CN114386310A - Subway train energy-saving schedule optimization method under time-space passenger flow network distribution - Google Patents

Subway train energy-saving schedule optimization method under time-space passenger flow network distribution Download PDF

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CN114386310A
CN114386310A CN202111463586.1A CN202111463586A CN114386310A CN 114386310 A CN114386310 A CN 114386310A CN 202111463586 A CN202111463586 A CN 202111463586A CN 114386310 A CN114386310 A CN 114386310A
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胡文斌
刘彤
张磊
许久奇
李华轩
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Nanjing University of Science and Technology
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Abstract

The invention discloses a subway train energy-saving schedule optimization method under space-time passenger flow network distribution, which comprises the following steps: under the complex physical network of urban rail transit, a train energy consumption optimization model based on a Pareto curved surface multi-objective improved genetic algorithm under the space-time passenger flow characteristic is provided based on a least square estimation frame and a train operation mechanical model; taking the interval running traction energy consumption and the interval running time as optimization targets; aiming at the maximization of passenger service quality indexes and the minimization of total traction energy consumption of the whole-line train, a schedule optimization model based on an improved genetic algorithm is established, and the energy-saving optimal adjustment strategy of the whole-line train under different passenger flow space-time characteristics is obtained. The method comprehensively considers the time-space network distribution characteristics of the passenger flow of the rail transit network, adjusts the train operation schedule, maximally meets the passenger service level, simultaneously maximally reduces the total traction energy consumption of the whole train, and has higher use value and application prospect.

Description

Subway train energy-saving schedule optimization method under time-space passenger flow network distribution
Technical Field
The invention relates to the technical field of urban rail transit, in particular to an energy-saving schedule optimization method for subway trains under space-time passenger flow network distribution.
Background
With the continuous expansion of the urban rail transit network scale, huge energy consumption is brought, and although the energy consumption per unit turnover amount of urban rail transit is relatively lower compared with road traffic, the total energy consumption is high due to the large total amount of passengers transported and long operation duration. Under the background that rail transit is the largest potential stock of future traffic infrastructure construction, how to reduce train traction energy consumption while meeting passenger service quality requirements is researched from a transportation organization level, and the rail transit has important significance for improving the transportation organization level and realizing sustainable development of urban rail transit. The train operation diagram is taken as a comprehensive plan of the operation of the urban rail transit system, the setting of technical parameters of the train operation diagram has important influence on both passenger service quality and train operation energy consumption, and the operation diagram of the existing stage mainly has the following problems:
1) the current departure interval mode mainly adopted by time-interval balance cannot well meet the requirement of passenger service level of high-peak and low-peak time interval energy transportation caused by the imbalance of time-space distribution of passenger flow;
2) in order to reduce train delay and avoid the platform detention phenomenon of passengers, particularly passengers in rush hours, the punctuation rate of the train is ensured by improving the running speed of each interval and shortening the running time of the interval, and the optimization of the running energy consumption of the train is less considered.
3) The contradiction between the passenger service level and the minimization of the train energy consumption cannot be well solved, on one hand, from the improvement of the passenger service level, the shorter the travel time is, the better the travel time is, but the higher the maximum running speed target value of the train is possibly caused, and the running energy consumption cost of the train is increased; on the other hand, the operating unit wants the train operation energy consumption cost to be as low as possible, but this may result in an increase in the travel time of passengers and a reduction in the service level.
Therefore, how to present complex and various characteristics through passenger flow distribution and evolution rules thereof, construct a space-time passenger flow network distribution model, and optimize a train schedule aiming at different passenger flow space-time distribution situations so as to meet the maximization of the traffic demand and the minimization of total energy consumption of train traction of the whole line is a great problem to be solved urgently in the technical field of urban rail transit.
Disclosure of Invention
The invention aims to provide an energy-saving schedule optimization method for a subway train under the space-time passenger flow network distribution, which optimizes the schedule under the condition of meeting the maximum demand of the passenger quantity, the comfort level of the passenger, the safe running and the normal operation scheduling of the train under the space-time passenger flow network distribution and maximally reduces the total traction energy consumption of the whole train.
