CN106651010A - Shortest path-based network division method - Google Patents
Shortest path-based network division method Download PDFInfo
- Publication number
- CN106651010A CN106651010A CN201611048460.7A CN201611048460A CN106651010A CN 106651010 A CN106651010 A CN 106651010A CN 201611048460 A CN201611048460 A CN 201611048460A CN 106651010 A CN106651010 A CN 106651010A
- Authority
- CN
- China
- Prior art keywords
- gauze
- voronoi
- point
- shortest path
- network
- 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.)
- Granted
Links
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
- G06Q10/00—Administration; Management
- G06Q10/04—Forecasting or optimisation specially adapted for administrative or management purposes, e.g. linear programming or "cutting stock problem"
- G06Q10/047—Optimisation of routes or paths, e.g. travelling salesman problem
Abstract
The present invention relates to an undirected connected network shortest path-based network division method. The objective of the invention is to solve practical problems. When a Voronoi diagram is generated on the network, the L2 Euclidean distance is replaced by a shortest path in connected lines between nodes along the network. According to the undirected connected network shortest path-based network division method, after a group of randomly distributed seed points are provided, Voronoi units on the current network are calculated based on the shortest path; a Voronoi diagram in the Euclidean space is generalized into the Voronoi diagram in the connected network through a CVT (centroidal Voronoi tessellation) algorithm; and iteration is performed, the weighting length of the network corresponding to each seed point on the network is made to be identical as much as possible, and therefore, the optimal division of the network model is obtained. With the method of the invention adopted, problems in the distribution of public infrastructure such as gas stations, charging stations and sanitation facilities, and the distribution of logistics warehouse nodes on urban road can be solved.
Description
Technical field
The present invention relates to a kind of gauze division methods based on shortest path.
Background technology
It is an important mathematical problem that the point set how being based in given plane carries out the division of plane, and it is in communication section
The key areas such as point optimization, logistics distribution, urban planning suffer from important practical value.Plane is carried out by Voronoi diagram
Division be most commonly seen form.Voronoi diagram is a kind of mathematically critically important geometry, in physics, chemistry, life
Many fields such as thing, engineering are all widely used as important abstract model method for expressing.In given plane from
Scatterplot collection P, wherein each point are referred to as seed point, and one division unit of correspondence.If any point is to this seed in division unit
Less than the distance to other seed points, we claim the plane to be divided into Voronoi subdivisions to point distance, and corresponding division unit just claims
For Voronoi units (Voronoi Cell), 1850, Dirichlet 2 peacekeeping 3-dimensionals used in the quadratic form research
Voronoi diagram.1908, Georgy Voronoy defined and have studied the Voronoi diagram problem of general n dimension space.In order to seek
Optimum space division result is sought, Voronoi diagram can be first calculated, then constantly by the geometric center of gravity of Voronoi units, is made
For new seed point, Voronoi diagram is recalculated, by continuous iteration, so that it may the phase so that area of Voronoi units is tried one's best
Deng.Here it is center of gravity Voronoi subdivision (abbreviation CVT).The fast algorithm of the Wang Wen equality research CVT of Hong Kong University and it is based on
The acceleration of GPU, the Wang Xiao CVT problems that have studied on triangle gridding such as peaceful.
In actual applications, such as when being distributed electric motorcar charging station in city, typically may require that covering for each charging station
The area in the region of lid is as far as possible equal, and this just can be solved with the CVT methods of Voronoi diagram.But in the city of reality, charge
Standing can only be distributed on kerbside, and electric automobile also can only be travelled on street, therefore can not be with traditional employing Euclidean distance
The method for calculating Voronoi diagram is divided to plane.But need to consider real road situation, the partition problem of plane is turned
Turn to the partition problem on road network.And in view of practical situations such as congestions, we cover without requiring each seed point
Geometric areas area equation, and total weighting equal length of the road that each seed point is covered should be required.Therefore we
Propose the optimized Voronoi partition problems on a kind of undirected connection gauze.
