CN104331738A - Network reconfiguration algorithm based on game theory and genetic algorithm - Google Patents

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

Based on the Network Reconfiguration Algorithm of game and genetic algorithm

Technical field

The invention belongs to complex network technical field, relate to reconstruct and the data mining technology of complex network, specifically a kind of Network Reconfiguration Algorithm based on game and genetic algorithm.

Background technology

Complex network is the abstract a kind of form of expression out of complication system in real world, a lot of such complex network is there is in real world, such as, neural network and metabolic network etc. in the friends network in community network, power network, WWW, bio-networks.In real world network, we are abstracted into the independent individual in system the node in network, and in system, between individuality, according to certain rule, a kind of relation of self-assembling formation or arteface is abstracted into the limit between node.

Since within 1998,1999, to have delivered two sections of articles about small-world network and Scale-free network on " Nature " and " Science " two publications, worldwide start the research boom of one complex network.After this in the past few years, the research about complex network achieves much important achievement in research, and complex network has become a key areas of scientific research.

Because complex network node is numerous, complex structure, makes its research very difficult.In many fields of Science and engineering, the interested system that people run into is made up of the element of networking, and these elements are called node, but the interaction of the node of this pattern and node or network topology structure are complete the unknowns.The network topology structure wherein do not disclosed can be extracted and somely to obtain based on seasonal effect in time series data from experiment or observed result.

In the past few years, network reconfiguration problem receives increasing concern, the algorithm that great majority exist is all based on compressed sensing algorithm, it utilizes the openness of network, with compressed sensing model reconstruction network, fine for sparse network effect, but the shortcoming meanwhile existed is exactly openness constraint, just can not reconstruct correctly for the network such as community network etc. that complexity is not sparse, and time complexity is very high, very time-consuming for macroreticular reconstruct, for the shortcoming of existing algorithm, the deficiency of the existing algorithm that this algorithm solves, not by sparsity constraints, and greatly reduce time complexity.

Summary of the invention

The object of the invention is to the attribute information according to network node, reconstruct the whole topological structure of network, a kind of Network Reconfiguration Algorithm based on game and genetic algorithm is provided.

Technical scheme of the present invention is: based on the Network Reconfiguration Algorithm of game and genetic algorithm, comprise the steps:

(1) 0-1 matrix matrix [N] [N] [A] of first random initializtion A N*N, A=100;

(2) under prisoners' dilemma game, the N number of node of initialization game strategies state [N], then the nodes revenue of real network under game strategies state [N] and total revenue payoff_real [N+1] is calculated, and income payoff [N+1] [A] of A matrix matrix [N] [N] [A];

(3) computation process of genetic algorithm:

(3.1) each random without repeating extraction two matrix matrix [N] [N] [a] and matrix [N] [N] [b] from A matrix matrix [N] [N] [A], wherein a ≠ b, a, b represent the matrix randomly drawed respectively;

(3.2) first filial generation txt [N] [N] [a] obtains:

Choose total revenue and the minimum parent of actual total revenue difference as first filial generation, when | payoff [N] [a]-payoff_real [N] |≤| payoff [N] [b]-payoff_real [N] | time, 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] obtains:

For txt [i] [N] [b] i-th the choosing of row, namely the choosing of adjacency vector of i-th node:

Intersect: choose i-th nodes revenue comparatively close to the i-th row of the parent of payoff_real [i], namely

When | payoff [i] [a]-payoff_real [i] |≤| payoff [i] [b]-payoff_real [i] | time,

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 matrix [i] [N] [b] i-th N number of value of row be all assigned to txt [i] [N] [b];

Variation: after the i-th row is chosen, as txt [i] [j] [b] ≠ txt [j] [i] [b], choose with Probability p rop: $\mathrm{prop}=\frac{|\mathrm{payoff}\_\mathrm{txt}[i]-\mathrm{payoff}\_\mathrm{real}[i\left]\right|}{|\mathrm{payoff}\_\mathrm{txt}[i]-\mathrm{payoff}\_\mathrm{real}[i\left]\right|+|\mathrm{payoff}\_\mathrm{txt}[j]-\mathrm{payoff}\_\mathrm{real}[j\left]\right|}$

As the random number random<prop generated, txt [i] [j] [b]=txt [j] [i] [b], upgrade node i financial value payoff_txt [i], otherwise txt [j] [i] [b]=txt [i] [j] [b], upgrades 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) step (3) 50 times are repeated;

(4) repeat T step (2) and (3), T=100, i.e. population recruitment iteration 100 times, obtain A adjacency matrix matrix [N] [N] [A];

(5) randomly draw a matrix matrix [N] [N] [m], the difference of computing node and actual gain also presses descending sort d_value [N] [2], first row memory node, and secondary series stores the income difference of this node;

(6) with the restructing algorithm based on compressed sensing and game, node x=d_value [1] [1] is reconstructed, obtains the adjacency vector avrage [x] of x:

(7) 100 matrix matrix [N] [N] [A] that the adjacency vector avrage [x] of node d_value [1] [1] obtains to step (4) according to the corresponding assignment of symmetry principle, obtain 100 new initial population, run once according to step (3);

(8) repeat step (5), (6), (7) until nodes revenue value is equal with reality, obtain the network reconstructed.

The income of the computing node described in above-mentioned steps (2) is by formulae discovery below:

$F_{\mathrm{ij}}=S_i^{T}P{S}_j$ $G_i=\underset{j\&Element;{\mathrm{\&Gamma;}}_i}{\mathrm{\&Sigma;}}{S}_i^{T}P{S}_j$

S(C)＝(1，0) ^TS(D)＝(0，1) ^T

Wherein, P is a 2*2 gain matrix: $P=\left(\begin{array}{cc}0.95& -0.14\\ 1.56& 0.6\end{array}\right)$

F _ijrepresent the financial value that node i and node j game posterior nodal point i obtain;

G _irepresent node i and the financial value sum with the game of i connected node;

Г _irepresent the set having the node be connected with node i;

S _i, S _jrepresent the strategy matrix of node i and node j;

The transposition symbol of the T representing matrix in formula;

S (C) is expressed as the strategy matrix of cooperation, and S (D) is expressed as the strategy matrix of betrayal.

Beneficial effect of the present invention: the present invention is according to the cross and variation of nodes revenue value to random 100 the sample adjacency matrix produced, obtain good sample adjacency matrix, then according to compression sensing method reconstructing part partial node, the adjacency matrix that final network is correct.Present invention incorporates the method for theory of games and genetic algorithm, can be quick, reconstruct the true topological structure of network accurately.In the reconstruct of gene regulatory network, the fields such as net engineering science and territorial protection are organized to have important application based on social discrete data or information illustration.The present invention is not only few to node, spends little network implementation use, also very practical for macroreticular, and efficiency is high, not by the constraint that network is openness.

Below with reference to accompanying drawing, the present invention is described in further details.

Accompanying drawing explanation

Fig. 1 is FB(flow block) of the present invention;

Fig. 2 is Optimization Steps of the present invention;

Fig. 3 is the figure that in the embodiment of the present invention, has 34 nodes;

Fig. 4 is the reconstruction result of network in the embodiment of the present invention.

Embodiment

Software runtime environment of the present invention is MicrosoftVisualC++6.0, and the concrete steps of enforcement see figures.1.and.2, and the present invention is based on the Network Reconfiguration Algorithm of game and genetic algorithm, comprises the following steps:

(1) 0-1 matrix matrix [N] [N] [A] of first random initializtion A N*N, A=100;

(2) under prisoners' dilemma game, the N number of node of initialization game strategies state [N], then the nodes revenue of real network under game strategies state [N] and total revenue payoff_real [N+1] is calculated, and income payoff [N+1] [A] of A matrix matrix [N] [N] [A];

The income of computing node is by formulae discovery below:

$F_{\mathrm{ij}}=S_i^{T}P{S}_j$ $G_i=\underset{j\&Element;{\mathrm{\&Gamma;}}_i}{\mathrm{\&Sigma;}}{S}_i^{T}P{S}_j$

S(C)＝(1，0) ^TS(D)＝(0，1) ^T

Wherein, P is a 2*2 gain matrix: $P=\left(\begin{array}{cc}0.95& -0.14\\ 1.56& 0.6\end{array}\right)$

F _ijrepresent the financial value that node i and node j game posterior nodal point i obtain;

G _irepresent node i and the financial value sum with the game of i connected node;

Г _irepresent the set having the node be connected with node i;

S _i, S _jrepresent the strategy matrix of node i and node j;

The transposition symbol of the T representing matrix in formula;

S (C) is expressed as the strategy matrix of cooperation, and S (D) is expressed as the strategy matrix of betrayal.

(3) computation process of genetic algorithm:

(3.1) each random without repeating extraction two matrix matrix [N] [N] [a] and matrix [N] [N] [b] from A matrix matrix [N] [N] [A], wherein a ≠ b, a, b represent the matrix randomly drawed respectively;

(3.2) first filial generation txt [N] [N] [a] obtains:

Choose total revenue and the minimum parent of actual total revenue difference as first filial generation, when | payoff [N] [a]-payoff_real [N] |≤| payoff [N] [b]-payoff_real [N] | time, 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] obtains:

For txt [i] [N] [b] i-th the choosing of row, namely the choosing of adjacency vector of i-th node:

Intersect: choose i-th nodes revenue comparatively close to the i-th row of the parent of payoff_real [i], namely

When | payoff [i] [a]-payoff_real [i] |≤| payoff [i] [b]-payoff_real [i] | time,

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 matrix [i] [N] [b] i-th N number of value of row be all assigned to txt [i] [N] [b];

Variation: after the i-th row is chosen, as txt [i] [j] [b] ≠ txt [j] [i] [b], choose with Probability p rop: $\mathrm{prop}=\frac{|\mathrm{payoff}\_\mathrm{txt}[i]-\mathrm{payoff}\_\mathrm{real}[i\left]\right|}{|\mathrm{payoff}\_\mathrm{txt}[i]-\mathrm{payoff}\_\mathrm{real}[i\left]\right|+|\mathrm{payoff}\_\mathrm{txt}[j]-\mathrm{payoff}\_\mathrm{real}[j\left]\right|}$

As the random number random<prop generated, txt [i] [j] [b]=txt [j] [i] [b], upgrade node i financial value payoff_txt [i], otherwise txt [j] [i] [b]=txt [i] [j] [b], upgrades 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) step (3) 50 times are repeated;

(4) repeat T step (2) and (3), T=100, i.e. population recruitment iteration 100 times, obtain A adjacency matrix matrix [N] [N] [A];

(5) randomly draw a matrix matrix [N] [N] [m], the difference of computing node and actual gain also presses descending sort d_value [N] [2], first row memory node, and secondary series stores the income difference of this node;

(6) with the restructing algorithm based on compressed sensing and game, node x=d_value [1] [1] is reconstructed, obtains the adjacency vector avrage [x] of x:

According to compressed sensing model G _x=Φ _xy _x, wherein G _xfor the actual gain of node x, the known conditions of this algorithm; Φ _xfor the financial value of node x and all the other N-1 node game, tried to achieve by game; Y _xfor the adjacency vector of node x, it is the solution that we require.By G _x, Φ _xknown, by inverse of a matrix computing, obtain the adjacency vector Y of node x _x, i.e. avrage [x].

(7) 100 matrix matrix [N] [N] [A]: matrix [x] [N] [A]=avrage [x] that the adjacency vector avrage [x] of node d_value [1] [1] obtains to step (4) according to the corresponding assignment of symmetry principle, matrix [N] [x] [A]=avrage [x], obtain 100 new initial population, run once according to step (3);

(8) repeat step (5), (6), (7) until nodes revenue value is equal with reality, obtain the network reconstructed.

To sum up, the present invention, according to the cross and variation of nodes revenue value to random 100 the sample adjacency matrix produced, obtains good sample adjacency matrix, then according to compression sensing method reconstructing part partial node, and the adjacency matrix that final network is correct.Present invention incorporates the method for theory of games and genetic algorithm, can be quick, reconstruct the true topological structure of network accurately.In the reconstruct of gene regulatory network, the fields such as net engineering science and territorial protection are organized to have important application based on social discrete data or information illustration.The present invention is not only few to node, spends little network implementation use, also very practical for macroreticular, and efficiency is high, not by the constraint that network is openness.

Effect of the present invention can be further illustrated by following experiment:

1. simulated conditions:

Be core22.4GHZ at CPU, internal memory 4G, WINDOWS7 system uses Microsoft visual c++ 6.0 to emulate.

2. emulate content:

Choose one and have 34 nodes, the karate club network on 78 limits, node degree is minimum is 1, is 17 to the maximum.In experiment, stochastic generation 100 sample adjacency matrix, after the evolution in 100 generations intersects, obtain 100 good sample adjacency matrix, then in conjunction with compressed sensing restructing algorithm, often reconstruct a node, Population Regeneration, an iteration generation, stops when the nodes revenue value extracting population is worth equal with actual gain, namely obtain network of network, after in experiment, we are reconstructed 17 nodes, financial value is just equal.

In experiment, the true connection of Tu3Shi karate club network, Fig. 4 is the correct situation of the method reconstruct by us.From experimental result, adopt the network reconstruction method proposed in the present invention, can well topology of networks be reconstructed.

Above-mentioned embodiment is only an example of the present invention, does not form any limitation of the invention, such as, can also be applied to the reconstruct of other networks by the inventive method, as 62 nodes, article 159, the dolphin network on limit, 100 nodes that computer random produces, the EA network etc. on 301 limits.

3. experimental result

At the simulation result that Fig. 4 is corresponding experiment, horizontal ordinate represents the nodes of reconstruct, and ordinate represents wrong limit number, and can find out that namely the wrong limit number when reconstructing after reconstruct 18 nodes reaches 0, network reconfiguration is correct.

To sum up, the present invention, according to the cross and variation of nodes revenue value to random 100 the sample adjacency matrix produced, obtains good sample adjacency matrix, then according to compression sensing method reconstructing part partial node, and the adjacency matrix that final network is correct.Present invention incorporates the method for theory of games and genetic algorithm, can be quick, reconstruct the true topological structure of network accurately.In the reconstruct of gene regulatory network, the fields such as net engineering science and territorial protection are organized to have important application based on social discrete data or information illustration.The present invention is not only few to node, spends little Web vector graphic, also very practical for macroreticular, and efficiency is high.

The part that the present embodiment does not describe in detail belongs to the known conventional means of the industry, does not describe one by one here.More than exemplifying is only illustrate of the present invention, does not form the restriction to protection scope of the present invention, everyly all belongs within protection scope of the present invention with the same or analogous design of the present invention.

Claims (2)

1., based on the Network Reconfiguration Algorithm of game and genetic algorithm, it is characterized in that: comprise the steps:

(1) 0-1 matrix matrix [N] [N] [A] of first random initializtion A N*N, A=100;

(2) under prisoners' dilemma game, the game strategies state [N] of the N number of node of initialization, then the nodes revenue of real network under game strategies state [N] and total revenue payoff_real [N+1] is calculated, and income payoff [N+1] [A] of A matrix matrix [N] [N] [A];

(3) computation process of genetic algorithm:

(3.1) each random without repeating extraction two matrix matrix [N] [N] [a] and matrix [N] [N] [b] from A matrix matrix [N] [N] [A], wherein a ≠ b, a, b represent the matrix randomly drawed respectively;

(3.2) first filial generation txt [N] [N] [a] obtains:

Choose total revenue and the minimum parent of actual total revenue difference as first filial generation, when | payoff [N] [a]-payoff_real [N] |≤| payoff [N] [b]-payoff_real [N] | time, 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] obtains:

For txt [i] [N] [b] i-th the choosing of row, namely the choosing of adjacency vector of i-th node:

Intersect: choose i-th nodes revenue comparatively close to the i-th row of the parent of payoff_real [i], namely

When | payoff [i] [a]-payoff_real [i] |≤| payoff [i] [b]-payoff_real [i] | time,

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 matrix [i] [N] [b] i-th N number of value of row be all assigned to txt [i] [N] [b];

Variation: after the i-th row is chosen, as txt [i] [j] [b] ≠ txt [j] [i] [b], choose with Probability p rop: $\mathrm{prop}=\frac{|\mathrm{payoff}\_\mathrm{txt}[i]-\mathrm{payoff}\_\mathrm{real}[i\left]\right|}{|\mathrm{payoff}\_\mathrm{txt}[i]-\mathrm{payoff}\_\mathrm{real}[i\left]\right|+|\mathrm{payoff}\_\mathrm{txt}[j]-\mathrm{payoff}\_\mathrm{real}[j\left]\right|}$

As the random number random<prop generated, txt [i] [j] [b]=txt [j] [i] [b], upgrade node i financial value payoff_txt [i], otherwise txt [j] [i] [b]=txt [i] [j] [b], upgrades 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) step (3) 50 times are repeated;

(4) repeat T step (2) and (3), T=100, i.e. population recruitment iteration 100 times, obtain A adjacency matrix matrix [N] [N] [A];

(5) randomly draw a matrix matrix [N] [N] [m], the difference of computing node and actual gain also presses descending sort d_value [N] [2], first row memory node, and secondary series stores the income difference of this node;

(6) with the restructing algorithm based on compressed sensing and game, node x=d_value [1] [1] is reconstructed, obtains the adjacency vector avrage [x] of x:

(7) 100 matrix matrix [N] [N] [A] that the adjacency vector avrage [x] of node d_value [1] [1] obtains to step (4) according to the corresponding assignment of symmetry principle, obtain 100 new initial population, run once according to step (3);

(8) repeat step (5), (6), (7) until nodes revenue value is equal with reality, obtain the network reconstructed.

2. the Network Reconfiguration Algorithm based on game and genetic algorithm according to claim 1, is characterized in that: the income of the computing node wherein described in step (2) is by formulae discovery below:

$\begin{array}{cc}{F}_{\mathrm{ij}}=S_i^{T}P{S}_j& G_i\text{=}\underset{j\&Element;{\mathrm{\&Gamma;}}_i}{\mathrm{\&Sigma;}}{S}_i^{T}P{S}_j\end{array}$

$\begin{array}{cc}S\left(C\right)={\left(\mathrm{1,0}\right)}^T& S\left(D\right)={\left(\mathrm{0,1}\right)}^T\end{array}$

Wherein, P is a 2*2 gain matrix: $P=\left(\begin{array}{cc}0.95& -0.14\\ 1.56& 0.6\end{array}\right)$

F _ijrepresent the financial value that node i and node j game posterior nodal point i obtain;

G _irepresent node i and the financial value sum with the game of i connected node;

Г _irepresent the set having the node be connected with node i;

S _i, S _jrepresent the strategy matrix of node i and node j;

The transposition symbol of the T representing matrix in formula;

S (C) is expressed as the strategy matrix of cooperation, and S (D) is expressed as the strategy matrix of betrayal.