CN112465205B - Rail transit train running density optimization method for single-wire multi-station cooperative current limiting - Google Patents
Rail transit train running density optimization method for single-wire multi-station cooperative current limiting Download PDFInfo
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Abstract
The invention discloses a rail transit train running density optimization method with single-line multi-station cooperative current limiting, which takes the minimum total waiting time of passengers in a passenger flow peak period as an optimization target, constructs a rail transit train running density optimization model with multi-station cooperative current limiting, and obtains the overall optimal running interval between the number of passengers controlled by each station and the train by using a simulated annealing algorithm. Compared with the prior art, the invention provides an optimization method for the running density of urban rail transit trains under the background of large passenger flow by taking cooperative current limiting as a theoretical basis, and the optimization method effectively relieves the peak passenger flow pressure, reduces the waiting time of passengers and ensures the service level on the basis of ensuring the transportation efficiency and the safety of the rail transit.
Description
Technical Field
The invention relates to the field of train operation organization under the background of large passenger flows of urban rail transit, in particular to a rail train operation density optimization method with single-wire multi-station cooperative current limiting.
Background
The urban rail transit has the outstanding advantages of safety, rapidness, comfort, large traffic volume, small pollution, lower operation cost, no interference with other traffic modes and the like, and improves the problem of road traffic jam on the basis of meeting the travel demands of passengers to the greatest extent, improves the traffic and transportation efficiency, and occupies an important skeleton position in urban traffic. In large and medium-sized cities, urban rail transit becomes a preferred traffic mode for short-distance travel, the direct passenger flow and the passenger flow of transfer are synchronously increased, large passenger flows can appear in the peaks, holidays, large movable gathering and scattering sites and the like of travel, partial passengers can be detained in stations when a single train is in insufficient full-load operation, and the delay scale of the train is diffused to a single line from a station. When accidental events such as train faults and bad weather occur, large passenger flows possibly cause the problems that the personal safety of passengers cannot be guaranteed, passengers stay in a large scale, the delay scale of the train is enlarged, the security capacity and the bearing capacity of the station are insufficient, and the like. When a certain station is in passenger retention or large passenger flow gathering, the train sent out from the station is basically in a full state, the adjacent station, the adjacent section or the transfer station can be influenced, the large passenger flow is transmitted by the large passenger flow in a 'line' mode formed by 'points', and the passenger retention phenomenon exists in a single track traffic line. Therefore, the adjustment and optimization of the train running density under the multi-station cooperative current limiting condition are beneficial to guaranteeing the overall coordination of transportation, guaranteeing the safety of transportation service, promoting the maximization of transportation capacity and avoiding the waste of transportation energy.
Aiming at the background of large passenger flow in the peak period, the prior art at home and abroad mainly focuses on analyzing the space-time characteristics of the passenger flow, dynamically distributing the passenger flow in a rail transit network, further optimizing a rail train grouping scheme, a size-crossing adjustment organization scheme and the like, but lacks a technical scheme for simultaneously considering single-wire multi-station cooperative current limiting and train running density adjustment optimization.
Disclosure of Invention
The invention aims to: aiming at the problems, the invention provides a rail transit train running density optimization method with single-line multi-station cooperative current limiting, which aims at minimizing the total waiting time of passengers in a whole line station, builds a multi-station cooperative current limiting optimization model, and solves the problem of obtaining the train optimal running density under the cooperative current limiting effect, thereby relieving the peak large passenger flow single-line rail transit transportation pressure, providing reference for reducing the train scale delay, ensuring the overall coordination of transportation as far as possible, ensuring the safety of transportation service, and avoiding the waste of transportation energy.