The technical solution for realizing the purpose of the invention is as follows: an energy-saving schedule optimization method for subway trains under space-time passenger flow network distribution comprises the following steps:
step1, establishing a unified state estimation framework model based on an urban rail transit complex network, integrating Lagrange observation values and Euler observation values of different data sources, different structures, different time and space accuracies, and accurately estimating and restoring network passenger flow states;
step2: establishing a unified network passenger flow estimation model, estimating the state of network passenger flow by adopting an estimation framework of a generalized least square method, and solving to obtain a passenger flow space-time estimation matrix;
step3, establishing a vehicle-mounted ATO model, a train mechanical model and a train energy consumption calculation model by combining the line basic parameters with the passenger flow state space-time estimation matrix, and deducing a train traction operation model under the passenger flow network at the moment;
step4, establishing a space-time passenger flow network schedule optimization model by aiming at the maximization of the demand of the passenger capacity and the minimization of total traction energy consumption of the whole-line train;
step5, based on the Pareto multi-target fuzzy optimization problem, improving an adaptive function on the basis of a genetic algorithm, avoiding the defect that the genetic algorithm is easy to fall into a local optimal solution when solving a more complex optimization problem, solving the optimal solution, outputting an energy-saving timetable optimization result, and determining an energy-saving optimal adjustment strategy of the whole-line train;
compared with the prior art, the invention has the following remarkable advantages: (1) according to the method, the passenger travel space-time trajectory is expressed as commodity flow in a space-time network, and an urban rail transit energy-saving train operation diagram optimization model based on space-time network passenger flow distribution is established by aiming at meeting the demand of riding quantity to the maximum and minimizing total traction energy consumption of a whole-line train; (2) the invention starts from the operation angle of the urban rail transit system, only makes small adjustment on the basis of the original operation plan, can realize consumption reduction and energy conservation, and is simple and easy to implement; (3) the invention does not need to invest additional equipment and has low cost; (4) the method has strong applicability, and the train operation timetable is adjusted to strictly meet passenger riding quantity, passenger comfort level indexes, train safe operation indexes, train operation scheduling indexes and the like; (5) the energy-saving optimization method designed by the invention is based on the genetic algorithm of the improved self-adaptive operator, the premature convergence phenomenon of the basic genetic algorithm is effectively avoided, the algorithm is prevented from being changed into a pure random search algorithm, the local search capability of the algorithm is enhanced, and the algorithm can search the global optimal solution.
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Fig. 1 is a general schematic diagram of an energy-saving schedule optimization method of a subway train under the distribution of a space-time passenger flow network.
FIG. 2 is a decomposition block diagram of a spatiotemporal network passenger flow estimation model in the present invention.
FIG. 3 is a schematic diagram of the space-time distribution of the speed curve of the train operation condition in the invention.
FIG. 4 is a flow chart of the improved adaptive function genetic algorithm calculation in the present invention.
Detailed Description
The invention is described in detail below with reference to the drawings and specific embodiments to enable the functions and features of the invention to be better understood. The present embodiment is implemented on the premise of the technical solution of the present invention, and a detailed implementation manner and a specific operation process are given, but the scope of the present invention is not limited to the following embodiments.
With reference to fig. 1, a method for optimizing an energy-saving schedule of a subway train under space-time passenger flow network distribution according to an embodiment of the present invention includes the following steps:
step1, establishing a unified state estimation framework model based on an urban rail transit complex network, integrating Lagrange observation values and Euler observation values of different data sources, different structures, different time and space accuracies, and accurately estimating and restoring network passenger flow states;
in the field of multi-source data fusion of an urban rail transit system, a unified state estimation framework is constructed by utilizing Lagrange observation values and Euler observation values, Lagrange observation values and Euler observation values of different data sources, different structures, different time and space accuracies are integrated, the state of network passenger flow is accurately estimated and restored, and the method mainly comprises the steps of 1) reconstructing travel space-time tracks of all passengers from a starting point to a terminal point in a system; 2) high-precision time-varying traffic states (traffic density, congestion level) at all stations, in-train, and in-transfer lanes are estimated. The method specifically comprises the following substeps:
(1) construction of a passenger flow distribution spatiotemporal state network (V) based on timetables and discrete passenger flow statessts,Ests) Coupling passenger travel process and network passenger flow state, each time-space state arc has its own attribute including flow
Figure BDA0003389514830000031
Density of
Figure BDA0003389514830000032
Speed of rotation
Figure BDA0003389514830000033
(a) The computation spatio-temporal arc (i, j, t, t ') is expanded into a series of spatio-temporal state arcs (i, j, t, t ', m, m '),
(b) the time interval sequence number t 'and the (i, j, t, t', m, m ') time checking sequence number t' in the calculation state m are calculated as follows:
t′＝t+TTi,j(m)
wherein the travel time TT through (i, j) in the state mi,j(m) is calculated as follows:
Figure BDA0003389514830000034
(c) traverse all state transition processes (from state m to m')
(2) Constructing a state transition space-time state network of the fixed detector, adopting a space-time state arc to represent the state transition process of an observed target of the fixed detector, and aiming at a physical point ia′The corresponding time state network is constructed, and the observation target located at the physical point i is transferred from the state m (time t) to the state m ' (time t +1) by using a time space state arc (i, i, t, t +1, m, m '), wherein (i, j) ═ i (i, j) ═ m ' (time t +1)a′,ja′)。
Step2: with reference to fig. 2, a unified network passenger flow estimation model is established, a network passenger flow state estimation problem of the urban rail transit system is modeled into a high-dimensional network distribution model under a generalized least square estimation framework, the most probable network passenger flow state is estimated by the target under the constraint condition of consistency in substeps (1) and (2) of step1, and a passenger flow space-time estimation matrix is obtained by solving;
the method specifically comprises the following substeps:
(1) constructing a discrete passenger flow state: constructing a discrete passenger flow state according to the types and properties of different physical arcs, wherein the discrete passenger flow state mainly comprises the following steps;
(a) and constructing passenger flow balance constraint. In a spatiotemporal state network, the passenger flow balance constraint may be formulated. Wherein Lagrange observations of passengers (i.e. data of swiping cards of passengers at the starting point and the ending point) are boundary conditions of passenger flow balance constraint and are matched with the starting point (o) in the time-space state networka,DTa,m0) And at the end point (d)a,ATa,m0)；
Figure BDA0003389514830000041
(b) And (4) listing an observation equation between the passenger flow density and the network passenger flow state. Collective passenger flow density of physical arcs (i, j) over an arbitrary time interval t
Figure BDA0003389514830000042
Through density
Figure BDA0003389514830000043
And matching with the network passenger flow state variable z (i, j, t, m) as shown in a formula.
