CN109150629B - Road network multi-type monitoring equipment combined layout method - Google Patents

Road network multi-type monitoring equipment combined layout method Download PDF

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CN109150629B
CN109150629B CN201811190850.7A CN201811190850A CN109150629B CN 109150629 B CN109150629 B CN 109150629B CN 201811190850 A CN201811190850 A CN 201811190850A CN 109150629 B CN109150629 B CN 109150629B
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刘建蓓
单东辉
张志伟
叱干都
骆中斌
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CCCC First Highway Consultants Co Ltd
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04W—WIRELESS COMMUNICATION NETWORKS
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Abstract

The invention belongs to the technical field of traffic information acquisition and discloses a combined optimized layout method for various types of monitoring equipment of a road network. The method comprises the steps of firstly establishing a road traffic network topological relation graph according to a specific road network structure, establishing a multi-type monitoring equipment combined layout nonlinear programming model according to the road network topological relation graph and according to a combined cost minimization principle, a combined layout path full coverage principle and a combined layout path distinguishing principle, and solving the model to obtain a road section set provided with continuous monitoring equipment and a road section set provided with installation point type monitoring equipment. According to the method provided by the invention, various types of monitoring equipment are combined and distributed, so that the combination cost can be minimized under the condition of realizing the full coverage of the road network flow information, and the construction and maintenance cost of a road network information acquisition system is reduced. In addition, the path flow information obtained by the method is the only flow, so that the condition that the different paths are not distinguished due to blind pursuit of full coverage can be avoided, and the economy and the technology of the traffic information acquisition system are improved.

Description

Road network multi-type monitoring equipment combined layout method
Technical Field
The invention relates to the technical field of traffic information acquisition, in particular to a road network multi-type monitoring equipment combined layout method.
Background
In a traffic system, road traffic monitoring equipment is the most important way to acquire road network traffic flow information, so the arrangement mode of the road traffic monitoring equipment in a road network directly influences the quantity and quality of the acquired road network traffic flow information. The road network refers to a road system formed by interconnecting and interlacing various roads in a certain area.
At present, the commonly used road traffic monitoring equipment comprises point monitoring equipment (such as a sensing coil) and continuous monitoring equipment (such as a video monitoring system). The point-type monitoring equipment can acquire traffic flow information such as traffic volume, speed, occupancy and the like, and is low in installation cost and maintenance cost; compared to a point monitoring device, a continuous monitoring device can acquire traffic flow information other than traffic volume, speed, occupancy, and the like, for example, time when a vehicle passes through a road section, a license plate, and the like, but its installation cost and maintenance cost are high. Therefore, it is not practical to install advanced continuous monitoring devices on every road segment in a large road network.
In consideration of the above, two types of monitoring equipment can be combined and distributed in the road network, so that the road network flow information is fully covered, and meanwhile, the installation and maintenance cost is ensured to be low. However, the existing traffic monitoring device layout methods are all directed at the layout of a single type of monitoring device (such as a single sensing coil), the combined layout of more than two types of monitoring devices is not considered, and the full coverage of the road network flow information is not realized.
Disclosure of Invention
In view of this, the invention provides a method for arranging a plurality of types of road network monitoring devices in a combined manner, which can minimize the combined cost and reduce the construction and maintenance costs of a road network information acquisition system under the condition of realizing the full coverage of road network flow information. In addition, the path flow information obtained by the method is the only flow, so that the condition that the different paths are not distinguished due to blind pursuit of full coverage can be avoided, and the economy and the technology of the traffic information acquisition system are improved.
In order to achieve the purpose, the invention adopts the following scheme:
step 1, establishing a road network topological relation graph according to a road network structure. The road network topological relation graph comprises intersections in a road network and road sections among the intersections, wherein at least 1 starting point and at least 1 end point exist in the intersections of the road network, 1 starting point and 1 end point form 1 OD pair, the road sections passing through from 1 starting point to 1 end point form 1 path, and at least 1 path exists among the 1 OD pair.
Step 2, aiming at any path r in the road network topological relation graphiDefine Boolean variables
Figure BDA0001827460370000023
Represents a path riWhether to pass through the road section a; if path riPassing through the section a, then
Figure BDA0001827460370000024
Taking 1; if path riNot passing through the section a, then
Figure BDA0001827460370000025
Taking 0; the road section a is any road section in the road network topological relation graph.
Defining a Boolean variable x for any road section a in the road network topological relation graphaIndicating whether or not a continuous monitoring device is installed on the road section a, a boolean variable y is definedaIndicating whether a point type monitoring device is installed on the road section a; wherein, when the road section a is installed with a continuous monitoring device, xaTaking 1; when the road section a is not installed with the continuous monitoring device, xaTaking 0; when the road section a is installed with a point type monitoring device, yaTaking 1; when the section a is not installed with the spot monitoring device, yaTaking 0; x is the number ofaAnd yaNot taking 1 at the same time.
