CN112465205A - Single-line multi-station cooperative current limiting rail transit train running density optimization method - Google Patents

Single-line multi-station cooperative current limiting rail transit train running density optimization method Download PDF

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CN112465205A
CN112465205A CN202011309788.6A CN202011309788A CN112465205A CN 112465205 A CN112465205 A CN 112465205A CN 202011309788 A CN202011309788 A CN 202011309788A CN 112465205 A CN112465205 A CN 112465205A
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陈茜
张玥妍
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Abstract

The invention discloses a single-line multi-station cooperative current-limiting rail transit train running density optimization method, which takes the minimum waiting total time of passengers in a passenger flow peak period as an optimization target, constructs a multi-station cooperative current-limiting rail train running density optimization model, and obtains the globally optimal number of passengers at each station for controlling the passenger flow and the train running interval by applying a simulated annealing algorithm. Compared with the prior art, the method for optimizing the train running density of the urban rail transit based on the cooperative current limiting theory is provided, the peak passenger flow pressure is effectively relieved, the waiting time of passengers is reduced, and the service level is ensured on the basis of ensuring the rail transit transportation efficiency and safety.

Description

Single-line multi-station cooperative current limiting rail transit train running density optimization method
Technical Field
The invention relates to the field of train operation organization under the background of large passenger flow of urban rail transit, in particular to a single-line multi-station cooperative current-limiting rail train operation density optimization method.
Background
The urban rail transit has the outstanding advantages of safety, rapidness, comfort, large transportation volume, small pollution, lower operation cost, no interference with other traffic modes and the like, and on the basis of meeting the traveling demands of passengers to the maximum extent, the urban rail transit also improves the problem of road traffic jam, improves the efficiency of traffic transportation and occupies an important framework position in urban traffic. In large and medium-sized cities, urban rail transit has become a preferred traffic mode for short-distance travel, the direct passenger flow and the transfer passenger flow are increased synchronously, large passenger flows can occur in the early and late peaks, holidays, large-scale activity gathering scattered places and the like of travel, when the single train is in full-load operation due to insufficient transport capacity, part of passengers can be detained at a station, and the train delay scale is diffused from the station to a single line. When accidental events such as train faults and severe weather occur, the large passenger flow may cause the problems that the personal safety of passengers cannot be guaranteed, the passengers are detained in a large scale, the train delay scale is enlarged, the safety protection capability and the bearing capacity of a station are insufficient, and the like. When passengers are detained or large passenger flows are gathered at a certain station, the train sent out from the station is basically in a full state, the train is influenced by the adjacent station, the adjacent area or the transfer station, the large passenger flows form linear large passenger flow propagation by the points, and the passenger detention phenomenon exists in a single track traffic line. Therefore, the adjustment and optimization of the train running density under the multi-station coordinated flow limiting condition is beneficial to guaranteeing the coordination of the whole transportation, the safety of transportation service is guaranteed, the maximization of the transportation capacity is promoted, and the transportation energy waste is avoided.
Against the background of large passenger flow in peak period, the prior art at home and abroad mainly focuses on analyzing the space-time characteristics of the passenger flow and dynamically distributing the passenger flow in a rail transit network so as to optimize a rail train marshalling scheme, a large-small traffic route adjustment organization scheme and the like, but a technical scheme for simultaneously considering single-line multi-station cooperative current limiting and train operation density adjustment optimization is lacked.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems, the invention provides a method for optimizing the running density of a single-line multi-station coordinated current limiting rail transit train, which is characterized in that a multi-station coordinated current limiting optimization model is constructed by taking the minimum total waiting time of passengers in the whole line train station as a target, and the optimal running density of the train under the coordinated current limiting effect is obtained through solving, so that the pressure of the single-line rail transit transportation of the rush hour and large passenger flow is relieved, a reference is provided for reducing the scale delay of the train, the coordination of the whole transportation is ensured as much as possible, the safety of the transportation service is ensured, and the waste of transportation energy is avoided.
