CN112950015B - 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

Info

Publication number
CN112950015B
CN112950015B CN202110214646.XA CN202110214646A CN112950015B CN 112950015 B CN112950015 B CN 112950015B CN 202110214646 A CN202110214646 A CN 202110214646A CN 112950015 B CN112950015 B CN 112950015B
Authority
CN
China
Prior art keywords
particle
value
adaptive
particles
gradient
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Expired - Fee Related
Application number
CN202110214646.XA
Other languages
Chinese (zh)
Other versions
CN112950015A (en
Inventor
李梦莹
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Wuhan University WHU
Original Assignee
Wuhan University WHU
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Wuhan University WHU filed Critical Wuhan University WHU
Priority to CN202110214646.XA priority Critical patent/CN112950015B/en
Publication of CN112950015A publication Critical patent/CN112950015A/en
Application granted granted Critical
Publication of CN112950015B publication Critical patent/CN112950015B/en
Expired - Fee Related legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
    • G06Q10/00—Administration; Management
    • G06Q10/06—Resources, workflows, human or project management; Enterprise or organisation planning; Enterprise or organisation modelling
    • G06Q10/063—Operations research, analysis or management
    • G06Q10/0631—Resource planning, allocation, distributing or scheduling for enterprises or organisations
    • G06Q10/06315—Needs-based resource requirements planning or analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06N—COMPUTING ARRANGEMENTS BASED ON SPECIFIC COMPUTATIONAL MODELS
    • G06N3/00—Computing arrangements based on biological models
    • G06N3/004—Artificial life, i.e. computing arrangements simulating life
    • G06N3/006—Artificial life, i.e. computing arrangements simulating life based on simulated virtual individual or collective life forms, e.g. social simulations or particle swarm optimisation [PSO]
    • G06Q50/40—

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 optimizes the railway fare pre-dividing strategy by using a Particle Swarm Optimization (PSO) based on Adaptive motion Estimation (Adam).
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 has a relatively stable passenger flow base 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 to the line cannot exceed the maximum passenger capacity of the railway for 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
is assigned to the ith schemeTicket amount of the d-th section. The random initial solutions of n particles represent n different random initial fare allocation schemes, and iterative optimization is carried out by taking the scheme 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 particles 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, countingCalculating the adaptive value of all the particles and the historical optimal position 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.
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 returned iThe 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 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 a 1Is an exponentially weighted average coefficient.
mij＝β1mi，j-1+(1-β1)gij#(4)
Second, defining an exponentially weighted average v of the sum of squared 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)ijWhere α and β are adjustment coefficients.
Figure BDA0002952716620000045
The ticket distribution is based on the passenger flow prediction, and assuming that the passenger flow follows normal distribution, the probability density is based on which the integral is used to convert the passenger flow density into the expected sales volume of the ticket. The passenger flow demand density of the section (i, j) is:
Figure BDA0002952716620000046
x is the time elapsed since the time of sale, f ij(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.
When the Adam-PSO algorithm is used for realizing the railway fare distribution strategy, firstly, a solving model under the particle swarm optimization algorithm needs 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, which starts to initialize a group of random solutions and updates the optimal value 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 algorithms, particles represent potential solutions. When searching in the D-dimensional space, each particle i has a position vector
Figure BDA0002952716620000061
Sum 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, c 1And 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).
Gradient g of particle i in dimension 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 assigned 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 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
Namely, the position of the particle with the maximum adaptive function value under the label of the particle from iteration to the present; 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. The offset correction result is calculated by the formulas (6) and (7)
Figure BDA0002952716620000084
Calculating the self-adaptive inertia weight w of each dimension of the particles 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).
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 returned iThe positions of the particles and the calculated objective function, the positions representing the optimal allocation scheme, the objective functionThe values represent 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 (1)