Step 3, according to the road network topological relation graph, according to a combination cost minimization principle, a combination layout path full coverage principle and a combination layout path distinguishing principle, establishing a multi-type monitoring equipment combination layout nonlinear programming model:
minΣa∈Ac1xa+Σa∈Ac2ya
Figure BDA0001827460370000022
wherein, c1Cost of a single continuous monitoring device, c2The cost of the device is monitored in a single point mode; a is a set formed by all road sections in the network topological relation graph, and R is a set formed by all paths in the network topological relation graph; r isjAnd rkAny path in the road network topological relation graph is taken; rsTo pass through UcSet of identifiable paths, RcTo pass through UcA set of identifiable paths; u shapeSFor installing sets of road sections of continuous monitoring equipment, UcA collection of installation point type monitoring device road sections; u is the union set, n is the intersection set,
Figure BDA0001827460370000031
is an empty set; xicIs a Boolean variable and represents HcWhether full rank, HcFull rank time is 1, Hc0 when the rank is not full; hcIs UcA matrix associated with the path;
and 4, solving the nonlinear programming model of the combined layout of the multi-type monitoring equipment to obtain a road section set for installing the continuous monitoring equipment and a road section set for installing the point-type monitoring equipment.
The method comprises the steps of firstly establishing a road traffic network topological relation graph according to a specific road network structure, establishing a multi-type monitoring equipment combined layout nonlinear programming model according to a combined cost minimization principle, a combined layout path full coverage principle and a combined layout path distinguishing principle, and then solving the multi-type monitoring equipment combined layout nonlinear programming model to obtain a road section set for installing continuous monitoring equipment and a road section set for installing point type monitoring equipment.
When the model is established, the invention is based on the principle of minimizing the combination cost, the principle of fully covering the combined layout path and the principle of distinguishing the combined layout path, therefore, the set of the continuous monitoring equipment and the installation point type monitoring equipment solved according to the method provided by the invention can minimize the combination cost under the condition of realizing the full coverage of the road network flow information, and reduce the construction and maintenance cost of the road network information acquisition system. In addition, the path flow information obtained by the method is the only flow, so that the condition that the different paths are not distinguished due to blind pursuit of full coverage can be avoided, and the economy and the technology of the traffic information acquisition system are improved.
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In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a schematic flow chart of a method for arranging combinations of multiple types of monitoring devices in a road network according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a topology relationship of a router network according to an embodiment of the present invention;
fig. 3 is a schematic flowchart of a process for solving a full-coverage layout planning model of a single continuous monitoring device according to an embodiment of the present invention;
fig. 4 is a schematic flowchart of a process for solving a nonlinear programming model for combined layout of multiple types of monitoring devices according to an embodiment of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
Fig. 1 is a schematic flow chart of a method for arranging combinations of multiple types of road network monitoring devices according to an embodiment of the present invention.
Referring to fig. 1, the method for arranging the combinations of the road network multi-type monitoring devices provided by the embodiment of the present invention includes the following steps:
step 1, establishing a road network topological relation graph according to a road network structure.
The road network topological relation graph comprises intersections in a road network and road sections among the intersections, wherein at least 1 starting point and at least 1 end point exist in the intersections of the road network, 1 starting point and 1 end point form 1 OD pair, the road sections passing through from 1 starting point to 1 end point form 1 path, and at least 1 path exists among the 1 OD pair.
Illustratively, taking the road network topological relation graph shown in fig. 2 as an example, the road network comprises five intersections, namely an intersection (i) to an intersection (v), wherein the intersection (i) is a starting point, and the intersections (iv) and (v) are end points; seven road sections, namely road section 1 to road section 7; two OD pairs, namely an OD pair (r) -an OD pair (r) and an OD pair (r) -a (r); six paths, path r1 to path r6, respectively, where path r1 is comprised of links 1 and 4, path r2 is comprised of links 1,3, and 6, path r3 is comprised of links 2 and 6, path r4 is comprised of links 1 and 5, path r5 is comprised of links 1,3, and 7, and path r6 is comprised of links 2 and 7. Paths r1, r2, and r3 are paths between OD pairs (r) - (r), and paths r4, r5, and r6 are paths between OD pairs (r) - (r).
Step 2, aiming at any path r in the road network topological relation graphiDefine Boolean variables
Figure BDA0001827460370000054
Represents a path riWhether to pass through the road section a; defining a Boolean variable x for any road section a in the road network topological relation graphaIndicating whether or not a continuous monitoring device is installed on the road section a, a boolean variable y is definedaIndicating whether the link a is installed with a spot monitoring device.