The technical scheme is as follows: in order to realize the purpose of the invention, the technical scheme adopted by the invention is as follows: a single-line multi-station cooperative current-limiting rail transit train running density optimization method comprises the following specific steps:
step 1, calibrating conditions of urban rail transit lines, stations, trains and passenger flows and extracting key indexes; the key indexes comprise the getting-off rate and the getting-in passenger flow demand of the station, the maximum bearing capacity of the station platform and the section passenger flow in the interval;
step 2, determining constraint conditions by taking the minimum sum of the residence time of passengers in the current-limiting time period and the waiting time of the passenger flow entering as an optimization target and the minimum sum of the residence time of passengers in the current-limiting time period and the waiting time of the passenger flow entering the station as decision variables, and establishing a single-line multi-station cooperative current-limiting train density optimization model;
and 3, constructing input parameters of the model according to the step 2, wherein the input parameters comprise initial station entering passenger flow, platform number, number of getting-on and getting-off persons and number of remaining persons of each station, applying a simulated annealing algorithm to carry out iterative search on the number of station entering persons and train running intervals in a plurality of current-limiting periods, solving a multi-station cooperative current-limiting train density optimization model, and outputting an optimal train running interval and the number of current-limiting persons of each station.
Further, the step 1 is specifically set as follows:
in the same time period and section of passenger flow control, the operation of the train at the same time is carried out according to a train operation diagram which is actually planned; the initial bearing and passing capacity of each station meets the requirement of passengers for entering the station, the transfer passenger flow is converted into the passenger flow entering the station on the basis of one-way line analysis, and the rest passenger flows are regarded as the passenger flow leaving the station as a control point; the method comprises the following steps that the situation that passengers entering a station are skilled in using station facility equipment is assumed, and extra time spent in the station caused by individual subjective factors is not considered; neglecting the traffic of giving up travel of passengers, and getting on the bus in principle of first-come first, and not considering vicious congestion; the train type selection and the train marshalling train number are not changed when the multi-station cooperation is carried out on the same line, and the maximum passenger carrying number of the train is a fixed value.
Further, the step 1 specifically includes:
firstly, defining that a large passenger flow control cycle is a peak time period, dividing the large passenger flow control cycle into a plurality of small passenger flow control time periods, and carrying out station calibration on all stations of a single line to be limited to obtain a station label set;
secondly, obtaining the getting-off rate and the getting-in passenger flow demand of the ith station according to the original passenger flow data of different stations, and acquiring the maximum bearing capacity of the station and the maximum passing capacity calibration value under the limitation of passing facilities of the gate machine of the station;
secondly, according to the personnel-fixed carrying capacity of each train and the set full load rate limit, calculating the section passenger flow from the ith station to the (i + 1) th station, comparing the section passenger flow with the maximum carrying capacity of the section, and determining whether the section conveying constraint is met;
and finally, limiting the initial value of the train operation interval according to the normal rail transit train operation plan, and setting the initial interval and the number of initial stations at the ith station.
Further, in the train density optimization model in step 2, the objective function is expressed as follows:
Figure BDA0002789433680000021
where Z represents the sum of waiting times of passengers in the station,
Figure BDA0002789433680000022
for the passenger flow entering the station at the ith station under the control of current limit,
Figure BDA0002789433680000023
is the total number of passengers in the ith station, AtThe time length of the passenger flow control time interval is the train running interval, and T is the passenger flow control time interval which comprises a plurality of passenger flow control time intervals of the time length T; n ═ N i1,2,3, …, N, wherein N is the total number of all stations of a single line, and N represents a station set of the one-way rail transit line;
the constraint conditions include: station passenger flow demand constraint, station platform capacity constraint, interval passenger flow conveying capacity constraint, boarding passenger flow constraint, train tracking interval time constraint and line conveying capacity constraint, as shown in formulas (2) to (11):
Figure BDA0002789433680000024
Figure BDA0002789433680000031
Figure BDA0002789433680000032
Figure BDA0002789433680000033
Figure BDA0002789433680000034
At≥tm (7)
At≤ts (8)
At≥tr (9)
At≥tb (10)
Figure BDA0002789433680000035
the formula (2) is station passenger flow demand constraint, and lambda represents the minimum proportion of the passenger flow demand; the formula (3) and the formula (4) are station capacity constraints,
Figure BDA0002789433680000036
the maximum number of people accommodated in the platform of the station,
Figure BDA0002789433680000037
the maximum number of people passing through the gate machine is limited by facilities; equation (5) is a regional passenger flow transport capacity constraint, Mi-1,iRepresenting the cross-sectional passenger flow when traveling from station i-1 to station i,3 is the maximum passing capacity in the unit hour interval; y is n m d, m is the train formation number, the unit is a train, d is the train fixed member, n is the passing number of the train in unit hour, and the unit is a train; n 3600/max (t)b,tr)，tbTime interval for minimum departure of train at return station, trTo track train time intervals; equation (6) is the boarding passenger flow constraint, where:
Figure BDA0002789433680000038
Figure BDA0002789433680000039
in the formula Pr(i+1)For the remaining capacity of the train at the i +1 st station, PriNumber of train transporters at i-th station, KmaxThe maximum number of persons that can be accommodated by the train, giThe getting-off rate of the train passenger at the ith station is obtained;
equations (7) to (10) are train tracking interval time constraints, tmTime interval for which the train must stay at the station, tsMaximum limit of waiting time for passengers to endure, trTo track train time intervals, tbThe minimum departure time interval of the train at the return station is defined; train must stay for time tmRepresented by the following formula:
Figure BDA00027894336800000310
in the formula t0The opening time of the shielding door is the time when the train stops; mu is the coefficient of the unbalanced degree of the passenger distribution in front of the shielding door; t is t1The time for each passenger to get on or off the train; x is the number of vehicle doors; w is the width of the vehicle door; t is t2The train door closing time; t is t3The time from closing the door of the train to leaving the station;
equation (11) is a line transport capacity constraint, nminFor each section row of peak hourMinimum operating logarithm of vehicle operation, nmaxIs the number of operating logarithms at maximum line capacity.