The technical scheme is as follows: in order to achieve the purpose of the invention, the technical scheme adopted by the invention is as follows: a rail transit train running density optimization method of single-wire multi-station cooperative current limiting comprises the following specific steps:
step 1, calibrating urban rail transit lines, stations, trains and passenger flow conditions and extracting key indexes; the key indexes comprise the getting-off rate of a station and the incoming passenger flow demand of the station, the maximum bearing capacity of the station and the section passenger flow in a section;
step 2, taking the minimum sum of the residence time of passengers in the current limiting time period and the waiting time of the entering passenger flow as an optimization target, taking the running time interval of the train and the passenger flow limiting the entering station as decision variables, determining constraint conditions, and establishing a single-wire multi-station cooperative current limiting train density optimization model;
and 3, constructing input parameters of a model according to the step 2, including initial arrival passenger flow of each station, station number, boarding and disembarking number and remaining passenger number, applying a simulated annealing algorithm to perform iterative search on arrival number and train operation intervals of a plurality of current limiting periods, solving a multi-station collaborative current limiting train density optimization model, and outputting an optimal train operation interval and current limiting number 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 same-time train is carried out according to an actual planned train operation diagram; the initial bearing and passing capacity of each station meets the passenger arrival demand, the transfer passenger flow is converted into the local line arrival passenger flow based on unidirectional line analysis, the rest passenger flows are regarded as the outbound passenger flow, and the stations are regarded as control points; assuming that the inbound passengers are skilled in using the vehicle station facility equipment, not considering the extra stay time in the station caused by individual subjective factors; neglecting the flow of giving up the traveling of passengers, and driving according to the principle of first-come first-go, without considering malignant congestion; the number of the train group is not changed when the multi-station cooperative same line is carried out, and the maximum passenger carrying number of the train is a fixed value.
Further, the step 1 specifically includes:
firstly, defining a large period of passenger flow control as a peak period, dividing the period into a plurality of small passenger flow control 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 get-off rate and the get-in passenger flow demand of the ith station according to the original passenger flow data of different stations, and collecting the maximum bearing capacity of the station and the maximum passing capacity calibration value of the get-in gate under the limit of passing facilities;
then, according to the dead man carrying capacity of each train and setting full load rate limit, calculating the section passenger flow in the section from the ith station to the (i+1) th station, comparing with the maximum carrying capacity of the section, and determining whether section conveying constraint is met;
and finally, limiting initial values of train operation intervals according to a normal rail transit train operation plan, and setting initial intervals and initial platform population of an ith station.
Further, the train density optimization model in the step 2, the objective function is expressed as follows:
where Z represents the sum of waiting times of passengers in the station,passenger flow of i station in limited flow control,/->For the total passenger flow number in the ith station, A t The time length of the passenger flow control time period is the train running interval, and T is the passenger flow control time period, wherein the passenger flow control time period comprises a plurality of passenger flow control time periods with the time length of T; n= { N i I=1, 2,3, …, N }, N being the total number of all stations of a single line, N representing a set of stations of a unidirectional track traffic line;
the constraint conditions include: station passenger flow demand constraint, station platform capability constraint, interval passenger flow conveying capability constraint, boarding passenger flow constraint, train tracking interval time constraint and line conveying capability constraint, as shown in the formulas (2) to (11):
A t ≥t m (7)
A t ≤t s (8)
A t ≥t r (9)
A t ≥t b (10)
the formula (2) is a station passenger flow demand constraint, and lambda represents the minimum proportion of passenger flow demands; the formulas (3) and (4) are station capability constraints,for the maximum number of accommodations at the station platform +.>The maximum number of people passing through the facility limit for the entrance gate; formula (5) is an interval passenger flow conveying capacity constraint, M i-1,i The section passenger flow quantity from station i-1 to station i is represented, and 3 is the maximum passing capacity of unit hour interval; y=n×m×d, m is the number of train groups, the unit is the number of trains, d is the number of trains passing in unit hour, and n is the number of trains passing in unit hour; n=3600/max (t b ,t r )，t b For the minimum departure time interval of the train at the turn-back station, t r To track train time intervals; formula (6) is an boarding flow restriction, wherein:
p in the formula r(i+1) To the remaining capacity of the train when reaching the (i+1) th station, P ri For the number of train transportation people, K, at the ith station max G is the maximum number of people which can be accommodated by the train i The getting-off rate of the train passenger at the ith station is set;
formulas (7) to (10) are train tracking interval time constraint, t m For the time interval the train must stay at the station, t s Maximum limit of waiting time for passengers, t r To track train time intervals, t b A time interval for minimum departure of the train at the return station; train must stay time t m Represented by the following formula:
t is in 0 For stopping the train, shielding the time when the door is opened; mu is the imbalance degree coefficient of the distribution of the passengers at the station in front of the shielding door; t is t 1 The time for getting on and off each passenger; x is the number of vehicle doors; w is the width of the vehicle door; t is t 2 The closing time of the train door; t is t 3 The time to close the door to leave the station for the train;
formula (11) is a line conveying capacity constraint, n min For minimum operation logarithm of train operation in each section of peak hour, n max Is the logarithm of operation at maximum line capacity.