Wherein if the path riPassing through the section a, then
Figure BDA0001827460370000055
Taking 1; if path riNot passing through the section a, then
Figure BDA0001827460370000056
Taking 0; the road section a is any road section in the road network topological relation graph; when the road section a is installed with a continuous monitoring device, xaTaking 1; when the road section a is not installed with the continuous monitoring device, xaTaking 0; when the road section a is installed with a point type monitoring device, yaTaking 1; when the section a is not installed with the spot monitoring device, yaTaking 0; x is the number ofaAnd yaNot taking 1 at the same time.
And 3, establishing a combined layout nonlinear programming model of the multi-type monitoring equipment according to the road network topological relation graph and according to a combined cost minimization principle, a combined layout path full coverage principle and a combined layout path distinguishing principle.
The nonlinear programming model for the combined layout of the multi-type monitoring equipment is as follows:
minΣa∈Ac1xa+Σa∈Ac2yaformula (1)
Figure RE-GDA0001877394690000051
Wherein, c1Cost of a single continuous monitoring device, c2The cost of the device is monitored in a single point mode; a is a set formed by all road sections in the network topological relation graph, and R is a set formed by all paths in the network topological relation graph; r isjAnd rkFor any path in the topological relation graph of the road network, RsTo pass through UsSet of identifiable paths, RcTo pass through VcA set of identifiable paths; u is the union set, n is the intersection set,
Figure BDA0001827460370000061
is an empty set; xicIs a Boolean variable and represents HcWhether full rank, H c1 when full rank is present, 0 when not full rank is present, HcIs UcA matrix associated with the path.
The formula (1) is an objective function, the formulas (2) to (4) are constraint conditions, the formula (1) is a combination cost minimization constraint, the formula (2) is a combination path full coverage constraint, the formula (3) is a combination path layout distinguishing constraint, and the formula (4) is a logic constraint.
And 4, solving the nonlinear programming model of the combined layout of the multi-type monitoring equipment to obtain a road section set for installing the continuous monitoring equipment and a road section set for installing the point-type monitoring equipment.
The solving process of the nonlinear programming model distributed by the combination of the multi-type monitoring equipment comprises two layers: the method comprises the steps that firstly, a full-coverage layout planning model of single continuous monitoring equipment is solved, and a road section set for installing the single continuous monitoring equipment is obtained; and the second layer outputs a road section set for installing the continuous monitoring equipment and a road section set for installing the point type monitoring equipment under the condition of not losing monitoring information, namely, meeting the requirements of full coverage of combined layout paths and division of the combined layout paths, replacing the continuous monitoring equipment with cheaper point type monitoring equipment.
Specifically, the step 4 comprises the following steps:
and (4.1) establishing a full-coverage layout planning model of the single continuous monitoring equipment according to the network topological relation diagram and the layout path full-coverage principle and the layout path distinguishing principle.
The model for planning the full-coverage layout of the single continuous monitoring equipment comprises
minΣa∈AxaFormula (5)
Figure 2
The formula (5) is an objective function, the formulas (6) to (7) are constraint conditions, the formula (6) is a combined path full coverage constraint, and the formula (7) is a combined path layout distinguishing constraint.
And (4.2) solving the full-coverage layout planning model of the single continuous monitoring equipment to obtain a road section set for installing the single continuous monitoring equipment.
Preferably, referring to the flow chart of solving the single continuous monitoring device full coverage layout planning model shown in fig. 3, the step (4.2) specifically includes the following sub-steps:
(4.2a) initialization: let U represent the set of road segments where a single continuous monitoring device is installed, and initialize U as an empty set; order to
Figure BDA0001827460370000075
Representing the complement of set U in set a.
(4.2b) calculating and inputting a path-road section incidence matrix H of the network topological relation graphrl。
Wherein the path-section association matrix HrlCan be expressed as:
Figure BDA0001827460370000071
wherein m represents the number of paths in the network topological relation graph, n represents the number of road sections in the network topological relation graph,
Figure BDA0001827460370000072
represents a path riWhether to pass the Boolean variable of the first road section, if the path riThe first road segment is passed through the first road segment,
Figure BDA0001827460370000073
taking 1; if path riInstead of passing through the first route segment,
Figure BDA0001827460370000074
taking 0; i is an element of [1,2]，l∈[1,2,...,n]。
It should be noted that the network topology relation graph is obtained from an actual road network, and the path-road segment association matrix HrlCalculated and input by artificial observation, and HrlIs a sparse matrix of n x m consisting of 0 and 1.