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 FDA0003614692520000011
for the formula (10) expected sales of tickets, pi1j1Fare for segment (i1, j 1);
constraint conditions
Figure FDA0003614692520000012
The maximum passenger capacity of the line is represented by the constraint, and 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 FDA0003614692520000013
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 FDA0003614692520000014
And velocity of particles
Figure FDA0003614692520000015
Each particle represents a scheme for the allocation of the ticket,
Figure FDA0003614692520000016
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 FDA0003614692520000017
I.e. the position of the particle at which the fitness function value is maximal under the particle label from iteration to now,
Figure FDA0003614692520000018
representing the particle pbestiA value in the d-dimension; updating global optimal location vectors for population discovery
Figure FDA0003614692520000019
I.e. the position of the particle with the largest fitness function value among all particles,
Figure FDA00036146925200000110
denotes the particle gbestiA value in the d-dimension;
step 3, 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 FDA0003614692520000021
Calculating the self-adaptive inertia weight w of each dimension of the particle according to the formula (8)ij；
Step 4, updating the next speed and position of each particle by the inertia weight calculated in the step 3 through formulas (1) and (2);
in the step 3, the used improved particle swarm algorithm Adam-PSO is to perform self-adaptive setting on the inertia weight coefficient w in the particle swarm algorithm by using a self-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 weights are set according to information on different dimensions of different particles, a momentum concept is introduced, and a self-adaptive updating strategy is 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 jijConsidered as a global optimum for the current dimension of the particle
Figure FDA0003614692520000022
To xijIs a distance of
Figure FDA0003614692520000023
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 FDA0003614692520000031
gradient inertia value mijSum gradient squared sum exponentially weighted average vijConsidered as an approximation to the mean of the gradient and the gradient squared, 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 FDA0003614692520000032
And
Figure FDA0003614692520000033
Figure FDA0003614692520000034
Figure FDA0003614692520000035
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 FDA0003614692520000036
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 integral; the passenger flow demand density of the section (i1, j1) is:
Figure FDA0003614692520000037
x is the time elapsed from the time of sale, fi1j1(x) As a function of the passenger demand density for section (i1, j1), ui1j1Mean passenger flow demand, σ, for segment (i1, j1)i1j1Is the object of section (i1, j1)A stream demand standard deviation; according to the passenger flow demand density function, the expected sales volume of the passenger tickets of the train in the section can be obtained as
Figure FDA0003614692520000041
ai1j1Setting the initial value as the initial demand of passenger flow for the allocated ticket amount of the section (i1, j1) at the deadline time;
in step 4, updating the next velocity and position of each particle is based on the following formula:
Figure FDA0003614692520000042
Figure FDA0003614692520000043
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 of the particle found in its history search, is set to 2; c. C2Is the weight coefficient for the particle to find the optimum value in the group search, c1And c2Referred to as the acceleration constant; r is1And r2Is two randomly distributed values in the range of (0, 1);
step 5, after the position updating is finished, calculating the adaptive values of all the particles and the historical optimal positions pbest of the particlesiComparing the calculated adaptive values; 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 6, the adaptive values of all the particles in the particle swarm and 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 7, checking whether the iteration times reach the set maximum iteration times; if not, returning to the step 3 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.
CN202110214646.XA 2021-02-25 2021-02-25 Railway ticket amount pre-classifying method based on self-adaptive learning rate particle swarm optimization Expired - Fee Related CN112950015B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202110214646.XA CN112950015B (en) 2021-02-25 2021-02-25 Railway ticket amount pre-classifying method based on self-adaptive learning rate particle swarm optimization

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202110214646.XA CN112950015B (en) 2021-02-25 2021-02-25 Railway ticket amount pre-classifying method based on self-adaptive learning rate particle swarm optimization

Publications (2)

Publication Number Publication Date
CN112950015A CN112950015A (en) 2021-06-11
CN112950015B true CN112950015B (en) 2022-06-14

Family

ID=76246330

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202110214646.XA Expired - Fee Related CN112950015B (en) 2021-02-25 2021-02-25 Railway ticket amount pre-classifying method based on self-adaptive learning rate particle swarm optimization

Country Status (1)

Country Link
CN (1) CN112950015B (en)

Families Citing this family (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN113627971B (en) * 2021-06-30 2024-04-02 中国铁道科学研究院集团有限公司电子计算技术研究所 Ticket allocation method and device
CN116882705B (en) * 2023-08-02 2024-04-16 西南交通大学 Train seat optimal allocation method

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104517187A (en) * 2014-12-22 2015-04-15 中铁程科技有限责任公司 Railway ticket quota allocating method and device
CN109872009A (en) * 2019-03-14 2019-06-11 西安电子科技大学 A kind of interference increment method method for improving particle swarm algorithm
CN110570128A (en) * 2019-09-09 2019-12-13 西南交通大学 Nesting control method for multi-level ticket price seat storage of high-speed railway train
CN110807651A (en) * 2019-09-26 2020-02-18 北京交通大学 Intercity railway passenger ticket time-sharing pricing method based on generalized cost function
CN111582624A (en) * 2020-03-16 2020-08-25 中国铁道科学研究院集团有限公司电子计算技术研究所 Train ticket amount pre-dividing method and device, storage medium and computer equipment

Family Cites Families (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US8238924B2 (en) * 2010-04-30 2012-08-07 The United States Of America As Represented By The Secretary Of The Navy Real-time optimization of allocation of resources