Further, the step 3 specifically includes the following steps:
firstly, setting model initialization parameters, determining an initial passenger flow data matrix, and determining initial number of passengers at each station of a single line, maximum carrying capacity of a train and initial running interval of the single line train;
according to the simulated annealing algorithm, an initial operation interval and a passenger flow initial value are randomly set, constraint conditions of a model are input, and the total cost of the single-wire multi-station cooperative current limiting train running density and the total passenger waiting time is calculated through a global optimal solution finally output by the simulated annealing algorithm.
Further, the method for solving and calculating the simulated annealing algorithm in the step 3 is as follows:
3-1, in a current limiting period, setting a platform aggregation number and a train running interval of an initial train before each station starts, 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;
3-2, selecting a new train running interval A by using a random probability function in an algorithm mechanism t ' control of number of passengers entering station with each stationCalculating an objective function value, i.e., an energy value E (x (j)), and calculating an energy difference Δej=e (x (j)) -E (x (i)); if ΔEj is less than or equal to 0, let ∈ ->A t ＝A t 'A'; if delta Ej>0, returning to the step 3-1;
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, stopping calculation, and obtaining the optimal single-wire multi-station cooperative current limiting train operation interval and the current limiting number of each station.
The beneficial effects are that: compared with the prior art, the technical scheme of the invention has the following beneficial technical effects:
under the background of high passenger flow, the invention is used as an urban rail transit train running density optimization method of single-line multi-station cooperative current limiting, and compared with the traditional rail train running density, the invention combines with 'station-line' passenger flow control, associates the waiting time of passengers staying in a station, the waiting time of passengers entering the station and the running interval of a train, and establishes an optimization model with the minimum total waiting time. According to the characteristics of decision variables, the invention uses a simulated annealing algorithm to iterate and screen for a plurality of times to obtain the globally optimal train running interval and the passenger flow volume which is limited to enter by 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 an optimizing model of the running density of a rail transit train with multi-station cooperative current limiting;
FIG. 2 is a flow chart of a simulated annealing optimization algorithm of the present invention;
FIG. 3 is a flow chart of a single-wire multi-station cooperative current limiting solving method based on an annealing optimization algorithm;
FIG. 4 is a diagram showing the comparison of the actual demand and the passenger flow of the line control according to the present invention;
FIG. 5 is a ratio of station passenger retention implementing cooperative restriction in accordance with the present invention;
FIG. 6 is a graph showing the comparison of the number of people retained at the stations before and after the line co-current limiting according to the present invention.
Detailed Description
The invention is described in further detail below with reference to the drawings and the detailed description.
The invention discloses a rail transit train running density optimization method with single-line multi-station cooperative current limiting, which is shown in a figure 1 and comprises the following specific steps:
step 1, calibrating urban rail transit lines, stations, trains and passenger flow conditions and extracting key indexes; the parameter indexes and the conditions of the single track traffic line are calibrated, and the method comprises the following steps:
the cooperative current limiting is realized by implementing passenger flow control measures on a plurality of stations in a single line from the global angle based on the characteristic of 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 a large period of passenger flow control as a peak period, dividing the period into a plurality of small passenger flow control 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 get-off rate and the get-on passenger flow demand of the ith station according to the original passenger flow (OD) data of different stations, and collecting the maximum bearing capacity of the station and the maximum passing capacity calibration value under the limit of passing facilities of the get-on gate; then, according to the dead man carrying capacity of each train and setting full load rate limit, calculating the section passenger flow in the section from the ith station to the (i+1) th station, comparing with the maximum carrying capacity of the section, and determining whether section conveying constraint is met; and finally, limiting initial values of train operation intervals according to a normal rail transit train operation plan, and setting initial intervals and initial platform population of an ith station.
In the same time period and section of passenger flow control, the operation of the same-time train is carried out according to an actual planned train operation diagram; the initial bearing and passing capacity of each station meets the passenger arrival demand, the transfer passenger flow is converted into the local line arrival passenger flow based on unidirectional line analysis, the rest passenger flows are regarded as the outbound passenger flow, and the stations are regarded as control points; assuming that the inbound passengers are skilled in using the vehicle station facility equipment, not considering the extra stay time in the station caused by individual subjective factors; neglecting the flow of giving up the travel of passengers, and driving according to the principle of 'first come first get on', without considering malignant congestion; the number of the train group is not changed when the multi-station cooperative same line is carried out, and the maximum passenger carrying number of the train is a fixed value.