Illustratively, taking the road network topological relation graph shown in fig. 2 as an example, the path-road segment association matrix H is taken as the next examplerlThe calculation method of (2): assume a path-segment association matrix HrlLine 1 to line 7 of (1) correspond to road segments 1 to 7, respectively, and the path-road segment association matrix HrlRow 1 to row 6 of (1) correspond to the route r1 to the route r6, respectively, and taking the route r1 as an example, as can be seen from fig. 2, the route r1 passes through the link 1 and the link 4, and does not pass through the rest of the links, so the route-link association matrix HrlElement number 1 in the first column
Figure BDA0001827460370000081
And the 4 th element
Figure BDA0001827460370000082
Is 1, and the rest elements are 0. By analogy, the point shown in FIG. 2 can be obtainedRoad network topological relation graph corresponding path-road section incidence matrix HrlAs shown in table 1. In table 1, "1, 2,3,4,5,6, 7" represents seven road segments in the road network, r1-r6 represent six paths in the road network, and the data in the table is a matrix HrlOf (2) is used.
TABLE 1
Figure BDA0001827460370000083
(4.2c) according to the path-section correlation matrix HrlAnd generating a path distinguishing matrix H _ differential.
Wherein, the path distinguishing matrix H _ differential is a path-road section association matrix HrlThe column vectors of (1) are subtracted from each other to form a matrix
Figure BDA0001827460370000084
Then the path discrimination matrix
Figure BDA0001827460370000085
i. j is in the set of {1, 2.,. m } and i is not equal to j, H _ buffer is
Figure BDA0001827460370000086
The matrix of (a) is,
Figure BDA0001827460370000087
represents the number of combinations of 2 elements arbitrarily selected from m different elements and grouped together.
Illustratively, in the previous example, it is assumed that the path-segment association matrix obtained in step (4.2b) is H in the previous examplerlA specific process of generating the path distinguishing matrix H _ difference is explained: according to Table 1, a path-section association matrix H is formedrlEvery two rows in the middle are differenced and the absolute value is taken, resulting in table 2:
TABLE 2
Figure BDA0001827460370000088
Figure BDA0001827460370000091
The data in table 2 is the element of the path distinguishing matrix H _ difference, that is, the path distinguishing matrix H _ difference is:
Figure BDA0001827460370000092
(4.2d) judging whether the path distinguishing matrix H _ buffer is not empty: if the path distinguishing matrix H _ buffer is empty, executing the step 4.2 f); if the path discrimination matrix H _ buffer is not empty, step 4.2e) is performed.
It should be noted that, as those skilled in the art will readily understand, the path distinguishing matrix H _ buffer being empty means that all rows and columns of H _ buffer are eliminated, i.e., no element exists in H _ buffer.
(4.2e) computing a set according to a path differentiation criterion
Figure BDA0001827460370000094
The maximum value of the Differ (U, b) is determined, any section c corresponding to the max _ Differ is added into the set U, and the b represents the set
Figure BDA0001827460370000095
Any road segment in (1); and eliminating the row of which the element on the row corresponding to the road section c in the path distinguishing matrix H _ differential is 1 to obtain a matrix H _ differential ', and turning to the step (4.2d) to make H _ differential equal to H _ differential'.
Wherein Differ (U, b) represents the total number of paths that can be uniquely determined additionally when a segment b is additionally added in a segment set U where a single continuous monitoring device is installed.
It will be readily appreciated that for any one column of the path discrimination matrix H _ diff
Figure BDA0001827460370000093
When the element in one row is 1, it represents path riAnd pathrjWhen the road sections corresponding to the row are not passed by the same time, continuous monitoring equipment is arranged on the road sections, and the path r can be formediAnd a path rjAnd (4) unique distinction. Therefore, the elements of each row in the path distinguishing matrix H _ differential are added to obtain the Differ (U, b) of the road section corresponding to the row elements, and the road section layout monitoring equipment corresponding to the maximum value max _ Differ is selected, so that the most paths r can be distinguishediAnd a path rjAnd the number of the monitoring devices is reduced to the greatest extent.
Illustratively, in the previous example, taking H _ difference obtained in the previous example as an example, a specific process of calculating the matrix H _ difference' in step (4.2e) is described as follows:
adding each row element in the H _ Differ to obtain Differ (U, b) of the link corresponding to the row element, where Differ (U,1) is 8, Differ (U,2) is 8, Differ (U,3) is 8, Differ (U,4) is 5, Differ (U,5) is 5, Differ (U,6) is 8, and Differ (U,7) is 8. It is easy to know that the maximum value is 8, then the maximum value max _ Differ is 8, any link corresponding to max _ Differ is selected here as link 1, and added into the set U, it is easy to know that the columns with elements of 1 on the row corresponding to link 1 in H _ differential are respectively the 2 nd, 5 th, 6 th, 9 th, 10 th, 11 th, 14 th, 15 th columns, and these columns are eliminated, so as to obtain a matrix H _ differential' as:
Figure BDA0001827460370000101
(4.2f) reacting Hrl'＝HrlElimination of Hrl' all the links in the set U in the set correspond to columns with elements 1 on the rows.