Figure BDA0003389514830000044
(c) And constructing uniqueness constraint of the network passenger flow state. Assuming that any physical arc (i, j) in the urban rail transit system has a unique discrete passenger flow state in any time interval t, the constraint can be expressed as a formula.
Figure BDA0003389514830000045
(d) And constructing a balance constraint of the state transition flow of the fixed detector. The state transition process of the fixed detector is modeled as a spatio-temporal state path in the spatio-temporal state network, so the state transition flow balance constraint of the fixed detector can be formulated as:
Figure BDA0003389514830000051
(2) constructing a spatio-temporal state network: and constructing a space-time state three-dimensional network based on the physical network, the train running schedule and the discrete network passenger flow state. In a space-time state three-dimensional network, Lagrange observation values are matched into space-time state points, and Euler observation value fixed points constrain state solving space.
Assuming a flow observed value obsq(a', t), observed Density values obsk(a', t), velocity observed value obsv(a ', t) may each be obtained from a fixed detector a', where (i, j) ═ ia′,ja′). If the observation error and the approximation error of the discrete state are not considered, the Euler observation value should be matched with the state transition process of the fixed detector, such as the formulaAs shown, the estimated flow, density, velocity (right term) should be equal to the corresponding observation (left term).
Figure BDA0003389514830000052
(3) Constructing a unified framework for state estimation: and (3) adopting a generalized least square estimation model to build a problem decomposition framework and solve the problem decomposition framework iteratively, and estimating the network passenger flow state. And establishing a model estimation objective function as follows to finish solving:
generalized least squares estimation model objective function:
Minα×L(Xl,Z)+β×L(Obse,Xe)+γ×L(Xe,Z)
Figure BDA0003389514830000053
Figure BDA0003389514830000061
Figure BDA0003389514830000062
step3, combining the basic line parameters with the passenger flow state space-time estimation matrix in combination with the graph 3, wherein the basic line parameters in step3 comprise a line data module, a train parameter module, an ATO parameter module and a subway operation data module, and combining the passenger flow state space-time estimation matrix in step2, establishing a vehicle-mounted ATO model, a train mechanics model and a train energy consumption calculation model, and deducing a train traction operation model under the passenger flow network at the moment;
the train dynamic model is combined with the traction power supply calculation model to obtain a train interval running traction energy consumption calculation model, and the method specifically comprises the following substeps:
(1) estimating the passenger capacity I of the train k in the interval n' based on the passenger flow state space-time estimation matrix in the step2kn′Average mass m of passengers0Mass of unloaded train is M0Mass M of trainkn′Comprises the following steps:
Mkn′＝M0+Ikn′,m0
(2) under the condition of space distribution in an interval, the maximum traction, cruising, coasting and maximum braking operation conditions of the train are as follows:
Figure BDA0003389514830000071
wherein rho is a revolution mass coefficient; v. ofkn′tAnd xkn′tRespectively the speed and position of the train k running in the interval n' at the moment t; dknThe moment when the train k leaves the station n; a isk(n+1)The moment when the train k reaches the station n + 1;
Figure BDA0003389514830000072
and
Figure BDA0003389514830000073
respectively the moments of traction running cruise, cruise running coasting and coasting running braking when the train k runs in the interval n'; fT(vkn′t)、 R(vkn′t,xkn′t)FB(vkn′t) Respectively traction force, resistance force and braking force, the same direction as the train movement is defined as positive, the reverse direction is defined as negative, and R (v)kn′t,xkn′t) Including the basic train drag and the additional drag caused by changing line conditions such as ramps, curves and tunnels.
(3) Calculating the train traction energy consumption, assuming that the regenerative braking energy can go up and down in the same power supply zone and mutually transmit among a plurality of trains in the direction, and the conversion efficiency rho of the electric energy and the mechanical energymeMechanical energy to electrical energy conversion efficiency ρmeAnd line loss ρ1All are constants, Q is defined as power supply partition index, Q is total number of power supply partitions, and time interval [ t ] is divided at equal intervals of delta ts,te]At [ t, t + Δ t]Traction energy consumption of internal power supply subarea q
Figure BDA0003389514830000074
Figure BDA0003389514830000075
(4) Calculating the regenerative braking energy of the train, recording Q as the total number of power supply subareas under the Q power supply subareas, and dividing the time period [ t ] at equal intervals of delta ts,te]At [ t, t + Δ t]Regenerative braking energy consumption of internal power supply subarea q
Figure BDA0003389514830000076
Δ t represents the simulation step size
Figure BDA0003389514830000077
Figure BDA0003389514830000078
Is a variable from 0 to 1, if the interval n' belongs to the supply partition q,
Figure BDA0003389514830000079
otherwise
Figure BDA00033895148300000710
vcCritical speed for regenerative braking and air braking, if and only if vkn′t>vcRegenerative braking energy is generated.