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104517187A (en) * 2014-12-22 2015-04-15 中铁程科技有限责任公司 Railway ticket quota allocating method and device
CN109872009A (en) * 2019-03-14 2019-06-11 西安电子科技大学 A kind of interference increment method method for improving particle swarm algorithm
CN110570128A (en) * 2019-09-09 2019-12-13 西南交通大学 Nesting control method for multi-level ticket price seat storage of high-speed railway train
CN110807651A (en) * 2019-09-26 2020-02-18 北京交通大学 Intercity railway passenger ticket time-sharing pricing method based on generalized cost function
CN111582624A (en) * 2020-03-16 2020-08-25 中国铁道科学研究院集团有限公司电子计算技术研究所 Train ticket amount pre-dividing method and device, storage medium and computer equipment

Non-Patent Citations (7)

* Cited by examiner, † Cited by third party
Title
A Hybrid Algorithm of Adaptive Particle Swarm Optimization Based on Adaptive Moment Estimation Method;JIANG Yan等;《Intelligent Computing Theories and Application》;doi.org/10.1007/978-3-319-63309-1_58;20170720;全文 *
Adam: a method for stochastic optimization;Kingma D等;《Proceeding of the 3rd International Conference on Learning Representations》;20151231;全文 *
Optimization Design of Quad-Rotor Flight Controller Based on Improved Particle Swarm Optimization Algorithm;Yinliang Yang等;《International Conference on Intelligent and Interactive Systems and Applications》;20191130;全文 *
基于收益管理的票额动态分配方案研究;王洋;《交通科技与经济》;20200731;第22卷(第4期);全文 *
基于混合PSO-Adam神经网络的外协供应商评价决策模型;李益兵等;《控制与决策》;20181231;第33卷(第12期);全文 *
多列车多停站方案条件下高速铁路票额分配研究;赵翔等;《铁道学报》;20161130;第38卷(第11期);全文 *
神经网络梯度下降与粒子群组合的训练算法;郭松林等;《黑龙江科技大学学报》;20200731;第30卷(第4期);全文 *

Also Published As

Publication number Publication date
CN112950015A (en) 2021-06-11

Similar Documents

Publication Publication Date Title
CN112950015B (en) Railway ticket amount pre-classifying method based on self-adaptive learning rate particle swarm optimization
CN111862579B (en) Taxi scheduling method and system based on deep reinforcement learning
CN109034468B (en) Logistics distribution path planning method with time window based on cuckoo algorithm
CN106134136A (en) Calculate the long-term dispatch transmitted for the data on wide area network
Lees-Miller Minimising average passenger waiting time in personal rapid transit systems
CN107194491A (en) A kind of dynamic dispatching method based on Forecasting of Travel Time between bus passenger flow and station
CN112183812B (en) Finished cigarette logistics vehicle scheduling method considering short-time and low-cost
CN105302858B (en) A kind of the cross-node enquiring and optimizing method and system of distributed data base system
CN110516871B (en) Dynamic vehicle path optimization method based on fuzzy rolling time domain control strategy
CN113487220A (en) Static target observation-oriented space-sky heterogeneous earth observation resource cooperative scheduling method
Li et al. Optimization of number of operators and allocation of new lines in an oligopolistic transit market
CN111861279B (en) Multi-target high-speed toll station class car scheduling method considering transfer
Javidi et al. A multi-objective optimization framework for online ridesharing systems
CN111091286B (en) Public bicycle scheduling method
Li et al. Optimal combinations and variable departure intervals for micro bus system
Han et al. Real-time rideshare driver supply values using online reinforcement learning
CN114363996B (en) Heterogeneous wireless network service access control method and device based on multiple targets
CN113705891B (en) Urban commercial complex building parking demand prediction method based on MRA-BAS-BP algorithm
CN113313451A (en) Multi-objective optimization logistics scheduling method based on improved cuckoo algorithm
CN114118724A (en) Electric vehicle charging scheduling method considering requirement matching degree
CN114066503A (en) Method for forecasting taxi demand based on virtual service area construction
CN109919379B (en) Method, system and storage medium for allocating gate for flight
CN111538333B (en) Dynamic vehicle path optimization method based on fixed integral rolling time domain control strategy
Iravani et al. Developing an urban congestion pricing model by considering sustainability improvement and using a multi-objective optimization approach
CN108985658A (en) One kind cooperateing with method for down loading based on fuzzy evaluation and the desired car networking of client

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant
CF01 Termination of patent right due to non-payment of annual fee
CF01 Termination of patent right due to non-payment of annual fee

Granted publication date: 20220614