(4.2g) judgment matrix Hrl' if it is not null, if matrix HrlIf' is empty, then step (4.2i) is performed; if the matrix HrlIf not, step (4.2h) is performed.
(4.2h) computing the sets according to the path coverage criterion
Figure BDA0001827460370000102
The maximum value max _ Cover is determined, and max _ Cover is corresponded toAdding any road section d into the set U, wherein d represents any road section in the set; elimination of Hrl' middle road section d corresponds to the column with element 1 on the row and goes to step (4.2 g).
Wherein Cover (U, d) represents the sum of the number of paths that can be additionally covered when a road segment d is additionally added in the road segment set U where a single continuous monitoring device is installed.
It should be noted that, as those skilled in the art will readily understand, the path-segment association matrix HrlBeing null means that H is eliminatedrlAll rows and columns of `, i.e. Hrl' there is no element present.
Illustratively, assume the set obtained after performing step (4.2g)
Figure BDA0001827460370000111
Is {2,5,7}, the path-segment association matrix H is formedrlAdding the elements on the line corresponding to the middle road section 2 to obtain a set
Figure BDA0001827460370000112
Cover (U, b) corresponding to the middle road segment 2, that is, Cover (U,2) ═ 2; similarly, the path-segment association matrix HrlAdding the elements on the line corresponding to the middle road section 5 to obtain a set
Figure BDA0001827460370000113
Cover (U, b) corresponding to the middle road segment 5, namely, Cover (U,5) ═ 1; associating the path-road section with the matrix HrlAdding the elements on the line corresponding to the middle road section 7 to obtain a set
Figure BDA0001827460370000114
Cover (U, b) corresponding to the middle link 7, that is, Cover (U,7) is 1. It is easy to know that the maximum value is 2, then the maximum value max _ Cover is 2, any road section corresponding to max _ Cover, here, the road section 2 is selected, the set U is added, and H is eliminatedrl' middle road section 2 corresponds to a column with an element on the row of 1.
(4.2i) outputting a set of road segments U in which a single continuous monitoring device is installed.
Preferably, referring to the flow chart of solving the nonlinear programming model for the combined deployment of the multi-type monitoring devices shown in fig. 4, the step (4.3) specifically includes the following sub-steps:
(4.3a) initialization: and Q is used for taking the number of elements in the road section set U provided with the single continuous monitoring equipment.
(4.3b) deleting the p-th element a in the set U in sequencepTo obtain a corresponding set
Figure BDA0001827460370000115
p is all integers between 1 and Q.
Judging all Q sets
Figure BDA0001827460370000116
Whether each set meets a preset condition is that a joint identification coefficient matrix H corresponding to the set meets the preset conditionsAnd UcWith path correlation matrix HcThe ranks are all full.
If Q sets
Figure BDA0001827460370000117
If the partial sets meet the preset condition, Q sets are discarded
Figure BDA0001827460370000118
Does not satisfy the set of preset conditions and goes to step (4.3 c).
If Q sets
Figure BDA0001827460370000119
If the preset conditions are not met, the step (4.3d) is carried out.
Step (4.3c), for Q sets
Figure BDA0001827460370000121
In any set satisfying a predetermined condition
Figure BDA0001827460370000122
Each satisfying a predetermined condition
Figure BDA0001827460370000123
The sets are respectively used as new sets U, Q is reduced by 1, and the step (4.3b) is repeatedly executed until Q sets
Figure BDA0001827460370000124
All do not satisfy the preset condition, and simultaneously record Q sets
Figure BDA0001827460370000125
When the current set U does not meet the preset condition, the deleted elements corresponding to the current set U form a set U corresponding to the current set Uc。
Specifically, in step (4.3c), the joint identification matrix H is judged by adopting a scanogram methodsWhether the rank is full:
the scanning graph method specifically comprises the following steps: defining a path riThe set of passing road sections a is RiFor any path riDefinition of
Figure BDA0001827460370000126
For any two paths ri、rjJudgment of
Figure BDA0001827460370000127
Whether or not: if not, then
Figure BDA0001827460370000128
Corresponding joint identification coefficient matrix HsA not full rank; if so, then
Figure BDA0001827460370000129
Corresponding joint identification coefficient matrix HsThe full rank.
