CN112950015A - Railway ticket amount pre-classifying method based on self-adaptive learning rate particle swarm optimization - Google Patents

Railway ticket amount pre-classifying method based on self-adaptive learning rate particle swarm optimization Download PDF

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CN112950015A
CN112950015A CN202110214646.XA CN202110214646A CN112950015A CN 112950015 A CN112950015 A CN 112950015A CN 202110214646 A CN202110214646 A CN 202110214646A CN 112950015 A CN112950015 A CN 112950015A
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李梦莹
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Abstract

In order to realize intelligent allocation of the ticket amount based on the railway passenger flow demand, the invention discloses a railway ticket amount pre-allocation method based on a self-adaptive learning rate particle swarm algorithm.

Description

Railway ticket amount pre-classifying method based on self-adaptive learning rate particle swarm optimization
Technical Field
The invention uses a Particle Swarm algorithm (PSO) based on Adaptive motion Estimation (Adam) to optimize the railway fare pre-dividing strategy.
Background
The traditional railway fare distribution strategy adopts a mode of manually fixing the distribution fare of each station, the situation that the distribution fare is not matched with the actual demand is often generated, the ticket purchasing demand of a user cannot be met, and the income of a one-way railway line is also influenced. With the rapid development of Chinese economy, the running density of passenger trains on high-speed railways is gradually improved, and the traditional mode that tickets are fixedly distributed by stations manually is cancelled in the ticket distribution of passenger trains on high-speed railways. The full-row tickets are stored in the originating station in a centralized way, and the problem of transport capacity of stations along the way is solved through a ticket pre-dividing way and a ticket public and multiplexing way.
The ticket amount pre-distribution strategy is a new ticket selling organization strategy, and ticket amount pre-distribution is carried out according to inter-station passenger flow prediction on the basis of analyzing historical passenger flow and recent passenger flow of a train. The passenger flow form based on the passenger train has the characteristic of regularity, and although the passenger flow form has certain time variation, the passenger flow form is relatively stable in general. Therefore, on the basis of passenger flow prediction, the ticket amount pre-classifying strategy based on the passenger flow form of the passenger train has certain feasibility.
The existing ticket amount pre-sorting strategy adopts a pre-sorting principle of 'following definition', and pre-sorting is carried out according to the sequence of a bus station from small to large and a bus station from large to small. The pre-sorting scheme pre-sorts the tickets of each seat of the train according to the principle of ensuring the starting and giving consideration to the way. The pre-classification principle ensures short-distance passenger flow with vigorous demand along the way and reduces the impact on the initial ticket amount. The pre-classification process comprises the steps that a railway group company sets a common definition for a pre-classified train common use ticket amount, a railway group company marketing system automatically generates a pre-classification scheme in a time division mode, the pre-classification scheme is issued to the centers of all railway bureau group companies two days before the pre-sale period, and the system automatically pre-classifies seats in the morning one day before the pre-sale period.
The passenger flow form of the passenger train has certain uncertainty and time variability, so that the ticket amount pre-dividing strategy is possibly inconsistent with the actual situation. The research on the dynamic ticket amount pre-dividing strategy under uncertainty is a further expansion of the current ticket amount intelligent pre-dividing strategy, and has important significance on the practical feasibility of the whole ticket amount distribution scheme.
The method has the advantages that the particle swarm optimization (Adam-PSO) improved through the adaptive optimization algorithm Adam is used for establishing the railway fare pre-dividing strategy, the Adam-PSO algorithm has the capability of jumping out of local optimum, and the problem that the railway fare pre-dividing strategy is inconsistent with actual requirements under the passenger flow state under uncertainty and time variation can be well solved.
Disclosure of Invention
The invention provides a particle swarm algorithm (Adam-PSO) railway fare pre-dividing strategy based on an adaptive learning rate Adam, and solves the problem that the railway fare pre-dividing strategy is not consistent with actual requirements under the passenger flow form under uncertainty and time variation.