Further, the step 3 specifically includes:
firstly, setting model initialization parameters, determining an initial passenger flow data matrix, the initial number of people at each station of a single line, the maximum carrying capacity of a train and the initial value of the running interval of the single line train;
according to the simulated annealing algorithm, the initial operation interval and the initial passenger flow value are randomly set, the constraint conditions of the model are input, and the total cost of the train operation density and the passenger waiting time of the single-line multi-station cooperative current limiting is calculated through the global optimal solution finally output by the simulated annealing algorithm.
Further, the simulated annealing algorithm solving calculation method in the step 3 is as follows:
3-1, setting the number of station gathering people and the train running interval of the initial train before each station starts in the current limiting period, calculating an initial objective function value, namely an energy initial value E (x (i)), and judging whether the value exceeds the limit of a constraint condition or not;
3-2, selecting a new solution train running interval A by using a random probability function in an algorithm mechanismt' controlling the number of passengers entering the station with each station
Figure BDA0002789433680000041
Calculating an objective function value, i.e. an energy value E (x (j)), and calculating an energy difference Δ Ej ═ E (x (j)) to E (x (i)); if Δ Ej is less than or equal to 0, let
Figure BDA0002789433680000042
At＝At'; if Δ Ej>0, returning to the step 3-1;
and 3-3, repeating the step 3-1 and the step 3-2 until the change rate of the difference value between the current objective function value and the last objective function value is smaller than a set threshold value or the maximum iteration number is reached, and stopping calculation to obtain the optimal single-line multi-station coordinated current-limiting train operation interval and the current-limiting number of people at each station.
Has the advantages that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
compared with the traditional rail train running density, the method is combined with 'station-line' passenger flow control, the waiting time of passengers staying in the station, the waiting time of passengers entering the station and the train running interval are linked, and an optimization model with the minimum total waiting time is established. According to the characteristics of the decision variables, the invention applies a simulated annealing algorithm and iterates and screens for multiple times to obtain the globally optimal train driving interval and the limited passenger flow volume of each station of the track line, thereby effectively reducing the waiting time of passengers and relieving the pressure of large passenger flow.
