CN111915890B - Network connection optimization control method for main road traffic signals - Google Patents

Network connection optimization control method for main road traffic signals Download PDF

Info

Publication number
CN111915890B
CN111915890B CN202010720893.2A CN202010720893A CN111915890B CN 111915890 B CN111915890 B CN 111915890B CN 202010720893 A CN202010720893 A CN 202010720893A CN 111915890 B CN111915890 B CN 111915890B
Authority
CN
China
Prior art keywords
vehicle
variable
intersection
dual
updating
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202010720893.2A
Other languages
Chinese (zh)
Other versions
CN111915890A (en
Inventor
李升波
李克强
李文宇
郜嘉鑫
许庆
刘敏俊
郑剑峰
张博
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Tsinghua University
Beijing Didi Infinity Technology and Development Co Ltd
Original Assignee
Tsinghua University
Beijing Didi Infinity Technology and Development Co Ltd
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Tsinghua University, Beijing Didi Infinity Technology and Development Co Ltd filed Critical Tsinghua University
Priority to CN202010720893.2A priority Critical patent/CN111915890B/en
Publication of CN111915890A publication Critical patent/CN111915890A/en
Application granted granted Critical
Publication of CN111915890B publication Critical patent/CN111915890B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0125—Traffic data processing
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/01—Detecting movement of traffic to be counted or controlled
    • G08G1/0104—Measuring and analyzing of parameters relative to traffic conditions
    • G08G1/0137—Measuring and analyzing of parameters relative to traffic conditions for specific applications
    • G—PHYSICS
    • G08—SIGNALLING
    • G08G—TRAFFIC CONTROL SYSTEMS
    • G08G1/00—Traffic control systems for road vehicles
    • G08G1/07—Controlling traffic signals
    • G08G1/081—Plural intersections under common control
    • Y—GENERAL TAGGING OF NEW TECHNOLOGICAL DEVELOPMENTS; GENERAL TAGGING OF CROSS-SECTIONAL TECHNOLOGIES SPANNING OVER SEVERAL SECTIONS OF THE IPC; TECHNICAL SUBJECTS COVERED BY FORMER USPC CROSS-REFERENCE ART COLLECTIONS [XRACs] AND DIGESTS
    • Y02—TECHNOLOGIES OR APPLICATIONS FOR MITIGATION OR ADAPTATION AGAINST CLIMATE CHANGE
    • Y02T—CLIMATE CHANGE MITIGATION TECHNOLOGIES RELATED TO TRANSPORTATION
    • Y02T10/00—Road transport of goods or passengers
    • Y02T10/10—Internal combustion engine [ICE] based vehicles
    • Y02T10/40—Engine management systems

Landscapes

  • Physics & Mathematics (AREA)
  • General Physics & Mathematics (AREA)
  • Chemical & Material Sciences (AREA)
  • Analytical Chemistry (AREA)
  • Traffic Control Systems (AREA)

Abstract

The invention relates to a network connection optimization control method for a main road traffic signal, and belongs to the technical field of intelligent traffic flow control. The method comprises the steps of modeling a network connection control problem, decoupling the problem by introducing a consistency variable to construct a consistency optimization problem, realizing parallel calculation by using an alternative direction multiplier method, updating an original variable, a consistency variable and a dual variable in parallel until a set termination condition is met, and sending signal lamp control quantity obtained by calculation to each signal lamp for execution. Each step of calculation of the method can be respectively carried out on the calculation nodes of the signal lamps, and parallelization of problem solving is achieved. The method effectively improves the calculation and solving efficiency, and the calculation complexity is irrelevant to the number of intersections, thereby being more suitable for the cooperative control of large-scale trunk road traffic signals. The network connection optimization control method of the main road traffic signal improves the control efficiency, realizes real-time control, relieves the problems of traffic jam and the like, and is beneficial to improving the traffic efficiency.

