CN109005048A - Point layout optimization algorithm based on power guidance - Google Patents
Point layout optimization algorithm based on power guidance Download PDFInfo
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Abstract
The invention belongs to visualized data technical field, the point layout optimization algorithm based on power guidance is disclosed, includes the following steps: step (1): definition node set, line set and non-directed graph G；Step (2): the total size of attraction in setting system, the total size of repulsive force and total magnitude function in system；Step (3): it defines M (0)；Step (4): it is indicated with the sum of the sum of algorithm aggregation stage iteration and algorithm division stage iteration；Step (5): the component of attraction and repulsive force in X-direction and Y direction is calculated；Step (6): in X in cartesian coordinate space, Y direction repulsive force and attraction indicate node is subject in X, Y direction when the t times iteration resultant force, then obtain the coordinate after node iteration；Step (7): when the number of iterations is equal to a fixed value, iteration stopping, algorithm terminates.The present invention solves the problems, such as that the number of iterations is more in traditional algorithm, has better scalability.
Description
Technical field
The invention belongs to visualized data technical fields, more particularly to the point layout optimization algorithm based on power guidance.
Background technique
Power guidance algorithm refers to the resultant force that gravitation and repulsive force synthesis are calculated by the calculating to each node, then thus
Resultant force comes the position of mobile node.
For the algorithm suitable for general reticular structure map data, power guidance algorithm is a kind of side often applied
Method.By the calculating to each node, the resultant force of gravitation and repulsive force synthesis is calculated, then thus comes the position of mobile node with joint efforts
It sets.New energy value is calculated according to the new position of node after executing once, such as mechanical concept, energy value is smaller, indicates entire net
Network more tends towards stability.In general energy value is smaller, and the configuration of network is shown will be more clear, therefore when energy value reaches
When minimum value, the configuration status of network diagramming is exactly the result that we want.
The shortcomings that this method is not restrain, and always has node to vibrate back and forth on two different locations, although will not receive
Configuration when holding back, but vibrating back and forth generally also may ultimately reach certain stable state, therefore actual execution is all with specified
The number of execution come determine stop condition.When another question is exactly that the number of nodes of network diagramming is too many, order can not be also acquired
The satisfied result of people.
When be initially configured it is bad in the case where, the configuration result of usually power guidance algorithm is not very good, thus use
Power guidance algorithm would generally be with the algorithm for unifying an initial configuration, to reach relatively satisfactory net-like configuration.
Multi-level algorithm most importantly represents the selection of node, thus will have a direct impact on execution efficiency and result.
The idea of power guidance algorithm is very simple, and is easy to use and modify with meet demand.We can change network diagramming
To accelerate to restrain different types of power can also be added according to different requirements, although in addition, not having in algorithmic procedure in initial position
There is the symmetry particular for network diagramming to be configured, but when preferable there are can also be obtained when symmetric relation in network diagramming
As a result.The defect of power guidance algorithm is that obtained network diagramming will not be fine when initial configuration is bad, so can root
The algorithm whether is selected according to the characteristic of mesh data.
Classical power guiding placement algorithm has extremely wide application in network visualization field, algorithm regulation:
All there is charge repulsion effect between any two node, all there is spring graviational interaction between two arbitrarily connected nodes.But
There is also some shortcomingss, for example, in an iteration, when the effect for the power for calculate node to be subject to, need the node with
The distance of other all nodes and the size of charge repulsion, in this way, which it is longer to cause algorithm to spend in each iteration
Time.Furthermore under the reset condition of layout, all nodes are random distributions, so as to cause the layout distance under stochastic regime
Layout reaches stable state and needs to undergo more the number of iterations.In addition, having higher in the biggish complex network of number of nodes
A possibility that occur it is a large amount of while with while interlock, it is difficult to the problem of seeing clearly.
Application No. is 201611249511.2 patents to disclose the adaptive data visualization method and dress of network topology
It sets, the adaptive data visualization method of the network topology includes: to pre-process to node, output pretreatment node；Using
Power guidance placement algorithm handles the pretreatment node, forms initial network topology figure；To the initial network topology
The pretreatment node being overlapped in figure carries out duplicate removal processing, and multiple knot is removed in output；Multiple knot formation target network is gone to open up based on described
Flutter figure.The adaptive data visualization method of the network topology can realize that data visualization automates, and simplify at data visualization
Process is managed, manual intervention is not necessarily to, can effectively save manual intervention cost, and improve treatment effeciency.But the algorithm iteration number
More, iteration cycle is long.
Summary of the invention
It is few it is an object of the invention to disclose the number of iterations, the strong point layout optimization algorithm based on power guidance of scalability.
The object of the present invention is achieved like this:
Based on the point layout optimization algorithm of power guidance, comprise the following steps:
Step (1): defining non-directed graph G=(V, E) and be made of node set V and line set E, node set V={ vi|1
≤ i≤n }, n > 0；Line set E={ ei| 0≤i≤m }, m >=0；viIt is the node of non-directed graph G, eiIt is the side of non-directed graph G；
If defining node vi,vj∈ V, j ∈ [1, n], and vi,vj∈ E, then node vi,vjIt is adjacent；If defining two sides
Public same node, then this two sides are adjacent；N indicates the quantity of node, and m indicates the quantity on side；
Step (2): attraction is dimensioned to mM (t)μ, μ=0.9；
Ma(t)=2M (t)0.9m2；
Mr(t)=M (t) n (n-1)；
F (t)=2M (t)0.9m2-M(t)n(n-1)；
In above formula, Ma(t) be attraction in system total size, Mr(t) be repulsive force in system total size, f (t) is
Total magnitude function；
Step (3): t=t is setpMoment, total magnitude function f (t) are equal to 0；
T be algorithm iteration number, t ∈ [1 ,+∞)；
When defining t=0, M (0)=1/m；
When t > 1, M (t) monotonic increase；M (1) < M (tp)；
It enables
Step (4): the sum of imputation method aggregation stage iteration is s, and algorithm divides the sum of stage iteration as b, and 0 < s <
b。
It enables
M (t) is indicated with m, n, t and s:
Step (5): the component of attraction and repulsive force in X-direction and Y direction is calculated:
In above formula, fa(vi, t) and .x indicates the attraction in cartesian coordinate space in X-direction, fa(vi, t) and .y expression
Attraction in cartesian coordinate space in Y direction, θij(t) indicate in the t times iteration X-axis with connect vertex viAnd vj
Straight line between angle；aijBelong to adjacency matrix A, aij=1 indicates node vi,vjIt is adjacent；aij=0 indicates node vi,vjNo
It is adjacent；
In above formula, fr(vi, t) and .x indicates the repulsive force in cartesian coordinate space in X-direction, fr(vi, t) and .y expression
Repulsive force in cartesian coordinate space in Y direction；
Step (6): by vi(t) .x and vi(t) .y obtains iteration posterior nodal point viCoordinate:
Node v when the t times iterationiThe resultant force v being subject in the X-axis directioni(t) .x:
vi(t) .x=fa(vi,t).x+fr(vi,t).x；
Node v when the t times iterationiThe resultant force v being subject in the Y-axis directioni(t) .y:
vi(t) .y=fa(vi,t).y+fr(vi,t).y；
By vi(t) .x and vi(t) .y more new node viCoordinate；
Step (7): as t=s+b, iteration stopping.
The invention has the benefit that
The present invention solves the problems, such as that the number of iterations is too many in traditional algorithm and iteration cycle is long, also solves in number of nodes
Measure in biggish complex network it is a large amount of while with while interlock, it is difficult to the problem of seeing clearly.Compared with traditional algorithm, the present invention has more
Good scalability.
Detailed description of the invention
Fig. 1 is the point layout optimization algorithm based on power guidance in m=4, n=4, the situation of change of f (t) in M (t)=t；
Fig. 2 is that the point layout optimization algorithm of power guidance and FR algorithm cross edge quantitative comparison scheme；
Fig. 3 is the point layout optimization algorithm and FR algorithm side length standard deviation comparison diagram of power guidance；
Fig. 4 is minimum range comparison diagram between the point layout optimization algorithm and FR algorithm node that power guides；
Fig. 5 is the point layout optimization algorithm and FR algorithm Node distribution comparison diagram of power guidance；
Fig. 6 is that the point layout optimization algorithm of power guidance and FR algorithm hand over iteration time comparison diagram；
Fig. 7 is application of the point layout optimization algorithm of power guidance to the common random network figure of 8*8；
Fig. 8 is application of the FR algorithm to the common random network figure of 8*8；
Fig. 9 is application of the point layout optimization algorithm of power guidance to the QueenGraph network of 15*5；
Figure 10 is application of the FR algorithm to the QueenGraph network of 15*5.
Specific embodiment
Further describe the present invention with reference to the accompanying drawing:
Based on the point layout optimization algorithm of power guidance, macroscopically it is divided into two stages, i.e. aggregation stage and division stage.
It defines non-directed graph G=(V, E) to be made of node set V and line set E, node set V={ vi| 1≤i≤n },
Wherein n > 0, line set E={ ei| 0≤i≤m }, wherein m >=0, viAnd eiIt is node and the side of figure G respectively.Node { vi,vj}∈
V, if { vi,vj∈ E, then this two node is adjacent.If the public same node in two sides, then this two sides are adjacent
's.
It defines in adjacency matrix A, indicates whether two nodes are adjacent using 0 or 1, if adjacent, i.e. { vi,vj∈ E, then
(a)ij=1；If non-conterminous, then (a)ij=0.
For simplicity, non-directed graph is simply referred as figure in the remainder of this chapter.Pass through the layout of figure, it is known that
The position of all nodes, i.e. X-coordinate and Y coordinate in given plan view area.Assuming that attraction and repulsive force are defined on a pair
Between node, and regard figure as a physical system, then the placement algorithm of classical power guidance from one it is random just
The layout that begins starts, and then iteratively finds the smallest layout of gross energy, the mechanical balance state corresponding to system.It uses
Variable t indicates the number of algorithm iteration, wherein t ∈ [1 ,+∞).
Present invention fa(vi, t) and it indicates in the t times iteration of power guiding placement algorithm, node viAdjacent node to vi
Total attraction.Similar, use fr(vi, t) and indicate the v in the t times iterationiThe total repulsive force for other nodes being subject to.Due to
Power is the vector with size and Orientation, so using fa(vi, t) and .x, fa(vi, t) and .y, fr(vi, t) and .x, fr(vi, t) and .y points
Attraction fa (v in cartesian coordinate space in X-direction and Y direction is not describedi, t) and repulsive force fr(vi, t), together
Reason, vi(t) .x and vi(t) node v when .y respectively indicates the t times iterationiThe resultant force being subject in X-direction and Y direction.
Similar with FR algorithm, this algorithm needs to calculate the row between attraction and any pair of node between connected node
Repulsion.Repulsive force size between any specific iteration t moment assembled and divided, any two vertex is consistent, fixed
Adopted h (t) > 0, h (t) monotonic increase with the growth of the number of iterations t.Similarly, any in any particular iteration t moment
Attraction between a pair of of adjacent vertex also calculating function g (t) > 0 having the same, g (t) with the number of iterations t increase
And monotonic increase.That is, compared with FR algorithm, this algorithm takes simplified algorithm, i.e., the attraction between vertex and
The size of repulsive force is not dependent on the distance between they.
Firstly, trying the predominant intermolecular forces for allowing attraction to become in system in the first iteration, so that the section being connected
Point attracts one another in layout, close.Then, with the increase of the number of iterations, try that repulsive force is allowed to increase faster with one
Speed pursues and surmounts attraction, and makes vertex mutually exclusive, separate.Want to reach this effect, it can be by making a pair
The size of attraction between vertex increases slowly to realize than the size of repulsive force.In this task, herein by attraction
It is dimensioned to mM (t)μ, parameter μ can be adjusted to appropriately sized value during the experiment, fixed tentatively here and be
0.9。
Under the selection of such parameter size, the total size M of the attraction in certain specific iteration t moment, systema
(t) and the total size M of repulsive forcer(t) and difference f (t)=M of attraction and repulsive forcea(t)-Mr(t), using following etc.
Formula definition, wherein f (t) is total magnitude function:
Ma(t)=2M (t)0.9m2；
Mr(t)=M (t) n (n-1)；
F (t)=2M (t)0.9m2-M(t)n(n-1)；
Such as Fig. 1, the case where curve of X-axis upper section represents when attraction is better than repulsive force, attraction is two at this time
Stronger active force in kind power, node interconnected is upper close to each other in layout, is now in " aggregation " stage of algorithm.
But some nodes may lean on too close each other, to the case where overlapping occur, so that the layout result in this stage exists
It is unacceptable for visualizing on Aesthetic Standards, therefore algorithm also needs to continue iteration.The curve of X-axis section below represents
The case where when repulsive force is better than attraction, repulsive force is stronger strength between two kinds of power at this time, and growth rate is than attracting
Power faster when, indicate when vertex be spaced apart be used to realize beautiful layout result when, exactly " division " stage of algorithm.
The turning point of aggregation stage and division step transition is when total magnitude function f (t) becomes zero.In case of in t
=tpMoment, then M (tp) it is defined as value shown in following equalities.For any one n > 2, figure G, the M (t of m >=np)
> 1.Therefore, by Selection of Function, enable t since 1, so that M (1) < M (tp), then M (t) starts monotonic increase.First
When secondary iteration, the aggregation stage of algorithm, the vertex of interconnection is drawn into due to the effect of attraction, then, when M (t) becomes
It obtains and is greater than M (tp) when, the division stage of algorithm is arrived, node is separated under the action of repulsive force to be come.
The selection of this algorithm M (t) function should be the function of a monotonic increase, it can be seen in fig. 1 that if network G
The quantity of middle m=4, n=4, i.e. node and side are all 4, when the size of repulsive force " pulls up to " size of attraction,
It experienced 18000 successive ignitions, so high iteration number of words is clearly cannot be received, it is therefore desirable to adjust in M (t) function
It is found while adjustment algorithm parameter by preliminary experiment about the order of t, Aggregation-Division algorithm exists
It undergoes the relatively short aggregation stage and the longer division stage is undergone to produce more beautiful effect of visualization later.Cause
This, if predefining the number of iterations, the conception of this algorithm is the function that M (t) is a rapid growth, so as in aggregation rank
Iteration more less than the division stage is spent in section.In order to which the power guidance algorithm for keeping our algorithm classical with other compares favourably, I
Wish iteration phase time complexity be O (n) rank.It obviously, can be with shadow by changing the rate of rise of M (t) function
It rings algorithm and reaches value M (t in M (t)p) how many times iteration is executed before.
Assuming that the sum of algorithm aggregation stage iteration is s, the sum of division stage iteration is b, wherein 0 < s <b.Wish M
(t) be a rapid growth monotonically increasing function.So can be power function or exponential function for M (t) appropriate.?
M (t) is enabled in this algorithm are as follows:
It is replaced, is further indicated that using m and n are as follows:
In order to assess Aggregation-Division algorithm, we will also be total by experiment adjustment M (t) function and iteration
The value of parameter in number (s+b).
In each iteration, according in node viThe total attraction f being subject in iteration t each timea(vi, t) and total repulsion
Power fr(vi, t), update each node viCoordinate.Enable θij(t) indicate in the t times iteration X-axis with connect vertex viAnd vj's
Angle between straight line.Then f is calculated separatelya(vi, t) and component in X-direction and in the Y-axis direction, as follows:
Its intermediate value aijIt is a in the adjacency matrix A of figureijElement.It is similar with FR algorithm, node by from it is all and its
The attraction effect that adjacent node applies, works as aijWhen=0, it is believed that viAnd vjAttraction is not present between node, works as aij=1
When, it is believed that viAnd vjThere are attractions between node.Similarly, fr(vi, t) and component in X-direction and in the Y-axis direction is as follows
Shown calculating:
Think node viAll there is repulsive force effect with other all nodes, as a result, node viIn Descartes after movement under force
Coordinate in system can be obtained by calculation:
vi(t) .x=fa(vi,t).x+fr(vi,t).x；
vi(t) .y=fa(vi,t).y+fr(vi,t).y；
Unlike the placement algorithm of typical power guidance, in iteration given every time, Aggregation-
Division algorithm will not be by vertex viPosition before from it begins to move into new position.Node viNew position indirectly according to
Rely the number of iterations in its pervious position, executed with algorithm, connect vertex viAnd vjStraight line between angle it is related, it by
All vertex are relative to viThe influence of position, by calculating angle, θ in preceding an iterationijTo obtain.
The description of the sequencing of the point layout optimization algorithm based on power guidance is given below:
For scheming G=(V, E), | V |=n, | E |=m
Input a: primitive network
Output: the network after algorithm layout
1: all vertex are in a random site in plane domain
2:t ← 0
3:M (0) ← 1/m
4:for t ← 1 to (s+b) do
5:M (t) ← (2tm2/sn2)n-1))10
The to n of 6:for I ← 1 do
7:
8:
The to n of 9:for j ← 1 do
10:if { vi, vj}∈E then
11:
12:
13:end if
14:if i ≠ j then
15:
16:
17:end if
18:end for
19:
20:
21:end for
22:end for
The main body of the outmost for-loop circulation of 5-20 row is the number of iterations of AD algorithm, and a total of (s+b) is secondary repeatedly
In generation, wherein s and b is the number for indicating the aggregation stage and dividing stage iteration respectively.Algorithm is opened from an initial arbitrary placement
Begin.Since the first time iteration of AD algorithm needs an initial value, i.e. M (0) provides M (0)=1/m in this algorithm, it is meant that
Algorithm starts to calculate with a value strictly less than 1.When then, for t >=1, the value of M (t) is calculated.For each vertex vi,
The component for being applied to total attraction X-direction and Y direction thereon calculates in the 10-13 row of algorithm, in algorithm
The total repulsive force being applied to thereon is calculated in 14-17 row.Vertex v is calculated in algorithm 19-20 rowiAfter the t times iteration
Coordinate.
The time complexity of AD algorithm is O (n3), outermost circulation performs (s+b) secondary iteration, its main body includes
Two circulations, i.e., each other all nodes of node cyclic access.Therefore, AD algorithm and other classical power guidance algorithms
(including FR algorithm) time complexity having the same, but due between node active force it is unrelated with euclidean distance between node pair, it is big
Difficulty in computation is simplified greatly.In addition, being found through experiments that, in more than 20 iteration, AD can show beautiful result.
AD algorithm proposed by the present invention belongs to classical power guidance algorithm scope.When following the general modfel of FR algorithm,
AD algorithm uses the attraction and repulsive force unrelated with the distance between node.In each iteration, active force is even variation
, and the monotonic increase with the increase of the number of iterations.In addition, the present invention can be also illustrated by experiment, AD algorithm tool
Have to the cross edge of FR algorithm Similar numbers and similar adjacent side angle, the layout result of algorithm is generally rounded, is visualizing
This may be an advantage of AD algorithm in effect.In entire drawing area ratio FR algorithm more uniformly distribution node,
Such characteristic may be such that FR algorithm has better scalability, and can generate what some FR algorithms can not be reached
High degree of symmetry layout, the symmetric configuration of these figures generally requires relatively long side, for example, some hamiltonian graphs include
Queen's figure, Wagner figure and heawood graph, for the figure of symmetrical configuration, algorithm achieves ideal effect.
In order to verify the validity and applicability of AD algorithm, experiment is compared to AD algorithm and FR algorithm respectively, is tested
Object is that number of vertex is to randomly select the cyberrelationship non-directed graph of 5 to 100 nodes composition.It is made that corresponding AD is calculated simultaneously
The adjustment of method parameter, by experiment discovery AD algorithm using the selection of above-mentioned M (t) function, more than 20
More beautiful result is obtained in secondary iteration.Aggregation stage and division stage are explored during the experiment in total iteration time
Accounting in number, carrys out the layout result of the satisfaction in real currently all pilot experiment, and discovery algorithm undergoes relatively short aggregation
More beautiful effect of visualization is produced after stage and experience longer division stage, the aggregation stage generally occupies whole
20-30% in 20 iteration.
Experiment chooses some Aesthetic Standards to draw a network as the performance indicator for measuring AD algorithm and FR algorithm, in reality
It tests and middle respectively records the layout character that AD algorithm is realized with FR algorithm.Such as the quantity that side intersects, iteration time and section
Point distribution situation.A kind of method of quantization Node distribution situation is the minimum range found in layout between two nodes, then
Read group total mean value is i.e.:
Value D1It is higher, illustrate that node is distributed more uniform in entire drawing area.Another kind quantization Node distribution situation
Method, be enableFor vertex riIn network at a distance from its nearest node, enableFor node viOn layout boundary
Nearest node distance, enable
It calculates with riThe area ratio of the sum of area of circle surrounded for radius and the 2 dimensional region to draw a network, as
Quantify the second method of Node distribution situation.That is:
Value D2It more levels off to 1, illustrates that node is distributed more uniform in entire drawing area.
The performance for mainly comparing AD algorithm and FR algorithm respectively from the following aspects is respectively: the quantity figure of cross edge
2, standard deviation Fig. 3 of edge lengths, average minimum range Fig. 4, vertex distribution map 5, Riming time of algorithm Fig. 6 etc. between node.
In the title of each line chart, Aggregation-Division algorithm is indicated with AD, indicates Fruchterman- with FR
Reingold algorithm.
It summarizes to result, as shown in Fig. 2, two kinds of placement algorithms are controlling when being related to comparing the quantity of cross edge
Almost neck and neck on this esthetic index of cross edge quantity, AD algorithm is special relative to not highlighting between FR algorithm
Apparent advantage, is only somewhat below FR algorithm in cross edge quantity, and the number of nodes of AD algorithm layout is reported to the leadship after accomplishing a task on side at 55 or more
Quantity start less than FR algorithm, but difference almost can be ignored.It can be obvious in side length standard deviation shown in Fig. 3
Find out that the side length standard deviation of FR algorithm is less than the side length standard deviation after AD algorithm layout, tentatively conjecture is that FR algorithm generates in ground
Edge lengths are more unified, and the side length gap generated after AD algorithm layout is larger.However in figures 4 and 5, with network node
The growth of quantity, it may be clearly seen that the actual variance between two kinds of algorithms, from Node distribution characteristic, AD algorithm
Can preferably be evenly distributed node in entire drawing area, therefore it can be concluded that, the side length standard deviation of AD algorithm greatly compared with
It is in order to enable the more uniform reason of Node distribution greatly.Classical power guiding FR algorithm, which realizes edge lengths, has opposite one
The compact drawing layout caused, however, the cloth for often also thering is large stretch of unused storage space and dense subgraph more to tangle entanglement
Office.And AD algorithm proposed in this paper can preferably be made using entire drawing area by allowing to generate longer side
The distribution on vertex is more uniform.Fig. 4 and Fig. 5 also indicates that AD algorithm may preferably amplify than FR algorithm, because big with figure
Small growth, it tends to provide the result become better and better in terms of Node distribution.Fig. 6 shows that the iteration ratio FR's of AD algorithm changes
In generation, is fast, this is that this algorithm is desired, because AD algorithm uses simpler attraction repulsive force computation model, it is not
Dependent on the distance between node, therefore calculating speed is faster, is better than FR algorithm in terms of time performance.
Fig. 7-Figure 10 applies FR algorithm and AD to the QueenGraph of the common random network figure of 8*8 and 15*5 respectively respectively
Algorithm.It was found that AD algorithm generates circular layout by allowing to generate longer side, and it is uniformly distributed in entire drawing area
Vertex.When data set is the figure of symmetrical configuration, AD algorithm often will form more preferably to be laid out than FR algorithm, forms phase
As minor structure, the effect of visualization of minor structure is similar, whole to keep symmetrical.It can be seen that after node layout figure readability
It is more preferable compared with FR algorithm, and the scalability of algorithm is better than FR algorithm.
The above is not intended to restrict the invention, and for those skilled in the art, the present invention can have various
Change and variation.All within the spirits and principles of the present invention, any modification, equivalent replacement, improvement and so on should all wrap
Containing within protection scope of the present invention.
Claims (8)
1. the point layout optimization algorithm based on power guidance, it is characterised in that: comprise the following steps:
Step (1): definition node set, line set and non-directed graph G；
Step (2): the total size of attraction in setting system, the total size of repulsive force and total magnitude function in system；
Step (3): it defines M (0)；
Step (4): M (t) is indicated with the sum of the sum of algorithm aggregation stage iteration and algorithm division stage iteration；
Step (5): the component of attraction and repulsive force in X-direction and Y direction is calculated；
Step (6): in X in cartesian coordinate space, Y direction repulsive force and attraction indicate the t times iteration when node vi
Then the resultant force being subject in X, Y direction obtains the coordinate after node iteration；
Step (7): when the number of iterations is equal to a fixed value, iteration stopping, algorithm terminates.
2. the point layout optimization algorithm according to claim 1 based on power guidance, it is characterised in that: the step (1)
Specifically:
It defines non-directed graph G=(V, E) to be made of node set V and line set E, node set V={ vi| 1≤i≤n }, n > 0；Side
Set E={ ei| 0≤i≤m], m >=0；viIt is the node of non-directed graph G, eiIt is the side of non-directed graph G；
If defining node vi,vj∈ V, j ∈ [1, n], and vi,vj∈ E, then node vi,vjIt is adjacent；If it is public to define two sides
Same node, then this two sides are adjacent；N indicates the quantity of node, and m indicates the quantity on side.
3. the point layout optimization algorithm according to claim 1 based on power guidance, it is characterised in that: the step (2)
Specifically:
Attraction is dimensioned to mM (t)μ, μ=0.9；
Ma(t)=2M (t)0.9m2；
Mr(t)=M (t) n (n-1)；
F (t)=2M (t)0.9m2-M(t)n(n-1)；
In above formula, Ma(t) be attraction in system total size, Mr(t) be repulsive force in system total size, f (t) is total amount
Grade function.
4. the point layout optimization algorithm according to claim 1 based on power guidance, it is characterised in that: the step (3)
Specifically:
When defining t=0, M (0)=1/m；T be algorithm iteration number, t ∈ [1 ,+∞).
5. the point layout optimization algorithm according to claim 1 based on power guidance, it is characterised in that: the step (4)
Specifically:
The sum that imputation method assembles stage iteration is s, and algorithm divides the sum of stage iteration as b, and 0 < s <b；
It enables
M (t) is indicated with m, n, t and s:
6. the point layout optimization algorithm according to claim 1 based on power guidance, it is characterised in that: the step (5)
Specifically:
In above formula, fa(vi, t) and .x indicates the attraction in cartesian coordinate space in X-direction, fa(vi, t) and .y expression Descartes
Attraction in coordinate space in Y direction, θij(t) indicate in the t times iteration X-axis with connect vertex viAnd vjStraight line it
Between angle；aijBelong to adjacency matrix A, aij=1 indicates node vi,vjIt is adjacent；aij=0 indicates node vi,vjIt is non-conterminous；
In above formula, fr(vi, t) and .x indicates the repulsive force in cartesian coordinate space in X-direction, fr(vi, t) and .y expression Descartes
Repulsive force in coordinate space in Y direction.
7. the point layout optimization algorithm according to claim 1 based on power guidance, it is characterised in that: the step (6)
Specifically:
Node v when the t times iterationiThe resultant force v being subject in the X-axis directioni(t) .x:
vi(t) .x=fa(vi,t).x+fr(vi,t).x；
Node v when the t times iterationiThe resultant force v being subject in the Y-axis directioni(t) .y:
vi(t) .y=fa(vi,t).y+fr(vi,t).y；
By vi(t) .x and vi(t) .y more new node viCoordinate.
8. the point layout optimization algorithm according to claim 1 based on power guidance, it is characterised in that: the step (7)
Specifically:
As t=s+b, iteration stopping, algorithm terminates.
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