The following technical scheme is mainly adopted:
a railway ticket pre-classifying method based on a self-adaptive learning rate particle swarm algorithm is characterized by comprising the following steps: based on the following objective function, constraint and fitness function:
an objective function:
Figure BDA0002952716620000021
sijfor the formula (10) expected sales of tickets, pijIs the fare for segment (i, j).
Constraint conditions
Figure BDA0002952716620000022
CmaxFor the maximum passenger capacity of the line, the constraint indicates that the sum of the tickets allocated by the line cannot exceed the maximum passenger capacity of the railway of the line.
The adaptive value function combines the target function and the constraint by using a penalty function method, the adaptive value function is set as follows, and t is the current iteration algebra.
Figure BDA0002952716620000023
The method comprises the following steps:
step 1, setting the maximum iteration times T, the particle number N and the particle dimension D. Randomly generating N particles within a defined search space
Figure BDA0002952716620000024
And velocity of particles
Figure BDA0002952716620000025
Each particle represents a scheme for the allocation of the ticket,
Figure BDA0002952716620000026
the ticket to the d-th section is assigned for the ith proposal. The random initial solutions of n particles represent n different random initial ticket allocation schemes, and iterative optimization is carried out by taking the n different random initial ticket allocation schemes as a starting point.
Step 2, calculating the adaptive function values of all the particles, and updating the historical optimal position vector of a single particle
Figure BDA0002952716620000027
Figure BDA0002952716620000028
I.e. the position of the particle at which the fitness function value is maximal under the particle label from iteration to now,
Figure BDA0002952716620000029
representing the particle pbestiA value in the d-dimension; updating global optimal location vectors for population discovery
Figure BDA00029527166200000210
Figure BDA00029527166200000211
I.e. the position of the particle with the largest fitness function value among all particles,
Figure BDA00029527166200000212
denotes the particle gbestiValue in the d-th dimension.
Step 4, calculating the gradient g of each particle in each dimension according to the formula (3)ijCalculating the inertia value m of the particle gradient according to the formulas (4) and (5)ijSum gradient squared sum exponentially weighted average vij. Calculating the offset correction result by the formulas (6) and (7)
Figure BDA00029527166200000213
Calculating the self-adaptive inertia weight w of each dimension of the particle according to the formula (8)ij。
And 5, updating the next speed and position of each particle by the inertia weight calculated in the step four through the formulas (1) and (2).
Step 6, after the position updating is finished, calculating the adaptive values of all the particles and the historical optimal positions pbest of the particlesiThe calculated adaptation values are compared. The adaptive value calculated as the current particle is excellentIn the historical optimum position pbestiCalculated adaptive value, historical optimum position pbestiSet to the current particle position.
Step 7, matching the adaptive values of all the particles in the particle swarm with the global optimal position gbest searched by the whole swarmiThe calculated adaptation values are compared. Comparing the fitness value of the particle with the global optimal position gbestiCalculated adaptive value, if better then global optimum position gbestiSet to the current particle position.
And 8, checking whether the iteration times reach the set maximum iteration times. If not, returning to the step 4 to continuously update the position and the speed of the particle; if the global optimal position gbest is reached, the algorithm flow is ended, and the global optimal position gbest is returnediThe positions of the particles represent the optimal allocation scheme and the calculated objective function value represents the maximum benefit.
In the method for pre-classifying the railway ticket based on the adaptive learning rate particle swarm algorithm, in the step 1, the used improved particle swarm algorithm Adam-PSO is to adaptively set the inertia weight coefficient w in the particle swarm algorithm by using the adaptive learning rate method Adam. And (3) taking the positions of the single particles in different dimensions and the distance of the optimal solution in the iterative process of the algorithm as gradient information, and introducing momentum and exponential weighted average to realize a self-adaptive setting strategy. Appropriate inertia weight is set according to information on different dimensions of different particles, a momentum concept is introduced, and a self-adaptive updating strategy can be more stable. The adaptive setting of the inertia weight coefficient w is shown in equations (3) to (8).