The content of the invention
This method focuses on the optimal dividing problem on undirected connection gauze.Give first the description of wire mesh models with
Definition.Towards need solve practical problem, this method carry out wire mesh models Voronoi diagram generate when, with gauze two
The shortest path distance for connecting route between point along between node on gauze instead of L2 Euclidean distances, therefore line considered here
Net space does not have the property of convex space.This method based on it is undirected connection gauze on shortest path first, be given one group it is random
After the seed point of distribution, the Voronoi units calculated based on shortest path are calculated on current gauze；Again by Euclidean space
Voronoi diagram CVT algorithms be generalized to it is undirected connection gauze on Voronoi diagram on, by iteration so that each on gauze
The weighting length of the gauze corresponding to seed point is as far as possible equal, so as to the optimization for having obtained the wire mesh models is divided.The method
Can be with distribution, the logistic storage section of public infrastructure on effectively solving urban road (gas station, charging station, sanitary installation) etc.
The problems such as point distribution.
Description of the drawings
With reference to the accompanying drawings and detailed description the present invention is further detailed explanation:
Fig. 1 is the Voronoi diagram definition in wire mesh models and gauze.Wherein (a) gauze；Voronoi diagram on (b) gauze,
S1, s2, s3 represent respectively three seed points, and respective color identifies the corresponding Voronoi units of each seed point.
Fig. 2 is Voronoi unit computational methods step schematic diagrams on gauze.
Fig. 3 is application schematic diagram.Wherein comprising main within urban area of Beijing main traffic satellite mapping (a upper left side) and six rings
(upper right, black side's point is road junction to the connection of traffic route, and straight line is gauze connection.A kind of initial charge
Stand setting (in), and convergence result of the context of methods after 35 iteration (under).
Specific embodiment
Wire mesh models are defined：
Wire mesh models illustrate one group of annexation between summit and summit, have widely at aspects such as path plannings
Using.We define N-dimensional gauze G=(V, E) spatially, such as shown in Fig. 1 (a).Wherein vertex set is：
Line set is：
In one have limit for length full curve γijWith viAnd vjEnd points and without
It is also typically each edge (the v of gauze in shortest route problemi,vj) ∈ E imparting weights wi,j.From vertex viArrive
vjThe weight sum on the side sequentially passed through on path claims the weight in the path.From vertex viTo vjPath with minimal weight claims
For vertex viTo vjShortest path, corresponding weight is referred to as vertex viTo vjBeeline, be designated as di,j.If in vertex set
There is path between any two points, then claim gauze to be connection, otherwise gauze is unconnected.If while be it is directive, i.e.,
(vi,vj) and (vj,vi) representing different directed edges, then gauze is called oriented gauze, is otherwise undirected gauze.For undirected line
Net, it is believed that (vi,vj) and (vj,vi) represent identical side and have wi,j=wj,i。
Voronoi diagram on gauze
This method considers the Voronoi diagram problem on undirected connection gauze, defines the line in N-dimensional connection gauze G=(V, E)
Net space ΩGFor:
In curve γijUpper and (vi,vj)∈E}. (3)
Note dG(p1,p2) it is gauze space ΩGUpper 2 points p1,p2Between distance metric, w (p1,p2) for 2 points on same curves
p1,p2Between weight.Given ΩGOn discrete point setPoint skCorresponding Voronoi unitsIt is defined as：
ClaimFor gauze space ΩGA Voronoi divide.Fig. 1 (b) illustrates three kinds on a gauze
The Voronoi units that son point determines.
The center of gravity of gauze
For the Voronoi subdivisions on gauze, we also are intended to " area " of each Voronoi unit --- weight it
With --- it is as far as possible equal, such as in actual applications, it is intended that charging station is equably set so that each electric automobile arrives it
Time needed for nearest charging station is as far as possible equal；For another example, it is intended that refuse receptacle is put in park so that each visitor arrives
It is as far as possible equal that the refuse receptacle of its nearest neighbours walks distance.