For example, taking the road network topological relation graph shown in fig. 2 as an example, assuming that the set U obtained in step (4.2) in which a single continuous monitoring device is installed is {1,2,3,4,6}, and deleting the first element road segment 1 therein to obtain the map
Figure BDA00018274603700001210
The specific process of the scanogram method is explained as follows: defining a path riThe set of passing road sections a isRiPath r1Passing through road segment 1 and road segment 4, R1By analogy, R is {1,4}, and so on2-R6Are respectively R2＝{1,3.6}，R3＝{2,6}，R4＝{1,5}，R5＝{1,3,7}， R6For {2,7}, then
Figure BDA00018274603700001211
Figure BDA00018274603700001212
Figure BDA00018274603700001213
Corresponding to CRiThe two of the raw materials are not equal to each other,
Figure BDA00018274603700001214
corresponding joint identification coefficient matrix HsThe full rank.
Preferably, in step (4.3c), UsWith path correlation matrix HcFor deleting path-road segment association matrix HrlA matrix obtained by a specific row and a specific column, a specific row set
Figure BDA00018274603700001215
The specific column is HsFull rank time RsThe column for the path in (1).
In particular, RsThe path in (A) is
Figure BDA00018274603700001216
Path r of time correspondencei。
Step (4.3d), adding each UcSet U with the largest number of middle elementsc_maxDetermining a set of road sections U as a point-of-installation monitoring devicecSet Uc_maxThe corresponding current set U is determined as a road section set U for installing continuous monitoring equipments。
As an example, in the following example, assuming that the set of installed single continuous monitoring devices obtained in step (4.2) is U ═ 1,2,3,4,6}, step (4.3) is described:
initializing Q to 5, and deleting the 1 st element 1 in the set U in sequence to obtain
Figure BDA0001827460370000131
The second element 2 is obtained
Figure BDA0001827460370000132
The third element 3 is obtained
Figure BDA0001827460370000133
The fourth element 4 is obtained
Figure BDA0001827460370000134
Element 5 to element 6
Figure BDA0001827460370000135
Judging whether the 5 sets meet preset conditions or not, and easily knowing
Figure BDA0001827460370000136
And
Figure BDA0001827460370000137
abandoning the rest sets when the preset conditions are met, and enabling the sets meeting the preset conditions
Figure BDA0001827460370000138
And
Figure BDA0001827460370000139
each is executed as a new set U, Q-1 ═ 4 (4.3 b). For U ═ {1,3,4,6}, we assume its corresponding one
Figure BDA00018274603700001310
All the deleted element road sections 2 corresponding to the current set U are recorded to form a set U corresponding to the current set U c2. For the set U ═ {2,3,4,6},
Figure BDA00018274603700001311
judging whether the 4 sets meet preset conditions or not, and assuming that
Figure BDA00018274603700001312
And (4) when the preset condition is met, executing the step (4.2 b). Suppose that a set U is obtainedc＝{1,2,4}，UcIf 1,3,4, then each U will be assignedcSet U with the largest number of middle elementsc_maxDetermining a set of road sections U as a point-of-installation monitoring devicecSet Uc_maxThe corresponding current set U is determined as a road section set U for installing continuous monitoring equipmentsEasy to know UcWhen 1,2,4, Us＝{2,6}，UcWhen 1,3,4, UsI.e., {3,6}, there are a variety of combinatorial layout methods.
Based on the scheme, when the model is established, the combination cost minimization principle, the combination layout path full coverage principle and the combination layout path distinguishing principle are relied on, so that the method provided by the embodiment of the invention solves the obtained set of the installation continuous monitoring equipment and the installation point type monitoring equipment, can minimize the combination cost under the condition of realizing the full coverage of the road network flow information, and reduces the construction and maintenance cost of the road network information acquisition system. In addition, the path flow information obtained by the method is the only flow, so that the condition that the different paths are not distinguished due to blind pursuit of full coverage can be avoided, and the economy and the technology of the traffic information acquisition system are improved.
In summary, the method provided by the invention can obtain the set of road segments for installing the continuous monitoring equipment and the installation point type monitoring equipment only by inputting the path road segment incidence matrix, and corresponding equipment is arranged on the road segments, so that the combination cost is minimized under the condition of realizing the full coverage of the road network flow information, the construction and maintenance cost of the road network information acquisition system is reduced, the path flow information obtained by the method is the unique flow, the condition that the full coverage is not required to be tracked blindly and the differentiation of different paths is lacked can be avoided, and the economy and the technology of the traffic information acquisition system are improved. The road management department can also combine the model method of the invention to supplement and optimize the monitoring road section according to the existing condition of laying monitoring equipment, thereby realizing the full coverage of road network monitoring. In addition, as can be understood by those skilled in the art, by arranging the monitoring equipment by the method, the OD flow information and the unmonitored road segment flow information can be automatically extracted by the conservation equation.
Those of ordinary skill in the art will understand that: all or part of the steps for implementing the method embodiments may be implemented by hardware related to program instructions, and the program may be stored in a computer readable storage medium, and when executed, the program performs the steps including the method embodiments; and the aforementioned storage medium includes: various media that can store program codes, such as ROM, RAM, magnetic or optical disks.