(5) Calculating the net energy consumption of the train in the interval, and defining the net energy consumption as the difference between the total traction energy consumption and the utilized regenerative braking energy:
Figure BDA00033895148300000711
step4, aiming at the maximization of the traffic demand and the minimization of total energy consumption of train traction on the whole line, establishing a space-time passenger flow network energy-saving schedule optimization model, considering passenger flow demand constraints and train operation relevant constraints at known unit time intervals of each station, and solving the arrival and departure time of the train at each station and the maximum operation speed of the train in the interval, so that the total travel time of passengers and the train operation energy consumption are optimal, and specifically comprising the following substeps:
(1) effective riding time window of kth train at station i
Figure BDA0003389514830000081
Determining the number of people capable of riding the k-th train and the effective riding time window of the k-th train
Figure BDA0003389514830000082
The number of passengers from station i to station j is calculated as follows, in which
Figure BDA0003389514830000083
Figure BDA0003389514830000084
(2) Calculating the number of passengers getting on the train at the station i and taking the train k, wherein i belongs to S \ S, 2S; j belongs to S \ 1, S +1, j equals to i + 1; k is equal to Π;
Figure BDA0003389514830000085
Figure BDA0003389514830000086
(3) calculating the number of passengers getting off from the kth train at the station i, wherein i belongs to S; k is equal to Π;
Figure BDA0003389514830000087
Figure BDA0003389514830000088
(4) the k-th train starts from the i-th station,counting the number of passengers in the train and the number of passengers in the train after the train departs from the previous station
Figure BDA0003389514830000089
Number of passengers getting off at station
Figure BDA00033895148300000810
And the number of persons getting on the bus
Figure BDA00033895148300000811
In relation, the calculation is as follows:
Figure BDA00033895148300000812
(5) effective end-of-ride time of kth train at station i
Figure BDA00033895148300000813
Figure BDA00033895148300000814
i∈S\{s,2s}；j∈S\{1,s+1},j＝i+1；k∈Π；
Figure BDA00033895148300000815
(6) At the station i, the kth train arrives at the station i, the activities of getting on and off passengers and the like are completed within a certain stop time, and then the train stops from the station i and is expressed in a constraint manner:
Figure BDA00033895148300000816
(7) after the kth train starts from the ith station, recording the time of the ith interval as the interval operation time
Figure BDA0003389514830000091
Through
Figure BDA0003389514830000092
Can arrive at the (i +1) th station, the calculation is as follows
Figure BDA0003389514830000093
(8) Recording the interval running time of the k-th train starting from the ith station and arriving at the middle of the (i +1) th station
Figure BDA0003389514830000094
Recording run time of acceleration phase
Figure BDA0003389514830000095
Cruising time
Figure BDA0003389514830000096
And braking time
Figure BDA0003389514830000097
The sum, calculated as follows:
Figure BDA0003389514830000098
(9) the train operates in a cruising stage, and the maximum operating speed of the interval is restricted to
Figure BDA0003389514830000099
(10) When adjacent trains at the same platform run, the constraint that the departure and arrival of the trains need to meet the safety interval is as follows
Figure BDA00033895148300000910
Figure BDA00033895148300000911
(11) After the train runs for one uplink, if the train needs to continuously run for one downlink, the train can start only after a certain turn-back time, the turn-back time of the train is represented by tau, the number of the trains is represented by n, and tau is satisfied
Figure BDA00033895148300000912
(12) Establishing a time-space passenger flow network schedule optimization model objective function, and taking the minimization of train operation energy consumption and the minimization of passenger total travel time as optimization objectives, then:
keeping the passenger platform detention penalty coefficient alpha, the passenger total travel time minimization objective function can be expressed as:
Figure BDA00033895148300000913
the minimum objective function of the running energy consumption of all trains on the line can be expressed as follows:
Figure BDA00033895148300000914
step5, based on the space-time passenger flow curved surface Pareto multi-target fuzzy optimization problem, improving an adaptive function on the basis of a genetic algorithm, avoiding the defect that the genetic algorithm is easy to fall into a local optimal solution when solving a more complex optimization problem, solving the optimal solution, outputting an energy-saving timetable optimization result, and determining an energy-saving optimal adjustment strategy of the all-line train;
with reference to fig. 4, the improved adaptive function genetic algorithm design calculation steps are as follows:
(1) the method mainly comprises the following steps of inputting algorithm data such as train parameters, passenger flow OD data, line basic parameters and the like:
a. researching departure quantity, train passenger carrying capacity and maximum train full load rate in a time range;
b. technical parameters of a part of train operation diagrams: the train is stopped at each station, the minimum running interval, the minimum preparation time of the train at the retracing station and the value upper and lower limits of the maximum running speed of the interval are defined;
c. passenger flow demand data: the OD passenger flow demand matrix of each station in a unit time interval needs to be obtained by preprocessing AFC passenger ticket data;
d. line and train data: interval mileage between each station, train mass, vehicle basic resistance equation coefficient, traction acceleration and brake deceleration data;
e. setting genetic algorithm parameters: initial feasible population scale, genetic algebra, cross probability and mutation probability.