For this purpose, undirected connection gauze G=(V, E) is given, and gauze space ΩGOn probability density function ρ, for giving
M fixed seed pointCorresponding Voronoi subdivisionsWe define " the weight of each Voronoi unit
The heart " is
Wherein, EkFor subnet GkLine set.
The computational methods of the Voronoi diagram subdivision on undirected connection Weight gauze
Give undirected connection gauze G=(V, E), weight W and gauze space ΩGOn m seed point
Voronoi subdivisions on gauze G, seek to calculate the corresponding Voronoi units of each seed pointCalculate undirected company
Voronoi diagram on logical gauze it is critical only that the length for calculating shortest path between any two points in gauze, that is, define online
Net spaceThe distance of upper any two points.For this purpose, we are first considered seed point setAddition gauze G=(V,
E), and update obtain gauze GS=(VS,ES) and corresponding weight WS, then calculate gauze GSShortest path path length between upper summit
Degree.Next, it is possible to calculate GS=(VS,ES) in the affiliated Voronoi units in summit and side cut-point.Finally according to point
Cutpoint forms the Voronoi subdivisions on gauze.Concrete grammar is as follows：
(1) by seed point setGauze G=(V, E) is added, and renewal obtains gauze GS=(VS,ES) and
Corresponding weight WS：Each point s in S, it is assumed that s places side is (vI,vj), then have：
ES=ES∪{(s,vi),(s,vj)}\{(vi,vj)},WS(s,vi)=w (s, vi) (6)
WS(s,vj)=w (s, vj),WS(vi,vj)=+ ∞, WS(s, s)=0 (7)
(2) new shortest path is obtained.This method only considers that non-negative right connects the situation of gauze.For non-negative right connection
Gauze, we travel through each summit of gauze, and the summit is calculated to the shortest path on remaining summit using dijkstra's algorithm, obtain
Shortest path between any two summit.
(3) Voronoi diagram is calculated：
Give undirected connection gauze G=(V, E), Voronoi seed point setsPoint set S is calculated with regard to gauze
Space ΩGOne Voronoi is dividedIt is in gauze GS=(Vs,Es) and its gauze spaceUpper determination VsIn each
Voronoi units belonging to summit, and each edge EsOn point belonging to Voronoi units.
3.1 calculate VsThe affiliated Voronoi units on middle summit
DefinitionFor gauze spaceTo the mapping of the subset of Voronoi seed point set S, gauze is represented
SpaceIn each point and affiliated Voronoi units seed point set corresponding relation.
Due to VsIn point be divided into two parts --- the vertex set V and Voronoi seed point set S in gauze G.ForVor (s)={ s }；ForHave,
3.2 calculate EsThe affiliated Voronoi units put on middle side
Should if an end points of a line is passed through to the shortest path of the seed point of its affiliated Voronoi unit
Side, then any point belongs to the Voronoi units on the side.Otherwise, the Voronoi that the point on the side may belong to different is mono-
Unit.So adopting judge with the following method which Voronoi unit it belongs to：
If (vi,vj)∈ES, note
Sij=Vor (vi)∩Vor(vj), (9)
diFor viTo Vor (vi) in seed point distance, djFor vjTo Vor (vj) in seed point distance,
If (i) | di-dj|=wi,j, then to curve γijUpper any point p (does not contain end points vi,vj), have
Vor (p)=Sij (10)
(ii) if | di-dj|≠wi,j, curve γijUpper existence anduniquess cut-point pcSo that Vor (pc)=Vor (vi)∪Vor
(vj), and curve γijUpper pcTo end points viWeight be：
w(pc,vi)=(wi,j+dj-di)/2。 (11)
The proof of the formula of the above two is as follows：
Prove：First prove (i).Without loss of generality, it is assumed that
dj=di+wi,j。 (12)
It is rightObviously haveThen have
Due to djFor vertex vjTo the minimum range of all seed points, then there are s ' ∈ Vor (vj), i.e.,
Then have,
Sij=Vor (vi)。 (15)
According to (13), from the subpath property of shortest path, from vjShortest path to s ' is through side (vi,vj).By
Shortest path property is known, to curve γijUpper any point p (does not contain end points vi,vj), p belongs to s ' places Voronoi units, then
Have
ConsiderAnd curve γijUpper any point p (does not contain end points vi,vj), Wo Menyou
Known by shortest path property again
Known by (12) again
Had by (17)～(20),
Known by (21), it is rightHave
Known by closure again,
Just there is Vor (p)=S by (15) (16) (22) (23)ij.I () must be demonstrate,proved.