In the line of the present embodiment, there are 20 station nodes in total, and the OD passenger flow plan data of the peak passenger flow period in a single direction is known, and since the actual incoming demand includes the number of people in each station, the initial number of people in each station control period is set to 100, and the initial value of the actual passenger flow demand is shown in table 1 and table 2.
Table 1 parameter calibration and definition
Table 2 initial number of people at each station
And according to the passenger flow OD schedule, the existing passenger flow data are arranged to obtain the get-off rate of each station, and the get-off rate is shown in Table 3.
Table 3 rate of departure for each station
Because the train has overload phenomenon in the peak period of passenger flow, the train dispatcher is 1460, the maximum overload rate is set to 120%, and when the maximum overload rate exceeds the maximum overload rate, the train is regarded as having no residual capacity, namely the limit condition residual capacity value is 0.
When passengers stay in the 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 in a large passenger flow time period is generally 6 minutes.
And 2, optimizing the running density of the single-wire train from the cooperative current limiting angle, wherein the implementation of the current limiting of a plurality of stations can lead to relatively long waiting time of passengers, and according to the determination of the initial number of the single-wire track line in the step 1, taking the minimum sum of the residence time of the passengers in the current limiting time period and the waiting time of the entering passenger flow as an optimization target, taking the running time interval of the train and the passenger flow of the entering stations as decision variables, determining constraint conditions, and establishing a single-wire multi-station cooperative current limiting train density optimization model.
The objective function is expressed as follows:
wherein Z represents the sum of waiting times of passengers in the station; passenger flow in the station is divided into two types, one type is that partial passengers stay in the station due to extremely high full rate of arrival of the train on duty, and the passenger flow can be expressed asThe other category is passenger flow entering the ith station under the control of current limiting, namely +.>For total passenger flow people in the ith stationThe waiting time of the two passengers is different, the waiting time of the passenger 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 period t The invention adopts the empirical mean value to set the waiting time of the passenger flow to be A as the running interval of the train and the irregularity of the arrival time of the second passenger t 2; t is a passenger flow control period, wherein the passenger flow control period comprises a plurality of passenger flow control periods with T time length; n= { N i I=1, 2,3, …, N }, N being the total number of all stations of a single route, N representing a unidirectional track traffic route station set.
The constraint conditions include: station passenger flow demand constraint, station platform capability constraint, interval passenger flow conveying capability constraint, boarding passenger flow constraint, train tracking interval time constraint and line conveying capability constraint, as shown in the formulas (2) to (11):
A t ≥t m (7)
A t ≤t s (8)
A t ≥t r (9)
A t ≥t b (10)
the formula (2) is a constraint of the passenger flow demand of the station, when the station is limited, the continuity of the passenger flow of the road network is considered, the entering passenger flow is ensured to be not 0, when an extreme condition occurs, the upper limit of the passenger flow demand is set to be 0, the actual passenger flow of the station is set to be the upper limit of the passenger flow demand, lambda represents the minimum proportion of the passenger flow demand, and when the large-scale passenger flow is actually controlled, 0.5 is generally taken.
The formulas (3) and (4) are station capability constraints,for the maximum number of accommodations at the station platform +.>The maximum number of people passing through the facility limit for the entrance gate; the capacity of the two aspects of the entering process and the waiting process is generally divided, the passing capacity of a gate is generally used as the entering time of the passenger flow, and the accommodation of a platform is mainly from the constraint condition that the number of people is the waiting time of the passenger flow at the station; in the design criteria of the actual urban rail transit infrastructure, the gate types are shown in table 4:
TABLE 4 subway gate types
The area of the platform for urban rail transit construction is determined according to the maximum number of people gathered in the long-term peak passenger flow period, the accommodation rate is generally 2 to 4 people per square meter considering the area of the platform occupied by people, and the platform of a subway station can generally accommodate 1500 to 2000 people.