Description

Network connection optimization control method for main road traffic signals
Technical Field
The invention relates to a network connection optimization control method for a main road traffic signal, and belongs to the technical field of intelligent traffic flow control.
Technical Field
The main traffic flows in urban street networks are on thoroughfares and roads along thoroughfares. The optimal timing control of traffic signals along the main road has important significance for solving the problems of traffic jam, energy conservation, emission reduction, traffic safety and the like. The cooperative control of traffic lights along the arterial road has a number of advantages: the method can provide higher-level traffic service, improve the overall speed of the traffic flow and reduce the parking times of the vehicles. And secondly, the traffic flow is smoother, the vehicle distance can be reduced, and the road capacity can be improved. Thirdly, by reasonably controlling the signal lamps, the duration of the green light when the traffic flow reaches the intersection is maximized, and the rear-end collision phenomenon caused by the stop of the traffic light is reduced. Fourthly, the distance between traffic flows is reduced by reasonably controlling the signal lamps, and the phenomenon that pedestrians cross the road within the duration of green light can also be reduced.
At present, the control modes aiming at the main road traffic signals are mainly divided into two modes of maximizing the passing time, minimizing the integral delay time and the parking times of vehicles. Because the mode of minimizing the overall delay time and the number of times of stopping the vehicle needs to evaluate variables such as time delay, the number of times of stopping and the like, the model is more complex and involves nonlinearity, and the traditional method mostly adopts the mode of maximizing the passing time. For the traffic signal lamp control mode of maximizing the traffic time, the current mainstream solving mode comprises two modes of constructing an optimization problem solution and adopting a heuristic algorithm to solve the optimization problem solution. For a solution mode constructed as an optimization problem, most of the existing work constructs the problem as a mixed integer linear programming problem (MILP), the calculation complexity of the problem is greatly increased along with the increase of the scale of the problem, the online control of traffic signals has a certain real-time requirement, and the mode constructed as the optimization problem is difficult to be applied to the large-scale traffic signal control problem. The solving method adopting the heuristic algorithm aims to improve the solving speed of the problem so that the problem can meet the real-time requirement of control, but the heuristic algorithm often cannot find the optimal solution or only finds a certain feasible solution due to time limitation. Both the two solving methods cannot well solve the control problem of the large-scale main road traffic signals.
Disclosure of Invention
The invention aims to provide a network connection optimization control method of a main road traffic signal, which decouples the network connection optimization control problem by introducing a consistency variable, and realizes the parallel computation of sub-nodes by using an alternative direction multiplier algorithm so as to effectively reduce the computation complexity increased along with the number of controlled intersections, thereby improving the computation efficiency and achieving better computation instantaneity.
The invention provides a network connection optimization control method of main road traffic signals, which considers three different intersection conditions and has three different control methods, wherein the first method comprises the following steps:
(1) setting N intersections in the trunk road, and establishing a trunk road signal lamp cooperative control optimization model when any two continuous intersections in the N intersections are green, wherein the trunk road signal lamp cooperative control optimization model comprises the following steps:
Figure GDA0003516525220000021
satisfies the following conditions: a is (i) ≤x (i) -t i ≤y (i) -t i ≤a (i) +g i-1
b (i) ≤x (i) ≤y (i) ≤b (i) +g i
Figure GDA0003516525220000022
Figure GDA0003516525220000023
Figure GDA0003516525220000024
i＝1，2，...，N-2
Wherein i is the serial number of the crossing, N is the total number of the crossings on the main road, and w i And
Figure GDA0003516525220000025
weight coefficient, Δ, for forward and reverse travel of the vehicle i Starting a green time interval, eta, for forward and reverse running of the vehicle i Already running in reverse direction for vehicleCrossing the cycle number, c represents a signal lamp cycle;
x and
Figure GDA0003516525220000026
respectively representing the starting position, y and y of the current road section when the vehicle drives forward and the vehicle drives backward to share the green light timing
Figure GDA0003516525220000027
Indicating the end position of the current road section, a and
Figure GDA0003516525220000028
green light start time, b and
Figure GDA0003516525220000029
green light start time, o and
Figure GDA00035165252200000210
indicating the periodic interval between adjacent road sections, g and g, between which the vehicle is travelling in the forward direction and in the reverse direction
Figure GDA00035165252200000211
Indicating the duration of the green light, t, and
Figure GDA00035165252200000212
represents the time required for the vehicle to reach the intersection from the previous intersection in the forward direction and the reverse direction, wherein x (i) ，y (i) ，
Figure GDA00035165252200000220
a (i) ，b (i)
Figure GDA00035165252200000221
For variables to be optimized, the subscript i in the formulaThe ith intersection;
(2) setting the relationship between intersections on the main road as follows: the starting time b of the green light of the current road section when the vehicle at the upper intersection in the forward running process of the vehicle runs in the forward direction is the same as the starting time a of the green light of the upper road section in the forward running process of the vehicle plus the time t required by the vehicle to reach the current intersection from the upper intersection, namely b (i) ＝a (i) +t i At the current crossing in reverse direction
Figure GDA00035165252200000214
At the next crossing when travelling in the reverse direction of the vehicle
Figure GDA00035165252200000215
Plus the time required for the vehicle to reach the current intersection from the next intersection
Figure GDA00035165252200000219
Are identical, i.e. that
Figure GDA00035165252200000216
Decoupling the coupling part in the model in the step (1) by introducing a consistency variable Z, wherein the decoupled submodel is as follows:
Figure GDA00035165252200000217
satisfies the following conditions:
Figure GDA00035165252200000218
F 1 X 1i ＝Δ 1i
A 1 X 1i ＝Z 1i
i＝1，2，...，N-2
wherein the content of the first and second substances,
Figure GDA0003516525220000031
Figure GDA0003516525220000032
Figure GDA0003516525220000033
F 1 ＝[0 0 0 -1 0 0 0 1]
Figure GDA0003516525220000034
Figure GDA0003516525220000035
Figure GDA0003516525220000036
Figure GDA0003516525220000037
(3) and (3) further simplifying the sub-model decoupled in the step (2) into a model with an indication function:
Figure GDA0003516525220000038
satisfies the following conditions: a. the 1 X 1i ＝Z 1i
Wherein Z is 1i In order to be a consistent variable, the data rate,
Figure GDA0003516525220000039
to limit the range of the variable, the indicator function is:
Figure GDA00035165252200000310
wherein S represents a set of feasible solutions for the optimization function, i.e., a set of feasible solutions that satisfy the following constraints:
Figure GDA00035165252200000311
F1X 1i ＝Δ 1i
(4) using dual variables lambda in augmented Lagrange form 1 And a penalty factor rho, the consistency optimization model in the step (3) is rewritten into an augmented Lagrange form L 1ρ (X 1 ,Z 1 ,λ 1 ) The following were used:
Figure GDA00035165252200000312
wherein, the superscript T is a matrix transposition;
(5) by using an alternating direction multiplier method (ADMM for short), iteratively solving the augmented Lagrange formal model in the step (4), realizing the network connection type group cooperative control on the trunk signal lamp, and comprising the following steps:
sequential updating of the consistency variable Z using an alternate direction multiplier method 1 Original variable X 1 And a dual variable λ 1 And setting the iteration number k to be 1 during initialization:
(5-1) at each intersection of the trunk road, for the original variable X 1 And performing parallel updating, wherein an updating formula is as follows:
Figure GDA0003516525220000041
wherein the content of the first and second substances,
Figure GDA0003516525220000042
show to get
Figure GDA0003516525220000043
X to a minimum 1i ；
(5-2)Updating the original variable X according to the step (5-1) 1 For the consistency variable Z 1 Updating is carried out, and an updating formula is as follows:
Figure GDA0003516525220000044
wherein Ω represents and Z 1i Associated X 1i A set of (a);
(5-3) updating the original variable X according to the step (5-1) 1 And step (5-2) updating the consistency variable Z 1 Update the dual variable lambda 1 The update formula is as follows:
Figure GDA0003516525220000045
(5-4) setting an original threshold value epsilon according to a convergence judgment condition of an alternative direction multiplier method for solving the augmented Lagrange formal model pri And dual threshold e dual Separately calculating the original error
Figure GDA0003516525220000046
And dual error
Figure GDA0003516525220000047
If r k+1 ≤∈ pri And s is k+1 ≤∈ dual Then will be
Figure GDA0003516525220000048
As the optimal solution of the main road cooperative control, x, y,
Figure GDA0003516525220000049
a (i) ，b (i) ，
Figure GDA00035165252200000410
realize the network connection type cooperative control of the main road traffic signal, if r k+1 ＞∈ pri Or s k+1 ＞∈ dual Then go back to step(5-1), and continuing the steps of (5-1) to (5-4).
The second method comprises the following steps:
(1) setting N intersections in the trunk road, and establishing a trunk road signal lamp cooperative control optimization model when any three continuous intersections in the N intersections are green, wherein the trunk road signal lamp cooperative control optimization model comprises the following steps:
Figure GDA00035165252200000411
satisfies the following conditions: a is a (i) +t i ≤x (i) ≤y (i) ≤a (i) +g i-1 +t i
b (i) ≤x (i) ≤y (i) ≤b (i) +g i
d (i) -t i+1 ≤x (i) ≤y (i) ≤d (i) +g i+1 -t i+1
Figure GDA00035165252200000412
Figure GDA00035165252200000413
Figure GDA00035165252200000414
Figure GDA00035165252200000415
Figure GDA00035165252200000416
Figure GDA0003516525220000051
i＝1，2，...，N-2
Wherein i is the serial number of the road junction, N is the total number of the road junctions on the main road, w i And
Figure GDA00035165252200000524
weighting coefficients for forward running and reverse running of the vehicle; delta i Starting a green time interval, eta, for both forward and reverse running of the vehicle i C represents a signal light period for the number of crossing periods that the vehicle has crossed when driving in reverse.
x and
Figure GDA00035165252200000511
respectively representing the starting position, y and y of the current road section when the vehicle drives forward and the vehicle drives backward to share the green light timing
Figure GDA00035165252200000512
Indicating the end position of the current road section, a and
Figure GDA00035165252200000513
green light start time, b and
Figure GDA00035165252200000514
green light start time, d and d indicating that the vehicle is driving in forward direction and the vehicle is driving in reverse direction on the current road section
Figure GDA00035165252200000515
A green light start time indicating that the vehicle is traveling in the forward direction and the vehicle is traveling in the reverse direction on the next road section, and
Figure GDA00035165252200000517
indicating the periodic interval between adjacent road sections, g and g, between which the vehicle is travelling in the forward direction and in the reverse direction
Figure GDA00035165252200000516
Indicating the duration of the green light, t, and
Figure GDA00035165252200000518
represents the time required for the vehicle to reach the intersection from the previous intersection in the forward direction and the reverse direction, wherein x (i) ,y (i) ,
Figure GDA0003516525220000052
a (i) ,b (i) ,
Figure GDA0003516525220000053
For the variables to be optimized, the corner mark i in the formula represents the ith intersection;
(2) setting the relationship between the main road intersections as follows: the starting time b of the green light of the current road section when the vehicle is running in the forward direction is the same as the starting time a of the green light of the previous road section when the vehicle is running in the forward direction plus the time t required for the vehicle to reach the current intersection from the previous intersection, namely b (i) ＝a (i) +t i And the starting time b of the green light of the current road section when the vehicle is running in the forward direction is the same as the time t required by the vehicle to reach the next road section from the current road section by subtracting the starting time d of the green light of the next road section when the vehicle is running in the forward direction, namely b (i) ＝d (i) -t i+1 At the current crossing when the vehicle is travelling in the reverse direction