Drawings
FIG. 1 is a flow chart of a design of a multi-station coordinated current limiting rail transit train operation density optimization model according to the present invention;
FIG. 2 is a flow chart of a simulated annealing optimization algorithm of the present invention;
FIG. 3 is a single-line multi-station cooperative current-limiting solving flow chart based on an annealing optimization algorithm;
FIG. 4 is a comparison of line controlled passenger flow versus actual demand in accordance with the present invention;
FIG. 5 is a diagram of the passenger retention ratio of a station implementing cooperative current limiting according to the present invention;
fig. 6 is a comparison of the number of people staying in the platform before and after the implementation of the coordinated current limiting of the line.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
The invention relates to a single-line multi-station cooperative current limiting rail transit train operation density optimization method, which comprises the following specific steps of:
step 1, calibrating conditions of urban rail transit lines, stations, trains and passenger flows and extracting key indexes; the parameter indexes and condition calibration of the single rail transit line are as follows:
the cooperative current limiting is realized by taking passenger flow control measures on a plurality of stations in a single line from the perspective of the whole situation based on the characteristics of the passenger flow propagation rule, so that the large passenger flow pressure of the whole subway line is relieved, the linear scale propagation is prevented, and the transportation efficiency is ensured. Firstly, defining that a large passenger flow control cycle is a peak time period, dividing the large passenger flow control cycle into a plurality of small passenger flow control time periods, and carrying out station calibration on all stations of a single line to be limited to obtain a station label set; secondly, obtaining the getting-off rate and the getting-in passenger flow demand of the ith station according to original passenger flow (OD) data of different stations, and acquiring the maximum carrying capacity of the station and the maximum passing capacity calibration value under the limitation of passing facilities of the gate machine of the station; secondly, according to the personnel-fixed carrying capacity of each train and the set full load rate limit, calculating the section passenger flow from the ith station to the (i + 1) th station, comparing the section passenger flow with the maximum carrying capacity of the section, and determining whether the section conveying constraint is met; and finally, limiting the initial value of the train operation interval according to the normal rail transit train operation plan, and setting the initial interval and the number of initial stations at the ith station.
In the same time period and section of passenger flow control, the operation of the train at the same time is carried out according to a train operation diagram which is actually planned; the initial bearing and passing capacity of each station meets the requirement of passengers for entering the station, the transfer passenger flow is converted into the passenger flow entering the station on the basis of one-way line analysis, and the rest passenger flows are regarded as the passenger flow leaving the station as a control point; the method comprises the following steps that the situation that passengers entering a station are skilled in using station facility equipment is assumed, and extra time spent in the station caused by individual subjective factors is not considered; neglecting the traffic of giving up traveling of passengers, and getting on the bus in the principle of 'first come first get on the bus', and not considering vicious congestion; the train type selection and the train marshalling train number are not changed when the multi-station cooperation is carried out on the same line, and the maximum passenger carrying number of the train is a fixed value.
In the route of the present embodiment, there are 20 station nodes, and the OD passenger flow planning data in the peak passenger flow time slot in a single direction is known, and since the actual inbound demand includes the original number of people of each station, the present embodiment sets the initial number of people in each station control time slot to 100, and the initial value of the actual passenger flow demand is as shown in table 1 and table 2.
TABLE 1 parameter calibration and definition
Figure BDA0002789433680000051
Figure BDA0002789433680000061
TABLE 2 initial number of people at each station
Figure BDA0002789433680000062
And (4) sorting the existing passenger flow data according to the passenger flow OD schedule to obtain the getting-off rate of each station, which is shown in a table 3.
TABLE 3 rate of getting-off at each station
Figure BDA0002789433680000063
The train is determined to be 1460 persons, the maximum overload rate is set to be 120%, and when the overload rate exceeds the maximum overload rate, the train is regarded as having no residual capacity, namely the residual capacity value of the limited condition is 0.
When passengers are detained in a station, in order to ensure the safety of getting on and off the train, the stop time of the train at the station is increased, and the maximum waiting tolerance time of the passengers is generally 6 minutes in a large passenger flow time period.
And 2, considering that the single-line train running density is optimized from a cooperative current limiting angle, the waiting time of passengers is relatively long due to the implementation of the current limiting of a plurality of stations, according to the determination of the initial number of the single track line in the step 1, the minimum sum of the residence time of the passengers in the current limiting time period and the waiting time of the passenger flow entering is taken as an optimization target, the train running time interval and the passenger flow limiting entering the stations are taken as decision variables, constraint conditions are determined, and a single-line multi-station cooperative current limiting train density optimization model is established.
The objective function is expressed as follows:
Figure BDA0002789433680000071
wherein Z represents the sum of waiting time of passengers in the station; the passenger flow in the station is divided into two types, one type is that partial passengers are detained at the platform due to the extremely high full load rate of arriving trains on duty, and the passenger flow can be expressed as
Figure BDA0002789433680000072
The other is the passenger flow entering the ith station under the control of current limiting, namely the passenger flow is
Figure BDA0002789433680000073
The waiting time of the passengers staying at the platform is the time difference between the arrival of the next train and the departure of the train, namely the time length A of the passenger flow control time intervaltNamely train running interval, the second passenger is irregular due to station entering time, the waiting time of the part of passenger flow is set as A by adopting experience mean value t2; t is a passenger flow control time period which comprises a plurality of passenger flow control time periods with the duration of T; n ═ NiAnd i is 1,2,3, …, N is the total number of all stations of a single line, and N represents a station set of the one-way track traffic line.