(2) Generating an initial population, wherein a special binary coding method is selected for a departure moment part of a train at a departure station, genes of the part in a chromosome correspond to discrete time intervals in a research period, each gene can only be randomly generated from 0 and 1 number according to a certain rule, a speed-limiting running speed coding section of the train adopts floating point number coding, and the upper limit and the lower limit of the maximum running speed of the train in each interval are randomly generated according to the value of the maximum running speed of the train.
One chromosome can be represented as:
Figure BDA0003389514830000101
tp is the time interval, xtA variable of 0-1 indicating whether a train departs from the origin at the end of the t-th time interval, x if a train departs from the origin at the end of the t-th time intervaltIs 1, otherwise is 0,
Figure BDA0003389514830000102
and taking an upper limit and a lower limit for the maximum running speed of the train in the ith interval.
On the premise of considering the train departure time of the urban rail transit departure station and various constraints of the maximum running speed of the train, the method for generating the initial feasible solution is designed, and the specific implementation steps are as follows:
step1: initializing, namely generating a vector A containing tp zero elements, and enabling the vector A to be an initial starting station train departure time scheme, wherein each element in the vector A represents a gene value of a corresponding time interval;
step2: from 1 to tp-hmin-(hmin-1) × (K-2) random sequence arr, the elements in arr corresponding to the numbering of the loci in a, hminIs the minimum departure interval.
Step3: randomly taking out K-1 gene positions from a random sequence arr generated in Step2, carrying out ascending arrangement on the K-1 gene positions, and putting the K-1 gene positions into a set pos, wherein j is 0, and i is 1;
step 4: based on the randomly taken K-1 gene positions, according to the minimum departure interval hminThe restriction of (2) assigns the number of cars to the corresponding gene position in A. Let A (pos (i) + j) be 1, and let j be j + hmin-1,i＝i+1；
Step 5: repeating Step4, stopping when i is larger than K, namely finishing the random distribution of the previous K-1 times of train numbers according to the minimum interval constraint;
step 6: and fixing the departure time of the K-th train. Let the tp th element in vector A be 1;
step 7: produce s-1
Figure BDA0003389514830000111
And
Figure BDA0003389514830000112
random numbers in the range form a random sequence V;
step 8: sequentially putting tp elements in the vector A and a random sequence V randomly generated in Step7 into the vector XqIn, XqNamely, the generated feasible solution which meets the constraint;
step 9: repeating the steps 1-8 pop _ size times to generate the initial feasible population with the size of pop _ size.
(3) Constructing a fitness function, wherein the evaluation of the fitness function needs to calculate the minimum value minPT of the total travel time of the passengers and the total operation energy consumption minE and d of the line train in the target function in the step4 and the step 121、d2Scaling indexes of each objective function; the method comprises the following steps:
(a) calculation of passenger total travel time:
step1: and (5) initializing. Setting vector TL1Represents the latest arrival time of passengers per train at the 1 st station, vector Num1Indicating number of passengers in train, TL, at 1 st station per train1And Num1Respectively containing K +1 elements, initializing the elements to be zero, and enabling K to be 2;
step2: let t be L1(k-1) +1, if t is less than or equal to D (1, k), then go to Step3, otherwise go to Step 6. D (1, k) represents the departure time of train k at the first stop.
Step3: and (6) judging. If the number of passengers Num in the k train at the time of t-11(k) And if the train capacity is smaller than the Cap, turning to Step4, otherwise, turning to Step5.
Step 4: let Num1(k) Plus the number of passengers arriving at the station at time t, i.e. Num1(k)＝Num1(k)+sum(P1(t,: t)) and let TL1(k) T, t +1, Step 2;
step 5: let Num1(k) The number of passengers arriving at the station at the moment of t-1 is subtracted, namely Num1(k)＝Num1(k)-sum(P1(t-1): and let TL1(k) T-2, Step 6;
step 6: a stop condition. And if K is equal to K +1, turning to Step2, and otherwise, stopping.
Step 7: after the latest arrival time of passengers of each train at the 1 st station is calculated, the latest arrival time of the passengers of each train at the 2 nd, 3 rd,.. multidot.s-1, s +1, … and 2s-1 stations is calculated and calculated according to Step 1-Step 6, but when the calculation initialization is needed at each Step1, the number of passengers in the train at the 2 nd, 3 rd.. multidot.s-1, s +1, … and 2s-1 stations needs to be subtracted by the number of passengers in the train at the corresponding station.
Step 8: the passenger travel time for each passenger to ride each train is calculated at each station according to steps 1 to 7, and the total passenger travel time PT can be calculated with reference to Step4.
(b) And (3) calculating the energy consumption of the train on the whole route: repeating the step (a) can estimate the number of people in the train after each train departs from each station, and referring to the step (5) in the step3, the net energy consumption E of the train in each section can be calculatedNReferring to (12) in step4, the whole-track train is calculatedEnergy consumption E;
(c) minimum and individual scaling index of the objective function: according to the model and the input data, the minimum value minPT and the respective telescopic indexes d of the single objective function can be obtained by considering the single objective function1、d2And calculating the membership degree of each objective function.
