CN109299813B - Method for calculating shortest path length of public transport network under minimum transfer - Google Patents

Method for calculating shortest path length of public transport network under minimum transfer Download PDF

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CN109299813B
CN109299813B CN201810998771.2A CN201810998771A CN109299813B CN 109299813 B CN109299813 B CN 109299813B CN 201810998771 A CN201810998771 A CN 201810998771A CN 109299813 B CN109299813 B CN 109299813B
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洪流
欧阳敏
钟欣
田辉
徐敏
刘创
章慧
叶博文
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Huazhong University of Science and Technology
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Abstract

The invention discloses a method for calculating the shortest path length of a public transport network under the condition of least transfer, which comprises the following steps: using a first adjacency matrix Tk×kAnd a second adjacency matrix Hk×kRespectively recording the minimum reachable lap number and the corresponding shortest path length between the sites, and initializing a first adjacency matrix Tk×kAnd a second adjacency matrix Hk×kTo do so by
Figure DDA0001778720450000011
And
Figure DDA0001778720450000012
representing a first adjacency matrix Tk×kAnd a second adjacency matrix Hk×kIn the initial state of the mobile terminal,
Figure DDA0001778720450000013
and
Figure DDA0001778720450000014
matrix element in (1)
Figure DDA0001778720450000015
And
Figure DDA0001778720450000016
setting to be + ∞; by using
Figure DDA0001778720450000017
And
Figure DDA0001778720450000018
matrix element in (1)
Figure DDA0001778720450000019
And
Figure DDA00017787204500000110
updating a matrix
Figure DDA00017787204500000111
And
Figure DDA00017787204500000112
to
Figure DDA00017787204500000113
And
Figure DDA00017787204500000114
iteration matrix
Figure DDA00017787204500000115
And
Figure DDA00017787204500000116
to
Figure DDA00017787204500000117
And
Figure DDA00017787204500000118
m is more than or equal to 2; further increasing the number of transfers does not change the second adjacency matrix H any morek×kLet us order
Figure DDA00017787204500000119
At this time, the second adjacency matrix Hk×kThe shortest path length of any two stations in the public transport network under the minimum transfer times is included. The invention iterates the adjacency matrix under the consideration of the minimum transfer times, thereby obtaining the shortest path length under the minimum transfer times.