The constraint conditions include: station passenger flow demand constraint, station platform capacity constraint, interval passenger flow conveying capacity constraint, boarding passenger flow constraint, train tracking interval time constraint and line conveying capacity constraint, as shown in formulas (2) to (11):
Figure BDA0002789433680000074
Figure BDA0002789433680000075
Figure BDA0002789433680000076
Figure BDA0002789433680000077
Figure BDA0002789433680000078
At≥tm (7)
At≤ts (8)
At≥tr (9)
At≥tb (10)
Figure BDA0002789433680000081
the formula (2) is station passenger flow demand constraint, when limiting the flow of the station, the continuity of the passenger flow of the road network is considered, the entering passenger flow is not 0, when an extreme condition occurs, the entering passenger flow can be set to be 0, the upper limit of the passenger flow demand is the actual passenger flow of the station, lambda represents the minimum proportion of the passenger flow demand, and when controlling the large-scale passenger flow actually, the maximum proportion is generally 0.5.
The formula (3) and the formula (4) are station capacity constraints,
Figure BDA0002789433680000082
the maximum number of people accommodated in the platform of the station,
Figure BDA0002789433680000083
the maximum number of people passing through the gate machine is limited by facilities; the capacity is generally divided into two aspects of an entering process and a waiting process, the passing capacity of a gate is generally used as the passenger flow entering time, and the accommodation of a platform mainly comes from the constraint condition that the number of people is the passenger flow waiting at the station; in the design criteria of an actual urban rail transit infrastructure, the gate types are as shown in table 4:
TABLE 4 subway Gate types
Figure BDA0002789433680000084
The area of the platform constructed by urban rail transit is determined according to the maximum number of people gathering at the long-term peak passenger flow period, the accommodation rate is generally 2 to 4 people per square meter, and the number of people accommodated in the platform of a general subway station is 1500 to 2000 people in consideration of the area of the platform occupied by all people.
Equation (5) is a regional passenger flow transport capacity constraint, Mi-1,iThe cross section passenger flow from the station i-1 to the station i is shown, and Y is the maximum passing capacity in the unit hour interval; y is n m d, m is the train formation number, the unit is a train, d is the train fixed member, n is the passing number of the train in unit hour, and the unit is a train; n 3600/max (t)b,tr)，tbTime interval for minimum departure of train at return station, trTo track train time intervals. The cross section passenger flow passing through any two stations cannot exceed the maximum passenger flow for conveying in the interval. The section passenger flow between two stations is the passenger traffic of the train running at the station, and the section passenger flow of the train running from the station i to the station i +1 consists of the residual passenger capacity and the inflow passenger flow of the train arriving at the station i.
The formula (6) is the restriction of the passenger flow on getting on the train, and when the current is limited, the actual number of people on getting on the train controlled by the station is required to be ensured not to exceed the maximum remaining capacity of the train; wherein the remaining capacity of each train is determined by the remaining capacity of the train at the previous station, the number of getting-off persons and the number of getting-in persons, and is represented as follows:
Figure BDA0002789433680000085
the cross-sectional passenger flow when traveling from station i-1 to station i is expressed as:
Figure BDA0002789433680000086
in the formula Pr(i+1)For the remaining capacity of the train at the i +1 st station, PriNumber of train transporters at i-th station, KmaxThe maximum number of persons that can be accommodated by the train, giAnd the getting-off rate of the train passenger at the ith station is obtained.
Equations (7) to (10) are train tracking interval time constraints, the urban rail transit line is used for ensuring that the passenger demand is met in the peak passenger flow period, and the running time interval must be within the waiting time endured by the passenger when train planning adjustment is carried out; the running time interval of the train is controlled by the time interval that the train has to stay in the station to meet the boarding and alighting behaviors of passengers, the time interval that the return operation of the train starts at the return station and the train tracking time interval; in the formula tmTime interval for which the train must stay at the station, tsMaximum limit of waiting time for passengers to endure, trTo track train time intervals, tbThe minimum departure time interval of the train at the return station is defined; train must stay for time tmRepresented by the following formula:
Figure BDA0002789433680000091
in the formula t0Taking 3s for the time of opening the shielding door when the train stops; mu is the coefficient of the unbalanced degree of the passenger in the station in front of the shielding door, and 1.7 is taken; t is t11.2 s/door is taken for the time of getting on or off each passenger; x is the number of vehicle doors; w is the width of the car door and is 1.3 m; t is t2Taking 5s for the closing time of the train door; t is t3The time from the closing of the train to the departure from the station was taken for 3 s.