Figure GDA00035165252200000525
At the next crossing when travelling in the reverse direction of the vehicle
Figure GDA00035165252200000523
Plus the time required for the vehicle to reach the current intersection from the next intersection
Figure GDA00035165252200000519
Are identical, i.e. that
Figure GDA0003516525220000054
And at the current intersection when the vehicle is travelling in the reverse direction
Figure GDA00035165252200000520
At the next crossing when travelling in the reverse direction of the vehicle
Figure GDA00035165252200000521
Minus the time required for the vehicle to reach the next intersection from the current intersection
Figure GDA00035165252200000522
Are identical, i.e. that
Figure GDA0003516525220000055
Decoupling the coupling part in the model in the step (1) by introducing a consistency variable, wherein the decoupled submodel is as follows:
Figure GDA0003516525220000056
satisfies the following conditions:
Figure GDA0003516525220000057
F 2 X 2i ＝δ i
A 2 X 2i ＝Z 2i
i＝1，2，...，N-2
wherein the content of the first and second substances,
Figure GDA0003516525220000058
Figure GDA0003516525220000059
Figure GDA00035165252200000510
Figure GDA0003516525220000061
Figure GDA0003516525220000062
Figure GDA0003516525220000063
Figure GDA0003516525220000064
Figure GDA0003516525220000065
Figure GDA0003516525220000066
(3) and further simplifying the decoupled submodel into a model with an indication function:
Figure GDA0003516525220000067
satisfies the following conditions: a. the 2 X 2i ＝Z 2i
Wherein Z is 2i In order to be a consistent variable, the data rate,
Figure GDA0003516525220000068
to limit the range of the variable, the indicator function is:
Figure GDA0003516525220000069
wherein S represents a set of feasible solutions for the optimization function, i.e., a set of feasible solutions that satisfy the following constraints:
Figure GDA00035165252200000610
F 2 X 2i ＝δ i
(4) using dual variables lambda in augmented Lagrange form 2 And a penalty factor rho, and rewriting the consistency optimization model in the step (3-2-1) into an augmented Lagrange form L 2ρ (X 2 ,Z 2 ,λ 2 ) The following were used:
Figure GDA00035165252200000611
wherein, the superscript T is a matrix transposition;
(5) and (3) iteratively solving the augmented Lagrange formal model in the step (4) by using an alternating direction multiplier method to realize the network connection type group cooperative control on the trunk signal lamp, wherein the method comprises the following steps:
updating the consistency variable Z in sequence 2 Original variable X 2 And a dual variable λ 2 And setting the iteration number k to be 1 during initialization:
(5-1) at each intersection of the trunk road, for the original variable X 2 And performing parallel updating, wherein an updating formula is as follows:
Figure GDA0003516525220000071
wherein the content of the first and second substances,
Figure GDA0003516525220000072
express get such that
Figure GDA0003516525220000073
X to a minimum 2i ；
(5-2) updating the original variable X according to the step (5-1) 2 For the consistency variable Z 2 Updating is carried out, and an updating formula is as follows:
Figure GDA0003516525220000074
wherein Ω represents and Z 2i Associated X 2i A set of (a);
(5-3) updating the original variable X according to the step (5-1) 2 And step (5-2) updating the consistency variable Z 2 Update the dual variable lambda 2 The update formula is as follows:
Figure GDA0003516525220000075
(5-4) setting an original threshold value epsilon according to a convergence judgment condition of an alternative direction multiplier method for solving the augmented Lagrange formal model pri And dual threshold e dual Separately calculating the original error
Figure GDA0003516525220000076
And dual error
Figure GDA0003516525220000077
If r is k+1 ≤∈ pri And s is k+1 ≤∈ dual Then will be
Figure GDA0003516525220000078
Obtaining x as the optimal solution of the main road cooperative control optimization model (i) ,y (i) ,a (i) ,b (i) ,d (i) ,
Figure GDA0003516525220000079
Realize the network connection type cooperative control of the main road traffic signal, if r k+1 ＞∈ pri Or s k+1 ＞∈ dual And returning to the step (5-1) and continuing to circulate the steps from (5-1) to (5-4).
The third method comprises the following steps:
(1) setting N intersections in the main road, and establishing a main road signal lamp cooperative control optimization model when green lamps of all the intersections in the N intersections are matched as follows:
Figure GDA00035165252200000710
satisfies the following conditions:
Figure GDA00035165252200000711
Figure GDA00035165252200000712
Figure GDA00035165252200000713
Figure GDA00035165252200000714
Figure GDA00035165252200000715
(i＝1,2,…,N-2)
wherein the content of the first and second substances,
Figure GDA00035165252200000716
(2) setting the relationship between intersections as follows: the starting time b of the green light of the current road section when the vehicle is running in the forward direction is the same as the starting time a of the green light of the previous road section when the vehicle is running in the forward direction plus the time t required for the vehicle to reach the current intersection from the previous intersection, namely b (i) ＝a (i) +t i At the current crossing when the vehicle is travelling in the reverse direction
Figure GDA00035165252200000814
At the next crossing when travelling in the reverse direction of the vehicle
Figure GDA00035165252200000815
Plus the time required for the vehicle to reach the current intersection from the next intersection
Figure GDA00035165252200000812
Are identical, i.e. that
Figure GDA00035165252200000813
Setting the timing x and y of green lights at all intersections to be the same, and adopting the timing x and y at the first intersection to obtain the starting time b of the green light at the ith intersection (i) X less than or equal to the first crossing plus the cumulative time of the first crossing to reach the ith crossing
Figure GDA00035165252200000816
Namely, it is
Figure GDA00035165252200000817
The vehicle can be obtained in the same way in the reverse driving process;
decoupling the coupling part in the model in the step (1) by introducing a consistency variable, wherein the decoupled submodel is as follows:
Figure GDA0003516525220000081
satisfies the following conditions:
Figure GDA0003516525220000082
F 3 X 3i ＝Δ 3i
X 3i ＝Z 3i
i＝0，1，...，N-2
wherein the content of the first and second substances,
Figure GDA0003516525220000083
Figure GDA0003516525220000084
Figure GDA0003516525220000085
F 3 ＝[0 0 0 -1 0 0 0 1]
Figure GDA0003516525220000086
Figure GDA0003516525220000087
Figure GDA0003516525220000088
(3) and further simplifying the decoupled submodel into a model with an indication function:
Figure GDA0003516525220000089
satisfies the following conditions: x 3i ＝Z 3i
Wherein Z is 3i In order to be a consistent variable,
Figure GDA00035165252200000810
to limit the range of the variable, the indicator function is:
Figure GDA00035165252200000811
wherein S represents a set of feasible solutions for the optimization function, i.e., a set of feasible solutions that satisfy the following constraints:
Figure GDA0003516525220000091
F 3 X 3i ＝Δ 3i
(4) using dual variables lambda in augmented Lagrangian form 3 And a penalty factor rho, the consistency optimization model in the step (2) is rewritten into an augmented Lagrange form L 3ρ (X 3 ,Z 3 ,λ 3 ) The following were used:
Figure GDA0003516525220000092
wherein, the superscript T is a matrix transposition;
(5) and (3) iteratively solving the augmented Lagrange formal model in the step (4) by using an alternating direction multiplier method to realize the network connection type group cooperative control on the trunk signal lamp, wherein the method comprises the following steps:
updating the consistency variable Z in sequence 3 Original variable X 3 And a dual variable λ 3 And setting the iteration number k to be 1 during initialization:
(5-1) at each intersection of the trunk road, for the original variable X 3 And performing parallel updating, wherein an updating formula is as follows:
Figure GDA0003516525220000093
wherein the content of the first and second substances,
Figure GDA0003516525220000094
express get such that
Figure GDA0003516525220000095
X to a minimum 3i ；
(5-2) updating the original variable X according to the step (5-1) 3 For the consistency variable Z 3 Updating is carried out, and an updating formula is as follows:
Figure GDA0003516525220000096
wherein Ω represents and Z 3i Associated X 3i A set of (a);
(5-3) updating the original variable X according to the step (5-1) 3 And step (5-2) updating the consistency variable Z 3 Update the dual variable lambda 3 The update formula is as follows:
Figure GDA0003516525220000097
(5-4) setting an original threshold value epsilon according to a convergence judgment condition of an alternative direction multiplier method for solving the augmented Lagrange formal model pri And dual threshold e dual Separately calculating the original error
Figure GDA0003516525220000098
And dual error
Figure GDA0003516525220000099
If r k+1 ≤∈ pri And s is k+1 ≤∈ dual Then will be
Figure GDA00035165252200000910
As the optimal solution of the main road cooperative control optimization model, obtaining x, y,
Figure GDA00035165252200000911
a (i) ,b (i) ,
Figure GDA00035165252200000912
realize the network connection type cooperative control of the main road traffic signal, if r k+1 ＞∈ pri Or s k+1 ＞∈ dual And returning to the step (5-1) and continuing to circulate the steps from (5-1) to (5-4).
The network connection optimization control method of the main road traffic signals under one, two or three or any two combinations of the three different conditions comprises the following steps:
(1) setting N intersections in the main road, and establishing a sub-model after the main road signal lamp cooperative control decoupling when green lights of all the intersections in the N intersections are matched as follows:
Figure GDA0003516525220000101
satisfies the following conditions:
Figure GDA0003516525220000102
F 1 X 1i ＝Δ 1i
A 1 X 1i ＝Z 1i
Figure GDA0003516525220000103
F 2 X 2i ＝δ i
A 2 X 2i ＝Z 2i
Figure GDA0003516525220000104
F 3 X 3i ＝Δ 3i
X 3i ＝Z 3i
Figure GDA0003516525220000105
Figure GDA0003516525220000106
i＝1，2，...，N-2
wherein, the first and the second end of the pipe are connected with each other,
Figure GDA0003516525220000107
in the first method, when the vehicle is driving in the forward direction, the green light at the ith intersection starts,
Figure GDA0003516525220000108
vehicle in the second methodWhen the vehicle is running forward, the green light starting time of the ith crossing,
Figure GDA0003516525220000109
indicating the green light start time of the ith intersection when the vehicle is traveling in the forward direction in the third method,
Figure GDA00035165252200001010
indicating the starting time of the green light at the ith intersection when the vehicle is traveling in reverse in the first method,
Figure GDA00035165252200001011
indicating the starting time of the green light at the ith intersection when the vehicle is traveling in reverse in the second method,
Figure GDA00035165252200001012
indicating the green light starting time of the ith intersection when the vehicle is driven in reverse in the third method,
further simplified as follows:
Figure GDA00035165252200001013
satisfies the following conditions: GX i ≤H (i)
FX i ＝ζ i
AX i ＝Z i
i＝1，2，...，N-2
Wherein the content of the first and second substances,
L＝[L 1 ，L 2 ，L 3 ]
X i ＝[X 1i， X 2i ，X 3i ] T
Z i ＝[Z 1i， Z 2i ，Z 3i l T
F＝[F 1 ，F 2 ，F 3 ]
Figure GDA0003516525220000111
Figure GDA0003516525220000112
ζ i ＝[Δ 1i ，δ i ，Δ 2i ] T
A＝[A 1 ，A 2 ，I] T
(2) and simplifying the decoupled submodel into a model with an indication function:
Figure GDA0003516525220000113
satisfies the following conditions: AX i ＝Z i
Wherein Z is i In order to be a consistent variable,
Figure GDA0003516525220000114
to limit the range of the variable, the indicator function is:
Figure GDA0003516525220000115
wherein S represents a set of feasible solutions for the optimization function, i.e., a set of feasible solutions that satisfy the following constraints:
GX i ≤H (i)
FX i ＝ζ i
(3) utilizing a dual variable lambda and a penalty factor rho in the augmented Lagrange form to rewrite the consistency optimization model in the step (2) into an augmented Lagrange form L ρ (X, Z, λ) is as follows:
Figure GDA0003516525220000116
wherein, the superscript T is a matrix transposition;
(4) and (3) iteratively solving the augmented Lagrange formal model in the step (3) by using an alternating direction multiplier method to realize the network connection type group cooperative control on the trunk signal lamp, wherein the method comprises the following steps:
sequentially updating a consistency variable Z, an original variable X and a dual variable lambda, and setting the iteration number k to be 1 during initialization:
(4-1) at each intersection of the main road, updating the original variable X in parallel, wherein the updating formula is as follows:
Figure GDA0003516525220000117
wherein the content of the first and second substances,
Figure GDA0003516525220000118
express get such that
Figure GDA0003516525220000119
X to a minimum i ；
(4-2) updating the consistency variable Z according to the original variable X updated in the step (4-1), wherein the updating formula is as follows:
Figure GDA0003516525220000121
wherein Ω represents and Z i Associated X i A set of (a);
(4-3) updating the dual variable lambda according to the original variable X updated in the step (4-1) and the consistency variable Z updated in the step (4-2), wherein the updating formula is as follows:
Figure GDA0003516525220000122