Recording an objective function:
minPT is the riding time requirement, and the smaller the minPT is, the better the minPT is for passengers;
the minE is the benefit of an operator, and an operation unit hopes that the smaller the train operation energy consumption is, the better the train operation energy consumption is;
minPT corresponding membership function of
Figure BDA0003389514830000121
minE corresponding membership function of
Figure BDA0003389514830000122
Converting the double target functions into a single target programming function by using an AHP fuzzy optimization theory two-stage method:
minZ＝λ1·Z1+λ2·Z2
PTmin、Emin: the optimal value of the single objective function under the constraint is satisfied;
d1、d2: scaling indexes of each objective function;
λ1、λ2: the importance degree of each objective function takes a value within 0-1;
let the fitness function as follows:
fit(X)＝Z
(4) the genetic manipulation is carried out on the plant,
a. selecting; roulette selection method using elite reservation based strategy, individual XqThe probability that it can be selected to be inherited to a new generation population is:
Figure BDA0003389514830000131
elite retention strategy roulette selection chromosomes: firstly, finding out individuals with optimal fitness values in the contemporary population; then, selecting all individuals by adopting a roulette selection method according to the fitness values of the individuals, and finding out the individual with the worst fitness value in the new population after the roulette selection; and replacing the worst individual with the optimal individual selected in advance from the current generation population, and continuously performing iterative computation on the obtained individual serving as the new population after evolution.
The specific calculation process is as follows:
step1, calculating the fitness value fit (X) of each individual in the contemporary populationq) And finding out the optimal individual X in the current generation of individuals according to the size of the fitness valueqLet Xq＝1。
Step2, calculating the probability of the individual being selected and the cumulative probability:
Figure BDA0003389514830000132
step3 generating random selection probabilities for the individuals. Randomly generating pop _ size [? 0,1]When a number in between is placed in vector R, R (q) is the individual XqIs selected randomly.
Step 4: individual XqComparing the random selection probability with the cumulative probability, and performing selective replication on the individuals.
Step4.1: if R (X)q)<cumprob(X1) Then the individual XqSelected, it is copied to the offspring population, and transferred to Step5.1.
Step4.2: if cumrob (X)q′)<R(Xq)≤cumprob(Xq′+1) Then the individual Xq+1Selected, it is copied to the offspring population, and transferred to Step5.2.
Step 5: stop condition
Step5.1: if q is not more than pop-size, let q be q +1, go to step4.1, otherwise, q be 1, q' be 1, go to step4.2.
Step5.2: if q is not more than pop-size and q 'is not more than pop _ size-1, then let q +1, q' +1, and Step4.2, otherwise, Step 6.
Step 6: calculating fitness values of individuals in the new population after roulette selection and finding the worst individual Xw；
Step 7: the worst individual X in the new populationwWith optimal individuals X in the current generation of the population selected in advanceuThe replacement was done, at which point pop size individuals were selected as the next generation population.
b. Crossing; setting a minimum departure interval h of a trainminDesigning self-adaptive crossover operator for the length of the crossover segment, and calculating the crossover probability to be PcFor two individuals cross-paired, the cross probability is calculated as follows:
Figure BDA0003389514830000141
Figure BDA0003389514830000142
the cross probability of the cross operation is the cross probability of the current time;
j: the number of cross operations;
fmax: is the maximum fitness value in the population;
favg: is the average fitness value;
f: the greater fitness value in the two chromosomes that are cross-paired;
the specific operation steps of the crossover operator are as follows:
step1: initializing, making q equal to 1, and calculating cross probability PcThe number of times j of the cross operation is 1;
step2: sequentially taking out two individuals X from the previous generation populationq,Xq+1Forming paired crossed individuals;
step3: calculating the cross probability of the paired crossed individuals
Figure BDA0003389514830000143
Step 4: generate a range of 0-1A random number p inrIf, if
Figure BDA0003389514830000144
Turning to Step5 for individual cross recombination, otherwise, directly adding the two taken individuals into the offspring population, turning to Step9, and judging whether all the individuals in the population are subjected to cross judgment;
step 5: from
Figure BDA0003389514830000145
Randomly selecting a gene site t as a cross starting point in the interval, and then the cross segment is
Figure BDA0003389514830000146
Step 6: judging whether the two individuals meet the crossing condition:
Figure BDA0003389514830000151
and two individual cross-segments
Figure BDA0003389514830000152
Both front and back are present with h min1 zero gene, if both conditions are met, then switching to Step7 for gene interchange; otherwise, turning to Step5 to reselect the crossing position;
step 7: performing cross gene recombination to generate two new individuals Xq,X(q+1)′；
Step 8: selecting better individuals, if it is (X)q)>fit(Xq) Then, the individual Xq′Adding to the offspring population, otherwise adding individual XqAdding to the offspring population, X(q+1)′And Xq+1Carrying out the same judgment operation;
step 9: a crossover operation stop condition, if q < pop _ size-1, let q be q +2, j be j +1, go to Step 2; otherwise, all the individuals in the parent are subjected to cross judgment, and the cross operation is finished.