Prove again (ii).Without loss of generality, it is assumed that di<dj, then must have
dj<di+wi,j。 (24)
Otherwise, if dj>di+wi,j, then we are vjTo finding the shorter path of bar between seed point, this and known djIt is vjArrive
The beeline contradiction of seed point.For curve γijUpper any point p, is known by closure,
As shown in Figure 2, it is considered tok≠l.Without loss of generality, it is assumed that
Then p to skShortest path must first be directly over end points viS is reached againk.If not, p to skShortest path elder generation Jing
Cross end points vjS is reached againk, have
Again by djIt is vjBeeline to seed point knows,
From the definition of (27) (28) and shortest path,
This and (26) contradiction.Now, from (25) (26) formula,
Known by (25) (30) and now have
Vor (p)=Vor (vi)。 (31)
Due to curve γijIt is continuous curve, point p is from an end points to another end points consecutive variations process on curve
In, the minimum range of p to all seed points also consecutive variations.Known by (24) again, the minimum range elder generation monotonic increase again pass by dullness
Subtract.Then curve γijUpper existence anduniquess cut-point pc, and have at the cut-point
Just known by (31) (32) again,
Vor(pc)=Vor (vi)∪Vor(vj)。 (33)
Due to now pcTo skShortest path through end points vi, then have
In the same manner, have
And due to
wi,j=w (pc,vi)+w(pc,vj), (36)
(34)～(36) substitution (32) are just obtained (11).
Card is finished
To EsIn any bar side (vi,vj), the side can determine whether with the presence or absence of cut-point according to above method, if existing
Cut-point, (11) formula gives the position of cut-point.The all such boundary segmentation point sets of note are combined into C.
From the definition and the definition of Voronoi units on gauze of Vor,
ConsiderThe subnet G that summit and cut-point in unit is constitutedk=(Vk,Ek), then have
This explanation, gauze spaceOn Voronoi divideCorrespond to gauze GSOne division
(4) the center of gravity Voronoi subdivision of given area is finally solved using the iterative manner in Lloyd algorithms, it leads to
Cross and constantly iteratively build Voronoi subdivisions and update seed point location.Given seed point number m, region Ω, and be defined on
Probability density function ρ on Ω, main process is as follows:
1) m initial seed point is selected at random
2) according to seed pointCalculate the Voronoi subdivisions with regard to region Ω
3) calculation procedure 2) in each Voronoi unitCenter of gravity, obtain new seed point set
If 4) new seed point collection meets given convergence criterion (generally uses new point set flat with previous step point set
Distance whether less than the method for given threshold value judging, the threshold value can be set to 0.1 times of unit length), then algorithm terminates, no
Then, execution step 2.
This iterative manner proves there is local convergence by Kieffer et al..Voronoi obtained by so is cutd open
Point, be exactly the wire mesh models in given point set as the optimal dividing in the case of seed point.
Method application
As electric automobile becomes the selection of more and more people, to the demand of electric automobile charging station also day in urban transportation
Benefit increases, and how to plan the position of charging station so that user can as early as possible find charging station nearby and improve each charging station
Utilization rate become designer need consider problem.Here by taking the main traffic road within the ring of Beijing six as an example, utilize
How this method demonstration determines 50 charging station locations.Show in Fig. 3 and generated by the road connection on the map of Beijing
Gauze (1034 summits, 1801 sides, side right weight is the length of corresponding road) and place 50 charging stations final optimization pass
As a result.By the application verification, this method can be uniformly distributed problem with the node on effectively solving road network.