Gradient g of particle i in dimension jijCan be regarded as the global optimum of the current dimension of the particle
Figure BDA0002952716620000031
To xijIs a distance of
Figure BDA0002952716620000032
First, a gradient value introducing momentum concept is defined as mijIntroduction of momentumAnd the new gradient inertia value adopts exponential weighted average, so that the closer inertia value has more influence, and the farther inertia value has less influence. The updating process is shown in formula (4). Beta is a1Is an exponentially weighted average coefficient.
mij＝β1mi，j-1+(1-β1)gij#(4)
Second defining an exponentially weighted average v of the sum of squares of its gradientsijAnd calculating the square of the distance from the current position of the particle to the optimal position to reflect the size of the current movement trend of the particle. By means of exponential weighted average calculation, the influence of the farther trend is weakened, the influence of the previous generations of trends is improved, and the calculation result is smoother. The updating process is shown as formula (5) < beta >2Is an exponentially weighted average coefficient.
Figure BDA0002952716620000033
Gradient inertia value mijSum gradient squared sum exponentially weighted average vijCan be considered as approximations to the mean of the gradient and the square of the gradient, respectively. In order to more accurately represent the desired unbiased estimation, bias correction is introduced, and correction values of the bias correction are respectively calculated
Figure BDA0002952716620000041
And
Figure BDA0002952716620000042
the offset correction values are taken to eliminate the inaccuracy of the approximation in the initial steps.
Figure BDA0002952716620000043
Figure BDA0002952716620000044
Finally, the inertia weight w on the dimension j of the particle i is updated according to the formula (8)ijWherein α and β areAnd adjusting the coefficient.
Figure BDA0002952716620000045
The ticket distribution is carried out on the basis of passenger flow prediction, and on the assumption that the passenger flow obeys normal distribution, the probability density is used for converting the passenger flow density into the expected sales volume of the ticket by using integration. The passenger flow demand density of the section (i, j) is:
Figure BDA0002952716620000046
x is the time elapsed from the time of sale, fij(x) As a function of the density of the passenger flow demand for the section (i, j), uijMean value of passenger flow demand, σ, for segment (i, j)ijIs the standard deviation of the passenger flow demand for section (i, j). According to the passenger flow demand density function, the expected sales volume of the passenger tickets of the train in the section is obtained
Figure BDA0002952716620000047
aijThe initial value of the allocated fare for the deadline section (i, j) is set as the initial demand for traffic.
In the foregoing method for pre-classifying railway tickets based on the adaptive learning rate particle swarm algorithm, in step 4, the gradient of each dimension is calculated based on the following formula:
Figure BDA0002952716620000048
in the foregoing method for pre-classifying railway tickets based on the adaptive learning rate particle swarm optimization, in step 4, the next speed and position of each particle are updated based on the following formulas:
Figure BDA0002952716620000051
Figure BDA0002952716620000052
where w is an inertial weight coefficient, and the inertial weight determines the degree of influence of the particle historical flight speed on the current flight speed. c. C1A weight coefficient, which is the optimal value that the particle finds in its historical search, is typically set to 2; c. C2Is the weight coefficient for the particle to find the optimum value in the group search, c1And c2Commonly referred to as the acceleration constant. r is1And r2Are two randomly distributed values in the range of (0, 1).
Therefore, the invention has the following advantages: the Adam-PSO algorithm has strong universality, high convergence speed and good capability of jumping out of local optimum, is convenient to model when solving practical problems, has fewer parameters needing to be adjusted and is easy to realize. The method has the advantages that the particle swarm optimization (Adam-PSO) improved through the adaptive optimization algorithm Adam is used for establishing the railway fare pre-dividing strategy, and the problem that the railway fare pre-dividing strategy does not accord with actual requirements under the passenger flow state under uncertainty and time variation can be well solved.
Drawings
Fig. 1 is a flow chart of a ticket allocation policy.
Detailed Description
The Adam-PSO algorithm is based on the traditional particle swarm optimization algorithm, and the inertia weight w in the particle speed updating formula is set in a self-adaptive mode by using the adaptive optimization algorithm Adam. Macroscopically, the inertia weight w is updated in an iterative way with an overall decreasing trend; microscopically, the inertia weight w sets different variation trends according to different particle information, and simultaneously introduces a concept of momentum in physics and bias correction work to ensure the stability of the adaptive strategy. The strategy not only utilizes the characteristics of the particles, but also meets the setting strategy of decreasing the inertial weight, so that the ADAM-PSO algorithm can ensure the convergence, diversity and stability of the particle swarm optimization, and can generate good effect when the optimization problem is processed.