c. Mutation; randomly selecting a plurality of unrepeated gene positions as possible variation positions for the train departure time coding section of the starting station,then judging whether the selected gene locus meets the variation condition, and if so, performing variation according to a certain rule; designing adaptive mutation operator, and setting the mutation probability of algorithm as PnFor an individual X to be mutatedqThe variation probability can be calculated according to the following formula:
Figure BDA0003389514830000153
Pm(Xq): to be mutated individual XqThe mutation probability of (2);
favg: is the average fitness value;
fit(Xq): is an individual XqA fitness value of;
the specific calculation steps of the mutation operation are as follows:
step1: initializing, making q equal to 1, mutation probability Pm；
Step2: calculating the variation probability P of the individual meaningm(Xq)；
Step3: generating a random number p in the range of 0-1rIf p isr<Pm(Xq) Then, turning to Step4 to perform individual variation operation, otherwise, turning to the individual XqDirectly adding the obtained product into a filial generation population, turning to Step8, and judging whether all individuals in the population have variation;
step 4: variation of the coding section at the departure time of the train;
Step4.1：
Figure BDA0003389514830000161
randomly selecting theta (theta is less than or equal to tp-h)min-1) non-repetitive loci as possible positions of variation, let i equal 1;
step4.2: sequentially judging whether the selected gene meets the variation condition or not, and for the selected gene
Figure BDA0003389514830000162
If it satisfies
Figure BDA0003389514830000163
And is
Figure BDA0003389514830000164
Exchanging the t and t +1 gene values; if it satisfies
Figure BDA0003389514830000165
And is
Figure BDA0003389514830000166
Then the t + h min1 and t + hminInterchanging individual gene values;
step 5: and (3) changing the stop condition of the coded segment variation at the departure time of the train, if i is less than theta, enabling i to be i +1, and turning to Step4.2, otherwise, turning to Step 6.
Step 6: the maximum running speed of train is varied to generate random sequence V' in the maximum running speed range and replace the gene in speed coding segment, and the varied individual is marked as Xq′；
Step 7: selecting better individuals, if it is (X)q)>fit(Xq) Then, the mutated individuals Xq′Adding to the offspring population, otherwise adding individual XqAdding the obtained product into a filial generation population;
step 8: stopping mutation operation, if q is less than pop-size, making q equal to q +1, and turning to Step 2; otherwise, all the individuals in the parent are subjected to mutation judgment, and the mutation operation is finished.
(5) The algorithm terminates the computation conditions.
And (4) recording GEN as a genetic algebra set by the algorithm termination condition, iterating according to the selection, intersection and variation designed in the step (4), finishing the algorithm when the maximum genetic algebra GEN is reached, and outputting the currently evolved optimal individual as an optimal solution. Outputting an energy-saving schedule optimization result, and determining an energy-saving optimal adjustment strategy of the whole train;
in conclusion, the method adopts a software simulation mode, considers the spatial-temporal network distribution characteristics of the passenger flow of the rail transit network from the view point of urban rail transit operation, can maximally meet the passenger service level and simultaneously maximally reduce the total traction energy consumption of the whole train under the conditions of platform passenger riding requirements, passenger comfort, safe train operation and normal operation scheduling, and has higher use value and application prospect.
The above embodiments are merely illustrative of the technical ideas of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like based on the technical ideas of the present invention should be included in the scope of the present invention.

Claims (6)

1. An energy-saving schedule optimization method for subway trains under space-time passenger flow network distribution is characterized by comprising the following steps:
step1, establishing a unified state estimation framework model based on an urban rail transit complex network, integrating Lagrange observation values and Euler observation values of different data sources, different structures, different time and space accuracies, and accurately estimating and restoring network passenger flow states;
step2: establishing a unified network passenger flow estimation model, estimating the state of network passenger flow by adopting an estimation framework of a generalized least square method, and solving to obtain a passenger flow space-time estimation matrix;
step3, establishing a vehicle-mounted ATO model, a train mechanical model and a train energy consumption calculation model by combining the line basic parameters with the passenger flow state space-time estimation matrix, and deducing a train traction operation model under the passenger flow network at the moment;
step4, establishing a space-time passenger flow network schedule optimization model by aiming at the maximization of the demand of the passenger capacity and the minimization of total traction energy consumption of the whole-line train;
and 5, based on the Pareto multi-target fuzzy optimization problem, improving an adaptive function on the basis of a genetic algorithm, avoiding the defect that the genetic algorithm is easy to fall into a local optimal solution when solving a more complex optimization problem, solving the optimal solution, outputting an energy-saving timetable optimization result, and determining an energy-saving optimal adjustment strategy of the whole-line train.
2. The method for optimizing the energy-saving schedule of the subway train under the time-space passenger flow network distribution as claimed in claim 1, wherein said unified state estimation framework of step1 establishes network passenger flow, reconstructs the travel time-space trajectory of all passengers from the starting point to the end point in the system and estimates high-precision time-varying passenger flow in all platforms, vehicles and transfer channels.