(4-4) setting an original threshold value epsilon according to the convergence judgment condition of the alternative direction multiplier method for solving the augmented Lagrange formal model pri And dual threshold e dual Separately calculating the original error
Figure GDA0003516525220000123
And dual error
Figure GDA0003516525220000124
If r k+1 ≤∈ pri And s is k+1 ≤∈ dual Then will be
Figure GDA0003516525220000125
Obtaining X as the optimal solution of the main road cooperative control optimization model 1i ,X 2i ,X 3i Realizing the network connection type cooperative control of the main road traffic signal, if r k+1 ＞∈ pri Or s k+1 ＞∈ dual And returning to the step (4-1) and continuing to circulate the steps from (4-1) to (4-4).
The network connection optimization control method of the main road traffic signal provided by the invention has the advantages that:
the network connection optimization control method of the main road traffic signals, provided by the invention, is used for decoupling the network connection optimization control problem on the basis of the construction of a central problem of cooperative control of the main road traffic signals, and in the step of updating the ADMM, the calculation of each step can be respectively carried out on the calculation nodes of respective signal lamps, so that the parallelization of problem solution is realized. Compared with a centralized solving mode, the method provided by the invention effectively improves the calculation solving efficiency. Particularly, the calculation complexity of the method is irrelevant to the number of intersections, so that the method is more suitable for cooperative control of large-scale trunk road traffic signals. The network connection optimization control method of the main road traffic signal improves the control efficiency, realizes real-time control, relieves the problems of traffic jam and the like, and is beneficial to improving the traffic efficiency.
Drawings
Fig. 1 is a schematic diagram of the cooperative control of main road signal lamps when any two continuous intersections or all intersections are matched in the method of the present invention.
Fig. 2 is a schematic diagram of the cooperative control of trunk signal lamps when any three continuous intersections match in the method of the present invention.
Fig. 3 is a schematic diagram of cooperative control of trunk signal lamps in three types of intersection timing combinations.
Fig. 4 is a flowchart of a network connection optimization control method for a main road traffic signal according to the present invention.
Detailed Description
The flow chart of the network connection optimization control method of the main road traffic signal provided by the invention is shown in fig. 4, the invention considers three different intersection conditions and has three different control methods, wherein the first method comprises the following steps:
(1) setting N intersections in the main road, and establishing a main road signal lamp control optimization model when any two continuous intersections in the N intersections are in green light timing as follows: the optimization model is shown in fig. 1.
Figure GDA0003516525220000131
Satisfies the following conditions: a is (i) ≤x (i) -t i ≤y (i) -t i ≤a (i) +g i-1
b (i) ≤x (i) ≤y (i) ≤b (i) +g i
Figure GDA0003516525220000132
Figure GDA0003516525220000133
Figure GDA0003516525220000134
i＝1，...，N-2
Wherein i is the serial number of the road junction, N is the total number of the road junctions on the main road, w i And
Figure GDA00035165252200001319
weight coefficient, Δ, for forward and reverse travel of the vehicle i For forward and reverse running of the vehicleStarting green time interval at running timing i C represents a signal lamp period;
x and
Figure GDA00035165252200001310
respectively representing the starting position, y and y of the current road section when the vehicle drives forward and the vehicle drives backward to share the green light timing
Figure GDA00035165252200001311
Indicating the end position of the current road section, a and
Figure GDA00035165252200001312
green light start time, b and
Figure GDA00035165252200001313
a green light start time indicating that the vehicle is traveling in the forward direction and the vehicle is traveling in the reverse direction on the current road section, and
Figure GDA00035165252200001314
indicating the periodic interval between adjacent road sections, g and g, between which the vehicle is travelling in the forward direction and in the reverse direction
Figure GDA00035165252200001315
Indicating the duration of the green light, t, and
Figure GDA00035165252200001316
represents the time required for the vehicle to reach the intersection from the upper intersection in the forward direction and the reverse direction, wherein x (i) ，y (i) ，
Figure GDA0003516525220000135
a (i) ，b (i) ，
Figure GDA0003516525220000136
For the variables to be optimized, the corner mark i in the formula represents the ith intersection;
(2) setting the relationship between intersections on the main road as follows: the starting time b of the green light of the current road section when the vehicle at the upper intersection in the forward running process of the vehicle runs in the forward direction is the same as the starting time a of the green light of the upper road section in the forward running process of the vehicle plus the time t required by the vehicle to reach the current intersection from the upper intersection, namely b (i) ＝a (i) +t i At the current crossing when the vehicle is travelling in the reverse direction
Figure GDA00035165252200001320
At the next crossing when travelling in the reverse direction of the vehicle
Figure GDA00035165252200001317
Plus the time required for the vehicle to reach the current intersection from the next intersection
Figure GDA00035165252200001318
Are identical, i.e. that
Figure GDA0003516525220000137
Decoupling the coupling part in the model in the step (1) by introducing a consistency variable Z, wherein the decoupled submodel is as follows:
Figure GDA0003516525220000138
satisfies the following conditions:
Figure GDA0003516525220000139
F 1 X 1i ＝Δ 1i
A 1 X 1i ＝Z 1i
i＝1，2，...，N-2
wherein the content of the first and second substances,
Figure GDA0003516525220000141
Figure GDA0003516525220000142
Figure GDA0003516525220000143
F 1 ＝[0 0 0 -1 0 0 0 1]
Figure GDA0003516525220000144
Figure GDA0003516525220000145
Figure GDA0003516525220000146
Figure GDA0003516525220000147
(3) and (3) further simplifying the sub-model decoupled in the step (2) into a model with an indication function:
Figure GDA0003516525220000148
satisfies the following conditions: a. the 1 X 1i ＝Z 1i
Wherein Z is 1i In order to be a consistent variable,
Figure GDA0003516525220000149
to limit the range of the variable, the indicator function is:
Figure GDA00035165252200001410
wherein S represents a set of feasible solutions for the optimization function, i.e., a set of feasible solutions that satisfy the following constraints:
Figure GDA00035165252200001411
F 1 X 1i ＝Δ 1i
(4) using dual variables lambda in augmented Lagrange form 1 And a penalty factor rho, the consistency optimization model in the step (3) is rewritten into an augmented Lagrange form L 1ρ (X 1 ,Z 1 ,λ 1 ) The following were used:
Figure GDA00035165252200001412
wherein, the superscript T is a matrix transposition;
(5) by using an alternating direction multiplier method (ADMM for short), iteratively solving the augmented Lagrange formal model in the step (4), realizing the network connection type group cooperative control on the trunk signal lamp, and comprising the following steps:
sequential updating of the consistency variable Z using an alternate direction multiplier method 1 Original variable X 1 And a dual variable λ 1 And setting the iteration number k to be 1 during initialization:
(5-1) at each intersection of the trunk road, for the original variable X 1 And performing parallel updating, wherein an updating formula is as follows:
Figure GDA0003516525220000151
wherein the content of the first and second substances,
Figure GDA0003516525220000152
express get such that
Figure GDA0003516525220000153
X to a minimum 1i ；
(5-2) updating the original variable X according to the step (5-1) 1 For the consistency variable Z 1 Updating is carried out, and an updating formula is as follows:
Figure GDA0003516525220000154
wherein Ω represents and Z 1i Associated X 1i A set of (a);
(5-3) updating the original variable X according to the step (5-1) 1 And step (5-2) updating the consistency variable Z 1 Update the dual variable lambda 1 The update formula is as follows:
Figure GDA0003516525220000155
(5-4) setting an original threshold value epsilon according to a convergence judgment condition of an alternative direction multiplier method for solving the augmented Lagrange formal model pri And dual threshold e dual Separately calculating the original error
Figure GDA0003516525220000156
And dual error
Figure GDA0003516525220000157
If r k+1 ≤∈ pri And s is k+1 ≤∈ dual Then will be
Figure GDA0003516525220000158
As the optimal solution of the main road cooperative control, x, y,
Figure GDA0003516525220000159
a (i) ，b (i) ，
Figure GDA00035165252200001510
network connection type for realizing main road traffic signalCo-operating under control of r k+1 ＞∈ pri Or s k+1 ＞∈ dual And returning to the step (5-1) and continuing to circulate the steps from (5-1) to (5-4).
The second method comprises the following steps:
(1) setting N intersections in the trunk road, and establishing a trunk road signal lamp cooperative control optimization model when any three continuous intersections in the N intersections are green, wherein the trunk road signal lamp cooperative control optimization model comprises the following steps: the optimization model is shown in FIG. 2
Figure GDA00035165252200001511
Satisfies the following conditions: a is (i) +t i ≤x (i) ≤y (i) ≤a (i) +g i-1 +t i
b (i) ≤x (i) ≤y (i) ≤b (i) +g i
d (i) -t i+1 ≤x (i) ≤y (i) ≤d (i) +g i+1 -t i+1
Figure GDA00035165252200001512
Figure GDA00035165252200001513
Figure GDA00035165252200001514
Figure GDA00035165252200001515
Figure GDA00035165252200001516
Figure GDA00035165252200001517
i＝1，2，...，N-2
Wherein i is the serial number of the road junction, N is the total number of the road junctions on the main road, w i And
Figure GDA00035165252200001624
weighting coefficients for forward running and reverse running of the vehicle; delta i Starting a green time interval, eta, for forward and reverse running of the vehicle i C represents a signal light period for the number of crossing periods that the vehicle has crossed when driving in reverse.
x and
Figure GDA0003516525220000169
respectively representing the starting position, y and y of the current road section when the vehicle drives forward and the vehicle drives backward to share the green light timing
Figure GDA00035165252200001610
Indicating the end position of the current road section when the vehicle has a green light in both forward and reverse directions, a and
Figure GDA00035165252200001611
green light start time, b and
Figure GDA00035165252200001612
green light start time, d and d indicating that the vehicle is driving in forward direction and the vehicle is driving in reverse direction on the current road section
Figure GDA00035165252200001613
A green light start time indicating that the vehicle is traveling in the forward direction and the vehicle is traveling in the reverse direction on the next road section, and
Figure GDA00035165252200001614
indicating forward and reverse travel of the vehiclePeriodic interval between adjacent road sections, g and
Figure GDA00035165252200001615
indicating the duration of the green light, t, and
Figure GDA00035165252200001616
represents the time required for the vehicle to reach the intersection from the previous intersection in the forward direction and the reverse direction, wherein x (i) ,y (i) ,
Figure GDA0003516525220000161
a (i) ,b (i) ,
Figure GDA0003516525220000162
For the variables to be optimized, the corner mark i in the formula represents the ith intersection;
(2) setting the relationship between the main road intersections as follows: the starting time b of the green light of the current road section when the vehicle is running in the forward direction is the same as the starting time a of the green light of the previous road section when the vehicle is running in the forward direction plus the time t required for the vehicle to reach the current intersection from the previous intersection, namely b (i) ＝a (i) +t i And the starting time b of the green light of the current road section when the vehicle is running in the forward direction is the same as the time t required by the vehicle to reach the next road section from the current road section by subtracting the starting time d of the green light of the next road section when the vehicle is running in the forward direction, namely b (i) ＝d (i) -t i+1 At the current crossing when the vehicle is travelling in the reverse direction
Figure GDA00035165252200001622
At the next crossing when travelling in the reverse direction of the vehicle
Figure GDA00035165252200001620
Plus the time required for the vehicle to reach the current intersection from the next intersection
Figure GDA00035165252200001617
Are identical, i.e. that
Figure GDA00035165252200001623
And at the current intersection when the vehicle is travelling in the reverse direction
Figure GDA00035165252200001621
At the next crossing when travelling in the reverse direction of the vehicle
Figure GDA00035165252200001618
Minus the time required for the vehicle to reach the next intersection from the current intersection
Figure GDA00035165252200001619
Are identical, i.e. that
Figure GDA0003516525220000163
