CN108171331A - A kind of modularity optimization method based on differential evolution algorithm - Google Patents
A kind of modularity optimization method based on differential evolution algorithm Download PDFInfo
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Abstract
The invention discloses a kind of modularity optimization method based on differential evolution algorithm, initialization of population；Network parameter is set, including number of nodes n, adjacency matrix adj, community correction threshold δ；DE algorithm parameters are set, including individual dimension D, Population Size NP, population iterations t and maximum iteration tmax；With the individual representation random initializtion population pop of community's label；Then it identifies and records optimal solution；When population iterations are less than population maximum iteration, population iterations are unsatisfactory for the cycle that condition then terminates 3.1 3.5 from adding one；Next community's amendment is carried out based on neighborhood information；Export the X in popgbest,tIt is divided as final optimal community, the present processes improve accuracy, stability and the scalability that optimal community divides, and have the complex network of very fuzzy community structure including those.
Description
Technical field
The present invention relates to a kind of optimization method, specifically a kind of modularity optimization method based on DE.
Background technology
Stochastic Optimization Algorithms in recent years, especially evolution algorithm (EvolutionaryAlgorithms, EAs), by into
Work(is applied to modularity optimization problem, such as genetic algorithm (GeneticAlgorithm, GA), particle swarm optimization algorithm
(ParticleSwarmOptimization, PSO), Memetic algorithms, ant colony optimization algorithm, Immune Clone Selection and differential evolution are calculated
Method (DifferentialEvolution, DE) etc..It is worth noting that the modularity optimization method based on EA is strong due to having
Big global optimization's ability, shows notable superiority on a variety of test problems.In addition, it is contemplated that in real world network
Prior information acquisition it is more difficult, such algorithm does not need to any prior information (such as community's number) and specific mathematical mould
Type.However, although the modularity optimization method based on EA achieves satisfactory knot on multiple network community test problems
Fruit, but do not solved adequately the problem of Premature Convergence and extreme value degeneration.
Quality is divided in order to overcome the above problem and improve optimal community, the modularity optimization based on EA should be further improved
Convergence energy.Previous experiments the result shows that, the constringency performance of the modularity optimization algorithm based on EA depends primarily on two
A key factor, primary factor are also most important factor is how to improve the global convergence abilities of EA in itself, and another factor is
How to efficiently use network topological information and reduce search space huge in modularity optimization process.However as far as we know, it is existing
Have in algorithm and basic EAs is usually ignored into its convergence capabilities directly as optimisation strategy, so as to cause the Premature Convergence of EAs,
It is also poor that the optimal community obtained divides quality.At the same time, although existing some algorithm carries out the evolutional operation in EAs
It improves, community's detection demand is met, but the inappropriate use of topology information destroys the overall situation most by converged network topology information
The search space that excellent community divides.
Invention content
In view of the deficiencies of the prior art, the present invention proposes a kind of modularity optimization method based on DE, can be effectively
It identifies the community structure of complex network, improves accuracy, stability and scalability that optimal community divides, have including those
The very complex network of fuzzy community structure.
To achieve the above object, the present invention provides a kind of modularity optimization method based on differential evolution algorithm, specifically
Including：
S1：Initialization of population；
S1.1 sets network parameter, including number of nodes n, adjacency matrix adj, community correction threshold δ；DE algorithms ginseng is set
Number, including individual dimension D, Population Size NP, population iterations t and maximum iteration tmax；
S1.2 is with the individual representation random initializtion population pop of community's label；
S2：It identifies and records optimal solution；
S2.1 is identified and is recorded t for the optimum individual X in population popgbest,t；
S2.2 is identified and is recorded t for individual X each in population popi,tHistory optimal solution Xpbesti,t；By all populations
The X of individualpbesti,tBuild initial population pbest_pop；
S3：When population iterations are less than population maximum iteration, population iterations are unsatisfactory for condition from adding one
Then terminate the cycle of S3.1-S3.5；
S3.1 passes through adaptive classification differential variation construction of strategy variation population mutation_pop；
When the value of i is arrived for 1 in Population Size numberical range, step a) is to cycle e) for progress, if the value of i is not arrived 1
In Population Size numberical range, then step a) is jumped out to e), end loop；
A) 3 different individual X are randomly selected from population popr1,t, Xr2,t, Xr3,t；
B) dynamic adjustment Mutation parameter Fi,t、wi,t、Ki,t；
C) according to fitness value Q to Xi,tClassify；
D) according to adaptive classification differential variation strategy generating variation individual Vi,t；
E) V is calculatedi,tModule angle value and and Xi,tIndividual is made comparisons, and more excellent individual is stored in pbest_pop；
If i is more than NP, leapfrog goes out a) suddenly to cycle e)；
S3.2 is based on neighborhood information and carries out community's amendment；
S3.3 is according to variation population mutation_pop and population pop structure cross-species crossover_pop；
When the value of i is arrived for 1 in Population Size numberical range, step a) is to cycle d) for progress, if the value of i is not arrived 1
In Population Size numberical range, then step a) is jumped out to d), end loop；
A) i-th of individual u in cross-species is initializedi,t=xi,t；
B) dynamic adjustment cross parameter CRi,t；
C) by from variation individual Vi,tIt inherits community information and carrys out Adjustment Tests individual ui,t；
D) u is calculatedi,tModule angle value and be compared with i-th of individual in pbest_pop, retain compared with the figure of merit extremely
pbest_pop；
S3.4 is based on neighborhood information and carries out community's amendment；
S3.5 is by replacing all individual update pop in pbest_pop；
S4：Export the X in popgbest,tIt is divided as final optimal community, otherwise returns to S3 steps.
Further, classification adaptive differential class Mutation Strategy, concrete operations are as follows：
For each target individual Xi,tIf its ideal adaptation angle value fiMore than current entire population at individual fitness
The average of value, then be classified as excellent individual, and globally optimal solution is closer in the position of search space；Therefore, in Xi,t
In good gene be reserved for strengthening local search around individual, the corresponding vector V that makes a variationi,tGenerating mode is as follows：
Vi,t=Fi,t.Xpbesti,t+Wi,t.(Xr2,t-Xr3,t)(1)
Wherein, Xpbesti,tRepresent individual Xi,tIn the history optimal solution in preceding t generations, for enhancing individual exploring ability；Xr2,tWith
Xr3,tIt is randomly selected two Different Individuals from population, and meets condition r2 ≠ r3 ≠ i；Fi,tAnd Wi,tIt is XiControl
Parameter, numerical value is according to evolutionary generation and Xi,tIdeal adaptation angle value dynamic adjust；
For each target individual Xi,tIf its ideal adaptation angle value fiLess than current entire population at individual fitness
The average of value is then classified as poor individual, in the position of search space and globally optimal solution farther out；Therefore, strengthen it
The exchanging to promote global search between excellent individual in population, the corresponding vector V that makes a variationi,tGenerating mode is as follows：
Vi,t=Wi,t.Xr1,t+Ki,t.(Xgbest,t-Xi,t)(2)
Wherein Xr1,tIt is the randomly selected individual from population, and meets condition r1 ≠ i；Xgbest,tRepresent current iteration kind
Optimal solution in group, for enhancing Xi,tExploring ability；Wi,tAnd Ki,tIt is XiControl parameter, numerical value is according to evolutionary generation
And Xi,tIdeal adaptation angle value carry out dynamic adjustment.
Further, dynamic, which adjusts Mutation parameter concrete operations, is：Three control parameters W, K, F, respectively mutation process
In random element, social ingredient and cognitive component；In addition, it is also used in crossover operation there are one crucial control parameter CR
Determine each experiment individual ui,tIn from variation individual Vi,tThe percentage of middle succession；Adjustment process is specific as follows：
1. parameter adaptive adjustment is carried out according to the fitness value of individual：To poor individual, strengthen variation and the journey intersected
Degree, to introduce more directivity informations during evolution.Therefore, the random element in mutation process, social ingredient with
And the succession in crossover process all enhances, the CR values in W and K and intersection in corresponding formula (2) are larger；On the contrary, for
For excellent individual, strengthen the cognition part in mutation process, parameter adjustment should defer to opposite principle, corresponding to formula (1)
In larger F values and smaller W values.
2. according to evolution iterations dynamic self-adapting：In early stage of evolving, strengthen the exploring ability of individual, with
Ensure fully to be searched in each individual neighborhood.On the contrary, in the later stage of evolution stage, strengthen the producing capacity of individual, strengthen
The convergence of entire group is accelerated in exchange between individual.According to this principle, F in evolutionary process, the value of W, CR is gradually reduced,
And K values gradually increase.
Based on mentioned above principle, parameter value can be adaptively adjusted, and each individual can obtain in evolutionary process
Dynamic control.Specific operation process is as follows：
Further, it is specifically based on the step of neighborhood information progress community's amendment：If a node, which meets community, corrects item
Part, then the node will likely be placed in again in its all affiliated community of neighborhood node, and the probability being placed in and neighborhood community
Scale it is directly proportional.
The present invention due to using the technology described above, can obtain following technique effect：
The application can efficiently identify the community structure of complex network, improve accuracy, stabilization that optimal community divides
Property and scalability, there is the complex network of very fuzzy community structure including thoseing.
TSP question based on classification will act on all individuals in every generation population to be terminated, therefore each until evolving
The variation of individual, which can access, targetedly to be adjusted.On the one hand, the exploring ability of excellent individual can be strengthened, to increase
Its neighborhood finds the possibility of global optimum；On the other hand, the producing capacity of poor individual can be strengthened, to accelerate it to the overall situation
The search speed of optimization.In short, the evolution demand with different fitness characteristic individuals, can be obtained by new Mutation Strategy
To better meeting.Under the guiding of directivity information, the blindness in search process can efficiently reduce, and offspring individual
It can also be improved with the quality of optimal solution.And the degree of variation of each individual of dynamic self-adapting during evolution.
Historical information will be saved as, and for follow-up evolutional operation by also achieving the outstanding solution generated in entire evolutionary process.
New correction strategy can effectively reduce search space, additionally it is possible to relax limitation when community is corrected, be global optimum
Solution provides sufficient search space, so as to preferably using topology information known to network, and promote the convergence of CDEMO algorithms.
Description of the drawings
Fig. 1 is the adaptive differential evolution algorithm flow chart based on classification；
Fig. 2 is the modularity optimization algorithm CDEMO flow charts based on differential evolution；
Fig. 3 is the CDEMO that the different zout of GN networks is worth to and the average NMI values figure of other algorithms；
Fig. 4 is the CDEMO that the different μ of LFR networks is worth to and the average NMI values figure of other algorithms；
Fig. 5 is that community structure of the CDEMO algorithms on Karate networks divides identification figure；
Fig. 6 is that community structure of the CDEMO algorithms on Dolphin networks divides identification figure；
Fig. 7 is that community structure of the CDEMO algorithms on Polbooks networks divides identification figure；
Fig. 8 is that community structure of the CDEMO algorithms on Football networks divides identification figure.
Specific embodiment
To make the objectives, technical solutions, and advantages of the present invention clearer, it is right in the following with reference to the drawings and specific embodiments
The present invention is described in detail.
Embodiment 1
The modularity optimization algorithm based on DE is present embodiments provided, is specifically included：
First, the modularity optimization algorithm based on DE：
(1) CDEMO algorithms, algorithm flow chart are as shown in Figure 2：
1：Initialization of population；
1.1 setting network parameters, including number of nodes n, adjacency matrix adj, community correction threshold δ.DE algorithm parameters are set,
Including individual dimension D, Population Size NP, population iterations t and maximum iteration tmax；
1.2 with the individual representation random initializtion population pop of community's label；
2：It identifies and records optimal solution
2.1 identify and record t for the optimum individual X in population popgbest,t；
2.2 identify and record t for individual X each in population popi,tHistory optimal solution Xpbesti,t.By all populations
The X of bodypbesti,tBuild initial population pbest_pop；
3：When population iterations are less than population maximum iteration, population iterations are unsatisfactory for condition from adding one
Then terminate the cycle of S3.1-S3.5；
3.1 pass through adaptive classification differential variation construction of strategy variation population mutation_pop；
When the value of i is arrived for 1 in Population Size numberical range, step a) is to cycle e) for progress, if the value of i is not arrived 1
In Population Size numberical range, then step a) is jumped out to e), end loop；
A) 3 different individual X are randomly selected from population popr1,t, Xr2,t, Xr3,t；
B) dynamic adjustment Mutation parameter Fi,t、wi,t、Ki,t；
C) according to fitness value Q to Xi,tClassify；
D) according to adaptive classification differential variation strategy generating variation individual Vi,t；
E) V is calculatedi,tModule angle value and and Xi,tIndividual is made comparisons, and more excellent individual is stored in pbest_pop；
If i is more than NP, leapfrog goes out a) suddenly to cycle e)；
3.2 carry out community's amendment based on neighborhood information；
3.3 according to variation population mutation_pop and population pop structure cross-species crossover_pop；
When the value of i is arrived for 1 in Population Size numberical range, step a) is to cycle d) for progress, if the value of i is not arrived 1
In Population Size numberical range, then step a) is jumped out to d), end loop；
A) i-th of individual u in cross-species is initializedi,t=xi,t；
B) dynamic adjustment cross parameter CRi,t；
C) by from variation individual Vi,tIt inherits community information and carrys out Adjustment Tests individual ui,t；
D) u is calculatedi,tModule angle value and be compared with i-th of individual in pbest_pop, retain compared with the figure of merit extremely
pbest_pop；
3.4 carry out community's amendment based on neighborhood information；
3.5 by replacing all individual update pop in pbest_pop.
4：Stop algorithm if stopping criterion is met, export the X in popgbest,tIt is divided as final optimal community,
Otherwise the 3rd step is returned.
The advantageous effect of generation：CDEMO algorithms can efficiently identify the community structure of complex network, improve optimal community
Accuracy, stability and the scalability of division have the complex network of very fuzzy community structure including those.
CDEMO algorithm performances are tested：
Strategy validity will be changed by experimental verification new communities, and verify whether DE algorithmic statements performance is promoted advantageous
In its application in modularity optimization.6 kinds of modularity optimization algorithms based on DE are built, are named as DEMO1-6.These algorithms
Using the optimisation strategy of different DE algorithms (there is different experiment individual generation strategies) modularity as an optimization.DEMO1-4
It is middle to apply different DE algorithms respectively, including DE/rand/2/dir, DE/rand/1/bin, DE/current-to-best/2/
Bin, DE/best/1/bin.DEMO5 employs a kind of widely used random variation strategy, i.e. node community ownership is with complete
Random manner is adjusted.DEMO6 is tactful as an optimization by improved DE_version2.It is combined on the basis of DEMO6
The improvement of preceding proposition is to improve the global convergence of algorithm and reduce algorithm search space on this basis and ensure global optimum
CDEMO is constructed in new communities' modification operation of solution search space.
All algorithms are tested on 4 real world social networks, as shown in table 3, including karate club net
Network, dolphin network, American politics books network and American university rugby network.Experimental result is as shown in table 4, including each calculation
The average value and standard deviation of method gained modularity Q values after 30 independent operatings on each test network.
From table 4 we it can be clearly seen that due to different convergences, the DE algorithms of different mode optimize in modularity
Performance has larger difference in problem.Compared with DEMO3 and DEMO4, in DEMO1-2 and DEMO5 Mutation Strategies it is random into
Divide and make it have stronger exploring ability, therefore better Qavg and Qstd values can be obtained.In addition, divided in optimal community
In terms of precision and stability, DEMO6 performances are better than DEMO1-5, it was demonstrated that DE convergences, which can be promoted, contributes to it in mould
Application in lumpiness optimization.Compared with DEMO6, CDEMO is obtained on Karate networks, Dolphin networks and PolBooks networks
Better Qavg and Qstd values are obtained, the accuracy of detected community is further promoted.
Based on above-mentioned test result, we may safely draw the conclusion, believes from promoting DE algorithm global convergence abilities and promoting topology
Two aspect enhancing algorithmic statement performance of service efficiency is ceased, contributes positively to improve what optimal community in modularity optimization problem divided
Quality.
2nd, the global convergence performance for raising DE algorithms, has redesigned three main evolutional operations：
(1) classification adaptive differential Mutation Strategy
Corrective measure mainly includes following several respects：
1. utilize current population optimal solution Xgbest,tWith the history optimal solution X of each individualpbesti,tChange randomly selected
Body guiding variation direction；
2. propose and balanced using a kind of new adaptive classification mechanism the spy of the individual with different compliance characteristics
Rope and producing capacity；
3. the degree of variation of each individual carries out dynamic self-adapting by parameter in evolutionary process.
New Mutation Strategy concrete operations are described as follows：
For each target individual Xi,tIf its ideal adaptation angle value fiMore than current entire population at individual fitness
The average of value, then be classified as excellent individual, and globally optimal solution is closer in the position of search space.Therefore, in Xi,t
In good gene should be reserved for strengthening the local search around individual, the corresponding vector V that makes a variationi,tGenerating mode is as follows：
Vi,t=Fi,t.Xpbesti,t+Wi,t.(Xr2,t-Xr3,t) (1)
Wherein Xpbesti,tRepresent individual Xi,tIn the history optimal solution in preceding t generations, for enhancing individual exploring ability.Xr2,tWith
Xr3,tIt is randomly selected two Different Individuals from population, and meets condition r2 ≠ r3 ≠ i.Fi,tAnd Wi,tIt is XiControl
Parameter, numerical value is according to evolutionary generation and Xi,tIdeal adaptation angle value dynamic adjust.
For each target individual Xi,tIf its ideal adaptation angle value fiLess than current entire population at individual fitness
The average of value is then classified as poor individual, in the position of search space and globally optimal solution farther out.Therefore, should strengthen
Its exchanging to promote global search between excellent individual in population, the corresponding vector V that makes a variationi,tGenerating mode is as follows：
Vi,t=Wi,t.Xr1,t+Ki,t.(Xgbest,t-Xi,t) (2)
Wherein Xr1,tIt is the randomly selected individual from population, and meets condition r1 ≠ i.Xgbest,tRepresent current iteration kind
Optimal solution in group, for enhancing Xi,tExploring ability.Wi,tAnd Ki,tIt is XiControl parameter, numerical value is according to evolutionary generation
With this Xi,tIdeal adaptation angle value dynamic adjust.
The advantageous effect of generation：It is straight that the above-mentioned TSP question based on classification will act on all individuals in every generation population
Terminate to evolution, therefore the variation of each individual can be accessed and targetedly be adjusted.On the one hand, excellent individual can be strengthened
Exploring ability, with increase its neighborhood find global optimum possibility；On the other hand, the exploitation of poor individual can be strengthened
Ability, to accelerate its search speed to global optimization.In short, the evolution demand with different fitness characteristic individuals, it can
To be better met by new Mutation Strategy.Under the guiding of directivity information, blindness in search process can be with
It efficiently reduces, and the quality of offspring individual and optimal solution can also be improved.
(2) dynamic self-adapting parameter adjustment
Three control parameters W, K, F correspond respectively to random element, social ingredient and cognitive component in mutation process.
In addition, also there are one crucial control parameter CR in crossover operation, for determining each experiment individual ui,tIn from variation individual
Vi,tThe percentage of middle succession.
1. parameter adaptive adjustment is carried out according to the fitness value of individual.To poor individual, it should strengthen variation and intersect
Degree, to introduce more directivity informations during evolution.Therefore, the random element in mutation process, society into
Point and crossover process in succession should all enhance, W and K in corresponding formula (2) and the CR values in intersecting are larger.
On the contrary, for excellent individual, it should strengthen the cognition part in mutation process, parameter adjustment should defer to opposite principle,
Corresponding to larger F values and smaller W values in formula (1).
2. according to evolution iterations dynamic self-adapting.In early stage of evolving, it should strengthen the exploration energy of individual
Power, to ensure fully to be searched in each individual neighborhood.On the contrary, in the later stage of evolution stage, it should strengthen the exploitation of individual
Ability strengthens the exchange between individual, accelerates the convergence of entire group.According to this principle, F in evolutionary process, the value of W, CR
It is gradually reduced, and K values gradually increase.
Based on mentioned above principle, parameter value can be adaptively adjusted, and each individual can obtain in evolutionary process
Dynamic control.Specific operation process is as follows：
The advantageous effect of generation：The degree of variation of each individual of dynamic self-adapting during evolution.
(3) the difference selection operation based on historical information
The outstanding solution generated in entire evolutionary process will be saved as historical information, and for follow-up evolutional operation.For
It realizes this target, introduces special population pbest_pop, by the history optimal solution X of individual each in populationpbesti,tForm population
Pbest_pop, and generated, and be updated after each evolutional operation in initial phase.To individual each in population
Xi,tIf its fitness value is improved during a certain evolutional operation, then newly-generated individual will be used as Xi,tWork as
Preceding history optimal solution, and be saved in pbest_pop.After every generation evolutional operation, all individuals will replace in pbest_pop
For all individuals in population pop, and current optimal solution X is selected from pbest_popgbest,t。
The advantageous effect of generation：Realize that the outstanding solution generated in entire evolutionary process will be saved as historical information, and
For follow-up evolutional operation.
Improved differential evolution Algorithm Convergence is tested：
Above-mentioned three corrective measures are provided to improve the global convergence of DE algorithms, algorithm flow chart such as Fig. 1 after improvement
It is shown.
Different from standard DE algorithms, more directivity informations are combined in new mutation operation, therefore individual can more have
Pointedly into row variation.Performed in addition, selection operation is not placed on after crossover operation, but by each evolutional operation it
Population Regeneration pbest_pop is selected and is retained outstanding solution afterwards.
In order to verify the above-mentioned corrective measure for DE, carried out using 18 standard Benchmark function pairs innovatory algorithms
Test, wherein f1-f5 is single mode state function, and f6-f14 is basic multi-modal function, and f15-f16 is spread function, and f17-f18
It is composite function.Table 1 provides the details of standard Benchmark functions.
Improved DE algorithms and 4 efficient and widely used DE algorithm patterns carry out performance comparison, including DE/
Rand/2/dir, DE/rand/1/bin, DE/current-to-best/2/bin and DE/best/1/bin.For ease of comparing,
DE_version1 is named as using the algorithm of new Mutation Strategy and parameter adaptive adjustable strategies, and uses all three improvement
The DE algorithms of measure are named as DE_version2.
During the experiment, all algorithms use same initial population scale NP=100 on each test problem, together
The variable dimension D=30 of sample and same stop criterion Max_FEs=5.0e+0.5.In addition, in the DE algorithms of all patterns
Parameter F and CR be adjusted all in accordance with the adaptive mode shown in formula (5) and (6).The value range of relevant parameter is W ∈
[0.1,0.9], K ∈ [0.3,0.9], F ∈ [0.3,0.9], CR ∈ [0.1,0.9].
The DE algorithms of six kinds of patterns carry out performance comparison in terms of optimal solution accuracy and robustness.Experimental result such as table 2
It is shown, acquire the average value of optimal solution and standard deviation including 30 independent operatings on each test function (in bracket).Each is surveyed
Optimal solution on trial function is shown with runic.It will be seen that DE_version1 and DE_version2 almost exist from table 2
It is better than other 4 kinds of algorithms on all test functions.DE_version2 is successfully converged to really in 50.0% test function
Globally optimal solution, and show on 88.9% test function optimal.The above results prove, the TSP question based on classification
Strategy can effectively improve the accuracy of offspring individual quality and optimal solution.In addition, compared with DE_version1, DE_
Version2 is significantly improved in terms of accuracy, illustrates that the new selection operation based on historical information can effectively improve DE algorithms
Global convergence ability.
Above-mentioned experimental result illustrates that improved method proposed in this paper is successfully effective, can effectively improve primary standard DE
The global convergence performance of algorithm, the modularity optimization problem in being detected for complex network community provide a kind of effective overall situation most
Optimization method.
3rd, preferably to utilize network topological information, it is proposed that a kind of improved community's adjustment plan based on neighborhood information
Slightly, enough search spaces are provided to ensure to divide as community of global optimum while DE search spaces are reduced.
For DE algorithms after improvement, preferably to utilize network topological information, it is proposed that a kind of improved based on neighborhood letter
Community's correction strategy of breath：
In order to avoid this inappropriate use to topology information, a kind of new community's correction strategy is proposed in CDEMO.
If a node meets community's correction conditions, then the node will likely be placed in again in its all affiliated community of neighborhood node,
And the probability of merging is directly proportional to the scale of neighborhood community.
The advantageous effect of generation：It can effectively reduce search space new correction strategy and former strategy, and heavier be
Limitation when community is corrected can be relaxed, sufficient search space is provided for globally optimal solution, so as to preferably utilize network
Know topology information, and promote the convergence of CDEMO algorithms.
4th, community's detection performance is tested
1. experimental setup
Performance Evaluation is carried out to CDEMO algorithms on artificial synthesized network and real world social networks.CDEMO algorithms exist
7.0 software programmings of MATLAB are realized, and in 7 systems of Windows for using Pentium Dual Core 2.5GHz processors and 2.0GB memories
On tested.Parameter setting in CDEMO is as follows：Population scale NP values 100, maximum iteration tmax values 200, control
The value range of parameter processed is set as, W ∈ [0.1,0.9], K ∈ [0.3,0.9], F ∈ [0.3,0.9], CR ∈ [0.1,0.9].
2. Performance evaluation criterion
(1) modularity Q：For the real world network of unknown community structure, usually refer to by the use of modularity function as performance
Mark weighs the significance degree of detection gained community structure.Modularity is defined as follows：
Wherein, M is the total number of edges of network；A=(aij) n*n is network adjacent matrix；Ki and kj represents node i and j's respectively
Degree；δ (i, j) represents community's attaching relation of node i and node j, if it is 1 that the two, which belongs to same community value, otherwise value
It is 0.It being represented in network there are community structure when Q values are more than 0, more than 0.3 when represents that the community structure of network is more apparent,
Q values are bigger to illustrate that community structure is more notable.It is that current use is most extensive although there are resolution ratio restricted problems for modularity
Community divide quality metric.
(2) normalized mutual information NMI：For the artificial synthesized network of known community structure, usually refer to by the use of NMI as performance
Mark weighs detection gained community and divides the approximation ratio divided with community content, and calculation formula is such as shown in (8).Assuming that A is network
Community content divide, B be detection gained community divide, define hybrid matrix C, wherein row represent A in community divide, list
Show that the community detected in B divides.Elements C ij represents the section identical with dividing j-th of community in B of i-th of community in division A
It counts out.According to the definition of C, evaluation criterion NMI is defined as follows：
Wherein, N represents the interstitial content in network；CA and CB represents to divide community's number in A and B respectively；Ci is mixed
The sum of i-th row element in Matrix C of confusing represents and divides i-th of community's interstitial content in A；Cj is jth column element in confusion matrix C
The sum of, it represents and divides j-th of community's interstitial content in B.If A is identical with B, NMI gets maximum value 1, if on the contrary,
A and B are entirely different, and NMI values are 0.
3. the experimental result of artificial synthesized network
Community's detection of verification CDEMO algorithms on the extension GN Benchmark networks of the propositions such as Lancichinetti
Performance.Comprising 128 nodes in each GN networks, it is divided into 4 communities, each community includes 32 nodes.Each node and society
Other nodes connect number of edges mesh for Zin inside area, and connect number of edges purpose for Zout with community's external node, and sum of the two is equal to node
The 16 of degree.Zout values are bigger, and the Lian Bianyue of node and community's external node is more, and community structure gets over unobvious, to detection
The detection performance requirement of algorithm is higher.
CDEMO algorithms are tested in Zout values gradually incremental 9 difference GN networks, only according to algorithm on each network
The accuracy and stability of the average value measure algorithm of vertical 30 gained NMI of operation, and calculated with 10 kinds of typical modularity optimizations
Method is compared (including CNM, GN, GATHB, ECGA, LGA, MA, UMDA, MOEA/D-Net, DECD and IDDE)), experimental result
As shown in Figure 3.
From figure 3, it can be seen that all algorithms can obtain optimal N MI values as Zout≤3, that is, it successfully is detected GN networks
Community structure.However, being gradually incremented by with Zout, the community structure of network, which becomes more to obscure, to be also more difficult to identify, is owned
NMI values obtained by algorithm all continuously decrease.It is worth noting that, CDEMO algorithms testing result is better than other 10 kinds of algorithms always, especially
It is to work as Zout>Afterwards, this illustrates that CDEMO algorithms are more accurate in community's detection of computer synthesis network and stablize.
It is further to test the Scalable Performance of CDEMO algorithms, it is gradually increased more massive in hybrid parameter μ
Test experiments are carried out on LFR Benchmark networks.The node degree of LFR networks is distributed as power-law distribution and community's scale can
Become, therefore closer real world network characteristic.Mixture of networks parameter μ is determined between community's interior nodes and other community's nodes altogether
The quantity on side is enjoyed, numerical value is bigger, and corresponding network community structure is fuzzyyer.0.7 interval is increased to from 0 using μ values in experiment
0.1 8 LFR networks, each LFR networks include 1000 nodes, community's scale value range be [10,50], each node
Average degree for 20, maximal degree 50.On each LFR networks, CDEMO algorithms independent operating 30 times, same to CNM, GATHB,
MOGA-Net, MPSOA, ECGA, UMDA, MOEA/D-Net and DECD8 kind algorithm are compared, and detection gained is measured using NMI
The accuracy and stability of community structure, experimental result are as shown in Figure 4.
From Fig. 4 we may notice that being compared with other modularity optimization algorithms, CDEMO algorithms can be in 8 LFR nets
Optimal NMI values are obtained on network.Work as μ<The performance advantage of CDEMO algorithms is not obvious when 0.2, and being incremented by with μ values,
Advantage in the accuracy and stability of CDEMO algorithms gradually highlights.It is above-mentioned the experimental results showed that, CDEMO is in artificial synthesized net
There is preferable accuracy, stability and scalability on community's test problems of network.
4. real world network experiment result
CDEMO algorithm performances are verified on the real world social networks shown in table 3, and use 16 kinds of module recognizers
Performance comparison is carried out with CDEMO.Comparison algorithm is divided into three groups：First group comprising 6 kinds of tradition, the optimization of Qualitative module degree is calculated really
Method, including Fast Nm, CNM, GN, BGLL, MSFCM, FMM/H1；Second group comprising 4 kinds the modularity optimization algorithm based on GA,
Including GATHB, MOGA-Net, ECGA, and MOEA/D-Net；The last one group is excellent comprising 5 kinds of modularities based on PSO and DE
Change algorithm, including Meme-Net, MODPSO, DECD, CCDECD and IDDE.All algorithms independent operating on each test network
30 times, and measure optimal community using modularity Q and divide quality, table 5-7 record CDEMO and optimal Q obtained by other comparison algorithms
Value.
It is in table 5-7 the experimental results showed that, although all algorithms can identify the community structure in live network, and
Algorithm performance in first category has no larger difference, but the modularity optimization algorithm based on EA is compared to traditional certainty
Modularity optimization algorithm has apparent superiority.In the algorithm based on EA, DECD, CCDECD, IDDE and CDEMO are obtained
Q values it is relatively high, it was demonstrated that superiority based on DE optimisation strategies.Although the modularity optimization algorithm (Meme- based on PSO
Net and MODPSO) it can detect the optimal communities of Karate networks, but their performances on other networks are not to the utmost such as people
Meaning.Compared with DECD, CCDECD and IDDE, only CDEMO algorithms can always obtain optimal Q values, especially in Dolphin and
On Polbooks networks.
Fig. 5-8 shows the optimal community division result that CDEMO algorithms detect in 4 real world social networks.
The experimental results showed that other than artificial synthesized network, CDEMO algorithms can also efficiently identify community's knot of true social networks
Structure, it is more accurate, more stable compared with the effective modularity optimization algorithm in a variety of forward positions, thus also further demonstrate that algorithm entirety
The validity and advance that constringency performance improves.
7 tables involved in the present embodiment are introduced below：
1 Benchmark function details of table
1 Benchmark function details (Continued) of table
Table 2.DE algorithmic statement performances compare
Table 3.Benchmark real world network characteristics
Table 4.DE algoritic modules degree optimization performance compares
The optimal Q values of 5 Fast Nm CNM of table, GN, BGLL, MSFCM and FMM/H1 on real world network
The optimal Q values of table 6 GATHB, MOGA-Net, ECGA and MOEA/D-Net on real world network
The optimal Q values of table 7 Meme-Net, MODPSO, DECD, CCDECD and IDDE on real world network
The foregoing is only a preferred embodiment of the present invention, but protection scope of the present invention be not limited thereto,
Any one skilled in the art in the technical scope of present disclosure, according to the technique and scheme of the present invention and its
Inventive concept is subject to equivalent substitution or change, should be covered by the protection scope of the present invention.
Claims (4)
1. a kind of modularity optimization method based on differential evolution algorithm, which is characterized in that specifically include：
S1：Initialization of population；
S1.1 sets network parameter, including number of nodes n, adjacency matrix adj, community correction threshold δ；DE algorithm parameters, packet are set
Include individual dimension D, Population Size NP, population iterations t and maximum iteration tmax；
S1.2 is with the individual representation random initializtion population pop of community's label；
S2：It identifies and records optimal solution；
S2.1 is identified and is recorded t for the optimum individual X in population popgbest,t；
S2.2 is identified and is recorded t for individual X each in population popi,tHistory optimal solution Xpbesti,t；By all population at individual
Xpbesti,tBuild initial population pbest_pop；
S3：When population iterations are less than population maximum iteration, population iterations are unsatisfactory for condition and then tie from adding one
The cycle of beam S3.1-S3.5；
S3.1 passes through adaptive classification differential variation construction of strategy variation population mutation_pop；
When i value for 1 to step a) in Population Size numberical range, is carried out to cycle e), if the value of i is not 1 to population
In the range of magnitude numerical value, then step a) is jumped out to e), end loop；
A) 3 different individual X are randomly selected from population popr1,t, Xr2,t, Xr3,t；
B) dynamic adjustment Mutation parameter Fi,t、wi,t、Ki,t；
C) according to fitness value Q to Xi,tClassify；
D) according to adaptive classification differential variation strategy generating variation individual Vi,t；
E) V is calculatedi,tModule angle value and and Xi,tIndividual is made comparisons, and more excellent individual is stored in pbest_pop；
If i is more than NP, leapfrog goes out a) suddenly to cycle e)；
S3.2 is based on neighborhood information and carries out community's amendment；
S3.3 is according to variation population mutation_pop and population pop structure cross-species crossover_pop；
When i value for 1 to step a) in Population Size numberical range, is carried out to cycle d), if the value of i is not 1 to population
In the range of magnitude numerical value, then step a) is jumped out to d), end loop；
A) i-th of individual u in cross-species is initializedi,t=xi,t；
B) dynamic adjustment cross parameter CRi,t；
C) by from variation individual Vi,tIt inherits community information and carrys out Adjustment Tests individual ui,t；
D) u is calculatedi,tModule angle value and be compared with i-th of individual in pbest_pop, retain compared with the figure of merit to pbest_
pop；
S3.4 is based on neighborhood information and carries out community's amendment；
S3.5 is by replacing all individual update pop in pbest_pop；
S4：Export the X in popgbest,tIt is divided as final optimal community, otherwise returns to S3 steps.
2. a kind of modularity optimization method based on differential evolution algorithm according to claim 1, which is characterized in that classification is certainly
Difference class Mutation Strategy is adapted to, concrete operations are as follows：
For each target individual Xi,tIf its ideal adaptation angle value fiIt is flat more than current entire population at individual fitness value
Mean is then classified as excellent individual, and globally optimal solution is closer in the position of search space；Therefore, in Xi,tIn it is good
Gene is reserved for strengthening the local search around individual, the corresponding vector V that makes a variationi,tGenerating mode is as follows：
Vi,t=Fi,t.Xpbesti,t+Wi,t.(Xr2,t-Xr3,t) (1)
Wherein, Xpbesti,tRepresent individual Xi,tIn the history optimal solution in preceding t generations, for enhancing individual exploring ability；Xr2,tAnd Xr3,t
It is randomly selected two Different Individuals from population, and meets condition r2 ≠ r3 ≠ i；Fi,tAnd Wi,tIt is XiControl ginseng
Number, numerical value is according to evolutionary generation and Xi,tIdeal adaptation angle value dynamic adjust；
For each target individual Xi,tIf its ideal adaptation angle value fiIt is flat less than current entire population at individual fitness value
Mean is then classified as poor individual, in the position of search space and globally optimal solution farther out；Therefore, strengthen it in population
In exchanging to promote global search between excellent individual, the corresponding vector V that makes a variationi,tGenerating mode is as follows：
Vi,t=Wi,t.Xr1,t+Ki,t.(Xgbest,t-Xi,t) (2)
Wherein Xr1,tIt is the randomly selected individual from population, and meets condition r1 ≠ i；Xgbest,tIt represents in current iteration population
Optimal solution, for enhancing Xi,tExploring ability；Wi,tAnd Ki,tIt is XiControl parameter, numerical value is according to evolutionary generation and Xi,t
Ideal adaptation angle value carry out dynamic adjustment.
3. a kind of modularity optimization method based on differential evolution algorithm according to claim 1, which is characterized in that dynamic is adjusted
Whole Mutation parameter concrete operations are：Three control parameters W, K, F, random element respectively in mutation process, social ingredient and
Cognitive component；In addition, also there are one crucial control parameter CR in crossover operation, for determining each experiment individual ui,tIn from
Make a variation individual Vi,tThe percentage of middle succession；Adjustment process is specific as follows：
4. a kind of modularity optimization method based on differential evolution algorithm according to claim 1, which is characterized in that based on neighbour
Domain information carry out community's amendment the step of be specifically：If a node meets community's correction conditions, then the node will be put again
Enter in its all affiliated community of neighborhood node, and the probability being placed in is directly proportional to the scale of neighborhood community.
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