The above description is only for the specific embodiments of the present invention, but the scope of the present invention is not limited thereto, and any person skilled in the art can easily conceive of the changes or substitutions within the technical scope of the present invention, and the changes or substitutions should be covered within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.

Claims (7)

1. A road network multi-type monitoring equipment combined layout method is characterized by comprising the following steps:
step 1, establishing a road network topological relation graph according to a road network structure; the road network topological relation graph consists of intersections in a road network and road sections among the intersections, at least 1 starting point and at least 1 end point exist in the intersections of the road network, 1 starting point and 1 end point form 1 OD pair, the road sections passing through from 1 starting point to 1 end point form 1 path, and at least 1 path exists between 1 OD pair;
step 2, aiming at any path r in the road network topological relation graphiDefine Boolean variables
Figure FDA0002988056540000012
Represents a path riWhether to pass through the road section a; if path riPassing through the section a, then
Figure FDA0002988056540000013
Taking 1; if path riNot passing through the section a, then
Figure FDA0002988056540000014
Taking 0; the road section a is any road section in the road network topological relation graph;
defining a Boolean variable x for any road section a in the road network topological relation graphaIndicating whether or not a continuous monitoring device is installed on the road section a, a boolean variable y is definedaIndicating whether a point type monitoring device is installed on the road section a; wherein, when the road section a is installed with a continuous monitoring device, xaTaking 1; when the road section a is not installed with the continuous monitoring device, xaTaking 0; when the road section a is installed with a point type monitoring device, yaTaking 1; when the section a is not installed with the spot monitoring device, yaTaking 0; x is the number ofaAnd yaTaking 1 at different times;
step 3, according to the road network topological relation graph, according to a combination cost minimization principle, a combination layout path full coverage principle and a combination layout path distinguishing principle, establishing a multi-type monitoring equipment combination layout nonlinear programming model:
Figure FDA0002988056540000011
wherein, c1Cost of a single continuous monitoring device, c2The cost of the device is monitored in a single point mode; a is a set formed by all road sections in the road network topological relation graph, and R is a set formed by all paths in the road network topological relation graph; r isjAnd rkAny path in the road network topological relation graph is taken; rsTo pass through UcSet of identifiable paths, RcTo pass through UcA set of identifiable paths; u shapeSFor installing sets of road sections of continuous monitoring equipment, UcA collection of installation point type monitoring device road sections; u is the union set, n is the intersection set,
Figure FDA0002988056540000021
is an empty set; xicIs a Boolean variable and represents HcWhether full rank, HcFull rank time is 1, Hc0 when the rank is not full; hcIs UcA matrix associated with the path;
and 4, solving the nonlinear programming model of the combined layout of the multi-type monitoring equipment to obtain a road section set for installing the continuous monitoring equipment and a road section set for installing the point-type monitoring equipment.
2. The method of claim 1, wherein step 4 comprises the steps of:
(4.1) according to the road network topological relation graph, according to a layout path full-coverage principle and a layout path distinguishing principle, establishing a single continuous monitoring equipment full-coverage layout planning model:
Figure FDA0002988056540000022
(4.2) solving the single continuous monitoring equipment full-coverage layout planning model to obtain a road section set for installing single continuous monitoring equipment;
and (4.3) solving the nonlinear programming model of the combined layout of the multi-type monitoring equipment by utilizing the road section set provided with the single continuous monitoring equipment to obtain the road section set provided with the continuous monitoring equipment and the road section set provided with the installation point type monitoring equipment.