Claims (4)
1. a kind of division methods based on shortest path.It is characterized in that the method comprises the steps:
A) by the data of actual scene, such as road is expressed as undirected connection gauze, and the factors such as road congestion conditions is abstract
For the weight on side in wire mesh models；
B) give seed point set, using point set as new node wire mesh models added, update the vertex set of gauze, line set and
Its weight；
C) method by calculating cut-point on shortest path and side, obtains the gauze Voronoi based on current point and divides；
D) center of gravity of current each Voronoi unit is calculated, and seed point is moved to position of centre of gravity, calculate new Voronoi
Divide；
E) c and Step d are repeated, until the convergence of seed point set position.
2. method according to claim 1, it is characterised in that：May finally search out based on the gauze the most in a balanced way of the point set
Divide so that each point is minimum apart from summation to final seed point location on gauze.
3. method and step c according to claim 1, it is characterised in that：Summit on calculating gauze is only needed (to include original vertices and kind
Sub- point) and side on cut-point Voronoi units, and according to cut-point constitute gauze Voronoi divide.
4. method and step c and d according to claim 1, it is characterised in that：Voronoi divisions and center of gravity calculation on gauze etc.
Series of steps, different from plane divide, need to carry out redefining based on the shortest path distance in wire mesh models with
Calculate.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611048460.7A CN106651010B (en) | 2016-11-22 | 2016-11-22 | Shortest path-based wire network dividing method |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201611048460.7A CN106651010B (en) | 2016-11-22 | 2016-11-22 | Shortest path-based wire network dividing method |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN106651010A true CN106651010A (en) | 2017-05-10 |
| CN106651010B CN106651010B (en) | 2020-05-12 |
Family
ID=58812582
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201611048460.7A Expired - Fee Related CN106651010B (en) | 2016-11-22 | 2016-11-22 | Shortest path-based wire network dividing method |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN106651010B (en) |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108776668A (en) * | 2018-05-04 | 2018-11-09 | 上海西井信息科技有限公司 | Path evaluation method, system, equipment and storage medium based on road-net node |
| CN108832668A (en) * | 2018-05-07 | 2018-11-16 | 北京三辰环卫机械有限公司 | Charging method, the device and system of dustbin |
| CN111062531A (en) * | 2019-12-13 | 2020-04-24 | 上海中通吉网络技术有限公司 | Method and device for generating express trunk transportation scheme |
Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102393869A (en) * | 2011-12-02 | 2012-03-28 | 河海大学 | Continuous physical distribution node layout optimization method based on weighted Voronoi diagram |
| CN103226804A (en) * | 2013-04-12 | 2013-07-31 | 山东大学 | Flow field visualization method based on flow line gravity center Voronoi diagram |
| CN105183855A (en) * | 2015-09-08 | 2015-12-23 | 浪潮(北京)电子信息产业有限公司 | Information classification method and system |
| CN106643783A (en) * | 2016-12-28 | 2017-05-10 | 国网天津市电力公司东丽供电分公司 | Shortest path Thiessen polygon-based electric vehicle charging station searching method |
-
2016
- 2016-11-22 CN CN201611048460.7A patent/CN106651010B/en not_active Expired - Fee Related
Patent Citations (4)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN102393869A (en) * | 2011-12-02 | 2012-03-28 | 河海大学 | Continuous physical distribution node layout optimization method based on weighted Voronoi diagram |
| CN103226804A (en) * | 2013-04-12 | 2013-07-31 | 山东大学 | Flow field visualization method based on flow line gravity center Voronoi diagram |
| CN105183855A (en) * | 2015-09-08 | 2015-12-23 | 浪潮(北京)电子信息产业有限公司 | Information classification method and system |