Equation (11) is a line transport capacity constraint, nminMinimum operation logarithm, n, for each section of train operation in peak hourmaxIs the number of operating logarithms at maximum line capacity. At peak hour, each section of train operates not less than 12 pairs, and the departure frequency meets the limitation of line capacity.
And 3, constructing input parameters of the model according to the step 2, wherein the input parameters comprise initial station entering passenger flow, platform number, number of getting-on and getting-off persons and number of remaining persons of each station, applying a simulated annealing algorithm to carry out iterative search on the number of station entering persons and train running intervals in a plurality of current-limiting periods, solving a multi-station cooperative current-limiting train density optimization model, and outputting an optimal train running interval and the number of current-limiting persons of each station. Firstly, setting model initialization parameters, determining an initial passenger flow data matrix, the initial number of people at each station of a single line, the maximum carrying capacity of a train and the initial value of the running interval of the single line train; according to the simulated annealing algorithm, the initial operation interval and the initial passenger flow value are randomly set, the constraint condition of the model is input, the overall optimal solution finally output by the simulated annealing algorithm is used for calculating the total cost of the train operation density and the passenger waiting time of the single-line multi-station cooperative current limiting, and the total waiting time of the passengers when the train operates at the minimum interval in the initial non-current limiting state is compared to achieve the optimization effect.
Referring to fig. 2 and 3, the simulated annealing algorithm solution calculation method is as follows:
3-1, setting the number of station gathering people and the train running interval of the initial train before each station starts in the current limiting period, calculating an initial objective function value, namely an energy initial value E (x (i)), and judging whether the value exceeds the limit of a constraint condition or not;
3-2, selecting a new solution train running interval A by using a random probability function in an algorithm mechanismt' controlling the number of passengers entering the station with each station
Figure BDA0002789433680000092
Calculating an objective function value, i.e. an energy value E (x (j)), and calculating an energy difference Δ Ej ═ E (x (j)) to E (x (i)); if Δ Ej is less than or equal to 0, let
Figure BDA0002789433680000093
At＝At'; if the delta Ej is larger than 0, returning to the step 3-1;
and 3-3, repeating the step 3-1 and the step 3-2 until the change rate of the difference value between the current objective function value and the last objective function value is smaller than a set threshold value or the maximum iteration number is reached, and stopping calculation to obtain the optimal single-line multi-station coordinated current-limiting train operation interval and the current-limiting number of people at each station.
The model solution results are shown below, and the variable group values satisfying the objective function are shown in table 5.
TABLE 5 Limit inbound passenger flow resolution results
Figure BDA0002789433680000101
As can be seen from the data in table 5 and fig. 4, under the goal of reducing the cost of the waiting time for passengers as much as possible, the total number of stations requiring current limiting in the line is 10, wherein, as shown in fig. 5, stations No. 4, 5, 6, 7, 8, 9, and 10 in the line perform current limiting cooperative control, the passenger retention proportion reaches 50%, multiple stations implement current limiting synchronously, the optimal train departure interval of the line in the rush hour is 2.52 minutes, the optimal solution of the waiting cost for passengers is met, and the waiting time for passengers that are retained meets the maximum tolerance time constraint, and the service level is met.
At the moment, the current-limiting cooperative effect of the whole line is met, and the obtained train meets the operation interval A under the constraint conditiontWas 2.52 minutes. Under the condition of the line multi-station current limiting, the train operation logarithm of the train operation density is calculated by the following formula:
Figure BDA0002789433680000102
to pair
During peak hours, the train density of the train running on the line is 24 pairs/hour.
In this embodiment, the minimum operation interval of the train is 2min, and the number of running pairs n of the train per hour is set without performing multi-station cooperative current limitingmaxAs shown in fig. 6, when the train is driven at the minimum running interval, the remaining capacity of the train is insufficient, the difference between the number of passengers staying at the station platform before and after the current limit and the total load rate of the train at this time is substantially 120% which is the limit condition, and the possibility that passengers cannot get on the train at the station is increased.
The total number of people staying in the peak hours and the cost of waiting time of passengers of the train in the running density of the train and the multi-station cooperative current limiting under the condition of minimum interval running are shown in the table 6.