3. Method according to claim 2, characterized in that step (4.2) comprises the following sub-steps:
(4.2a) initialization: let U represent the set of road segments where a single continuous monitoring device is installed, and initialize U as an empty set; order to
Figure FDA0002988056540000023
Representing the complement of the set U in the set A;
(4.2b) calculating and inputting the path-road section incidence matrix of the road network topological relation graphHrl：
Figure FDA0002988056540000031
Wherein m represents the number of paths in the road network topological relation graph, n represents the number of road sections in the road network topological relation graph,
Figure FDA0002988056540000032
represents a path riWhether to pass the Boolean variable of the first road section, if the path riThe first road segment is passed through the first road segment,
Figure FDA0002988056540000033
taking 1; if path riInstead of passing through the first route segment,
Figure FDA0002988056540000034
taking 0; i is an element of [1,2]，l∈[1，2，...，n]；
(4.2c) associating matrix H according to the path-road sectionrlGenerating a path distinguishing matrix H-divider;
wherein the path distinguishing matrix H _ differential is a path-road section association matrix HrlThe column vectors of (1) are subtracted from each other to form a matrix
Figure FDA0002988056540000035
The path discrimination matrix
Figure FDA0002988056540000036
i. j is in {1,2, …, m } and i ≠ j, H _ differ is
Figure FDA0002988056540000037
The matrix of (a) is,
Figure FDA0002988056540000038
represents a combination number of arbitrary 2 elements from m different elements and grouped;
(4.2d) judging whether the path distinguishing matrix H _ buffer is not empty: if the path distinguishing matrix H _ difference is empty, then step 4.2f) is executed; if the path distinguishing matrix H _ buffer is not empty, then step 4.2e) is executed;
(4.2e) computing a set according to a path differentiation criterion
Figure FDA0002988056540000039
The maximum value of the Differ (U, b) is determined, any section c corresponding to the max _ Differ is added into the set U, and the b represents the set
Figure FDA00029880565400000310
Any road segment in (1); eliminating the row of which the element on the row corresponding to the road section c in the path distinguishing matrix H _ differential is 1 to obtain a matrix H _ differential ', and turning to the step (4.2d) to make H _ differential be H _ differential';
wherein Differ (U, b) represents the total number of paths that can be uniquely determined additionally when a section b is additionally added in a section set U where a single continuous monitoring device is installed;
(4.2f) reacting Hrl′＝HrlElimination of Hrl' the row element corresponding to all the road sections in the set U is a column of 1;
(4.2g) judgment matrix Hrl' if it is not null, if matrix HrlIf' is empty, then step (4.2i) is performed; if the matrix HrlIf not, then step (4.2h) is performed;
(4.2h) computing the sets according to the path coverage criterion
Figure FDA0002988056540000041
Determining the maximum value max _ Cover corresponding to the Cover (U, d) corresponding to each road section, adding any road section e corresponding to the max _ Cover into the set U, wherein d represents any road section in the set; elimination of Hrl' column with element 1 on line corresponding to middle road section e, and go to step (4.2 g);
wherein Cover (U, d) represents the sum of the number of paths that can be additionally covered when a road segment d is additionally added in a road segment set U in which a single continuous monitoring device is installed;
(4.2i) outputting a set of road segments U in which a single continuous monitoring device is installed.
4. Method according to claim 2, characterized in that step (4.3) comprises the following sub-steps:
(4.3b) deleting the p-th element a in the set U in sequencepTo obtain a corresponding set
Figure FDA0002988056540000046
p is taken as all integers from 1 to Q;
judging all Q sets
Figure FDA0002988056540000042
Whether each set meets a preset condition is that a joint identification coefficient matrix H corresponding to the set meets the preset conditionsAnd said UcWith path correlation matrix HcThe average rank is full;
if the Q sets are
Figure FDA0002988056540000043
If the partial sets meet the preset condition, Q sets are discarded
Figure FDA0002988056540000044
Does not meet the set of preset conditions, and goes to step (4.3 c);
if the Q sets are
Figure FDA0002988056540000045
If the preset conditions are not met, the step (4.3d) is carried out;
step (4.3c), for said Q sets
Figure FDA0002988056540000051
In any set satisfying a predetermined condition
Figure FDA0002988056540000052
Each satisfying a predetermined condition
Figure FDA0002988056540000053
The sets are respectively used as new sets U, Q is reduced by 1, and the step (4.3b) is repeatedly executed until the Q sets
Figure FDA0002988056540000054
All the Q sets do not meet the preset condition, and the Q sets are recorded simultaneously
Figure FDA0002988056540000055
When the current set U does not meet the preset condition, the deleted elements corresponding to the current set U form a set U corresponding to the current set Uc；
Step (4.3d), adding each UcSet U with the largest number of middle elementsc_maxDetermining a set of road sections U as a point-of-installation monitoring devicecSet Uc_maxThe corresponding current set U is determined as a road section set U for installing continuous monitoring equipments。
5. The method according to claim 4, wherein in step (4.3c), the joint coefficient identification matrix H is determined by a scanogram methodsWhether the rank is full;
the scanning graph method specifically comprises the following steps: defining a path riThe set of passing road sections a is RiFor any path riDefinition of
Figure FDA0002988056540000056
For any two paths ri、rjJudgment of
Figure FDA0002988056540000057
Whether or not: if not, then the
Figure FDA0002988056540000058
Corresponding joint identification coefficient matrix HsA not full rank; if so, then the
Figure FDA0002988056540000059
Corresponding joint identification coefficient matrix HsThe full rank.
6. The method according to claim 4, wherein in step (4.3c), the U issWith path correlation matrix HcFor deleting the path-section association matrix HrlA matrix derived from a specific row and a specific column of (a), the specific row being a set of
Figure FDA00029880565400000510
The specific column is HsFull rank time RsThe column for the path in (1).
7. The method of claim 6, wherein R issThe path in (A) is
Figure FDA00029880565400000511
Path r of time correspondencei。
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