Decoupling the coupling part in the model in the step (1) by introducing a consistency variable, wherein the decoupled submodel is as follows:
Figure GDA0003516525220000164
satisfies the following conditions:
Figure GDA0003516525220000165
F 2 X 2i ＝δ i
A 2 X 2i ＝Z 2i
i＝1，2，...，N-2
wherein the content of the first and second substances,
Figure GDA0003516525220000166
Figure GDA0003516525220000167
Figure GDA0003516525220000168
Figure GDA0003516525220000171
Figure GDA0003516525220000172
Figure GDA0003516525220000173
Figure GDA0003516525220000174
Figure GDA0003516525220000175
Figure GDA0003516525220000176
(3) and further simplifying the decoupled submodel into a model with an indication function:
Figure GDA0003516525220000177
satisfies the following conditions: a. the 2 X 2i ＝Z 2i
Wherein, Z 2i In order to be a consistent variable, the data rate,
Figure GDA0003516525220000178
to limit the range of the variable, the indicator function is:
Figure GDA0003516525220000179
wherein S represents a set of feasible solutions for the optimization function, i.e., a set of feasible solutions that satisfy the following constraints:
Figure GDA00035165252200001710
F 2 X 2i ＝δ i
(4) using dual variables lambda in augmented Lagrange form 2 And a penalty factor rho, and rewriting the consistency optimization model in the step (3-2-1) into an augmented Lagrange form L 2ρ (X 2 ,Z 2 ,λ 2 ) The following were used:
Figure GDA00035165252200001711
wherein, the superscript T is a matrix transposition;
(5) and (3) iteratively solving the augmented Lagrange formal model in the step (4) by using an alternating direction multiplier method to realize the network connection type group cooperative control on the trunk signal lamp, wherein the method comprises the following steps:
updating the consistency variable Z in sequence 2 Original variable X 2 And dual variable lambda 2 And setting the iteration number k to be 1 during initialization:
(5-1) at each intersection of the trunk road, for the original variable X 2 And performing parallel updating, wherein an updating formula is as follows:
Figure GDA0003516525220000181
wherein the content of the first and second substances,
Figure GDA0003516525220000182
express get such that
Figure GDA0003516525220000183
X to a minimum 2i ；
(5-2) according to the stepsOriginal variable X after update of step (5-1) 2 For the consistency variable Z 2 Updating is carried out, and an updating formula is as follows:
Figure GDA0003516525220000184
wherein Ω represents and Z 2i Associated X 2i A set of (a);
(5-3) updating the original variable X according to the step (5-1) 2 And step (5-2) updating the consistency variable Z 2 Update the dual variable lambda 2 The update formula is as follows:
Figure GDA0003516525220000185
(5-4) setting an original threshold value epsilon according to a convergence judgment condition of an alternative direction multiplier method for solving the augmented Lagrange formal model pri And dual threshold e dual Separately calculating the original error
Figure GDA0003516525220000186
And dual error
Figure GDA0003516525220000187
If r k+1 ≤∈ pri And s is k+1 ≤∈ dual Then will be
Figure GDA0003516525220000188
Obtaining x as the optimal solution of the main road cooperative control optimization model (i) ,y (i) ,a (i) ,b (i) ,d (i) ,
Figure GDA0003516525220000189
Realize the network connection type cooperative control of the main road traffic signal, if r k+1 ＞∈ pri Or s k+1 ＞∈ dual And returning to the step (5-1) and continuing to circulate the steps from (5-1) to (5-4).
The third method comprises the following steps:
(1) setting N intersections in the main road, and establishing a main road signal lamp cooperative control optimization model when green lamps of all the intersections in the N intersections are matched as follows: the optimization model is shown in FIG. 1
Figure GDA00035165252200001810
Satisfies the following conditions:
Figure GDA00035165252200001811
Figure GDA00035165252200001812
Figure GDA00035165252200001813
Figure GDA00035165252200001814
Figure GDA00035165252200001815
(i＝1，2，...，N-2)
wherein the content of the first and second substances,
Figure GDA00035165252200001816
(2) setting the relationship between intersections as follows: the starting time b of the green light of the current road section when the vehicle is running in the forward direction is the same as the starting time a of the green light of the previous road section when the vehicle is running in the forward direction plus the time t required for the vehicle to reach the current intersection from the previous intersection, namely b (i) ＝a (i) +t i At the current crossing when the vehicle is travelling in the reverse direction
Figure GDA00035165252200001916
At the next crossing when travelling in the reverse direction of the vehicle
Figure GDA00035165252200001917
Plus the time required for the vehicle to reach the current intersection from the next intersection
Figure GDA00035165252200001915
Are identical, i.e. that
Figure GDA0003516525220000191
Setting the timing x and y of green lights at all intersections to be the same, and adopting the timing x and y at the first intersection to obtain the starting time b of the green light at the ith intersection (i) X less than or equal to the first crossing plus the cumulative time of the first crossing to reach the ith crossing
Figure GDA0003516525220000192
Namely, it is
Figure GDA0003516525220000193
The vehicle can be obtained in the same way in the reverse driving process;
decoupling the coupling part in the model in the step (1) by introducing a consistency variable, wherein the decoupled submodel is as follows:
Figure GDA0003516525220000194
satisfies the following conditions:
Figure GDA0003516525220000195
F 3 X 3i ＝Δ 3i
X 3i ＝Z 3i
i＝1，...，N-2
wherein the content of the first and second substances,
Figure GDA0003516525220000196
Figure GDA0003516525220000197
Figure GDA0003516525220000198
F 3 ＝[0 0 0 -1 0 0 0 1]
Figure GDA0003516525220000199
Figure GDA00035165252200001910
Figure GDA00035165252200001911
(3) and further simplifying the decoupled submodel into a model with an indication function:
Figure GDA00035165252200001912
satisfies the following conditions: x 3i ＝Z 3i
Wherein Z is 3i In order to be a consistent variable,
Figure GDA00035165252200001913
an indication function for limiting the value range of the variable, namely:
Figure GDA00035165252200001914
wherein S represents a set of feasible solutions for the optimization function, i.e., a set of feasible solutions that satisfy the following constraints:
Figure GDA0003516525220000201
F 3 X 3i ＝Δ 3i
(4) using dual variables lambda in augmented Lagrange form 3 And a penalty factor rho, the consistency optimization model in the step (2) is rewritten into an augmented Lagrange form L 3ρ (X 3 ,Z 3 ,λ 3 ) The following were used:
Figure GDA0003516525220000202
wherein, the superscript T is a matrix transposition;
(5) and (3) iteratively solving the augmented Lagrange formal model in the step (4) by using an alternating direction multiplier method to realize the network connection type group cooperative control on the trunk signal lamp, wherein the method comprises the following steps:
updating the consistency variable Z in sequence 3 Original variable X 3 And a dual variable λ 3 And setting the iteration number k to be 1 during initialization:
(5-1) at each intersection of the trunk road, for the original variable X 3 And performing parallel updating, wherein an updating formula is as follows:
Figure GDA0003516525220000203
wherein the content of the first and second substances,
Figure GDA0003516525220000204
express get such that
Figure GDA0003516525220000205
X to a minimum 3i ；
(5-2) updating the original variable X according to the step (5-1) 3 For the consistency variable Z 3 Updating is carried out, and an updating formula is as follows:
Figure GDA0003516525220000206
wherein Ω represents and Z 3i Associated X 3i A set of (a);
(5-3) updating the original variable X according to the step (5-1) 3 And step (5-2) updating the consistency variable Z 3 Update the dual variable lambda 3 The update formula is as follows:
Figure GDA0003516525220000207
(5-4) setting an original threshold value epsilon according to a convergence judgment condition of an alternative direction multiplier method for solving the augmented Lagrange formal model pri And dual threshold e dual Separately calculating the original error
Figure GDA0003516525220000208
And dual error
Figure GDA0003516525220000209
If r is k+1 ≤∈ pri And s is k+1 ≤∈ dual Then will be
Figure GDA00035165252200002010
As the optimal solution of the main road cooperative control optimization model, x, y,
Figure GDA00035165252200002011
a (i) ,b (i) ,
Figure GDA00035165252200002012
realize the network connection type cooperative control of the main road traffic signal, if r k+1 ＞∈ pri Or s k+1 ＞∈ dual And returning to the step (5-1) and continuing to circulate the steps from (5-1) to (5-4).
The network connection optimization control method of the main road traffic signals under one, two or three or any two combinations of the three different conditions comprises the following steps:
(1) setting N intersections in the main road, and establishing a sub-model after the main road signal lamp cooperative control decoupling when green lights of all the intersections in the N intersections are matched as follows: the optimization model is shown in figure 3 of the drawings,
Figure GDA0003516525220000211
satisfies the following conditions:
Figure GDA0003516525220000212
F 1 X 1i ＝Δ 1i
A 1 X 1i ＝Z 1i
Figure GDA0003516525220000213
F 2 X 2i ＝δ i
A 2 X 2i ＝Z 2i
Figure GDA0003516525220000214
F 3 X 3i ＝Δ 3i
X 3i ＝Z 3i
Figure GDA0003516525220000215
Figure GDA0003516525220000216
i＝1，2，...，N-2
wherein the content of the first and second substances,
Figure GDA0003516525220000217
vehicle in the first methodWhen the vehicle is running forward, the green light starting time of the ith crossing,
Figure GDA0003516525220000218
in the second method, when the vehicle is driving in the forward direction, the green light at the ith intersection starts,
Figure GDA0003516525220000219
indicating the green light start time of the ith intersection when the vehicle is traveling in the forward direction in the third method,
Figure GDA00035165252200002110
indicating the starting time of the green light at the ith intersection when the vehicle is traveling in reverse in the first method,
Figure GDA00035165252200002111
indicating the starting time of the green light at the ith intersection when the vehicle is traveling in reverse in the second method,
Figure GDA00035165252200002112
indicating the green light starting time of the ith intersection when the vehicle is driven in reverse in the third method,
further simplification is as follows:
Figure GDA00035165252200002113
satisfies the following conditions: GX i ≤H (i)
FX i ＝ζ i
AX i ＝Z i
i＝1，2，...，N-2
Wherein the content of the first and second substances,
L＝[L 1 ，L 2 ，L 3 ]
X i ＝[X 1i， X 2i ，X 3i ] T
Z i ＝[Z 1i， Z 2i ，Z 3i ] T
F＝[F 1 ,F 2 ,F 3 ]
Figure GDA0003516525220000221
Figure GDA0003516525220000222
ζ i ＝[Δ 1i ，δ i ，Δ 2i ] T
A＝[A 1 ，A 2 ，I] T
(2) and simplifying the decoupled sub-model into a model with an indication function:
Figure GDA0003516525220000223
satisfies the following conditions: AX i ＝Z i
Wherein, Z i In order to be a consistent variable,
Figure GDA0003516525220000224
an indication function for limiting the value range of the variable, namely:
Figure GDA0003516525220000225
wherein S represents a set of feasible solutions for the optimization function, i.e., a set of feasible solutions that satisfy the following constraints:
GX i ≤H (i)
FX i ＝ζ i
(3) utilizing a dual variable lambda and a penalty factor rho in the augmented Lagrange form to rewrite the consistency optimization model in the step (2) into the augmented Lagrange form L ρ (X, Z, λ) is as follows:
Figure GDA0003516525220000226
wherein, the superscript T is a matrix transposition;
(4) and (3) iteratively solving the augmented Lagrange formal model in the step (3) by using an alternating direction multiplier method to realize the network connection type group cooperative control on the trunk signal lamp, wherein the method comprises the following steps:
sequentially updating a consistency variable Z, an original variable X and a dual variable lambda, and setting the iteration number k to be 1 during initialization:
(4-1) at each intersection of the main road, updating the original variable X in parallel, wherein the updating formula is as follows:
Figure GDA0003516525220000227
wherein the content of the first and second substances,
Figure GDA0003516525220000228
show to get
Figure GDA0003516525220000229
X to a minimum i ；
(4-2) updating the consistency variable Z according to the original variable X updated in the step (4-1), wherein the updating formula is as follows:
Figure GDA00035165252200002210
wherein Ω represents and Z i Associated X i A set of (a);
(4-3) updating the dual variable lambda according to the original variable X updated in the step (4-1) and the consistency variable Z updated in the step (4-2), wherein the updating formula is as follows:
Figure GDA0003516525220000231
(4-4) augmenting Lagrange according to solvingThe convergence judgment condition of the alternative direction multiplier method of the day-form model is set as an original threshold belonging to pri And dual threshold e dual Separately calculating the original error
Figure GDA0003516525220000232
And dual error
Figure GDA0003516525220000233
If r k+1 ≤∈ pri And s is k+1 ≤∈ dual Then will be
Figure GDA0003516525220000234
Obtaining X as the optimal solution of the main road cooperative control optimization model 1i ,X 2i ,X 3i Realize the network connection type cooperative control of the main road traffic signal, if r k+1 ＞∈ pri Or s k+1 ＞∈ dua1 And returning to the step (4-1) and continuing to circulate the steps from (4-1) to (4-4).