Formula (5) is an interval passenger flow conveying capacity constraint, M i-1,i The section passenger flow quantity from station i-1 to station i is represented, Y is the maximum passing capacity of unit hour interval; y=n×m×d, m is the number of train groupsThe unit is the number of trains passing in unit hour, d is the number of train operators, n is the number of trains passing in unit hour, and the unit is the train; n=3600/max (t b ,t r )，t b For the minimum departure time interval of the train at the turn-back station, t r To track train time intervals. The section passenger flow volume passing through any two stations cannot exceed the maximum transport passenger flow volume of the section. The section passenger flow volume between two stations is the passenger flow volume of the train running at the station, and the section passenger flow volume on the train running from station i to station i+1 consists of the residual passenger flow volume and the inflow passenger flow volume of the train reaching station i.
Formula (6) is a passenger flow constraint of boarding, and when limiting the current, the actual number of boarding control at the station must be ensured not to exceed the maximum remaining capacity of the train; the remaining capacity of each train is determined by the remaining capacity of the train at the boarding station, the number of alighting persons and the number of entering persons, and the remaining capacity is expressed as follows:
the section passenger flow when running from station i-1 to station i is expressed as:
p in the formula r(i+1) To the remaining capacity of the train when reaching the (i+1) th station, P ri For the number of train transportation people, K, at the ith station max G is the maximum number of people which can be accommodated by the train i The departure rate of the train passenger at the ith station is obtained.
The formulas (7) to (10) are constraint of train tracking interval time, and the urban rail transit line is used for ensuring the meeting of passenger demands in the peak passenger flow period, and the running time interval must be within the waiting time born by passengers when train planning adjustment is carried out; the running time interval of the train is controlled by the time interval of departure of the turning-back operation of the train at the turning-back station and the train tracking time interval, wherein the time of the train which must stay at the station to meet the boarding and disembarking actions of passengers; t is in m For the time interval the train must stay at the station, t s Maximum limit of waiting time for passengers, t r To track train time intervals, t b A time interval for minimum departure of the train at the return station; train must stay time t m Represented by the following formula:
t is in 0 For stopping the train, taking 3s when the shielding door is opened; mu is the unbalance degree coefficient of the station passengers distributed in front of the shielding door, and 1.7 is taken; t is t 1 Taking 1.2 s/door for getting on/off each passenger; x is the number of vehicle doors; w is the width of the vehicle door, and is 1.3m; t is t 2 Taking 5s for closing the train door; t is t 3 The time from closing the door to leaving the station was taken for 3s.
Formula (11) is a line conveying capacity constraint, n min For minimum operation logarithm of train operation in each section of peak hour, n max Is the logarithm of operation at maximum line capacity. The train operation of each section in the peak hour is not less than 12 pairs, and the departure frequency meets the line capacity limit.
And 3, constructing input parameters of a model according to the step 2, including initial arrival passenger flow of each station, station number, boarding and disembarking number and remaining passenger number, applying a simulated annealing algorithm to perform iterative search on arrival number and train operation intervals of a plurality of current limiting periods, solving a multi-station collaborative current limiting train density optimization model, and outputting an optimal train operation interval and current limiting number of each station. Firstly, setting model initialization parameters, determining an initial passenger flow data matrix, and determining initial number of passengers at each station of a single line, maximum carrying capacity of a train and initial running interval of the single line train; according to the simulated annealing algorithm, an initial operation interval and a passenger flow initial value are randomly set, constraint conditions of a model are input, and a global optimal solution finally output by the simulated annealing algorithm is used for calculating the train running density and the total passenger waiting time cost of the single-wire multi-station cooperative current limiting, and compared with the total passenger waiting time sum of the train in the minimum interval under the initial non-current limiting state, the optimization effect is achieved.
Referring to fig. 2 and 3, the simulated annealing algorithm solving calculation method is as follows:
3-1, in a current limiting period, setting a platform aggregation number and a train running interval of an initial train before each station starts, 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;
3-2, selecting a new train running interval A by using a random probability function in an algorithm mechanism t ' control of number of passengers entering station with each stationCalculating an objective function value, i.e., an energy value E (x (j)), and calculating an energy difference Δej=e (x (j)) -E (x (i)); if ΔEj is less than or equal to 0, let ∈ ->A t ＝A t 'A'; if delta Ej is more than 0, returning to the step 3-1;
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, stopping calculation, and obtaining the optimal single-wire multi-station cooperative current limiting train operation interval and the current limiting number of each station.
The model solving results are shown below, and the variable array values satisfying the objective function are shown in table 5.