3. The method for optimizing the energy-saving schedule of the subway train under the space-time passenger flow network distribution as claimed in claim 1, wherein said step2 of establishing the high-dimensional network distribution model under the generalized least square estimation framework specifically comprises the following steps:
(1) constructing a discrete passenger flow state: constructing a discrete passenger flow state according to the types and properties of different physical arcs;
(2) constructing a spatio-temporal state network: constructing a space-time state three-dimensional network based on a physical network, a train running schedule and a discrete network passenger flow state; in a space-time state three-dimensional network, Lagrange observation values are matched into space-time state points, and Euler observation value fixed points constrain state solving space;
(3) constructing a unified framework for state estimation: and searching the optimal space-time state path of each passenger and the state transition of the fixed detector in the space-time state three-dimensional network, and estimating the network passenger flow state by adopting a problem decomposition frame and an iterative solution method.
4. The method for optimizing the energy-saving schedule of the subway trains under the time-space passenger flow network distribution as claimed in claim 1, wherein the line basic parameters in step3 comprise a line data module, a train parameter module, an ATO parameter module, a subway operation data module, and a passenger flow state time-space estimation matrix in step2, and a vehicle-mounted ATO model, a train mechanics model, a train energy consumption calculation model are established, and a train traction operation model under the time-space passenger flow network is deduced.
5. The method for optimizing the energy-saving schedule of the subway trains under the space-time passenger flow network distribution according to claim 1, wherein the step4 aims to maximize the passenger flow demand and minimize the total energy consumption of the traction of the whole-line train, and solves the maximum running speed of the train at the arrival and departure time of each station and the interval of the train in consideration of the passenger flow demand constraint and the train running relevant constraint on the known passenger flow demand and train relevant technical parameters of each station at unit time interval so as to optimize the total travel time of passengers and the train running energy consumption.
6. The method for optimizing the energy-saving schedule of the subway train under the space-time passenger flow network distribution according to claim 1, wherein the self-adaptive operator is improved and the optimal solution is found on the basis of the Pareto multi-objective fuzzy optimization problem based on the genetic algorithm in the step5, and the steps are as follows:
(1) inputting algorithm data such as train parameters, passenger flow OD data, line basic parameters and the like;
(2) generating an initial population;
the maximum running speed of the train is encoded by floating point numbers and is randomly generated according to the upper limit and the lower limit of the value of the maximum running speed of the train in each interval; one chromosome can be represented as:
Figure FDA0003389514820000021
tp is the time interval, xtA variable of 0-1 indicating whether a train departs from the origin at the end of the t-th time interval, x if a train departs from the origin at the end of the t-th time intervaltIs 1, otherwise is 0,
Figure FDA0003389514820000022
taking an upper limit and a lower limit for the maximum running speed of the train in the ith interval;
setting the initial population to contain pop _ size chromosome, then population qth chromosome can be represented as:
Figure FDA0003389514820000023
(3) constructing a fitness function;
recording an objective function:
minPT is the riding time requirement, and the smaller the minPT is, the better the minPT is for passengers;
the minE is the benefit of an operator, and an operation unit hopes that the smaller the train operation energy consumption is, the better the train operation energy consumption is;
minPT corresponding membership function of
Figure FDA0003389514820000024
minE corresponding membership function of
Figure FDA0003389514820000031
Converting the double target functions into a single target programming function by using an AHP fuzzy optimization theory two-stage method:
minZ＝λ1·Z1+λ2·Z2
PTmin、Emin: the optimal value of the single objective function under the constraint is satisfied;
d1、d2: scaling indexes of each objective function;
λ1、λ2: the importance degree of each objective function takes a value within 0-1;
let the fitness function as follows:
fit(X)＝Z
(4) genetic manipulation;
a. selecting; roulette selection method using elite reservation based strategy, individual XqThe probability that it can be selected to be inherited to a new generation population is:
Figure FDA0003389514820000032
the obtained individuals are used as a new population after evolution to continue iterative computation;
b. crossing; designing self-adaptive crossover operator with the crossover probability of PcFor two individuals cross-paired, the cross probability is calculated as follows:
Figure FDA0003389514820000033
Pc j: the cross probability of the cross operation is the cross probability of the current time;
j: the number of cross operations;
fmax: is the maximum fitness value in the population;
favg: is the average fitness value;
f: the greater fitness value in the two chromosomes that are cross-paired;
c. mutation; designing adaptive mutation operator, and setting the mutation probability of algorithm as PnFor an individual X to be mutatedqThe variation probability can be calculated according to the following formula:
Figure FDA0003389514820000041
Pm(Xq): to be mutated individual XqThe mutation probability of (2);
favg: is the average fitness value;
fit(Xq): is an individual XqA fitness value of;
(5) the algorithm terminates the calculation condition;
recording GEN as a genetic algebra set by an algorithm termination condition, iterating according to the selection, intersection and variation designed in the step (4), finishing the algorithm when the GEN reaches the maximum genetic algebra, and outputting the currently evolved optimal individual as an optimal solution; and outputting an energy-saving schedule optimization result, and determining an energy-saving optimal adjustment strategy of the whole train.
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