"Yu LiWhen the Adam-PSO algorithm is used for realizing the railway fare distribution strategy, firstly, a solving model under the particle swarm optimization is required to be established. Position of each particle
Figure BDA0002952716620000053
Represents a scheme for allocating the amount of ticket (among them)
Figure BDA0002952716620000054
The scheme is assigned to the ticket of the d-th section), the random initial solutions of n particles represent n different random initial ticket assignment schemes, and iterative optimization is carried out by taking the n different random initial ticket assignment schemes as a starting point. When the maximum iteration number is reached, the algorithm is terminated, and the final ticket amount distribution scheme and the passenger ticket income can be output. The profit value of the fare distribution scheme can be used as an adaptive value function of the algorithm, and when a fare distribution strategy is realized for a specific line, the passenger flow demand needs to be acquired. The passenger flow demand follows normal distribution, the expected sales volume of the current scheme is calculated by utilizing the expected and standard deviation of the distribution, and the product of the expected sales volume and the standard deviation is the income of the ticket amount distribution scheme, namely the adaptive value function of the algorithm.
The particle swarm optimization is an iterative optimization algorithm, a group of random solutions are initialized by the algorithm, and an optimal value is updated through iteration. The principle and mechanism of the particle swarm algorithm are simple and easy to understand, only the speed and the position are updated, the adaptive values are compared, and finally the global optimal solution is calculated. The particle swarm optimization is widely applied, and iterative optimization can be performed by using the particle swarm optimization as long as the problem to be optimized is modeled according to the characteristics of the particle swarm.
In particle swarm optimization, particles represent a potential solution. When searching in the D-dimensional space, each particle i has a position vector
Figure BDA0002952716620000061
And velocity vector
Figure BDA0002952716620000062
The current state is calculated. Furthermore the particle i will be along the historical optimal position vector of the individual
Figure BDA0002952716620000063
And the global optimal position vector gbest of the population discovery ═ { gbest ═ gbest1，gbest2，gbest3，...，gbestDAnd (6) moving. Position of the particle
Figure BDA0002952716620000064
And velocity
Figure BDA0002952716620000065
And (3) randomly initializing in a set interval, and updating the d dimension of the calculation particle i as shown in formula (1) and formula (2).
Figure BDA0002952716620000066
Figure BDA0002952716620000067
Where w is an inertial weight coefficient, and the inertial weight determines the degree of influence of the particle historical flight speed on the current flight speed. c. C1A weight coefficient, which is the optimal value that the particle finds in its historical search, is typically set to 2; c. C2The weight coefficient for the particle to find the optimal value in the group search is usually set to 2, c1And c2Commonly referred to as the acceleration constant. r is1And r2Are two randomly distributed values in the range of (0, 1).
The improved particle swarm algorithm Adam-PSO used in the invention is the self-adaptive setting of the inertia weight coefficient w in the particle swarm algorithm by using a self-adaptive learning rate method Adam. And (3) taking the positions of the single particles in different dimensions and the distance of the optimal solution in the iterative process of the algorithm as gradient information, and introducing momentum and exponential weighted average to realize a self-adaptive setting strategy. Appropriate inertia weight is set according to information on different dimensions of different particles, a momentum concept is introduced, and a self-adaptive updating strategy can be more stable. The adaptive setting of the inertia weight coefficient w is shown in equations (3) to (8).
Particle i in dimensionGradient g of jijCan be regarded as the global optimum of the current dimension of the particle
Figure BDA0002952716620000068
To xijIs a distance of
Figure BDA0002952716620000069
First, a gradient value introducing momentum concept is defined as mijAnd introducing momentum to update gradient inertia values, and adopting exponential weighted average, wherein closer inertia values have more influence, and farther inertia values have less influence. The updating process is shown in formula (4). Beta is a1Is an exponential weighted average coefficient, and the value is 0.9.
mij＝β1mi，j-1+(1-β1)gij#(4)
Second defining an exponentially weighted average v of the sum of squares of its gradientsijAnd calculating the square of the distance from the current position of the particle to the optimal position to reflect the size of the current movement trend of the particle. By means of exponential weighted average calculation, the influence of the farther trend is weakened, the influence of the previous generations of trends is improved, and the calculation result is smoother. The updating process is shown as formula (5) < beta >2Is an exponential weighted average coefficient, and the value is 0.999.
Figure BDA0002952716620000071
Gradient inertia value mijSum gradient squared sum exponentially weighted average vijCan be considered as approximations to the mean of the gradient and the square of the gradient, respectively. In order to more accurately represent the desired unbiased estimation, bias correction is introduced, and correction values of the bias correction are respectively calculated
Figure BDA0002952716620000072
And
Figure BDA0002952716620000073
Figure BDA0002952716620000074
Figure BDA0002952716620000075
finally, the inertia weight w on the dimension j of the particle i is updated according to the formula (8)ijWhere α and β are adjustment coefficients.
Figure BDA0002952716620000076
The ticket distribution is carried out on the basis of passenger flow prediction, and on the assumption that the passenger flow obeys normal distribution, the probability density is used for converting the passenger flow density into the expected sales volume of the ticket by using integration. The passenger flow demand density of the section (i, j) is:
Figure BDA0002952716620000077
x is the time elapsed from the time of sale, fij(x) As a function of the density of the passenger flow demand for the section (i, j), uijMean value of passenger flow demand, σ, for segment (i, j)ijIs the standard deviation of the passenger flow demand for section (i, j). According to the passenger flow demand density function, the expected sales volume of the passenger tickets of the train in the section is obtained
Figure BDA0002952716620000078
aijThe initial value of the allocated fare for the deadline section (i, j) is set as the initial demand for traffic.
The concrete implementation steps for solving the ticket distribution problem by using Adam-PSO are as follows:
the method comprises the following steps of firstly, setting the maximum iteration times T, the particle number N and the particle dimension D. Randomly generating N particles within a defined search space
Figure BDA0002952716620000079
And velocity of particles
Figure BDA00029527166200000710
Each particle represents a scheme for the allocation of the ticket,
Figure BDA00029527166200000711
the ticket to the d-th section is assigned for the ith proposal. The random initial solutions of n particles represent n different random initial ticket allocation schemes, and iterative optimization is carried out by taking the n different random initial ticket allocation schemes as a starting point.
Step two: in the ticket allotment problem, the objective function is
Figure BDA00029527166200000712
sijFor the formula (10) expected sales of tickets, pijIs the fare for segment (i, j). However, there are constraints
Figure BDA00029527166200000713
Figure BDA00029527166200000714
CmaxFor the maximum passenger capacity of the line, the constraint indicates that the sum of the tickets allocated by the line cannot exceed the maximum passenger capacity of the railway of the line. When the adaptive value function is set, a penalty function method is needed to combine the target function with the constraint, the adaptive value function is set as shown in a formula (11), and t is the current iteration algebra.
Figure BDA0002952716620000081
Step three: calculating the adaptive function values of all the particles according to the formula (11), and updating the historical optimal position vector of the single particle
Figure BDA0002952716620000082
I.e. the adaptation function value under the particle label from iteration to nowThe position of the largest particle; updating global optimal location vectors for population discovery
Figure BDA0002952716620000083
I.e. the position of the particle with the largest fitness function value among all particles.
Step four, calculating the gradient g of each particle in each dimension according to the formula (3)ijCalculating the inertia value m of the particle gradient according to the formulas (4) and (5)ijSum gradient squared sum exponentially weighted average vij. Calculating the offset correction result by the formulas (6) and (7)
Figure BDA0002952716620000084
Calculating the self-adaptive inertia weight w of each dimension of the particle according to the formula (8)ij。
And step five, updating the next speed and position of each particle by the inertia weight calculated in the step four through formulas (1) and (2).
Step six, after the position updating is finished, calculating the adaptive values of all the particles and the historical optimal positions pbest of the particlesiThe calculated adaptation values are compared. The adaptation value as calculated for the current particle is better than the historical optimal position pbestiCalculated adaptive value, historical optimum position pbestiSet to the current particle position.
Seventhly, the adaptive values of all the particles in the particle swarm and the global optimal position gbest searched by the whole swarmiThe calculated adaptation values are compared. Comparing the fitness value of the particle with the global optimal position gbestiCalculated adaptive value, if better then global optimum position gbestiSet to the current particle position.
And step eight, checking whether the iteration times reach the set maximum iteration times. If not, returning to the step 4 to continuously update the position and the speed of the particle; if the global optimal position gbest is reached, the algorithm flow is ended, and the global optimal position gbest is returnediThe positions of the particles represent the optimal allocation scheme and the calculated objective function value represents the maximum benefit.
The specific embodiments described herein are merely illustrative of the spirit of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (4)

1. A railway ticket pre-classifying method based on a self-adaptive learning rate particle swarm algorithm is characterized by comprising the following steps: based on the following objective function, constraint and fitness function:
an objective function:
Figure FDA0002952716610000011
sijfor the formula (10) expected sales of tickets, pijIs the fare for segment (i, j);
constraint conditions
Figure FDA0002952716610000012
CmaxThe maximum passenger capacity of the line is represented, and the constraint represents that the sum of the tickets distributed by the line cannot exceed the maximum passenger capacity of the railway of the line;
the adaptive value function combines the target function and the constraint by using a penalty function method, the adaptive value function is set as follows, and t is the current iteration algebra;
Figure FDA0002952716610000013
the method comprises the following steps:
step 1, setting a maximum iteration number T, a particle number N and a particle dimension D; randomly generating N particles within a defined search space
Figure FDA0002952716610000014
And velocity of particles
Figure FDA0002952716610000015
Each particle represents a scheme for the allocation of the ticket,
Figure FDA0002952716610000016
assigning a fare to the d-th section for the ith proposal; the random initial solutions of n particles represent n different random initial ticket allocation schemes, and iterative optimization is carried out by taking the schemes as starting points;
step 2, calculating the adaptive function values of all the particles, and updating the historical optimal position vector of a single particle
Figure FDA0002952716610000017
I.e. the position of the particle at which the fitness function value is maximal under the particle label from iteration to now,
Figure FDA0002952716610000018
representing the particle pbestiA value in the d-dimension; updating global optimal location vectors for population discovery
Figure FDA0002952716610000019
I.e. the position of the particle with the largest fitness function value among all particles,
Figure FDA00029527166100000110
denotes the particle gbestiA value in the d-dimension;
step 4, calculating the gradient g of each particle in each dimension according to the formula (3)ijCalculating the inertia value m of the particle gradient according to the formulas (4) and (5)ijSum gradient squared sum exponentially weighted average vij(ii) a Calculating the offset correction result by the formulas (6) and (7)
Figure FDA0002952716610000021
Calculating the self-adaptive inertia weight w of each dimension of the particle according to the formula (8)ij(ii) a Step 5, updating the next speed and position of each particle by the inertia weight calculated in the step four through formulas (1) and (2);
step 6, after the position updating is finished, calculating the adaptive values of all the particles and the historical optimal positions pbest of the particlesiCalculated adaptive value running ratioComparing; the adaptation value as calculated for the current particle is better than the historical optimal position pbestiCalculated adaptive value, historical optimum position pbestiSetting as a current particle position;
step 7, matching the adaptive values of all the particles in the particle swarm with the global optimal position gbest searched by the whole swarmiComparing the calculated adaptive values; comparing the fitness value of the particle with the global optimal position gbestiCalculated adaptive value, if better then global optimum position gbestiSetting as a current particle position;
step 8, checking whether the iteration times reach the set maximum iteration times; if not, returning to the step 4 to continuously update the position and the speed of the particle; if the global optimal position gbest is reached, the algorithm flow is ended, and the global optimal position gbest is returnediThe positions of the particles represent the optimal allocation scheme and the calculated objective function value represents the maximum benefit.
2. The railway fare pre-classifying method based on the adaptive learning rate particle swarm optimization algorithm according to claim 1, wherein in the step 1, the improved particle swarm optimization algorithm Adam-PSO is used for adaptively setting the inertia weight coefficient w in the particle swarm optimization algorithm by using the adaptive learning rate method Adam; taking the positions of the single particles in different dimensions and the distance of the optimal solution in the iterative process of the algorithm as gradient information, and introducing momentum and exponential weighted average to realize a self-adaptive setting strategy; appropriate inertia weight is set according to information on different dimensions of different particles, a momentum concept is introduced, and a self-adaptive updating strategy can be more stable; the adaptive setting of the inertia weight coefficient w is shown in formulas (3) to (8);
gradient g of particle i in dimension jijCan be regarded as the global optimum of the current dimension of the particle
Figure FDA0002952716610000031
To xijIs a distance of
Figure FDA0002952716610000032
First, a gradient value introducing momentum concept is defined as mijThe momentum is introduced to update the gradient inertia value, and the exponential weighted average is adopted, so that the closer inertia value has more influence, and the farther inertia value has less influence; the updating process is shown as formula (4); beta is a1Is an exponentially weighted average coefficient;
mij＝β1mi，j-1+(1-β1)gij#(4)
second defining an exponentially weighted average v of the sum of squares of its gradientsijCalculating the square of the distance from the current position of the particle to the optimal position to reflect the size of the current movement trend of the particle; by means of exponential weighted average calculation, the influence of a farther trend is weakened, the influence of previous generations of trends is improved, and a calculation result is smoother; the updating process is shown as formula (5) < beta >2Is an exponentially weighted average coefficient;
Figure FDA0002952716610000033
gradient inertia value mijSum gradient squared sum exponentially weighted average vijCan be considered as approximations to the mean of the gradient and the square of the gradient, respectively; in order to more accurately represent the desired unbiased estimation, bias correction is introduced, and correction values of the bias correction are respectively calculated
Figure FDA0002952716610000034
And
Figure FDA0002952716610000035
Figure FDA0002952716610000036
Figure FDA0002952716610000037
finally, the inertia weight w on the dimension j of the particle i is updated according to the formula (8)ijWherein α and β are adjustment coefficients;
Figure FDA0002952716610000041
the ticket amount distribution is carried out on the basis of passenger flow prediction, assuming that the passenger flow obeys normal distribution, and on the basis of probability density, converting the passenger flow density into the expected sales volume of the ticket by using integration; the passenger flow demand density of the section (i, j) is:
Figure FDA0002952716610000042
x is the time elapsed from the time of sale, fij(x) As a function of the density of the passenger flow demand for the section (i, j), uijMean value of passenger flow demand, σ, for segment (i, j)ijIs the standard deviation of the passenger flow demand for section (i, j); according to the passenger flow demand density function, the expected sales volume of the passenger tickets of the train in the section is obtained
Figure FDA0002952716610000043
aijThe initial value of the allocated fare for the deadline section (i, j) is set as the initial demand for traffic.
3. The method for pre-classifying railway tickets based on the adaptive learning rate particle swarm optimization algorithm according to claim 1, wherein in the step 4, the calculation of the gradient of each dimension is based on the following formula:
Figure FDA0002952716610000044
4. the method for pre-classifying railway tickets based on the adaptive learning rate particle swarm optimization algorithm as claimed in claim 1, wherein in the step 4, the next speed and position of each particle are updated based on the following formula:
Figure FDA0002952716610000045
Figure FDA0002952716610000051
w is an inertia weight coefficient, and the inertia weight determines the influence degree of the historical flight speed of the particles on the current flight speed; c. C1A weight coefficient, which is the optimal value that the particle finds in its historical search, is typically set to 2; c. C2Is the weight coefficient for the particle to find the optimum value in the group search, c1And c2Commonly referred to as the acceleration constant; r is1And r2Are two randomly distributed values in the range of (0, 1).
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