TABLE 6 comparison of maximum unrestricted capacity operation with multi-station coordinated restricted operation
Figure BDA0002789433680000111
When the train runs at intervals of 2min, the number of people staying on the line is far higher than the number of passengers staying at the line under the cooperative current limiting of multiple stations. The cost of the waiting time of the passengers entering the station and staying in the station of the line under the multi-station cooperative current limiting is reduced by 13.74%, the endurance time limit of the passengers is met, and the service level of the rail transit is ensured.
The above description is only a preferred example of the present invention, and is not intended to limit the present invention in any way, and any modifications or equivalent variations made in accordance with the technical spirit of the present invention are within the scope of the present invention as claimed.

Claims (6)

1. A single-line multi-station cooperative current limiting rail transit train operation density optimization method is characterized by comprising the following specific steps:
step 1, calibrating conditions of urban rail transit lines, stations, trains and passenger flows and extracting key indexes; the key indexes comprise the getting-off rate and the getting-in passenger flow demand of the station, the maximum bearing capacity of the station platform and the section passenger flow in the interval;
step 2, determining constraint conditions by taking the minimum sum of the residence time of passengers in the current-limiting time period and the waiting time of the passenger flow entering as an optimization target and the minimum sum of the residence time of passengers in the current-limiting time period and the waiting time of the passenger flow entering the station as decision variables, and establishing a single-line multi-station cooperative current-limiting train density optimization model;
and 3, constructing input parameters of the model according to the step 2, wherein the input parameters comprise initial station entering passenger flow, platform number, number of getting-on and getting-off persons and number of remaining persons of each station, applying a simulated annealing algorithm to carry out iterative search on the number of station entering persons and train running intervals in a plurality of current-limiting periods, solving a multi-station cooperative current-limiting train density optimization model, and outputting an optimal train running interval and the number of current-limiting persons of each station.
2. The method for optimizing the train running density of the single-line multi-station cooperative current limiting rail transit according to claim 1, wherein the method comprises the following steps: the step 1 is specifically set as follows:
in the same time period and section of passenger flow control, the operation of the train at the same time is carried out according to a train operation diagram which is actually planned; the initial bearing and passing capacity of each station meets the requirement of passengers for entering the station, the transfer passenger flow is converted into the passenger flow entering the station on the basis of one-way line analysis, and the rest passenger flows are regarded as the passenger flow leaving the station as a control point; the method comprises the following steps that the situation that passengers entering a station are skilled in using station facility equipment is assumed, and extra time spent in the station caused by individual subjective factors is not considered; neglecting the traffic of giving up travel of passengers, and getting on the bus in principle of first-come first, and not considering vicious congestion; the train type selection and the train marshalling train number are not changed when the multi-station cooperation is carried out on the same line, and the maximum passenger carrying number of the train is a fixed value.
3. The method for optimizing the train running density of the single-line multi-station cooperative current limiting rail transit according to claim 1, wherein the method comprises the following steps: the step 1 specifically comprises:
firstly, defining that a large passenger flow control cycle is a peak time period, dividing the large passenger flow control cycle into a plurality of small passenger flow control time periods, and carrying out station calibration on all stations of a single line to be limited to obtain a station label set;
secondly, obtaining the getting-off rate and the getting-in passenger flow demand of the ith station according to the original passenger flow data of different stations, and acquiring the maximum bearing capacity of the station and the maximum passing capacity calibration value under the limitation of passing facilities of the gate machine of the station;
secondly, according to the personnel-fixed carrying capacity of each train and the set full load rate limit, calculating the section passenger flow from the ith station to the (i + 1) th station, comparing the section passenger flow with the maximum carrying capacity of the section, and determining whether the section conveying constraint is met;
and finally, limiting the initial value of the train operation interval according to the normal rail transit train operation plan, and setting the initial interval and the number of initial stations at the ith station.
4. The method for optimizing the train running density of the single-line multi-station cooperative current limiting rail transit according to claim 1, wherein the method comprises the following steps: in the train density optimization model in the step 2, the objective function is expressed as follows:
Figure FDA0002789433670000011
where Z represents the sum of waiting times of passengers in the station,
Figure FDA0002789433670000021
for the passenger flow entering the station at the ith station under the control of current limit,
Figure FDA0002789433670000022
is the total number of passengers in the ith station, AtThe time length of the passenger flow control time interval is the train running interval, and T is the passenger flow control time interval which comprises a plurality of passenger flow control time intervals of the time length T; n ═ Ni1,2,3, a.
