CN109063837A - Genetic algorithm information flow network property analysis method based on complex network structures entropy - Google Patents
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Abstract
The present invention relates to the genetic algorithm information flow network property analysis method based on complex network structures entropy, including building genetic algorithm information flow network model, when edged simultaneously to by selection but without by intersecting, the individual progress edged of variation；Genetic algorithm information flow network structure entropy is calculated, genetic algorithm information flow network heterogeneity is analyzed.The method of the present invention, can be with the heterogeneity of more accurate succinct metric flow network relative to the network structure entropy directly calculated based on the scaling exponent being fitted in network power law degree distribution curve, foundation nodes number and node connectivity；The present invention will be helpful to understand the combination and distribution of outstanding genetic fragment in genetic algorithm evolutionary process, and provide new approaches and new method to design more efficient genetic algorithm；The present invention considered in genetic algorithm information flow network modeling process to by selection but without through intersection, variation individual progress edged, to more precisely describe genetic algorithm dynamic characteristic.
Description
Technical field
The present invention relates to a kind of genetic algorithm information flow network attributive analysis based on complex network structures entropy, belongs to heredity
Algorithmic technique field.
Background technique
Genetic algorithm based on Darwinian evolution and Mendelian inheritance theory is a kind of opening for natural imitation evolutionary process
Hairdo searching algorithm.Currently, genetic algorithm has been successfully applied to various different fields, solve the problems, such as many points such as image
It cuts and handles, function optimization, Combinatorial Optimization, machine scheduling, Machine Layout Design etc..But the performance of genetic algorithm need
It improves, the method for existing improved adaptive GA-IAGA performance is confined to the design of genetic operator, group's generation strategy etc. mostly, from something lost
Propagation algorithm aerodynamic point explore and improve algorithm performance research it is also considerably less, so the present invention is dynamic (dynamical) from genetic algorithm
Angle is further studied.
Complex network be one rapid development emerging cross discipline, the relationship that can be used in description system between individual with
And the collective behavior of system.Complex Networks Theory passes through the generation mechanism of Evolution of building complex network model research complication system,
The structure feature of various complex networks in real world is analyzed, the various dynamic behaviors in complex network occur for research.It is multiple
Miscellaneous network theory Network Virus Propagation, virtual community, temperature change, traffic system, disaster spreading, in terms of
Research work has been achieved for a large amount of achievement.
The present invention is based on Complex Networks Theory research genetic algorithm dynamics.It is existing research have been proven that genetic algorithm into
Change process can be modeled as complex network, i.e. information flow network.With each in the interpretation algorithm operational process of complex network
Kind phenomenon, for example what kind of trend of the outstanding gene between population be, changes the factors such as selection pressure, crossing-over rate or aberration rate
What kind of influence etc. can be generated on the topology of population on earth, is had between the performance and information flow network structure of genetic algorithm very tight
Close connection.Therefore, the genetic algorithm dynamics research based on Complex Networks Theory can be calculated for the more efficient heredity of design
Method provides new approaches and new method.
Document [1,2] is using the individual in population as the node in network, if two nodes, which occur to intersect, generates filial generation,
Edged between these nodes, but do not account for maintaining the multifarious variation behavior of Population Genetics.Document [3,4] is in information
Mutation operation is considered in the modeling process of flow network, but is not accounted for after those are selected not by intersecting, making a variation
Individual, these individuals are equally the important components of information flow network in information flow between generations.On the other hand
Existing research verifying discovery uses roulette selection method when genetic algorithm selection strategy, and obtained information flow network is uncalibrated visual servo
Network.In essence, the scaleless property of complex network is exactly a kind of nonhomogeneity, it is one kind " sequence " that network emerges.
There are only a fews to have with " core node " largely connected and largely " frontier node " connected on a small quantity in scales-free network,
So scales-free network is non-homogeneous or heterogeneous.Existing research is distributed using scales-free network power law degree
In scaling exponent portray this heterogeneity, scaling exponent is bigger, power law degree distribution curve decline it is faster, network it is non-homogeneous
Property is more obvious.But from the definition of scales-free network as can be seen that scaling exponent is only fitted network power law degree distribution curve
One estimation parameter.In fact, being abstracted in obtained complex network model in real world, power law degree distribution curve may be
Quite irregular curve, it is also possible to be not the curve of strictly decreasing, even the curve to successively decrease, by being fitted the mark obtained
It is also very inaccurate for spending index, and is calculated complicated.
Document [1] Oner M K, Garibay I I, Wu A S.Mating networks in steady state
genetic algorithms are scale free[C].Proceedings of the 8th annual conference
on Genetic and evolutionary computation.ACM,2006:1423-1424.
Document [2] Zelinka I, Davendra D, Lampinen J, et al.Evolutionary algorithms
dynamics and its hidden complex network structures[C].Evolutionary
Computation(CEC),2014 IEEE Congress on.IEEE,2014:3246-3251.
Document [3] Wu J, Shao X, Li J, et al.Scale-free properties of information
flux networks in genetic algorithms[J].Physica A Statistical Mechanics&Its
Applications,2012,391(4):1692-1701.
Document [4] Zhengping Wu, Qiong Xu, Gaosheng Ni, et al.The study of genetic
information flux network properties in genetic algorithms[J].International
Journal of Modern Physics C,2015,26(07):1550076-.
Summary of the invention
In view of the drawbacks of the prior art, the present invention provides it is a kind of different from existing research based on the information of scaling exponent
The genetic algorithm information flow network property analysis method based on complex network structures entropy of flow network heterogeneity Analysis method.
In order to solve the above technical problems, technology of the invention the following steps are included:
S1, building genetic algorithm information flow network model, when edged simultaneously to by selection but without by intersecting, variation
Individual carry out edged.
S2, genetic algorithm information flow network structure entropy is calculated, analyzes genetic algorithm information flow network heterogeneity.
Further, step S1 is specifically included:
Initialization population, defining N number of node in network is the individual in population, and individual is exactly the node in network.Each
Node one number i, i=1,2 ..., N are indicated.
Three main operators select, intersect, make a variation in genetic algorithm.Wherein, selection method uses roulette wheel selection,
It is a kind of method that individual is selected according to individual fitness.Crossover operation uses single point crossing method, the i.e. gene in individual
A point is randomly choosed in string, then exchanges the randomly selected subsequent gene of point in two parents.Mutation operation is using conventional
Position mutation is exactly one gene position of random selection in gene string, then negates the genic value on it.
An iteration is considered as a time step, and the line from node i to node j represents parent i by intersecting or making a variation
Genetic stew is contributed to filial generation j.In order to simplify modeling, the individual after selecting is intersecting and mutation process knot as father node
The new node generated after beam is child node, all establishes connection between every a pair of of father node and child node.The present invention is modeling
The improvements of aspect: after selection, intersection, mutation operation, some individuals are selected to remain into the next generation, still
Not by intersecting, making a variation, these individuals are equally the important composition portions of information flow network in information flow between generations
Point, so also must be considered that in the modeling process of genetic algorithm information flow network, it in this way could be to genetic algorithm information drift net
The more accurate analysis of network.
Further, step S2 is specifically included:
Output information flow network after S21, genetic algorithm end of run calculates the connection of each node in information flow network
Degree.
S22, the information integration degree that information flow network is calculated according to node connectivity.
S23, genetic algorithm information flow network structure entropy is calculated according to information integration degree and is normalized.Obviously, information
Flow network structure entropy is bigger, and network is more uniform, otherwise the smaller network of information flow network structure entropy is more uneven.
Change genetic algorithm crossing-over rate, aberration rate, it is total node number in corresponding genetic algorithm information flow network, total
Even changes will occur for number of edges, company's number of edges of each node etc., so that different information flow networks is generated, then to different letters
It ceases flow network and calculates network structure entropy.Finally, observing the information flow network structure entropy under different crossing-over rates, aberration rate is how to become
Change.
Heterogeneity of the present invention using network structure entropy research genetic algorithm information flow network, foundation nodes number
The network structure entropy that mesh and node connectivity calculate reflects the order degree of information flow network, the i.e. heterogeneity of network.Phase
For the estimation Parameter Scale index being fitted from network connection degree distribution curve, network structure entropy can be with more accurate succinct
The heterogeneity of metric flow network.This will be helpful to understand in genetic algorithm evolutionary process the combination of outstanding genetic fragment and
Distribution, and will be helpful to the more efficient genetic algorithm of design；The present invention is in genetic algorithm information flow network modeling process simultaneously
In consider to by selection but without through intersection, variation individual progress edged, to more precisely describe hereditary calculation
Method dynamic characteristic.
Detailed description of the invention
Fig. 1 is information flow network model framework schematic diagram of the invention；
Fig. 2 (a) is the information flow schematic diagram between the individual of the specific embodiment of the invention；
Fig. 2 (b) is the corresponding information flow network figure of Fig. 2 (a)；
Fig. 3 is the information flow network structure entropy schematic diagram under specific embodiment of the invention difference crossing-over rate；
Fig. 4 is the information flow network structure entropy schematic diagram under specific embodiment of the invention Different Variation rate.
Specific embodiment
In order to make the objectives, technical solutions, and advantages of the present invention clearer, below in conjunction with attached drawing to the present invention into
Row is further described.
As shown in Figure 1, being information flow network model framework schematic diagram of the invention.Heredity based on complex network structures entropy
Algorithm information flow network attributive analysis, comprising the following steps:
S1, building genetic algorithm information flow network model, when edged simultaneously to by selection but without by intersecting, variation
Individual carry out edged.
S2, genetic algorithm information flow network structure entropy is calculated, analyzes genetic algorithm information flow network heterogeneity.
In view of genetic algorithm is the algorithm for simulating biological evolution process, the iterative process between itself population can be constructed
Complex network model, but because the present invention is to genetic algorithm finally by the Structure Quantification of population into a network
Each step carries out detailed analysis and then programs, and finally exports an information flow network.
In step sl, initialization population, defining N number of node in network is the individual in population, and individual is exactly in network
Node.Each node one number i, i=1,2 ..., N are indicated.
Because of the not each variable of operation object in genetic algorithm, needs to encode each variable, will ask
The feasible solution of topic is converted into being known as encoding for the various codes (such as binary code, Gray code) of operatings of genetic algorithm.
Binary code is a kind of method of coding, and meaning is exactly that gene individual in population is by a string of binary string groups
At.The length of this gene string is related by the solving precision of required problem.To the gene string of the more high then individual of required precision
It is longer.It is [- 2,1] than section as requested, and the solving precision needed is to be accurate to 4 decimals.So solution procedure is just
Be: siding-to-siding block length is 1- (- 2)=3 first, it is contemplated that section [- 2,1] is at least divided into 3 × 10 by required precision4Equal portions, because
For 16384=214<3×104<215=32768, so the binary string encoded here at least wants 15.Binary system is simply grasped well
Make, facilitates the progress of each operator of genetic algorithm, therefore binary coding method is current most commonly used method, and the present invention
The method of use.
Initial population general recommendations population scale optimized scope is 20 to 100, and the population scale that the present invention chooses is 20.One
As initial population selection be it is random, the range of this random number be optimal solution take up space in entire problem space point
Cloth range.
The present invention is used to assess six classical test function such as 1 institutes of table of information flow network structure feature in genetic algorithm
Show.
1 test function of table
Three main operators select, intersect, make a variation in genetic algorithm.Wherein, selection method uses roulette wheel selection,
It is a kind of method that individual is selected according to individual fitness.Crossover operation uses single point crossing method, the i.e. gene in individual
A point is randomly choosed in string, then exchanges the randomly selected subsequent gene of point in two parents.Mutation operation is using conventional
Position mutation is exactly one gene position of random selection in gene string, then negates the genic value on it.
Genetic algorithm iterative process can be modeled as complex network, i.e. information flow network.Document [1,2] is in population
Body is as the node in network, if two nodes, which occur to intersect, generates filial generations, edged between these nodes, but do not examine
Consider and maintains the multifarious variation behavior of Population Genetics.Document [3,4] considers variation in the modeling process of information flow network
Operation, but do not account for not by the individual for intersecting, making a variation after those are selected, these individuals are in letter between generations
Breath flowing is equally the important component of information flow network.The present invention considers in genetic algorithm information flow network modeling process
These connect side, to more precisely describe genetic algorithm dynamic characteristic.
Individual in population is defined as the node in information flow network, each node corresponding number designation an i, i=
1,2...,N.An iteration is considered as a time step, and the line from node i to node j represents parent i by intersecting or making a variation
Genetic stew is contributed to filial generation j.In order to simplify modeling, the individual after selecting is intersecting and mutation process knot as father node
The new node generated after beam is child node, all establishes connection between every a pair of of father node and child node.The present invention is modeling
The improvements of aspect: after selection, intersection, mutation operation, some individuals are selected to remain into the next generation, still
Not by intersecting, making a variation, these individuals are equally the important composition portions of information flow network in information flow between generations
Point, so also must be considered that in the modeling process of genetic algorithm information flow network, it in this way could be to genetic algorithm information drift net
The more accurate analysis of network.
Fig. 2 (a) is the information flow schematic diagram between the individual of the specific embodiment of the invention；
As shown in Fig. 2 (a), by taking 6 individuals as an example, after selection, individual 11000 is eliminated, and individual 00011 is selected
It has selected twice.Then, individual 10111 intersects with individual 00011 and individual 00011 with individual 00110 respectively generates new individual
10011,00111,00010,00111.Then, individual 10011, which morphs, generates individual 10010.Wherein, individual 01100 He
10101 there is no intersecting and making a variation, but they can also enter the next generation, so carrying out them from ring edged.On the one hand,
This can show these individuals from a generation to the transmittance process in another generation.On the other hand, this can be individual these and be eliminated
Individual such as above-mentioned individual 11000 distinguishes.Fig. 2 (b) is the corresponding information flow network figure of Fig. 2 (a)；
Genetic algorithm information flow network is exported after meeting termination condition, and network structure then is calculated to information flow network
Entropy.
The related concept of entropy is first introduced below, is defined information flow network structure entropy and is carried out the non-homogeneous of quantitative study information flow network
Property.The Connected degree of node determines the significance level of node in a network in a sense.It is integrated that nodal information is provided first
The definition of degree.
1 present invention is defined to claim
For the information integration degree of i-th of node in information flow network, wherein N is the number of information flow network interior joint, Ci
For the Connected degree of i-th of node in information flow network.Note: work as CiWhen=0, the node is nonsensical to discussing, therefore assumes Ci> 0,
To Si>0。
Entropy is the measurement of " unordered ", if network connects at random, the information integration degree of each node is roughly the same, that
Think that network is " unordered "., whereas if network is uncalibrated visual servo, there are a small amount of " core node " and a large amount of " ends in network
The information integration degree of tip node ", node has differences, then it is assumed that this network is " orderly ".Information flow network is set forth below
The concept of structure entropy quantitatively measures this " sequence " with information flow network structure entropy.
2 present invention are defined to claim
For information flow network structure entropy, wherein N is information flow network interior joint number, SiIt is i-th in information flow network
The information integration degree of node.
It it is easy to show that, when network substantially uniformity, i.e.,When, IE is maximized
As it is assumed that Ci> 0 and CiFor integer, thus when in information flow network all nodes all with some central node phase
(might as well set and all be connected with first node), i.e. C1=N-1, CjNetwork is least uniform when=1 (j ≠ 1), information flow network structure
Entropy is minimum.When When, have
In order to exclude influence of the interstitial content N to IE, information flow network structure entropy is normalized.
3 present invention are defined to claim
For the standard structure entropy of information flow network, wherein N is nodes number, SiFor the information collection of i-th of node
Cheng Du.Obviously
With the heterogeneity of information flow network structure entropy research information flow network, it is not to say that with information flow network structure entropy
Replace Connected degree distribution.Information flow network structure entropy and Connected degree distribution relationship, just as stochastic variable numerical characters with
The relationship of its probability-distribution function, the two complement one another.Information flow network structure entropy is that determining, letter is distributed by Connected degree
Ceasing flow network structure entropy can be with the heterogeneity of more accurate succinct metric flow network.
As shown in Figure 3 and Figure 4, information flow network structure entropy is reducing when crossing-over rate increases, when aberration rate increases
When, information flow network structure entropy is to increase.Information flow network structure entropy increase means that information flow network is more and more equal
Even, the reduction of information flow network structure entropy means that information flow network is more and more uneven.It is therefore found that when crossing-over rate increases
Information flow network is more and more uneven when adding, and information flow network is more and more uniform when aberration rate increases.
Existing research describes the degree k in information flow network and the relationship between degree Probability p (k), finds node degree
Power-law distribution p (k) ∝ k is obeyed in distribution-α, wherein α is exactly scaling exponent.Existing research passes through the fitting estimation of maximum likelihood fitting process
Scaling exponent α out, thus the heterogeneity of research information flow network.Scaling exponent is bigger, and the decline of power law degree distribution curve is faster,
The heterogeneity of network is more obvious.But it can be seen that scaling exponent only to network power law degree point from the definition of scales-free network
One estimation parameter of cloth curve matching.In fact, in abstract obtained various complex network models, power law degree distribution curve
It may be quite irregular curve, it is also possible to not be the curve of strictly decreasing, even the curve to successively decrease, be obtained by fitting
Scaling exponent be also very inaccurate, and calculate complicated.It is directly counted according to nodes number and node connectivity
The network structure entropy of calculation reflects the order degree of information flow network, the i.e. heterogeneity of network.Relative to from network connection degree
The scaling exponent being fitted in distribution curve, network structure entropy can be with the non-homogeneous of more accurate succinct metric flow network
Property.This will be helpful to understand the combination and distribution of outstanding genetic fragment in genetic algorithm evolutionary process, and will be helpful to design more
Add efficient genetic algorithm.
The above is only a preferred embodiment of the present invention, it is noted that for the ordinary skill people of the art
For member, without departing from the technical principles of the invention, several improvement and deformations can also be made, these improvement and deformations
Also it should be regarded as protection scope of the present invention.
Claims (6)
1. the genetic algorithm information flow network attributive analysis based on complex network structures entropy characterized by comprising
S1, building genetic algorithm information flow network model, when edged simultaneously to by selection but without by intersecting, of variation
Body carries out edged；
S2, genetic algorithm information flow network structure entropy is calculated, analyzes genetic algorithm information flow network heterogeneity.
2. the genetic algorithm information flow network attributive analysis according to claim 1 based on complex network structures entropy, special
Sign is that step S1 is specifically included:
Initialization population, defining N number of node in network is the individual in population, and individual is exactly the node in network；Each node
With a number i, i=1,2 ..., N is indicated；
Select individual as father node, the new node generated after intersecting and mutation process is child node；
Connection is all established between every a pair of of father node and child node.
3. the genetic algorithm information flow network attributive analysis according to claim 1 based on complex network structures entropy, special
Sign is that step S2 is specifically included:
Output information flow network after S21, genetic algorithm end of run calculates the Connected degree of each node in information flow network；
S22, the information integration degree that information flow network is calculated according to node connectivity；
S23, genetic algorithm information flow network structure entropy is calculated according to information integration degree and is normalized.
4. genetic algorithm information flow network property analysis method according to claim 3, characterized in that believe in step S22
The expression formula for ceasing integrated level is as follows:
Wherein SiFor the information integration degree of i-th of node in information flow network, N is the number of information flow network interior joint, CiFor letter
Cease the Connected degree of i-th of node in flow network.
5. genetic algorithm information flow network property analysis method according to claim 4, characterized in that in step S23 according to
It is believed that the expression formula that breath integrated level calculates genetic algorithm information flow network structure entropy is as follows:
Wherein IE is information flow network structure entropy.
6. genetic algorithm information flow network property analysis method according to claim 5, characterized in that information flow network
The expression formula that structure entropy IE is normalized is as follows:
WhereinFor cease flow network standard structure entropy,
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| CN114582418A (en) * | 2022-03-08 | 2022-06-03 | 山东大学 | Biomarker identification system based on network maximum information flow model |
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| CN110136019A (en) * | 2019-04-22 | 2019-08-16 | 哈尔滨英赛克信息技术有限公司 | A kind of social media Anomaly groups user's detection method to be developed based on relationship |
| CN114582418A (en) * | 2022-03-08 | 2022-06-03 | 山东大学 | Biomarker identification system based on network maximum information flow model |
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