| CN106643783A (en) * | 2016-12-28 | 2017-05-10 | 国网天津市电力公司东丽供电分公司 | Shortest path Thiessen polygon-based electric vehicle charging station searching method |
Non-Patent Citations (2)
| Title |
|---|
| 易鸿杰 等: "基于AHP与广义最短距离的GIS选址方法", 《城市勘测》 * |
| 石悦悦: "纯电动汽车充电站选址布局研究", 《中国优秀硕士论文全文数据库工程科技II辑》 * |
Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108776668A (en) * | 2018-05-04 | 2018-11-09 | 上海西井信息科技有限公司 | Path evaluation method, system, equipment and storage medium based on road-net node |
| CN108776668B (en) * | 2018-05-04 | 2020-11-17 | 上海西井信息科技有限公司 | Path estimation method, system, equipment and storage medium based on road network nodes |
| CN108832668A (en) * | 2018-05-07 | 2018-11-16 | 北京三辰环卫机械有限公司 | Charging method, the device and system of dustbin |
| CN108832668B (en) * | 2018-05-07 | 2023-08-08 | 北京三辰环卫机械有限公司 | Charging method, device and system for garbage bin |
| CN111062531A (en) * | 2019-12-13 | 2020-04-24 | 上海中通吉网络技术有限公司 | Method and device for generating express trunk transportation scheme |
Also Published As
| Publication number | Publication date |
|---|---|
| CN106651010B (en) | 2020-05-12 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN109272170B (en) | A kind of traffic zone dividing system based on Louvain algorithm | |
| Yang et al. | Multi-objective highway alignment optimization incorporating preference information | |
| CN110009906B (en) | Dynamic path planning method based on traffic prediction | |
| Wagner et al. | Smart city planning-developing an urban charging infrastructure for electric vehicles | |
| CN112734176B (en) | Charging station building method and device, terminal equipment and readable storage medium | |
| CN112101676B (en) | Riding path planning method and device, computer equipment and storage medium | |
| CN112801399B (en) | Path generation method and device, terminal equipment and storage medium | |
| CN106651010A (en) | Shortest path-based network division method | |
| Yamamoto et al. | Structured random walk parameter for heterogeneity in trip distance on modeling pedestrian route choice behavior at downtown area | |
| Datta et al. | Spatial aggregation and compactness of census areas with a multiobjective genetic algorithm: a case study in Canada | |
| Yang et al. | A novel urban emergency path planning method based on vector grid map | |
| Aissat et al. | Dynamic ridesharing with intermediate locations | |
| CN116866931A (en) | Urban mobile edge server deployment method | |
| Qiao et al. | Fast-charging station location problem: A two-phase approach with mathematical program with equilibrium constraints considering charging choice behaviour | |
| Zavin et al. | Towards developing an intelligent system to suggest optimal path based on historic and real-time traffic data | |
| CN111008730B (en) | Crowd concentration prediction model construction method and device based on urban space structure | |
| Zhang et al. | Toward Large-Scale Graph-Based Traffic Forecasting: A Data-Driven Network Partitioning Approach | |
| Mahmud et al. | Facility location models development to maximize total service area | |
| CN110503234A (en) | A kind of method, system and the equipment of logistics transportation scheduling | |
| CN105701555A (en) | Method and system for dividing road network | |
| CN108199895A (en) | A kind of intelligent bayonet optimization placement method and device | |
| Saeidi | A genetic algorithm for route optimization in public transportation problem | |
| CN110738848A (en) | electric vehicle navigation method considering time-varying road resistance information | |
| CN111144612A (en) | Gas station position point prediction method and device, storage medium and terminal | |
| Xu et al. | Towards optimal free-of-charge trip planning in bike-sharing systems |
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 | ||
| CF01 | Termination of patent right due to non-payment of annual fee |
Granted publication date: 20200512 Termination date: 20211122 |
|
| CF01 | Termination of patent right due to non-payment of annual fee |