TABLE 5 solution to limiting inbound traffic
As can be seen from the data in table 5 and fig. 4, under the goal of meeting the requirement of reducing the cost of waiting time of passengers as much as possible, 10 stations are in total needed to be limited in the line, wherein, as shown in fig. 5, stations 4,5,6,7,8,9 and 10 in the line are subjected to the cooperative control of limiting the current, the passenger retention proportion reaches 50%, a plurality of stations synchronously implement the current limitation, the optimized train departure interval of the line in the peak period is 2.52 minutes, the optimal solution of waiting cost of passengers is met, the waiting time of the retained passengers meets the constraint of the maximum tolerance time, and the service level is met.
At the moment, the current limiting synergistic effect of the whole line is met, and the calculated running interval A of the train under the constraint condition is met t 2.52 minutes. Under the condition of multi-station current limiting of the line, the train operation logarithm of the train operation density is calculated by the following formula:
for a pair of
During peak hours, the density of the line running trains is 24 pairs/hour.
In this embodiment, the minimum running interval of the train is 2min, and the running log n of each train unit hour is calculated under the condition of not performing multi-station cooperative current limiting max For 30 pairs, as shown in fig. 6, when the number of passengers detained at station platforms before and after the current limiting of each station is as large as the current limiting due to insufficient remaining capacity of the train when the trains are at a minimum running interval, the full load rate of the trains basically reaches 120% of the limit condition at the moment, and the possibility that the passengers cannot get on the station is increased.
The total number of passengers remaining in the peak period and the cost of waiting time of the passengers at the running density of the train under the minimum interval running condition and the multi-station cooperative current limiting are shown in the table 6.
Table 6 comparison of unrestricted maximum capability operation and Multi-station coordinated Current limiting operation
When the trains are operated at intervals of 2min, the number of the detainers of the line is far higher than the detained passenger flow under the multi-station cooperative limiting flow. The overall passenger waiting time cost of the line incoming passenger flow and the passenger flow in the station under the multi-station cooperative limit is reduced by 13.74%, the tolerance time limit of passengers is met, and the service level of rail traffic is ensured.
The above description is only a preferred embodiment of the present invention, and is not intended to limit the present invention in any way, but any modifications or equivalent variations according to the technical spirit of the present invention are still within the scope of the present invention as claimed.
Claims (3)
1. A rail transit train running density optimization method of single-wire multi-station cooperative current limiting is characterized by comprising the following specific steps:
step 1, calibrating urban rail transit lines, stations, trains and passenger flow conditions and extracting key indexes; the key indexes comprise the getting-off rate of a station and the incoming passenger flow demand of the station, the maximum bearing capacity of the station and the section passenger flow in a section;
firstly, defining a large period of passenger flow control as a peak period, dividing the period into a plurality of small passenger flow control 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 get-off rate and the get-in passenger flow demand of the ith station according to the original passenger flow data of different stations, and collecting the maximum bearing capacity of the station and the maximum passing capacity calibration value of the get-in gate under the limit of passing facilities;
then, according to the dead man carrying capacity of each train and setting full load rate limit, calculating the section passenger flow in the section from the ith station to the (i+1) th station, comparing with the maximum carrying capacity of the section, and determining whether section conveying constraint is met;
finally, limiting initial values of train operation intervals according to a normal rail transit train operation plan, and setting initial intervals and initial station number of an ith station;
step 2, taking the minimum sum of the residence time of passengers in the current limiting time period and the waiting time of the entering passenger flow as an optimization target, taking the running time interval of the train and the passenger flow limiting the entering station as decision variables, determining constraint conditions, and establishing a single-wire multi-station cooperative current limiting train density optimization model;
the train density optimization model has the following objective function:
where Z represents the sum of waiting times of passengers in the station,passenger flow of i station in limited flow control,/->For the total passenger flow number in the ith station, A t The time length of the passenger flow control time period is the train running interval, and T is the passenger flow control time period, wherein the passenger flow control time period comprises a plurality of passenger flow control time periods with the time length of T; n= { N i I=1, 2,3, …, N }, N being the total number of all stations of a single line, N representing a set of stations of a unidirectional track traffic line;
the constraint conditions include: station passenger flow demand constraint, station platform capability constraint, interval passenger flow conveying capability constraint, boarding passenger flow constraint, train tracking interval time constraint and line conveying capability constraint, as shown in the formulas (2) to (11):
A t ≥t m (7)
A t ≤t s (8)