Description

Method for calculating shortest path length of public transport network under minimum transfer
Technical Field
The invention belongs to the field of public transportation, and particularly relates to a method for calculating the shortest path length of a public transportation network under the condition of minimum transfer.
Background
The public transportation system is an engineering facility for providing transportation service for resident trip and social material transportation, and plays a vital role in the economic development of the country or region and the life of people. In the planning and scheduling process of the public transportation system, the shortest path between stations is one of the factors to be considered. In the public transportation network, transfer has an important influence on the measurement of the path length, different transfer modes are usually corresponding to different path lengths, people generally prefer to reach a destination under a small number of transfer times, but the influence of the transfer on the path length is mostly ignored in the current calculation of the shortest path length of the public transportation network.
Disclosure of Invention
In view of the above drawbacks or needs for improvement in the prior art, the present invention provides a method for calculating a shortest path length of a public transportation network with minimal transfer, thereby solving the technical problem in the prior art that the influence of transfer on the path length is not considered.
In order to achieve the above object, the present invention provides a method for calculating a shortest path length of a public transportation network under minimum transfer, comprising:
(1) using a first adjacency matrix Tk×kAnd a second adjacency matrix Hk×kRespectively recording the minimum reachable lap number and the corresponding shortest path length between sites, and a first adjacent matrix Tk×kFirst element t of (1)i，jRepresenting a site niAnd njThe minimum number of reachable laps in between, (t)i，j-1) represents a site niAnd njMinimum transfer betweenDegree of second adjacency matrix Hk×kThe second element h in (1)i，jRepresenting a site niAnd njThe shortest path length under the minimum transfer between the stations, k represents the number of public transportation stations, i belongs to [1, k ]]，j∈[1，k]；
(2) Initializing a first adjacency matrix Tk×kAnd a second adjacency matrix Hk×kTo do so by
Figure BDA0001778720430000021
And
Figure BDA0001778720430000022
representing a first adjacency matrix Tk×kAnd a second adjacency matrix Hk×kIn the initial state of the mobile terminal,
Figure BDA0001778720430000023
and
Figure BDA0001778720430000024
matrix element in (1)
Figure BDA0001778720430000025
And
Figure BDA0001778720430000026
setting to be + ∞;
(3) by using
Figure BDA0001778720430000027
And
Figure BDA0001778720430000028
matrix element in (1)
Figure BDA0001778720430000029
And
Figure BDA00017787204300000210
updating a matrix
Figure BDA00017787204300000211
And
Figure BDA00017787204300000212
to
Figure BDA00017787204300000213
And
Figure BDA00017787204300000214
(4) based on
Figure BDA00017787204300000215
And
Figure BDA00017787204300000216
iteration matrix
Figure BDA00017787204300000217
And
Figure BDA00017787204300000218
to
Figure BDA00017787204300000219
And
Figure BDA00017787204300000220
m≥2；
(5) repeating the step (4) until
Figure BDA00017787204300000221
I.e. further increasing the number of transfers does not change the second adjacency matrix H any morek×kLet us order
Figure BDA00017787204300000222
At this time, the second adjacency matrix Hk×kThe shortest path length of any two stations in the public transport network under the minimum transfer times is included.
Further, the step (3) comprises:
if n isiAnd njTwo stations on a public transport line, i ≠ j, then
Figure BDA00017787204300000223
Element (1) of
Figure BDA00017787204300000224
For matrix
Figure BDA00017787204300000225
If the shortest travel distance between the stations is obtained, then
Figure BDA00017787204300000226
Element (1) of
Figure BDA00017787204300000227
If the shortest travel time between the stations is obtained, then
Figure BDA00017787204300000228
Where v and Δ represent the average traveling speed and average waiting time of the public transportation means, Dis (n), respectivelyi，nj) Representing a site niTo njIf n is a running distance ofiAnd njNot two stations on a public transport line, then
Figure BDA00017787204300000229
Element (1) of
Figure BDA00017787204300000230
Figure BDA00017787204300000231
Element (1) of
Figure BDA00017787204300000232
Further, the step (4) comprises:
(4-1) for site niAnd njIf, if
Figure BDA00017787204300000233
Element (1) of
Figure BDA00017787204300000234
Then
Figure BDA00017787204300000235
Element (1) of
Figure BDA00017787204300000236
Figure BDA00017787204300000237
Element (1) of
Figure BDA00017787204300000238
(4-2) if
Figure BDA00017787204300000239
Selecting a site nxAs niAnd njTransfer station between, where x ≠ i ≠ j, calculation
Figure BDA00017787204300000240
A value of (d);
(4-3) removing niAnd njRepeating the step (4-2) for all public transportation stations except the public transportation station, and performing the step for all transfer stations nxIs selected to make
Figure BDA0001778720430000031
N of minimum valuexAs a transfer station, the transfer station is,
Figure BDA0001778720430000032
Figure BDA0001778720430000033
if it is not
Figure BDA0001778720430000034
Then
Figure BDA0001778720430000035
If there is only one site nxMake it
Figure BDA0001778720430000036
The value is minimum, then the station nxAs transfer stations, and
Figure BDA0001778720430000037
Figure BDA0001778720430000038
if there are multiple sites nxMake it
Figure BDA0001778720430000039
The smallest value, then
Figure BDA00017787204300000310
And select
Figure BDA00017787204300000311
Corresponding site n when value of (d) is minimumxAs transfer stations.
In general, compared with the prior art, the above technical solution contemplated by the present invention can achieve the following beneficial effects:
(1) the invention introduces the adjacency matrix, iterates the adjacency matrix under the consideration of the minimum transfer times, considers the influence of transfer on the shortest path, and further obtains the shortest path length under the minimum transfer times. The shortest path obtained by the method is more accurate in length and stronger in reliability.
(2) The invention can finally obtain the shortest path length between any two stations in the public transport network under the minimum transfer times, including the shortest travel distance and the shortest travel time.
Drawings
Fig. 1 is a flowchart of a method for calculating a shortest path length of a public transportation network under minimal transfer according to an embodiment of the present invention;
fig. 2 is a schematic diagram of a public transportation network provided by an embodiment of the invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
As shown in fig. 1, a method for calculating shortest path length of public transportation network under minimum transfer includes:
(1) using a first adjacency matrix Tk×kAnd a second adjacency matrix Hk×kRespectively recording the minimum reachable lap number and the corresponding shortest path length between sites, and a first adjacent matrix Tk×kFirst element t of (1)i，jRepresenting a site niAnd njThe minimum number of reachable laps in between, (t)i，j-1) represents a site niAnd njThe minimum number of transitions between, the second adjacency matrix Hk×kThe second element h in (1)i，jRepresenting a site niAnd njThe shortest path length under the minimum transfer between the stations, k represents the number of public transportation stations, i belongs to [1, k ]]，j∈[1，k]；
(2) Initializing a first adjacency matrix Tk×kAnd a second adjacency matrix Hk×kTo do so by
Figure BDA0001778720430000041
And
Figure BDA0001778720430000042
representing a first adjacency matrix Tk×kAnd a second adjacency matrix Hk×kIn the initial state of the mobile terminal,
Figure BDA0001778720430000043
and
Figure BDA0001778720430000044
matrix element in (1)
Figure BDA0001778720430000045
And
Figure BDA0001778720430000046
setting to be + ∞;
(3) by using
Figure BDA0001778720430000047
And
Figure BDA0001778720430000048
matrix element in (1)
Figure BDA0001778720430000049
And
Figure BDA00017787204300000410
updating a matrix
Figure BDA00017787204300000411
And
Figure BDA00017787204300000412
to
Figure BDA00017787204300000413
And
Figure BDA00017787204300000414
(4) based on
Figure BDA00017787204300000415
And
Figure BDA00017787204300000416
iteration matrix
Figure BDA00017787204300000417
And
Figure BDA00017787204300000418
to
Figure BDA00017787204300000419
And
Figure BDA00017787204300000420
m≥2；
(5) repeating the step (4) until
Figure BDA00017787204300000421
I.e. further increasing the number of transfers does not change the second adjacency matrix H any morek×kLet us order
Figure BDA00017787204300000422
At this time, the second adjacency matrix Hk×kThe shortest path length of any two stations in the public transport network under the minimum transfer times is included.
Further, the step (3) comprises:
if n isiAnd njTwo stations on a public transport line, i ≠ j, then
Figure BDA00017787204300000423
Element (1) of
Figure BDA00017787204300000424
For matrix
Figure BDA00017787204300000425
If the shortest travel distance between the stations is obtained, then
Figure BDA00017787204300000426
Element (1) of
Figure BDA00017787204300000427
If the shortest travel time between the stations is obtained, then
Figure BDA00017787204300000428
Where v and Δ represent the average traveling speed and average waiting time of the public transportation means, Dis (n), respectivelyi，nj) Representing a site niTo njIf n is a running distance ofiAnd njNot two stations on a public transport line, then
Figure BDA00017787204300000429
Element (1) of
Figure BDA00017787204300000430
Figure BDA00017787204300000431
Element (1) of
Figure BDA00017787204300000432
Further, the step (4) comprises:
(4-1) for site niAnd njIf, if
Figure BDA00017787204300000433
Element (1) of
Figure BDA00017787204300000434
Then
Figure BDA00017787204300000435
Element (1) of
Figure BDA0001778720430000051
Figure BDA0001778720430000052
Element (1) of
Figure BDA0001778720430000053
(4-2) if
Figure BDA0001778720430000054
Selecting a site nxAs niAnd njTransfer station between, where x ≠ i ≠ j, calculation
Figure BDA0001778720430000055
A value of (d);
(4-3) removing niAnd njPlaces other than the aboveWith the step (4-2) repeated for all transfer stations nxIs selected to make
Figure BDA0001778720430000056
N of minimum valuexAs a transfer station, the transfer station is,
Figure BDA0001778720430000057
Figure BDA0001778720430000058
if it is not
Figure BDA0001778720430000059
Then
Figure BDA00017787204300000510
If there is only one site nxMake it
Figure BDA00017787204300000511
The value is minimum, then the station nxAs transfer stations, and
Figure BDA00017787204300000512
Figure BDA00017787204300000513
if there are multiple sites nxMake it
Figure BDA00017787204300000514
The smallest value, then
Figure BDA00017787204300000515
And select
Figure BDA00017787204300000516
Corresponding site n when value of (d) is minimumxAs transfer stations.
As shown in fig. 2, assuming that the public transportation network has 7 public transportation stations, there are three public transportation lines: lines 1(1-2-3-4), lines 2(1-2-5-3) and lines 3(6-4-7), the distances between adjacent stations being as shown in fig. 2. Based on the iteration process of the matrixes T and H, the shortest path length of any two stations of the public transportation network under the minimum transfer times can be obtained through three iterations, and the shortest travel distance under the minimum transfer times is taken as an example, and the specific calculation result is as follows:
Figure BDA00017787204300000517
the method for calculating the shortest path length of the public transport network under the minimum transfer times can calculate the shortest path length between any two stations in the public transport network under the condition of considering the minimum transfer, wherein the shortest path length comprises the shortest travel distance and the shortest travel time.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.