Claims (4)

1. A network connection optimization control method of a main road traffic signal is characterized by comprising the following steps:
(1) setting N intersections in the trunk road, and establishing a trunk road signal lamp cooperative control optimization model when any two continuous intersections in the N intersections are green, wherein the trunk road signal lamp cooperative control optimization model comprises the following steps:
Figure FDA0003599281000000011
satisfies the following conditions: a is (i) ≤x (i) -t i ≤y (i) -t i ≤a (i) +g i-1
b (i) ≤x (i) ≤y (i) ≤b (i) +g i
Figure FDA0003599281000000012
Figure FDA0003599281000000013
Figure FDA0003599281000000014
i＝1，2，...，N-2
Wherein i is the serial number of the road junction, N is the total number of the road junctions on the main road, w i And
Figure FDA0003599281000000015
weight coefficient, Δ, for forward and reverse travel of the vehicle i Starting a green time interval, eta, for forward and reverse running of the vehicle i C represents a signal lamp period;
x and
Figure FDA0003599281000000016
respectively representing the starting position, y and y of the current road section when the vehicle drives forward and the vehicle drives backward to share the green light timing
Figure FDA0003599281000000017
Indicating the end position of the current road section, a and
Figure FDA0003599281000000018
green light start time, b and
Figure FDA0003599281000000019
green light start time, o and
Figure FDA00035992810000000110
indicating the periodic interval between adjacent road sections, g and g, between which the vehicle is travelling in the forward direction and in the reverse direction
Figure FDA00035992810000000111
Indicating the duration of the green light, t, and
Figure FDA00035992810000000112
represents the time required for the vehicle to reach the intersection from the previous intersection in the forward direction and the reverse direction, wherein x (i) ，y (i) ，
Figure FDA00035992810000000113
a (i) ，b (i) ，
Figure FDA00035992810000000114
For the variables to be optimized, the corner mark i in the formula represents the ith intersection;
(2) setting the relationship between intersections on the main road as follows: the starting time b of the green light of the current road section when the vehicle at the upper intersection in the forward running process of the vehicle runs in the forward direction is the same as the starting time a of the green light of the upper road section in the forward running process of the vehicle plus the time t required by the vehicle to reach the current intersection from the upper intersection, namely b (i) ＝a (i) +t i At the current crossing when the vehicle is travelling in the reverse direction
Figure FDA00035992810000000115
At the next crossing when travelling in the reverse direction of the vehicle
Figure FDA00035992810000000116
Plus the time required for the vehicle to reach the current intersection from the next intersection
Figure FDA00035992810000000117
Are identical, i.e. that
Figure FDA00035992810000000118
Figure FDA00035992810000000119
Decoupling the coupling part in the model in the step (1) by introducing a consistency variable Z, wherein the decoupled submodel is as follows:
Figure FDA00035992810000000120
satisfies the following conditions:
Figure FDA0003599281000000021
F 1 X 1i ＝Δ 1i
A 1 X 1i ＝Z 1i
i＝1，2，...，N-2
wherein the content of the first and second substances,
Figure FDA0003599281000000022
Figure FDA0003599281000000023
Figure FDA0003599281000000024
F 1 ＝[0 0 0 -1 0 0 0 1]
Figure FDA0003599281000000025
Figure FDA0003599281000000026
Figure FDA0003599281000000027
Figure FDA0003599281000000028
(3) and (3) further simplifying the sub-model decoupled in the step (2) into a model with an indication function:
Figure FDA0003599281000000029
satisfies the following conditions: a. the 1 X 1i ＝Z 1i
Wherein Z is 1i In order to be a consistent variable,
Figure FDA00035992810000000210
to limit the range of the variable, the indicator function is:
Figure FDA00035992810000000211
wherein S represents a set of feasible solutions for the optimization function, i.e., a set of feasible solutions that satisfy the following constraints:
Figure FDA00035992810000000212
F 1 X 1i ＝Δ 1i
(4) using dual variables lambda in augmented Lagrange form 1 And a penalty factor rho, the consistency optimization model in the step (3) is rewritten into an augmented Lagrange form L 1ρ (X 1 ，Z 1 ，λ 1 ) The following were used:
Figure FDA00035992810000000213
wherein, the superscript T is a matrix transposition;
(5) and (3) iteratively solving the augmented Lagrange formal model in the step (4) by using an alternating direction multiplier method to realize the network connection type group cooperative control on the trunk signal lamp, wherein the method comprises the following steps:
sequential updating of the consistency variable Z using an alternate direction multiplier method 1 Original variable X 1 And a dual variable λ 1 And setting the iteration number k to be 1 during initialization:
(5-1) at each intersection of the trunk road, for the original variable X 1 And performing parallel updating, wherein an updating formula is as follows:
Figure FDA0003599281000000031
wherein the content of the first and second substances,
Figure FDA0003599281000000032
express get such that
Figure FDA0003599281000000033
X to a minimum 1i ；
(5-2) updating the original variable X according to the step (5-1) 1 For the consistency variable Z 1 Updating is carried out, and an updating formula is as follows:
Figure FDA0003599281000000034
wherein Ω represents and Z 1i Associated X 1i A set of (a);
(5-3) updating the original variable X according to the step (5-1) 1 And step (5-2) updating the consistency variable Z 1 Update dual variablesλ 1 The update formula is as follows:
Figure FDA0003599281000000035
(5-4) setting an original threshold value epsilon according to the convergence judgment condition of the alternative direction multiplier method for solving the augmented Lagrange formal model pri And dual threshold e dual Separately calculating the original error
Figure FDA0003599281000000036
And dual error
Figure FDA0003599281000000037
If r k+1 ≤∈ pri And s is k+1 ≤∈ dual Then will be
Figure FDA0003599281000000038
As the optimal solution of the main road cooperative control, x, y,
Figure FDA0003599281000000039
a (i) ，b (i) ，
Figure FDA00035992810000000310
realize the network connection type cooperative control of the main road traffic signal, if r k+1 ＞∈ pri Or s k+1 ＞∈ dual And returning to the step (5-1) and continuing to circulate the steps from (5-1) to (5-4).
2. A network connection optimization control method of a main road traffic signal is characterized by comprising the following steps:
(1) setting N intersections in the trunk road, and establishing a trunk road signal lamp cooperative control optimization model when any three continuous intersections in the N intersections are green, wherein the trunk road signal lamp cooperative control optimization model comprises the following steps:
Figure FDA00035992810000000311
satisfies the following conditions: a is (i) +t i ≤x (i) ≤y (i) ≤a (i) +g i-1 +t i
b (i) ≤x (i) ≤y (i) ≤b (i) +g i
d (i) -t i+1 ≤x (i) ≤y (i) ≤d (i) +g i+1 -t i+1
Figure FDA00035992810000000312
Figure FDA0003599281000000041
Figure FDA0003599281000000042
Figure FDA0003599281000000043
Figure FDA0003599281000000044
Figure FDA0003599281000000045
i＝1，2，...，N-2
Wherein i is the serial number of the road junction, N is the total number of the road junctions on the main road, w i And
Figure FDA0003599281000000046
weighting coefficients for forward running and reverse running of the vehicle; delta i Starting a green time interval, eta, for forward and reverse running of the vehicle i C represents a signal lamp period;
x and
Figure FDA0003599281000000047
respectively representing the starting position, y and y of the current road section when the vehicle drives forward and the vehicle drives backward to share the green light timing
Figure FDA0003599281000000048
Indicating the end position of the current road section, a and
Figure FDA0003599281000000049
green light start time, b and
Figure FDA00035992810000000410
green light start time, d and d indicating that the vehicle is driving in forward direction and the vehicle is driving in reverse direction on the current road section
Figure FDA00035992810000000411
Green light starting time, o and
Figure FDA00035992810000000412
indicating the periodic interval between adjacent road sections, g and g, between which the vehicle is travelling in the forward direction and in the reverse direction
Figure FDA00035992810000000413
Indicating the duration of the green light, t, and
Figure FDA00035992810000000414
represents the time required for the vehicle to reach the intersection from the previous intersection in the forward direction and the reverse direction, wherein x (i) ，y (i) ，
Figure FDA00035992810000000415
a (i) ，b (i) ，
Figure FDA00035992810000000416
For the variables to be optimized, the corner mark i in the formula represents the ith intersection;
(2) setting the relationship between the main road intersections as follows: the starting time b of the green light of the current road section when the vehicle is running in the forward direction is the same as the starting time a of the green light of the previous road section when the vehicle is running in the forward direction plus the time t required for the vehicle to reach the current intersection from the previous intersection, namely b (i) ＝a (i) +t i And the starting time b of the green light of the current road section when the vehicle is running in the forward direction is the same as the time t required by the vehicle to reach the next road section from the current road section by subtracting the starting time d of the green light of the next road section when the vehicle is running in the forward direction, namely b (i) ＝d (i) -t i+1 At the current crossing when the vehicle is travelling in the reverse direction
Figure FDA00035992810000000417
At the next crossing when travelling in the reverse direction of the vehicle
Figure FDA00035992810000000418
Plus the time required for the vehicle to reach the current intersection from the next intersection
Figure FDA00035992810000000419
Are identical, i.e. that
Figure FDA00035992810000000420
And at the current intersection when the vehicle is travelling in the reverse direction
Figure FDA00035992810000000421
At the next crossing when travelling in the reverse direction of the vehicle
Figure FDA00035992810000000422
Minus the time required for the vehicle to reach the next intersection from the current intersection
Figure FDA00035992810000000423
Are identical, i.e. that
Figure FDA00035992810000000424
Figure FDA00035992810000000425
Decoupling the coupling part in the model in the step (1) by introducing a consistency variable, wherein the decoupled submodel is as follows:
Figure FDA00035992810000000426
satisfies the following conditions:
Figure FDA00035992810000000427
F 2 X 2i ＝δ i
A 2 X 2i ＝Z 2i
i＝1，2，...，N-2
wherein the content of the first and second substances,
Figure FDA0003599281000000051
Figure FDA0003599281000000052
Figure FDA0003599281000000053
Figure FDA0003599281000000054
Figure FDA0003599281000000055
Figure FDA0003599281000000056
Figure FDA0003599281000000057
Figure FDA0003599281000000058
Figure FDA0003599281000000059
(3) and further simplifying the decoupled submodel into a model with an indication function:
Figure FDA00035992810000000510
satisfies the following conditions: a. the 2 X 2i ＝Z 2i
Wherein Z is 2i In order to be a consistent variable,
Figure FDA00035992810000000511
to limit the range of the variable, the indicator function is:
Figure FDA00035992810000000512
wherein S represents a set of feasible solutions for the optimization function, i.e., a set of feasible solutions that satisfy the following constraints:
Figure FDA00035992810000000513
F 2 X 2i ＝δ i
(4) using dual variables lambda in augmented Lagrange form 2 And a penalty factor rho, and rewriting the consistency optimization model in the step (3-2-1) into an augmented Lagrange form L 2ρ (X 2 ，Z 2 ，λ 2 ) The following:
Figure FDA0003599281000000061
wherein, the superscript T is a matrix transposition;
(5) and (3) iteratively solving the augmented Lagrange formal model in the step (4) by using an alternating direction multiplier method to realize the network connection type group cooperative control on the trunk signal lamp, wherein the method comprises the following steps:
updating the consistency variable Z in sequence 2 Original variable X 2 And a dual variable λ 2 And setting the iteration number k to be 1 during initialization:
(5-1) at each intersection of the trunk road, for the original variable X 2 And performing parallel updating, wherein an updating formula is as follows:
Figure FDA0003599281000000062
wherein the content of the first and second substances,
Figure FDA0003599281000000063
express get such that
Figure FDA0003599281000000064
X to a minimum 2i ；
(5-2) updating the original variable X according to the step (5-1) 2 For the consistency variable Z 2 Updating is carried out, and an updating formula is as follows:
Figure FDA0003599281000000065
wherein Ω represents and Z 2i Associated X 2i A set of (a);
(5-3) updating the original variable X according to the step (5-1) 2 And step (5-2) updating the consistency variable Z 2 Update the dual variable lambda 2 The update formula is as follows:
Figure FDA0003599281000000066
(5-4) setting an original threshold value epsilon according to a convergence judgment condition of an alternative direction multiplier method for solving the augmented Lagrange formal model pri And dual threshold e dual Separately calculating the original error
Figure FDA0003599281000000067
And dual error
Figure FDA0003599281000000068
If r k+1 ≤∈ pri And s is k+1 ≤∈ dual Then will be
Figure FDA0003599281000000069
Obtaining x as the optimal solution of the main road cooperative control optimization model (i) ，y (i) ，a (i) ，b (i) ，d (i) ，
Figure FDA00035992810000000610
Realize the network connection type cooperative control of the main road traffic signal, if r k+1 ＞∈ pri Or s k+1 ＞∈ dual And returning to the step (5-1) and continuing to circulate the steps from (5-1) to (5-4).
3. A network connection optimization control method of a main road traffic signal is characterized by comprising the following steps:
(1) setting N intersections in the main road, and establishing a main road signal lamp cooperative control optimization model when green lamps of all the intersections in the N intersections are matched as follows:
Figure FDA00035992810000000611
satisfies the following conditions:
Figure FDA00035992810000000612
Figure FDA00035992810000000613
Figure FDA00035992810000000614
Figure FDA0003599281000000071
Figure FDA0003599281000000072
i＝1，2，...，N-2
wherein the content of the first and second substances,
Figure FDA0003599281000000073
wherein i is the serial number of the road junction, N is the total number of the road junctions on the main road, w i And
Figure FDA0003599281000000074
weight coefficient, Δ, for forward and reverse travel of the vehicle i Starting a green time interval, eta, for forward and reverse running of the vehicle i C represents a signal lamp period;
x and
Figure FDA0003599281000000075
respectively representing the starting position, y and y of the current road section when the vehicle drives forward and the vehicle drives backward to share the green light timing
Figure FDA0003599281000000076
Indicating the end position of the current road section, a and
Figure FDA0003599281000000077
green light start time, b and
Figure FDA0003599281000000078
the green light start time, t, and
Figure FDA0003599281000000079
indicating the time required for the vehicle to reach the intersection from the previous intersection in the forward direction and the reverse direction,
Figure FDA00035992810000000710
and
Figure FDA00035992810000000711
cumulative transit time, g and g, representing the time the vehicle travels in the forward direction and in the reverse direction from the first intersection to the ith intersection
Figure FDA00035992810000000712
Indicating the duration of the green light, t, and
Figure FDA00035992810000000713
represents the time required for the vehicle to reach the intersection from the previous intersection in the forward direction and the reverse direction, wherein a (i) ，b (i) ，
Figure FDA00035992810000000714
For the variables to be optimized, the corner mark i in the formula represents the ith intersection;
(2) setting the relationship between intersections as follows: the starting time b of the green light of the current road section when the vehicle is running in the forward direction is the same as the starting time a of the green light of the previous road section when the vehicle is running in the forward direction plus the time t required for the vehicle to reach the current intersection from the previous intersection, namely b (i) ＝a (i) +t i At the current crossing when the vehicle is travelling in the reverse direction
Figure FDA00035992810000000715
At the next crossing when travelling in the reverse direction of the vehicle
Figure FDA00035992810000000716
Plus the time required for the vehicle to reach the current intersection from the next intersection
Figure FDA00035992810000000717
Are identical, i.e. that
Figure FDA00035992810000000718
Setting the timing x and y of green lights at all intersections to be the same, and adopting the timing x and y at the first intersection to start the green light at the ith intersectionTime b (i) X less than or equal to the first crossing plus the cumulative time of the first crossing to reach the ith crossing
Figure FDA00035992810000000719
Namely, it is
Figure FDA00035992810000000720
The vehicle can be obtained in the same way in the reverse driving process;
decoupling the coupling part in the model in the step (1) by introducing a consistency variable, wherein the decoupled submodel is as follows:
Figure FDA00035992810000000721
satisfies the following conditions:
Figure FDA00035992810000000722
F 3 X 3i ＝Δ 3i
X 3i ＝Z 3i
i＝1，...，N-2
wherein the content of the first and second substances,
Figure FDA00035992810000000723
Figure FDA0003599281000000081
Figure FDA0003599281000000082
F 3 ＝[0 0 0 -1 0 0 0 1]
Figure FDA0003599281000000083
Figure FDA0003599281000000084
Figure FDA0003599281000000085
(3) and further simplifying the decoupled submodel into a model with an indication function:
Figure FDA0003599281000000086
satisfies the following conditions: x 3i ＝Z 3i
Wherein Z is 3i In order to be a consistent variable,
Figure FDA0003599281000000087
to limit the range of the variable, the indicator function is:
Figure FDA0003599281000000088
wherein S represents a set of feasible solutions for the optimization function, i.e., a set of feasible solutions that satisfy the following constraints:
Figure FDA0003599281000000089
F 3 X 3i ＝Δ 3i
(4) using dual variables lambda in augmented Lagrange form 3 And a penalty factor rho, and rewriting the consistency optimization model in the step (2) into an augmented Lagrange form L 3ρ (X 3 ，Z 3 ，λ 3 ) The following were used:
Figure FDA00035992810000000810
wherein, the superscript T is a matrix transposition;
(5) and (3) iteratively solving the augmented Lagrange formal model in the step (4) by using an alternating direction multiplier method to realize the network connection type group cooperative control on the trunk signal lamp, wherein the method comprises the following steps:
updating the consistency variable Z in sequence 3 Original variable X 3 And a dual variable λ 3 And setting the iteration number k to be 1 during initialization:
(5-1) at each intersection of the trunk road, for the original variable X 3 And performing parallel updating, wherein an updating formula is as follows:
Figure FDA00035992810000000811
wherein the content of the first and second substances,
Figure FDA00035992810000000812
express get such that
Figure FDA00035992810000000813
X to a minimum 3i ；
(5-2) updating the original variable X according to the step (5-1) 3 For the consistency variable Z 3 Updating is carried out, and an updating formula is as follows:
Figure FDA0003599281000000091
wherein Ω represents and Z 3i Associated X 3i A set of (a);
(5-3) updating the original variable X according to the step (5-1) 3 And step (5-2) updating the consistency variable Z 3 Update the dual variable lambda 3 More, moreThe new formula is as follows:
Figure FDA0003599281000000092
(5-4) setting an original threshold value epsilon according to a convergence judgment condition of an alternative direction multiplier method for solving the augmented Lagrange formal model pri And dual threshold e dual Separately calculating the original error
Figure FDA0003599281000000093
And dual error
Figure FDA0003599281000000094
If r k+1 ≤∈ pri And s is k+1 ≤∈ dual Then will be
Figure FDA0003599281000000095
As the optimal solution of the main road cooperative control optimization model, x, y,
Figure FDA0003599281000000096
a (i) ，b (i) ，
Figure FDA0003599281000000097
realize the network connection type cooperative control of the main road traffic signal, if r k+1 ＞∈ pri Or s k+1 ＞∈ dual And returning to the step (5-1) and continuing to circulate the steps from (5-1) to (5-4).
4. A network connection optimization control method of a main road traffic signal is characterized by comprising the following steps:
(1) setting N intersections in the main road, and establishing a sub-model after the main road signal lamp cooperative control decoupling when green lights of all the intersections in the N intersections are matched as follows:
Figure FDA0003599281000000098
satisfies the following conditions:
Figure FDA0003599281000000099
F 1 X 1i ＝Δ 1i
A 1 X 1i ＝Z 1i
Figure FDA00035992810000000910
F 2 X 2i ＝δ i
A 2 X 2i ＝Z 2i
Figure FDA00035992810000000911
F 3 X 3i ＝Δ 3i
X 3i ＝Z 3i
Figure FDA00035992810000000912
Figure FDA00035992810000000913
i＝1，2，...，N-2
wherein the content of the first and second substances,
Figure FDA0003599281000000101
indicating the starting time of the green light at the ith intersection when the vehicle of claim 1 is traveling in the forward direction,
Figure FDA0003599281000000102
representing rightsThe vehicle in 2 is required to be driven forward at the starting moment of the green light at the ith intersection,
Figure FDA0003599281000000103
indicating the starting time of the green light at the ith intersection when the vehicle of claim 3 is traveling in the forward direction,
Figure FDA0003599281000000104
indicating the start time of the green light at the ith intersection when the vehicle of claim 1 is traveling in reverse,
Figure FDA0003599281000000105
indicating the starting time of the green light at the ith intersection when the vehicle of claim 2 is traveling in reverse,
Figure FDA0003599281000000106
indicating the green light start time, L, of the ith intersection when the vehicle of claim 3 is traveling in reverse 1 ，X 1i ，G 1 ，
Figure FDA0003599281000000107
F 1 ，Δ 1i ，A 1 ，Z 1i As defined in claim 1; l is 2 ，X 2i ，G 2 ，
Figure FDA0003599281000000108
F 2 ，δ i ，A 2 ，Z 2i Is as defined in claim 2; l is 3 ，X 3i ，G 3 ，
Figure FDA0003599281000000109
F 3 ，Δ 3i ，A 3 ，Z 3i Is as defined in claim 3;
further simplification is as follows:
Figure FDA00035992810000001010
satisfies the following conditions: GX i ≤H (i)
FX i ＝ζ i
AX i ＝Z i
i＝1，2，...，N-2
Wherein the content of the first and second substances,
L＝[L 1 ，L 2 ，L 3 ]
X i ＝[X 1i ，X 2i ，X 3i ] T
Z i ＝[Z 1i ，Z 2i ，Z 3i ] T
F＝[F 1 ，F 2 ，F 3 ]
Figure FDA00035992810000001011
Figure FDA00035992810000001012
ζ i ＝[Δ 1i ，δ i ，Δ 3i ] T
A＝[A 1 ，A 2 ，A 3 ] T
(2) and simplifying the decoupled submodel into a model with an indication function:
Figure FDA00035992810000001013
satisfies the following conditions: AX i ＝Z i
Wherein Z is i In order to be a consistent variable,
Figure FDA00035992810000001014
to take value ranges for variablesThe indicator function that limits, namely:
Figure FDA0003599281000000111
wherein S represents a set of feasible solutions for the optimization function, i.e., a set of feasible solutions that satisfy the following constraints:
GX i ≤H (i)
FX i ＝ζ i
(3) utilizing a dual variable lambda and a penalty factor rho in the augmented Lagrange form to rewrite the consistency optimization model in the step (2) into an augmented Lagrange form L ρ (X, Z, λ) is as follows:
Figure FDA0003599281000000112
wherein, the superscript T is a matrix transposition;
(4) and (3) iteratively solving the augmented Lagrange formal model in the step (3) by using an alternating direction multiplier method to realize the network connection type group cooperative control on the trunk signal lamp, wherein the method comprises the following steps:
sequentially updating a consistency variable Z, an original variable X and a dual variable lambda, and setting the iteration number k to be 1 during initialization:
(4-1) at each intersection of the main road, updating the original variable X in parallel, wherein the updating formula is as follows:
Figure FDA0003599281000000113
wherein the content of the first and second substances,
Figure FDA0003599281000000114
express get such that
Figure FDA0003599281000000115
X to a minimum i ；
(4-2) updating the consistency variable Z according to the original variable X updated in the step (4-1), wherein the updating formula is as follows:
Figure FDA0003599281000000116
wherein Ω represents and Z i Associated X i A set of (a);
(4-3) updating the dual variable lambda according to the original variable X updated in the step (4-1) and the consistency variable Z updated in the step (4-2), wherein the updating formula is as follows:
Figure FDA00035992810000001110
(4-4) setting an original threshold value epsilon according to a convergence judgment condition of an alternative direction multiplier method for solving the augmented Lagrange formal model pri And dual threshold e dual Separately calculating the original error
Figure FDA0003599281000000117
And dual error
Figure FDA0003599281000000118
If r k+1 ≤∈ pri And s is k+1 ≤∈ dual Then will be
Figure FDA0003599281000000119
Obtaining X as the optimal solution of the main road cooperative control optimization model 1i ，X 2i ，X 3i Realizing the network connection type cooperative control of the main road traffic signal, if r k+1 ＞∈ pri Or s k+1 ＞∈ dual And returning to the step (4-1) and continuing to circulate the steps from (4-1) to (4-4).
CN202010720893.2A 2020-07-24 2020-07-24 Network connection optimization control method for main road traffic signals Active CN111915890B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202010720893.2A CN111915890B (en) 2020-07-24 2020-07-24 Network connection optimization control method for main road traffic signals

