic requirement q of each OD pair is calculatedrs；
The time-varying requirement for each OD pair is calculated from equation (1)
Figure BDA0002829149700000152
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 solution and the worst solution in A and the corresponding evaluation function value Emin and Emax；
Initializing parameters, determining the initial temperature T according to the rule of thumb0The cooling iteration number a is 0;
Figure BDA0002829149700000151
Figure BDA0002829149700000161
preferably, the method can be expanded to the problem of price variation floating optimization of the multiple trains of tickets in the pre-sale period. The problem is that the selection behavior of the passenger is expanded by one dimension, the passenger not only needs to select among multiple trains, but also relates to the selection problem of the early ticket buying period, relevant data needs to be collected to solve the problem, and the influence condition of multi-row ticket price differential floating in the pre-sale period on the selection behavior of the passenger is analyzed.
Fig. 2 is a system architecture diagram of a multi-row vehicle differential pricing strategy optimization system according to the present invention. The invention relates to a multi-train differential pricing strategy optimization system, which comprises:
and the time-varying demand analysis unit 201 is used for analyzing the time-varying characteristics of the travel demand of the passenger by using the historical ticketing data.
In this step, the time-varying demand analysis unit 201 analyzes the time-varying characteristics of the passenger demand of the intercity high-speed railway, and determines the expression form of the passenger time-varying demand. In order to conveniently describe the time-varying characteristics of the passenger demands and obtain the time-varying demands of the passengers, the probability distribution of the departure time period of the passenger demands can be obtained by adopting a statistical regression method according to historical ticketing data.
Specifically, it is assumed that the amount of demand of passengers before 7 o 'clock and after 23 o' clock is small according to the historical ticketing data, and therefore, the passenger demand between 7 o 'clock and 23 o' clock is studied. For convenience of presentation, the operational time of day is divided into time periods, e.g., time periods [7:00,7:59 ], at hourly intervals]Referred to as period 7, time period [8:00,8:59 ]]Referred to as epoch 8 and so on, the time of day is divided into 16 epochs, epoch 7 through epoch 22. Marking the travel OD of the passenger as (r, s), wherein r is the upper station, s is the lower station, and the passenger demand of the OD for (r, s) within one day as qrsThe probability that the passenger demand is in the kth departure time period is recorded
Figure BDA0002829149700000171
The passenger's demand in departure time k is recorded as
Figure BDA0002829149700000172
Then
Figure BDA0002829149700000173
The time-share trip selection model construction unit 202 is configured to describe, by using multiple Logit models, selection behaviors of passengers in different departure time shares among differently priced multiple trains, obtain a time-share trip selection model, and estimate model parameters by using questionnaire survey data.
In the time-interval outgoing row selection model construction unit 202, a plurality of Logit models are adopted to analyze how the passenger time-varying demand selects a train from a plurality of trains with different pricing, so that the outgoing utility is maximized.
For convenience of description, the following symbols are designed: the set formed by all stations is marked as SN, and the set formed by all OD pairs is marked as RS. The set of all trains is denoted as W ═ j }. For the train j epsilon W, let h (j) be the stop number of the train j,
Figure BDA0002829149700000174
order set for train j stopping along the way
Figure BDA0002829149700000175
Train j is at stop
Figure BDA0002829149700000176
To a stop station
Figure BDA0002829149700000177
Is called a train section and is marked as
Figure BDA0002829149700000178
The running sections of train j form a set, denoted as LEGj. For x ≦ x′And y is′Less than or equal to y, weighing operation section
Figure BDA0002829149700000179
Covering a run section
Figure BDA00028291497000001710
Is marked as
Figure BDA00028291497000001711
The transport capacity of train j is noted CAjIn the running section of the train
Figure BDA00028291497000001712
The passenger flow rate is marked as F (j, x), x is more than or equal to 1 and less than or equal to h (j) -1.
According to the time-varying requirements of passengers, the selection of the passenger requirements in each departure time period is correspondingly limitedThe train which starts within the time interval. There are many factors that influence the selection of a train by passengers, and only the running time and fare of the train are considered here. Let the set of trains parked at OD pair (r, s) and departing from station r in the kth time period be denoted as
Figure BDA0002829149700000181
The running time of the train j between OD pairs (r, s) is denoted as trs(j) And the fare is recorded as crs(j) In that respect Then, the utility of the passenger selecting train j can be expressed as
Figure BDA0002829149700000182
wherein ,θ1 and θ2Is a parameter, epsilonjIs a random term.