Claims (1)

1. A method for calculating the shortest path length of a public transport network under the condition of minimum transfer is characterized by comprising the following steps:
(1) using a first adjacency matrix Tk×kAnd a second adjacency matrix Hk×kRespectively recording the minimum reachable lap number and the corresponding shortest path length between sites, and a first adjacent matrix Tk×kFirst element t of (1)i，jRepresenting a site niAnd njThe minimum number of reachable laps in between, (t)i，j-1) represents a site niAnd njThe minimum number of transitions between, the second adjacency matrix Hk×kThe second element h in (1)i，jRepresenting a site niAnd njThe shortest path length under the minimum transfer between the stations, k represents the number of public transportation stations, i belongs to [1, k ]]，j∈[1,k]；
(2) Initializing a first adjacency matrix Tk×kAnd a second adjacency matrix Hk×kTo do so by
Figure FDA0003247914910000011
And
Figure FDA0003247914910000012
representing a first adjacency matrix Tk×kAnd a second adjacency matrix Hk×kIn the initial state of the mobile terminal,
Figure FDA0003247914910000013
and
Figure FDA0003247914910000014
matrix element in (1)
Figure FDA0003247914910000015
And
Figure FDA0003247914910000016
setting to be + ∞;
(3) by using
Figure FDA0003247914910000017
And
Figure FDA0003247914910000018
matrix element in (1)
Figure FDA0003247914910000019
And
Figure FDA00032479149100000110
updating a matrix
Figure FDA00032479149100000111
And
Figure FDA00032479149100000112
to
Figure FDA00032479149100000113
And
Figure FDA00032479149100000114
(4) based on
Figure FDA00032479149100000115
And
Figure FDA00032479149100000116
iteration matrix
Figure FDA00032479149100000117
And
Figure FDA00032479149100000118
to
Figure FDA00032479149100000119
And
Figure FDA00032479149100000120
(5) repeating the step (4) until
Figure FDA00032479149100000121
I.e. further increasing the number of transfers does not change the second adjacency matrix H any morek×kLet us order
Figure FDA00032479149100000122
At this time, the second adjacency matrix Hk×kThe shortest path length of any two stations in the public transport network under the minimum transfer times is included;
the step (3) comprises the following steps:
if n isiAnd njTwo stations on a public transport line, i ≠ j, then
Figure FDA00032479149100000123
Element (1) of
Figure FDA00032479149100000124
For matrix
Figure FDA00032479149100000125
If the shortest travel distance between the stations is obtained, then
Figure FDA00032479149100000126
Element (1) of
Figure FDA00032479149100000127
If the shortest travel time between the stations is obtained, then
Figure FDA00032479149100000128
Where v and Δ represent the average traveling speed and average waiting time of the public transportation means, Dis (n), respectivelyi，nj) Representing a site niTo njIf n is a running distance ofiAnd njNot two stations on a public transport line, then
Figure FDA0003247914910000021
Element (1) of
Figure FDA0003247914910000022
Figure FDA0003247914910000023
Element (1) of
Figure FDA0003247914910000024
The step (4) comprises the following steps:
(4-1) for site niAnd njIf, if
Figure FDA0003247914910000025
Element (1) of
Figure FDA0003247914910000026
Then
Figure FDA0003247914910000027
Element (1) of
Figure FDA0003247914910000028
Figure FDA0003247914910000029
Element (1) of
Figure FDA00032479149100000210
(4-2) if
Figure FDA00032479149100000211
Selecting a site nxAs niAnd njTransfer station between, where x ≠ i ≠ j, calculation
Figure FDA00032479149100000212
A value of (d);
(4-3) removing niAnd njRepeating the step (4-2) for all public transportation stations except the public transportation station, and performing the step for all transfer stations nxIs selected to make
Figure FDA00032479149100000213
N of minimum valuexAs a transfer station, the transfer station is,
Figure FDA00032479149100000214
Figure FDA00032479149100000215
if it is not
Figure FDA00032479149100000216
Then
Figure FDA00032479149100000217
If there is only one site nxMake it
Figure FDA00032479149100000218
The value is minimum, then the station nxAs transfer stations, and
Figure FDA00032479149100000219
Figure FDA00032479149100000220
if there are multiple sites nxMake it
Figure FDA00032479149100000221
The smallest value, then
Figure FDA00032479149100000222
And select
Figure FDA00032479149100000223
Corresponding site n when value of (d) is minimumxAs transfer stations.
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CN105206037A (en) * 2014-05-30 2015-12-30 中国电信股份有限公司 Bus route analysis method and system
CN106779225A (en) * 2016-12-22 2017-05-31 福州大学 A kind of optimal path method for solving comprising Dominator collection
CN107808217A (en) * 2017-10-24 2018-03-16 山东大学 A kind of Public Transport Transfer optimization method based on Big Dipper positioning with the volume of the flow of passengers

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