The constraint conditions include: station passenger flow demand constraint, station platform capacity constraint, interval passenger flow conveying capacity constraint, boarding passenger flow constraint, train tracking interval time constraint and line conveying capacity constraint, as shown in formulas (2) to (11):
Figure FDA0002789433670000023
Figure FDA0002789433670000024
Figure FDA0002789433670000025
Figure FDA0002789433670000026
Figure FDA0002789433670000027
At≥tm (7)
At≤ts (8)
At≥tr (9)
At≥tb (10)
Figure FDA0002789433670000028
the formula (2) is station passenger flow demand constraint, and lambda represents the minimum proportion of the passenger flow demand; the formula (3) and the formula (4) are station capacity constraints,
Figure FDA0002789433670000029
the maximum number of people accommodated in the platform of the station,
Figure FDA00027894336700000210
the maximum number of people passing through the gate machine is limited by facilities; equation (5) is a regional passenger flow transport capacity constraint, Mi-1，iThe cross section passenger flow from the station i-1 to the station i is shown, and Y is the maximum passing capacity in the unit hour interval; y is n m d, m is the train formation number, the unit is a train, d is the train fixed member, n is the passing number of the train in unit hour, and the unit is a train; n 3600/max (t)b，tr)，tbTime interval for minimum departure of train at return station, trFor tracing trainSpacing; equation (6) is the boarding passenger flow constraint, where:
Figure FDA00027894336700000211
Figure FDA00027894336700000212
in the formula Pr(i+1)For the remaining capacity of the train at the i +1 st station, PriNumber of train transporters at i-th station, KmaxThe maximum number of persons that can be accommodated by the train, giThe getting-off rate of the train passenger at the ith station is obtained;
equations (7) to (10) are train tracking interval time constraints, tmTime interval for which the train must stay at the station, tsMaximum limit of waiting time for passengers to endure, trTo track train time intervals, tbThe minimum departure time interval of the train at the return station is defined; train must stay for time tmRepresented by the following formula:
Figure FDA0002789433670000031
in the formula t0The opening time of the shielding door is the time when the train stops; mu is the coefficient of the unbalanced degree of the passenger distribution in front of the shielding door; t is t1The time for each passenger to get on or off the train; x is the number of vehicle doors; w is the width of the vehicle door; t is t2The train door closing time; t is t3The time from closing the door of the train to leaving the station;
equation (11) is a line transport capacity constraint, nminMinimum operation logarithm, n, for each section of train operation in peak hourmaxIs the number of operating logarithms at maximum line capacity.
5. The method for optimizing the train running density of the single-line multi-station cooperative current limiting rail transit according to any one of claims 1 to 4, wherein the method comprises the following steps: the step 3 is specifically as follows:
firstly, setting model initialization parameters, determining an initial passenger flow data matrix, the initial number of people at each station of a single line, the maximum carrying capacity of a train and the initial value of the running interval of the single line train;
according to the simulated annealing algorithm, the initial operation interval and the initial passenger flow value are randomly set, the constraint conditions of the model are input, and the total cost of the train operation density and the passenger waiting time of the single-line multi-station cooperative current limiting is calculated through the global optimal solution finally output by the simulated annealing algorithm.
6. The rail transit train running density optimization method based on multi-station cooperative current limiting according to claim 5, characterized in that: the simulated annealing algorithm solving calculation method in the step 3 is as follows:
3-1, setting the number of station gathering people and the train running interval of the initial train before each station starts in the current limiting period, calculating an initial objective function value, namely an energy initial value E (x (i)), and judging whether the value exceeds the limit of a constraint condition or not;
3-2, selecting a new solution train running interval A by using a random probability function in an algorithm mechanismt' controlling the number of passengers entering the station with each station
Figure FDA0002789433670000033
Calculating an objective function value, i.e. an energy value E (x (j)), and calculating an energy difference Δ Ej ═ E (x (j)) to E (x (i)); if Δ Ej is less than or equal to 0, let
Figure FDA0002789433670000032
At＝At'; if the delta Ej is larger than 0, returning to the step 3-1;
and 3-3, repeating the step 3-1 and the step 3-2 until the change rate of the difference value between the current objective function value and the last objective function value is smaller than a set threshold value or the maximum iteration number is reached, and stopping calculation to obtain the optimal single-line multi-station coordinated current-limiting train operation interval and the current-limiting number of people at each station.
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