According to the principle of a plurality of Logit models, OD is used for the passenger time-varying requirement of (r, s)
Figure BDA0002829149700000183
Probability of selecting train j is
Figure BDA0002829149700000184
The above is a time-interval trip selection model.
Because the fare between the existing intercity railway trains does not show differentiation. Therefore, since the parameters of the model cannot be estimated from the historical ticketing data, in the present invention, an SP questionnaire is designed to investigate the passengers of the intercity railway. The method comprises the steps of surveying with Guangzhou interurban railway train stations and passengers of Guangzhou interurban railways, estimating parameters of a model and questionnaires, wherein 24 virtual ticket purchasing scenes are designed, each scene comprises 4 trains, and the information display of each train simulates ticket purchasing pages of a China 12306 website, namely the departure time, the arrival time, the on-board time and the ticket price of the train. The fare of the train is randomly floated up and down (floating up is not more than 20 percent and floating down is not more than 30 percent) on the basis of the existing fare, and the rest information is determined according to the current train schedule. According to the personal information filled by the passenger and the traveling habits, a virtual ticket purchasing scene is provided for the passenger, and the passenger can select one train. The questionnaire was unrolled onto the web in 3 months of 2020, and 1967 valid questionnaires were collected. And estimating the model parameters according to questionnaire survey data.
The passenger demand allocation unit 203 is designed by considering that the trip selection of passengers is limited by the transportation capacity of the train and considering capacity constraint, and allocates the passenger time-varying demand to the train with capacity constraint by combining the plurality of Logit models to obtain the passenger demand on each train.
Specifically, the passenger demand that can be accepted by each train is limited by transportation capacity, and when the demand is large, part of the passenger demand cannot be met. The passenger flow distribution method considering capacity constraint determines the probability of selecting trains according to the time-varying demands of passengers by designing a distribution rule according to the multiple logit models; and then determining the proportion of the passenger time-varying demands of each travel OD pair which can be allocated according to the transport capacity of the train, namely determining the ratio of the passenger time-varying demand which can be accepted by each OD pair to the total passenger time-varying demand of the OD pair, so as to determine the passenger demand F (j, x) allocated on each train, wherein x is more than or equal to 1 and less than or equal to h (j) -1, and j belongs to W, and the following capacity constraint conditions are met.
F(j,x)≤CAj (4)
Considering that the passenger selects the train and is determined in the ticket purchasing process, 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, some train segments become full and the alternative trains for some passengers change. Therefore, the time points of the change are divided into dividing nodes, and the ticket purchasing process is divided into a plurality of stages. Within each classification phase, the alternative trains to which passengers are not assigned do not change. When all the time-varying demand allocations are complete or there is no remaining train capacity to meet the demand for unallocated passengers, the passenger flow allocation process ends. The details of the mth passenger flow distribution phase are as follows:
1 stThe method comprises the following steps: for time varying demands
Figure BDA0002829149700000191
(r, s) ∈ RS, k ═ 7,8, …,22, and a set of alternative trains (with remaining capacity) is constructed and recorded as
Figure BDA0002829149700000192
Step 2: for time varying demands
Figure BDA0002829149700000193
(r, s) belongs to RS, k is 7,8, … and 22, and a multinomial Logit model is adopted to calculate in the set
Figure BDA0002829149700000194
The probability of selecting train j is denoted as P (j | r, s, k, m).
And 3, step 3: on the premise of meeting capacity constraint, unallocated passenger demands are allocated to the train as much as possible, the proportion of allocable demands of each O-D pair to the total demands of the O-D pairs is set to be the same, and the proportion is recorded as etamUntil either a certain train section is full or passenger demand is fully allocated.
And 4, step 4: the number of passengers allocated per train trip is calculated. For the passenger demand of the O-D pair (r, s) in the kth departure period, the number of passengers assigned to the train j in this stage is
Figure BDA0002829149700000195
And 5, step 5: if etam>0, the stage is finished and the (m +1) th stage is carried out, otherwise, the passenger flow distribution process is finished integrally.
For train option sets in step 1 and step 2
Figure BDA0002829149700000196
And a selection probability P (j | r, s, k, m) calculated according to the following formula
Figure BDA0002829149700000201
Figure BDA0002829149700000202
For calculating the assignable proportion eta of the mth stagemFor each train operating section
Figure BDA0002829149700000203
An intermediate variable is set, denoted as Δ Fm(j, x) and the initial value is 0. In the mth phase, for each OD pair (r, s), each departure period k, each train trip
Figure BDA0002829149700000204
Each train operating section
Figure BDA0002829149700000205
The following cumulative calculation is performed:
Figure BDA0002829149700000206
wherein ,
Figure BDA0002829149700000207
representing hypothetical time-varying requirements
Figure BDA0002829149700000208
The amount of passenger traffic assigned to train j is not limited by the transport capacity in the mth stage. Thus, after the above-mentioned cumulative calculation is completed, ηmΔFm(j, x) indicates that all passenger time varying demands can be actually allocated to the train operation section in the mth stage
Figure BDA0002829149700000209
The following capacity constraints are satisfied:
ηmΔFm(j,x)≤CAj-F(j,x) (8)
wherein CAj-F (j, x) represents a train operating section
Figure BDA00028291497000002010
Remaining transport capacity at the beginning of the mth stage. And the proportion of each stage distribution satisfies
Figure BDA00028291497000002011
Thus ηmCan be calculated by equation (9):
Figure BDA00028291497000002012
at the end of the mth phase, the train operating section
Figure BDA00028291497000002013
The amount of passenger flow above is updated by equation (10):
F(j,x)＝F(j,x)+ηmΔFm(j,x) (10)
the passenger flow distribution method for the time-varying passenger demand in the mth stage is abbreviated as PACC, where the total number of the divided stages is M, that is, the passenger flow distribution method considering capacity constraint. The results of the passenger flow assignment can be used to evaluate a train fare scheme.
The fare optimization adjusting unit 204 is used for constructing a differential pricing optimization model of double-layer multi-row trains of the intercity high-speed railway, evaluating a multi-row fare scheme by adopting a passenger flow distribution method considering capacity constraint of the passenger demand distribution unit 203 with the goal of maximizing passenger ticket income, calculating an optimization goal, and optimizing and adjusting the multi-row fare scheme according to the optimization goal.
The optimization method synergistically optimizes the fare of the multiple trains in each running section, namely a decision variable, which is recorded as crs(j),j∈W,(r,s)∈LEGj. The train fare not only influences the selection of passengers among multiple trains, but also influences whether the passengers select trains to go out, namely the elasticity requirement. Increasing the train fare may increase revenue, but an excessive train fare may result in loss of passenger flow and cause a loss of passenger flowPassengers are turning to other alternative vehicles, such as automobiles. Therefore, in the multi-train differential pricing optimization model, an exponential function is used to describe the influence of the train fare on the total passenger travel demand, as shown below.
Figure BDA0002829149700000211
wherein ,
Figure BDA0002829149700000212
represents the mean train fare of the OD pair (r, s); when OD is equal to (r, s) the average train fare is
Figure BDA0002829149700000213
The corresponding travel demand of the passengers is
Figure BDA0002829149700000214
Can be obtained according to historical ticket selling data; the parameter phi can measure the demand elasticity corresponding to the change of unit price, and the larger the value of phi is, the larger the price elasticity of the demand is.
Fare scheme c for a given trainrs(j) OD passenger demand for (r, s) in the kth departure period can be simply expressed as the train average fare
Figure BDA0002829149700000215
The probability of passenger demand in the kth departure time period is
Figure BDA0002829149700000216
Then the average train fare of the OD pair (r, s) is expressed as
Figure BDA0002829149700000217
Then, the two-tier multi-train differential pricing optimization model can be expressed as follows,
an upper layer model:
Figure BDA0002829149700000218
s.t.
the formulae (11) to (13), (r, s) ∈ RS
Figure BDA0002829149700000219
The lower layer model: PACC passenger flow distribution method
Wherein Z represents the income of the passenger ticket,
Figure BDA0002829149700000221
and
Figure BDA0002829149700000222
respectively representing the lower limit and the upper limit of the fare allowable value of the train in the running section (r, s). In the upper model, the railway transportation enterprise optimizes a train fare scheme; and in the lower-layer model, the train fare scheme is evaluated according to a passenger flow distribution method. And (3) calculating an optimization target formula (14) by the railway transportation enterprise according to the passenger flow distribution result, and further evaluating and optimizing the train fare scheme.
Preferably, in the embodiment of the present invention, for the double-layer multi-row differential pricing optimization model, an improved direct search simulated annealing algorithm is adopted to solve the optimization model.
In particular, the decision variable c in the optimization model described abovers(j),(r,s)∈LEGjThe number of j ∈ W is large (e.g. when the number of trains is 50, and there are 4 travel zones per train, the decision variables reach 200), so a high-dimensional combinatorial optimization problem needs to be solved.
The Simulated Annealing (SA) algorithm has global convergence and is widely used in engineering practice. Ai and
Figure BDA0002829149700000223
the DSA algorithm is designed by the people, and the calculation efficiency and the calculation precision of the algorithm are improved. In order to improve the convergence stability and the convergence efficiency of the algorithm in solving the high-dimensional optimization problem, the invention improves the new solution generation method and the algorithm structure, and designs an improved Direct Search Simulated Annealing (MDSA) algorithm.
The new solution generation method of the MDSA algorithm comprises the following 3 steps: (1) randomly generating a new solution by variable-scale Cauchy distribution, wherein the method randomly generates the new solution by adopting a variable-scale Cauchy distribution mode in a solution search space; (2) and combining the solution with the optimal solution to generate a new solution, wherein the method randomly selects a certain number of solutions in a solution set to be randomly combined with the current optimal solution to generate the new solution. (3) Self-adaptive optimization generates a new solution, and the method generates the new solution by random disturbance in normal distribution near the current optimal solution.
For the convenience of algorithm description, let C, C remember the total number of decision variables as cnL and CUThe vectors, respectively the decision variables and their lower and upper limits, are cn-dimensional column vectors, as shown below
Figure BDA0002829149700000224
Figure BDA0002829149700000225
Figure BDA0002829149700000231
Then
CL≤C≤CU (19)
The solution vector satisfying equation (19) constitutes a search space, denoted as S. According to the constraint conditions of the optimization model, all solution vectors C in the search space S are feasible solutions. Let E (C) ═ z (C), then the optimization objective formula (14) is equivalent to min E (C), E (C) as the evaluation function in the MDSA algorithm.
Three new solution generation methods in the MDSA algorithm are described below.
(1) Random generation of new solution by variable-scale Cauchy distribution
A new solution C generated in a varying-scale cauchy distribution within the search space S. The Cauchy distribution probability density function centered at the origin is:
Figure BDA0002829149700000232
in the formula
Figure BDA0002829149700000233
The iteration number based on the algorithm is calculated according to the following formula (21) as a scale parameter so as to realize large-range search in the initial optimization stage and small-range fine search in the later optimization stage.
Figure BDA0002829149700000234
Wherein a is the number of cooling iterations.
The calculation formula for the new solution C is as follows:
Figure BDA0002829149700000235
Figure BDA0002829149700000236
wherein the symbols
Figure BDA0002829149700000237
Representing a 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 taking function, and w is a random number generated in (0,1) in a uniform distribution.
(2) Combining with the best solution to generate a new solution
First from solution to solutionRandomly selecting RN solutions in the set, and marking as
Figure BDA0002829149700000238
The RN solutions are compared with the optimal solution CBestRandom combinations are performed to generate a new solution C, each component of which is determined according to equation (24).
Figure BDA0002829149700000241
wherein ,wiIs [0,1 ]]Random numbers generated in a uniform distribution. RN is determined according to solution set, and the size of the solution set can be about 8%. The method can improve the search efficiency of the optimal solution and improve the convergence stability of the algorithm.
(3) Adaptive methods generate new solutions
The new solution C in the adaptive method is the best solution C in the search space SBestThe random disturbance is generated in the neighborhood according to normal distribution, so that the algorithm can be prevented from falling into local extreme values too early.
Figure BDA0002829149700000242
Wherein the symbols
Figure BDA0002829149700000243
Representing a Hadamard product, b a search radius adjustment coefficient, I an adaptation factor, and y a column vector of cn dimension, determined according to equations (26) to (28), respectively:
Figure BDA0002829149700000244
Figure BDA0002829149700000245
Figure BDA0002829149700000246
wherein TaIs the current temperature, maIs a random number, gamma, uniformly distributed within the interval (0,5)iIs the interval [0,1]The random number is uniformly distributed, beta is the self-adaptive probability, and is generally 0.1. SY is a cn-dimensional column vector randomly obtained according to a standard normal distribution.
After calculation according to equation (25), the resulting new solution C may exceed the search space S, and the components in the new solution C are corrected according to the following equation:
Figure BDA0002829149700000247
the following describes the structural design of the MDSA algorithm of the present invention
In the MDSA algorithm of the present invention, the initial temperature T0The determination of (2) needs to satisfy that the reception probability of the new solution in the initial stage is greater than a predetermined value (generally between 0.8 and 0.9). Length of the Mahalanobis chain LaCalculated according to the following formula (30):
Figure BDA0002829149700000251
probability P of new solution being acceptedaccCalculated according to the following equation (31):
Figure BDA0002829149700000252
coefficient of temperature reduction thetaaHas a value range of [ theta ]min＝0.80,θmax＝0.9]Initial value of θ0＝0.85，θaReference [24 ]]. After a certain number of cooling cycles, the value of the function E is evaluated at the optimum point if several successive cooling cycles (marked with Delta a) are carried outminIs unchanged or has no obvious change (i.e. the product is not changed)
Figure BDA0002829149700000253
δ is a given positive real number) as a criterion for the algorithm to fall into a local extremum. When Δ a<τ (τ is given positiveInteger), randomly generating a new solution by variable-scale Cauchy distribution with probability scp or combining probability 1-scp with the optimal point; when delta a is larger than or equal to tau, a new solution is generated by adopting a self-adaptive method.
Specifically, the structure of the MDSA algorithm is as follows.
Figure BDA0002829149700000254
Figure BDA0002829149700000261
Figure BDA0002829149700000271
Examples
In the embodiment of the invention, numerical analysis is carried out by taking the Guangzhou intercity railway as an example, and the fare optimization conditions of multiple trains with different departure time periods under different elasticity demand coefficients are tested by using the method. The calculation result shows that: the mean square deviation of the optimized values is within 100, and the average cooling frequency is within 200, which shows that the optimization 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 the passenger ticket income is large; for 1.6, the ticket income is increased by 10.25%.
In conclusion, the multi-train differential pricing strategy optimization method and system provided by the invention analyze passenger time-varying demand characteristics according to historical ticketing data to determine a passenger time-varying demand expression form, describe the selection behavior of the passenger time-varying demand among differentially priced multi-train trains by adopting a plurality of Logit models, design a passenger flow distribution method considering capacity constraint to evaluate a pricing scheme, construct an intercity high speed railway multi-train differential pricing optimization model based on the pricing scheme, optimally design the fare of the multi-train in each train operation section by taking passenger ticket income maximization as a target, and finally solve the optimization model by an improved direct search simulated annealing algorithm, thereby achieving the purpose of intercity high speed railway multi-train differential pricing optimization.
The foregoing embodiments are merely illustrative of the principles and utilities of the present invention and are not intended to limit the invention. Modifications and variations can be made to the above-described embodiments by those skilled in the art without departing from the spirit and scope of the present invention. Therefore, the scope of the invention should be determined from the following claims.

Claims (10)

1. A multi-train differential pricing strategy optimization method comprises the following steps:
step S1, analyzing the time-varying characteristics of the travel demand of the passenger by using the historical ticketing data;
step S2, describing the selection behavior of passengers in different departure time periods among the differently priced multiple trains by adopting multiple Logit models to obtain a time-period trip selection model;
step S3, considering that the trip selection of passengers is limited by the transportation capacity of the train, designing a passenger flow distribution method considering capacity constraint, and combining the plurality of Logit models to distribute the passenger time-varying requirements to the trains with capacity constraint to obtain the passenger requirements on each train;
and S4, constructing a differential pricing optimization model of double-layer multi-row trains of the intercity high-speed railway, aiming at maximizing passenger ticket income, evaluating the multi-row ticket price scheme by adopting the passenger flow distribution method considering capacity constraint in the step S3, calculating an optimization target, and optimizing and adjusting the multi-row ticket price scheme according to the optimization target.
2. The multi-train differential pricing strategy optimization method according to claim 1, wherein: in step S1, a statistical regression method is used to obtain the probability distribution of departure time period required by the passenger according to the historical ticketing data.