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202010720893.2A CN111915890B (en) 2020-07-24 2020-07-24 Network connection optimization control method for main road traffic signals

Publications (2)

Publication Number Publication Date
CN111915890A CN111915890A (en) 2020-11-10
CN111915890B true CN111915890B (en) 2022-08-12

Family

ID=73280776

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202010720893.2A Active CN111915890B (en) 2020-07-24 2020-07-24 Network connection optimization control method for main road traffic signals

Country Status (1)

Country Link
CN (1) CN111915890B (en)

Family Cites Families (9)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN104575021B (en) * 2014-12-17 2016-06-15 浙江工业大学 Distributed model predictive control method based on neighborhood Optimizing City road network system
CN106504536B (en) * 2016-12-09 2019-01-18 华南理工大学 A kind of traffic zone coordination optimizing method
WO2018130307A1 (en) * 2017-01-13 2018-07-19 Huawei Technologies Co., Ltd. An architecture and coordination mechanism to distribute and parallelize any mcf solver
CN107545729B (en) * 2017-08-25 2020-02-18 华南理工大学 Traffic network distributed region control method based on data driving
CN109410606B (en) * 2018-03-22 2021-05-04 合肥革绿信息科技有限公司 Main road cooperative annunciator control method based on video
CN109035766A (en) * 2018-07-13 2018-12-18 北京工业大学 The dynamic traffic control and induction cooperative optimization method of variable cycle are considered under a kind of car networking environment
CN109889564B (en) * 2018-12-04 2020-10-09 清华大学 Centralized group cooperative control method for networked automobiles
CN109935079A (en) * 2019-03-19 2019-06-25 吉林大学 Intersection supply and demand cooperates with optimal control method
CN110942627B (en) * 2019-11-27 2020-11-03 北京建筑大学 Road network coordination signal control method and device for dynamic traffic

Also Published As

Publication number Publication date
CN111915890A (en) 2020-11-10

Similar Documents

Publication Publication Date Title
CN108847037B (en) Non-global information oriented urban road network path planning method
CN106875710B (en) A kind of intersection self-organization control method towards net connection automatic driving vehicle
CN110264757B (en) Intelligent networking automobile layered speed planning method based on continuous signal lamp information
CN110032782B (en) City-level intelligent traffic signal control system and method
CN114241778B (en) Multi-objective optimization control method and system for expressway internet of vehicles cooperating with ramp junction
CN109840641B (en) Method for quickly optimizing train multi-section operation curve
CN107016857B (en) Signal control intersection left-turn traffic combination design optimization method
CN104766484A (en) Traffic control and guidance system and method based on evolutionary multi-objective optimization and ant colony algorithm
CN103198673B (en) Bus green wave arrangement control system for controlling station stop and road section driving
CN112319461B (en) Hybrid electric vehicle energy management method based on multi-source information fusion
CN113269963B (en) Internet vehicle signal lamp control intersection economic passing method based on reinforcement learning
CN104485004A (en) Signal control method combining main trunk road bidirectional dynamic green wave and secondary trunk road semi-induction
CN106297329A (en) A kind of signal timing dial adaptive optimization method of networking signals machine
Lin et al. Traffic signal optimization based on fuzzy control and differential evolution algorithm
CN107331166B (en) A kind of dynamic restricted driving method based on path analysis
CN114038212A (en) Signal lamp control method based on two-stage attention mechanism and deep reinforcement learning
CN109544922B (en) Traffic network distributed predictive control method based on region division
CN103500511B (en) A kind of Intersections split control method based on car networking
Kong et al. Urban arterial traffic two-direction green wave intelligent coordination control technique and its application
CN113421439B (en) Single intersection traffic signal timing optimization method based on Monte Carlo algorithm
CN113593226A (en) Control method for automatic driving special road intersection in mixed traffic flow environment
CN112286212A (en) Vehicle network cooperative energy-saving control method
CN111915890B (en) Network connection optimization control method for main road traffic signals
CN115344972A (en) Method for optimizing signal timing of special road position and intersection for man-machine hybrid driving automatic driving
CN110021168B (en) Grading decision method for realizing real-time intelligent traffic management under Internet of vehicles

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant