CN104331738B - Network reconfiguration algorithm based on game theory and genetic algorithm - Google Patents
Network reconfiguration algorithm based on game theory and genetic algorithm Download PDFInfo
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Abstract
The invention belongs to the technical field of a complicated network, and particularly discloses a network reconfiguration algorithm based on a game theory and a genetic algorithm. The algorithm comprises the main realization steps: firstly, as for a network with N nodes, A 0-1 matrixes are initialized randomly, and a game theory strategy is initialized; secondly, according to the known node actual earnings values, node earnings values of the A matrixes are calculated, and the total earnings value of each node is calculated; thirdly, a population is updated according to the genetic algorithm, and T generations are iterated to obtain A new matrixes; and finally, according to improvement on a reconfiguration algorithm on a compressed sensing network, the algorithm is used for reconstruction on a single node until the earnings values of all nodes are equal to the actual earnings values, and an actual network is obtained. Reconstruction of a network with many nodes and a large degree can be totally correct, and the time is excessively fast.
Description
Technical field
The invention belongs to complex network technical field, it is related to the reconstruct of complex network and data mining technology, specifically one
Plant the Network Reconfiguration Algorithm based on game and genetic algorithm.
Background technology
Complex network is a kind of form of expression that complication system is abstracted in real world, is existed in real world a lot
Such complex network, such as, and the god in friendship network, power network, WWW, bio-networks in community network
Through network and metabolic network etc..In real world network, the independent individual in system is abstracted into network by we
In node, in system individuality between according to certain rule and a kind of relation of self-assembling formation or arteface be abstracted into node it
Between side.
Since, in 1998 in 1999 have been delivered on small-world network on " Nature " and " Science " two publications
Since two articles of Scale-free networks, the research boom of one complex network has worldwide been started.Hereafter
In the past few years, the research on complex network achieves many important achievements in research, and complex network has become scientific research
One key areas.
Because complex network node is numerous, complex structure so that its research is extremely difficult.In science and many necks of engineering
Domain, what the system interested that people run into was made up of the element of networking, these elements are referred to as node, but the pattern section
Point is totally unknown with the interaction of node or network topology structure.The network topology structure not disclosed wherein can be from experiment
Or some data based on time series are extracted in observed result obtain.
In the past few years, network reconfiguration problem is of increased attention, and most of algorithms for existing are all based on
Compressed sensing algorithm, it is openness using network, with compressed sensing model reconstruction network, for sparse network effect very
It is good, but the shortcoming at the same time existing is exactly openness constraint, for complicated not sparse network such as community network etc. just
Can not reconstruct correctly, and time complexity is very high, it is very time-consuming for big network reconfiguration, for the shortcoming of existing algorithm, this
The deficiency of the existing algorithm that algorithm is solved, not by sparsity constraints, and greatly reduces time complexity.
The content of the invention
It is an object of the invention to the attribute information according to network node, the whole topological structure of network is reconstructed, there is provided
A kind of Network Reconfiguration Algorithm based on game and genetic algorithm.
The technical scheme is that：Network Reconfiguration Algorithm based on game and genetic algorithm, comprises the following steps：
(1) 0-1 matrixes matrix [N] [N] [A] of A N*N of random initializtion first, A=100；
(2) under prisoners' dilemma game, the game strategies state [N] of N number of node is initialized, then calculates reality
Nodes revenue and total revenue payoff_real [N+1] of the network under game strategies state [N], and A matrix matrix
The income payoff [N+1] [A] of [N] [N] [A]；
(3) calculating process of genetic algorithm：
(3.1) it is random from A matrix matrix [N] [N] [A] every time to extract two matrix matrix [N] [N] without repetition
[a] and matrix [N] [N] [b], wherein a ≠ b, a, b represent the matrix randomly selected respectively；
(3.2) first filial generation txt [N] [N] [a's] obtains：
The parent of total revenue and actual total revenue difference minimum is chosen as first filial generation, when | payoff [N] [a]-
Payoff_real [N] | during≤| payoff [N] [b]-payoff_real [N] |, txt [N] [N] [a]=matrix [N] [N]
[a]；Otherwise txt [N] [N] [a]=matrix [N] [N] [b]；
(3.3) second filial generation txt [N] [N] [b's] obtains：
For the selection of the rows of txt [i] [N] [b] i-th, that is, i-th selection of the adjacency vector of node：
Intersect：The i-th row that i-th nodes revenue is closer to the parent of payoff_real [i] is chosen, i.e.,
As | payoff [i] [a]-payoff_real [i] |≤| payoff [i] [b]-payoff_real [i] |,
Txt [i] [N] [b]=matrix [i] [N] [a] and payoff_txt [i]=payoff [i] [a],
Otherwise txt [i] [N] [b]=matrix [i] [N] [b], payoff_txt [i]=payoff [i] [b], N tables in formula
Show and N number of value of the rows of matrix [i] [N] [b] i-th is all assigned to txt [i] [N] [b]；
Variation：After the selection of the i-th row, as txt [i] [j] [b] ≠ txt [j] [i] [b], chosen with Probability p rop:
As the random number random of generation<During prop, txt [i] [j] [b]=txt [j] [i] [b] updates node i income
Value payoff_txt [i], otherwise txt [j] [i] [b]=txt [i] [j] [b], update nodes revenue value payoff_txt [j]；
(3.4) final updating population, matrix [N] [N] [a]=txt [N] [N] [a], matrix [N] [N] [b]=txt
[N][N][b]。
(3.5) repeat step (3) 50 times；
(4) T step (2) and (3) are repeated, T=100, i.e. population recruitment iteration 100 times obtain A adjacency matrix
matrix[N][N][A]；
(5) a matrix matrix [N] [N] [m] is randomly selected, the difference of calculate node income and actual gain and by dropping
Sequence arranges d_value [N] [2], and first row memory node, secondary series stores the income difference of the node；
(6) node x=d_value [1] [1] is reconstructed with the restructing algorithm based on compressed sensing and game, obtains the neighbour of x
Meet vectorial avrage [x]：
(7) the adjacency vector avrage [x] of node d_value [1] [1] is assigned to step according to symmetry principle correspondence
(4) the 100 matrix matrix [N] [N] [A] for obtaining, obtain 100 new initial populations, according to step (3) operation once；
(8) repeat step (5), (6), (7) are until nodes revenue value and actual equal, the network for being reconstructed.
The income of the calculate node described in above-mentioned steps (2) is calculated by following formula：
Wherein, P is a 2*2 gain matrix：
FijRepresent the financial value that node i is obtained with node j game posterior nodal points i；
GiRepresent node i and the financial value sum with i connected node games；
ГiExpression has the set of the node being connected with node i；
Si、SjRepresent the strategy matrix of node i and node j；
The transposition symbol of the T representing matrixs in formula；
S (C) is expressed as the strategy matrix of cooperation, and S (D) is expressed as the strategy matrix betrayed.
Beneficial effects of the present invention：The present invention is according to nodes revenue value to 100 sample adjacency matrix randomly generating
Cross and variation, obtains preferable sample adjacency matrix, then reconstructs part of nodes according to compression sensing method, final to obtain network just
True adjacency matrix.Present invention incorporates theory of games and the method for genetic algorithm, can be quick, accurately reconstruct network
True topological structure.Reconstruct in gene regulatory network, based on social discrete data or information illustration tissue net engineering science with
And there is important application in the field such as territorial protection.The present invention is not only few to node, spends small network practicality, also non-for big network
Chang Shiyong, and efficiency high, are not constrained by network is openness.
The present invention is described in further details below with reference to accompanying drawing.
Brief description of the drawings
Fig. 1 is FB(flow block) of the invention；
Fig. 2 is Optimization Steps of the invention；
Fig. 3 be in the embodiment of the present invention one there are 34 figures of node；
Fig. 4 is the reconstruction result of network in the embodiment of the present invention.
Specific embodiment
Software runtime environment of the invention is Microsoft Visual C++6.0, the He of specific steps reference picture 1 of implementation
Fig. 2, Network Reconfiguration Algorithm of the present invention based on game and genetic algorithm, comprises the following steps：
(1) 0-1 matrixes matrix [N] [N] [A] of A N*N of random initializtion first, A=100；
(2) under prisoners' dilemma game, the game strategies state [N] of N number of node is initialized, then calculates reality
Nodes revenue and total revenue payoff_real [N+1] of the network under game strategies state [N], and A matrix matrix
The income payoff [N+1] [A] of [N] [N] [A]；
The income of calculate node is calculated by following formula：
Wherein, P is a 2*2 gain matrix：
FijRepresent the financial value that node i is obtained with node j game posterior nodal points i；
GiRepresent node i and the financial value sum with i connected node games；
ГiExpression has the set of the node being connected with node i；
Si、SjRepresent the strategy matrix of node i and node j；
The transposition symbol of the T representing matrixs in formula；
S (C) is expressed as the strategy matrix of cooperation, and S (D) is expressed as the strategy matrix betrayed.
(3) calculating process of genetic algorithm：
(3.1) it is random from A matrix matrix [N] [N] [A] every time to extract two matrix matrix [N] [N] without repetition
[a] and matrix [N] [N] [b], wherein a ≠ b, a, b represent the matrix randomly selected respectively；
(3.2) first filial generation txt [N] [N] [a's] obtains：
The parent of total revenue and actual total revenue difference minimum is chosen as first filial generation, when | payoff [N] [a]-
Payoff_real [N] | during≤| payoff [N] [b]-payoff_real [N] |, txt [N] [N] [a]=matrix [N] [N]
[a]；Otherwise txt [N] [N] [a]=matrix [N] [N] [b]；
(3.3) second filial generation txt [N] [N] [b's] obtains：
For the selection of the rows of txt [i] [N] [b] i-th, that is, i-th selection of the adjacency vector of node：
Intersect：The i-th row that i-th nodes revenue is closer to the parent of payoff_real [i] is chosen, i.e.,
As | payoff [i] [a]-payoff_real [i] |≤| payoff [i] [b]-payoff_real [i] |,
Txt [i] [N] [b]=matrix [i] [N] [a] and payoff_txt [i]=payoff [i] [a],
Otherwise txt [i] [N] [b]=matrix [i] [N] [b], payoff_txt [i]=payoff [i] [b], N tables in formula
Show and N number of value of the rows of matrix [i] [N] [b] i-th is all assigned to txt [i] [N] [b]；
Variation：After the selection of the i-th row, as txt [i] [j] [b] ≠ txt [j] [i] [b], chosen with Probability p rop:
As the random number random of generation<During prop, txt [i] [j] [b]=txt [j] [i] [b] updates node i income
Value payoff_txt [i], otherwise txt [j] [i] [b]=txt [i] [j] [b], update nodes revenue value payoff_txt [j]；
(3.4) final updating population, matrix [N] [N] [a]=txt [N] [N] [a], matrix [N] [N] [b]=txt
[N][N][b]。
(3.5) repeat step (3) 50 times；
(4) T step (2) and (3) are repeated, T=100, i.e. population recruitment iteration 100 times obtain A adjacency matrix
matrix[N][N][A]；
(5) a matrix matrix [N] [N] [m] is randomly selected, the difference of calculate node income and actual gain and by dropping
Sequence arranges d_value [N] [2], and first row memory node, secondary series stores the income difference of the node；
(6) node x=d_value [1] [1] is reconstructed with the restructing algorithm based on compressed sensing and game, obtains the neighbour of x
Meet vectorial avrage [x]：
According to compressed sensing model Gx=Φx·Yx, wherein GxIt is the actual gain of node x, the known conditions of this algorithm；
ΦxIt is node x and remaining N-1 financial value of node game, is tried to achieve by game；YxIt is the adjacency vector of node x, is us
It is required that solution.By Gx、Φx, it is known that by inverse of a matrix computing, obtaining the adjacency vector Y of node xx, i.e. avrage [x].
(7) the adjacency vector avrage [x] of node d_value [1] [1] is assigned to step according to symmetry principle correspondence
(4) the 100 matrix matrix [N] [N] [A] for obtaining：Matrix [x] [N] [A]=avrage [x], matrix [N] [x] [A]
=avrage [x], obtains 100 new initial populations, according to step (3) operation once；
(8) repeat step (5), (6), (7) are until nodes revenue value and actual equal, the network for being reconstructed.
To sum up, the present invention is obtained according to nodes revenue value to 100 cross and variations of sample adjacency matrix for randomly generating
Preferable sample adjacency matrix, then reconstructs part of nodes according to compression sensing method, final to obtain the correct adjacency matrix of network.
Present invention incorporates theory of games and the method for genetic algorithm, can be quick, accurately reconstruct the true topological structure of network.
Reconstruct in gene regulatory network, based on the neck such as social discrete data or information illustration tissue net engineering science and territorial protection
There is important application in domain.The present invention is not only few to node, spends small network practicality, Er Qiexiao also very useful for big network
Rate is high, is not constrained by network is openness.
Effect of the invention can be further illustrated by following experiment：
1. simulated conditions：
It is the 2.4GHZ of core 2, Microsoft Visual C++ is used in the system of internal memory 4G, WINDOWS 7 in CPU
6.0 are emulated.
2. emulation content：
Choosing one has 34 nodes, and 78 karate club networks on side, node degree minimum 1 is 17 to the maximum.
In experiment, 100 sample adjacency matrix of generation, after the evolution in 100 generations intersects, obtain 100 preferable samples adjacent at random
Matrix is connect, then in conjunction with compressed sensing restructing algorithm, a node, Population Regeneration, an iteration generation, when extraction population is often reconstructed
Terminate when nodes revenue value is equal with actual gain value, that is, obtain network of network, we receive after being reconstructed 17 nodes in experiment
Benefit value is just equal.
In experiment, the true connection of Tu3Shi karates club network, Fig. 4 is by the correct of our method reconstruct
Situation.From experimental result, using the network reconstruction method proposed in the present invention, can be very good to reconstruct the topology of network
Structure.
Above-mentioned implementation method is only an example of the present invention, does not constitute any limitation of the invention, for example, sent out with this
Bright method is also applied to the reconstruct of other networks, such as 62 nodes, and 159 dolphin networks on side, computer random is produced
100 nodes, 301 EA networks on side etc..
3. experimental result
It is the simulation result of corresponding experiment in Fig. 4, abscissa represents the nodes of reconstruct, and ordinate represents wrong side number,
It can be seen that the wrong side number of reconstruct is to reach 0 after 18 nodes are reconstructed, network reconfiguration is correct.
To sum up, the present invention is obtained according to nodes revenue value to 100 cross and variations of sample adjacency matrix for randomly generating
Preferable sample adjacency matrix, then reconstructs part of nodes according to compression sensing method, final to obtain the correct adjacency matrix of network.
Present invention incorporates theory of games and the method for genetic algorithm, can be quick, accurately reconstruct the true topological structure of network.
Reconstruct in gene regulatory network, based on the neck such as social discrete data or information illustration tissue net engineering science and territorial protection
There is important application in domain.The present invention is not only few to node, spends small Web vector graphic, Er Qiexiao also very useful for big network
Rate is high.
The part that the present embodiment is not described in detail belongs to the known conventional means of the industry, does not describe one by one here.With
On enumerate only to of the invention for example, do not constitute the limitation to protection scope of the present invention, it is every with it is of the invention
Same or analogous design is belonged within protection scope of the present invention.
Claims (2)
1. the Network Reconfiguration Algorithm of game and genetic algorithm is based on, it is characterised in that：Comprise the following steps：
(1) 0-1 matrixes matrix [N] [N] [A] of A N*N of random initializtion first, A=100；
(2) under prisoners' dilemma game, the game strategies state [N] of N number of node is initialized, then calculates real network and exist
Nodes revenue and total revenue payoff_real [N+1] under game strategies state [N], and A matrix matrix [N] [N]
The income payoff [N+1] [A] of [A]；
(3) calculating process of genetic algorithm：
(3.1) it is random from A matrix matrix [N] [N] [A] every time to extract two matrix matrix [N] [N] [a] without repetition
With matrix [N] [N] [b], wherein a ≠ b, a, b represent the matrix randomly selected respectively；
(3.2) first filial generation txt [N] [N] [a's] obtains：
The parent of total revenue and actual total revenue difference minimum is chosen as first filial generation, when | payoff [N] [a]-
Payoff_real [N] | during≤| payoff [N] [b]-payoff_real [N] |, txt [N] [N] [a]=matrix [N] [N]
[a]；Otherwise txt [N] [N] [a]=matrix [N] [N] [b]；
(3.3) second filial generation txt [N] [N] [b's] obtains：
For the selection of the rows of txt [i] [N] [b] i-th, that is, i-th selection of the adjacency vector of node：
Intersect：The i-th row that i-th nodes revenue is closer to the parent of payoff_real [i] is chosen, i.e.,
As | payoff [i] [a]-payoff_real [i] |≤| payoff [i] [b]-payoff_real [i] |,
Txt [i] [N] [b]=matrix [i] [N] [a] and payoff_txt [i]=payoff [i] [a],
Otherwise txt [i] [N] [b]=matrix [i] [N] [b], payoff_txt [i]=payoff [i] [b], in formula N represent by
N number of value of the rows of matrix [i] [N] [b] i-th is all assigned to txt [i] [N] [b]；
Variation：After the selection of the i-th row, as txt [i] [j] [b] ≠ txt [j] [i] [b], prop chooses:
As the random number random of generation<During prop, txt [i] [j] [b]=txt [j] [i] [b] updates node i financial value
Payoff_txt [i], otherwise txt [j] [i] [b]=txt [i] [j] [b], update nodes revenue value payoff_txt [j]；
(3.4) final updating population, matrix [N] [N] [a]=txt [N] [N] [a], matrix [N] [N] [b]=txt [N]
[N][b]；
(3.5) repeat step (3) 50 times；
(4) T step (2) and (3) are repeated, T=100, i.e. population recruitment iteration 100 times obtain A adjacency matrix matrix
[N][N][A]；
(5) a matrix matrix [N] [N] [m] is randomly selected, the difference of calculate node income and actual gain is simultaneously arranged in descending order
Row d_value [N] [2], first row memory node, secondary series stores the income difference of the node；
(6) node x=d_value [1] [1] is reconstructed with the restructing algorithm based on compressed sensing and game, obtain the adjoining of x to
Amount avrage [x]：
(7) the adjacency vector avrage [x] of node d_value [1] [1] step (4) is assigned to according to symmetry principle correspondence to obtain
The 100 matrix matrix [N] [N] [A] arrived, obtain 100 new initial populations, according to step (3) operation once；
(8) repeat step (5), (6), (7) are until nodes revenue value and actual equal, the network for being reconstructed.
2. the Network Reconfiguration Algorithm based on game and genetic algorithm according to claim 1, it is characterised in that：Wherein step
(2) income of the calculate node described in is calculated by following formula：
S (C)=(1,0)TS (D)=(0,1)T
Wherein, P is a 2*2 gain matrix：
FijRepresent the financial value that node i is obtained with node j game posterior nodal points i；
GiRepresent node i and the financial value sum with i connected node games；
ГiExpression has the set of the node being connected with node i；
Si、SjRepresent the strategy matrix of node i and node j；
The transposition symbol of the T representing matrixs in formula；
S (C) is expressed as the strategy matrix of cooperation, and S (D) is expressed as the strategy matrix betrayed.
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