3. The multi-train differential pricing strategy optimization method according to claim 2, wherein: the travel OD of the passenger is marked as (r, s), wherein r is the upper station and s is the lower stationStation, OD records the passenger demand within one day for (r, s) as qrsThe probability that the passenger demand is in the kth departure time period is recorded
Figure FDA0002829149690000011
The passenger's demand in departure time k is recorded as
Figure FDA0002829149690000012
Then
Figure FDA0002829149690000013
4. The multi-train differential pricing strategy optimization method according to claim 3, wherein: in step S2, the set of trains that stop at the OD pair (r, S) and depart from the station r in the kth time zone is recorded as
Figure FDA0002829149690000014
The running time of the train j between OD pairs (r, s) is denoted as trs(j) And the fare is recorded as crs(j) Then the passenger's utility of selecting train j is expressed as
Figure FDA0002829149690000015
wherein ,θ1 and θ2Is a parameter, epsilonjIn the case of the random term,
Figure FDA0002829149690000016
representing random utility
Figure FDA0002829149690000017
The part of (a) to be determined,
according to the principle of a plurality of Logit models, OD is used for the passenger time-varying requirement of (r, s)
Figure FDA0002829149690000018
Selecting the probability of the train j as;
Figure FDA0002829149690000021
5. the multi-train differential pricing strategy optimization method of claim 4, wherein: in step S2, a questionnaire survey is designed, and the time-interval row selection model parameters are estimated using questionnaire survey data.
6. The multi-train differential pricing strategy optimization method according to claim 5, wherein: in step S3, the passenger flow allocation method considering capacity constraint determines the probability of selecting trains according to the multiple logit models by designing allocation rules, and then determines the allocable proportion of the passenger time varying demand of each travel OD pair according to the transportation capacity of the trains, i.e. the ratio of the passenger time varying demand that each OD pair can accept to the total passenger time varying demand of the OD pair, thereby determining the passenger demand F (j, x) allocated to each train, where x is greater than or equal to 1 and less than or equal to h (j) -1, and j ∈ W, and satisfying the following capacity constraint conditions:
F(j,x)≤CAj
wherein CAjRepresenting the transport capacity of train j.
7. The multi-train differential pricing strategy optimization method of claim 6, wherein: in step S3, the details of the mth passenger flow distribution stage are as follows:
step 1, for time-varying requirements
Figure FDA0002829149690000022
Constructing a set of alternative trains, denoted
Figure FDA0002829149690000023
Step 2, for time-varying requirements
Figure FDA0002829149690000024
Computing in the set by adopting a plurality of Logit models
Figure FDA0002829149690000025
The probability of selecting train j is marked as P (j | r, s, k, m);
and 3, distributing the unallocated passenger demands to the train as much as possible on the premise of meeting the capacity constraint, setting the proportion of the distributable demands of each O-D pair to the total demands of the O-D pairs to be the same, and recording as etamUntil a certain train section is full or passenger demands are completely distributed;
and 4, step 4: the number of passengers allocated per train trip is calculated. For the passenger demand of the O-D pair (r, s) in the kth departure period, the number of passengers assigned to the train j in this stage is
Figure FDA0002829149690000026
Step 5, if etam>0, the stage is finished and the (m +1) th stage is carried out, otherwise, the passenger flow distribution process is finished integrally.
8. The multi-train differential pricing strategy optimizing method of claim 7, wherein in step S4, the two-layer multi-train differential pricing optimization model is,
an upper layer model:
Figure FDA0002829149690000031
s.t.
Figure FDA0002829149690000032
Figure FDA0002829149690000033
Figure FDA0002829149690000034
Figure FDA0002829149690000035
the lower layer model: the passenger flow distribution method considering the capacity constraint.
9. The multi-row differential pricing strategy optimizing method of claim 8, wherein in step S4, for the double-layer multi-row differential pricing optimization model, the optimization model is solved by using an improved direct search simulated annealing algorithm.
10. A multi-train differential 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 using historical ticketing data;
the time-interval trip selection model construction unit is used for describing the selection behavior of passengers in different starting time intervals among the differently priced multiple trains by adopting multiple Logit models to obtain a time-interval trip selection model;
the passenger demand distribution unit is used for designing a passenger flow distribution method considering capacity constraint in consideration of the limitation of train transportation capacity on trip selection of passengers, and distributing passenger time-varying demands to trains with capacity constraint by combining the plurality of Logit models to obtain the passenger demand on each train;
and the ticket price optimization adjusting unit is used for constructing a differential pricing optimization model of double-layer multi-row cars of the intercity high-speed railway, evaluating a multi-row ticket price scheme by adopting a passenger flow distribution method considering capacity constraint of the passenger demand distribution unit with the goal of maximizing passenger ticket income, calculating an optimization goal, and optimizing and adjusting the multi-row ticket price scheme according to the optimization goal.
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