A t ≥t r (9)
A t ≥t b (10)
the formula (2) is a station passenger flow demand constraint, and lambda represents the minimum proportion of passenger flow demands; the formulas (3) and (4) are station capability constraints,for the maximum number of accommodations at the station platform +.>The maximum number of people passing through the facility limit for the entrance gate; formula (5) is an interval passenger flow conveying capacity constraint, M i-1,i The section passenger flow quantity from station i-1 to station i is represented, Y is the maximum passing capacity of unit hour interval; y=n×m×d, m is the number of train groups, the unit is the number of trains, d is the number of trains passing in unit hour, and n is the number of trains passing in unit hour; n=3600/max (t b ,t r )，t b For the minimum departure time interval of the train at the turn-back station, t r To track train time intervals; formula (6) is an boarding flow restriction, wherein:
p in the formula r(i+1) To the remaining capacity of the train when reaching the (i+1) th station, P ri For the number of train transportation people, K, at the ith station max G is the maximum number of people which can be accommodated by the train i The getting-off rate of the train passenger at the ith station is set;
formulas (7) to (10) are train tracking interval time constraint, t m For the time interval the train must stay at the station, t s Maximum limit of waiting time for passengers, t r To track train time intervals, t b A time interval for minimum departure of the train at the return station; train must stay time t m Represented by the following formula:
t is in 0 For stopping the train, shielding the time when the door is opened; mu is the imbalance degree coefficient of the distribution of the passengers at the station in front of the shielding door; t is t 1 The time for getting on and off each passenger; x is the number of vehicle doors; w is the width of the vehicle door; t is t 2 The closing time of the train door; t is t 3 The time to close the door to leave the station for the train;
formula (11) is a line conveying capacity constraint, n miA For minimum operation logarithm of train operation in each section of peak hour, n maC The operation logarithm is the maximum line capacity;
step 3, constructing input parameters of a model according to the step 2, including initial arrival passenger flow of each station, station number, boarding and disembarking number and remaining passenger number, applying a simulated annealing algorithm to perform iterative search on arrival number and train running intervals of a plurality of current limiting periods, solving a multi-station collaborative current limiting train density optimization model, and outputting an optimal train running interval and current limiting number of each station, wherein the method comprises the following steps of:
firstly, setting model initialization parameters, determining an initial passenger flow data matrix, and determining initial number of passengers at each station of a single line, maximum carrying capacity of a train and initial running interval of the single line train;
according to the simulated annealing algorithm, an initial operation interval and a passenger flow initial value are randomly set, constraint conditions of a model are input, and the total cost of the single-wire multi-station cooperative current limiting train running density and the total passenger waiting time is calculated through a global optimal solution finally output by the simulated annealing algorithm.
2. The method for optimizing the running density of the rail transit train with single-wire multi-station cooperative current limiting according to claim 1, which is characterized by comprising the following steps of: the step 1 is specifically set as follows:
in the same time period and section of passenger flow control, the operation of the same-time train is carried out according to an actual planned train operation diagram; the initial bearing and passing capacity of each station meets the passenger arrival demand, the transfer passenger flow is converted into the local line arrival passenger flow based on unidirectional line analysis, the rest passenger flows are regarded as the outbound passenger flow, and the stations are regarded as control points; assuming that the inbound passengers are skilled in using the vehicle station facility equipment, not considering the extra stay time in the station caused by individual subjective factors; neglecting the flow of giving up the traveling of passengers, and driving according to the principle of first-come first-go, without considering malignant congestion; the number of the train group is not changed when the multi-station cooperative same line is carried out, and the maximum passenger carrying number of the train is a fixed value.
3. The method for optimizing the running density of the rail transit train with single-wire multi-station cooperative current limiting according to claim 1, which is characterized by comprising the following steps of: the method for solving and calculating the simulated annealing algorithm in the step 3 is as follows:
3-1, in a current limiting period, setting a platform aggregation number and a train running interval of an initial train before each station starts, 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;
3-2, selecting a new train running interval A by using a random probability function in an algorithm mechanism t ' control of number of passengers entering station with each stationCalculating an objective function value, i.e., an energy value E (x (j)), and calculating an energy difference Δej=e (x (j)) -E (x (i)); if ΔEj is less than or equal to 0, let ∈ ->A t ＝A t 'A'; if delta Ej>0, returning to the step 3-1;
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, stopping calculation, and obtaining the optimal single-wire multi-station cooperative current limiting train operation interval and the current limiting number of each station.
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