CN105160404A - Complex network balance clustering method based on multi-objective optimization - Google Patents
Complex network balance clustering method based on multi-objective optimization Download PDFInfo
- Publication number
- CN105160404A CN105160404A CN201510512727.2A CN201510512727A CN105160404A CN 105160404 A CN105160404 A CN 105160404A CN 201510512727 A CN201510512727 A CN 201510512727A CN 105160404 A CN105160404 A CN 105160404A
- Authority
- CN
- China
- Prior art keywords
- group species
- advanced group
- solution
- individuality
- value
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
Landscapes
- Measuring Or Testing Involving Enzymes Or Micro-Organisms (AREA)
Abstract
The present invention discloses a complex network balance clustering method based on multi-objective optimization and mainly solves the following problems in the prior art: (1) a clustering result is single and under the condition that cost of network balance conversion is changed, the requirement for searching the optimal clustering result cannot be met; (2) a polarization phenomenon exists; and (3) for a network with a complex topological structure, the obtained network structure has high unbalancedness. The complex network balance clustering method comprises the implementing steps of: (1) reading in a data set of an objective undirected symbolic network; (2) initializing an evolution population; (3) computing fitness of the evolution population; (4) initializing an external population; (5) initializing a reference point of the evolution population; (6) updating the population; (7) locally searching the external population; (8) determining the optimal network balance structure. According to the complex network balance clustering method disclosed by the present invention, two objective functions can be simultaneously optimized and unbalancedness of complex network partitioning is reduced.
Description
Technical field
The invention belongs to field of computer technology, further relate to a kind of complex network balance clustering method based on multiple-objection optimization in data mining technology field.The present invention take balancing information as objective function, can be complicated undirected symbolic network provide multiple balanced structure by cluster operation.
Background technology
Complicated undirected symbolic network is a kind of typical network type.Based on the practical significance of the system representated by the type network, each node on behalf related individuals in network, positive or passive relation is there is between individuality, abstract is that positive limit (actively) between nodes connects or marginal (passiveness) connects, while node between relation there is symmetry.
A kind of complex network clustering method based on joint core influence power is disclosed in patented technology " the complex network clustering method based on joint core influence power " (number of patent application 201210002128.2, Authorization Notice No. CN102571954B) that BJ University of Aeronautics & Astronautics has at it.The method is by the size sequence of the node in complex network according to degree, initial each node does not all determine affiliated community, using the current core node of maximal degree node as community not determining affiliated community, start to build this community, determine community's ownership of the adjacent node of this core node successively, complete the structure of this community; To not yet determining in network that the residue node that community belongs to repeats above-mentioned steps until all nodes all determine affiliated community, obtain final network clustering structure.The weak point of the method is: can only obtain single cluster result, and when the cost of network equalize conversion changes, the method can not meet the demand finding optimum cluster result.
The paper " Fastcomputingglobalstructuralbalanceinsignednetworksbase donmemeticalgorithm. " (" PhysicaA:StatisticalMechanicsanditsApplication " that Sun Yixiang, Du Haifeng, public morphothion, good, the Wang Shanfeng of Mali deliver at it, 2014, pages261-272) in propose the clustering method (prior art Meme-SB) of a kind of quick compute sign network based on memetic algorithm overall situation balance.The method regards symbolic network balance clustering problem as a single-objective problem, the paper " Computingglobalstructuralbalanceinlarge-scalesignedsocia lnetworks " (" ProceedingsoftheNationalAcademyofSciences " delivered at it with GiuseppeFacchetti, Giovannilacono and ClaudioAltafini, 2011, pages20953-20958) energy function proposed in is objective function, is minimized this objective function by memetic algorithm.The weak point of the method is: with strong level theory for cluster prerequisite, therefore network can only be divided into two parts, and such cluster result does not in most of the cases meet reality, easily produces polarization phenomena; For the network of topological structure complexity, the network structure unbalancedness that the method obtains is high.
Summary of the invention
The object of the invention is to the deficiency overcoming above-mentioned prior art, propose a kind of complex network balance clustering method based on multiple-objection optimization.
Technical scheme of the present invention is: the number of number and the positive fillet of imbalance that the imbalance reducing network clustering is born fillet is as target, adopt a kind of complex network clustering method of multiple-objection optimization, and the local search approach introduced for equilibrium problem, the balanced structure of search objective network
The concrete steps realizing the object of the invention are as follows:
(1) data set of the undirected symbolic network of target is read in;
(2) initialization Advanced group species:
Adopt positive abutment points real number coding method, generate and separate individual initial Advanced group species containing 200, each solution individuality is made up of m gene position, and m equals number of network node;
(3) fitness of Advanced group species is calculated:
(3a) initial value of count flag e is set to 1;
(3b) with the value of count flag e for sequence number, the solution choosing the Advanced group species corresponding with this sequence number is individual;
(3c) imbalance of the solution individuality of the Advanced group species according to the following formula, selected by calculating bears the number of fillet:
Wherein, f
1(X) imbalance of the solution individuality of the Advanced group species selected by expression bears the number of fillet, X represents that the solution of selected Advanced group species is individual, Σ represents sum operation, k represents the number of the class comprised in the solution individuality of selected Advanced group species, the value of k is determined by the solution individuality of selected Advanced group species, N (C
r, C
r) Advanced group species selected by expression solution individuality in belong to r class all nodes between the number of negative fillet, C
rthe set of all nodes of r class is belonged in the solution individuality of the Advanced group species selected by expression;
(3d) number of the positive fillet of imbalance of according to the following formula, selected in calculation procedure (3b) solution individuality:
Wherein, f
2(X) number of the positive fillet of imbalance of the solution individuality of the Advanced group species selected by expression, X represents that the solution of selected Advanced group species is individual, Σ represents sum operation, k represents the number of the class comprised in the solution individuality of selected Advanced group species, the value of k is determined by the solution individuality of selected Advanced group species, P (C
r, O
r) Advanced group species selected by expression solution individuality in belong in all nodes of r class and other classes between node positive fillet number, C
rthe set of all nodes of r class is belonged to, O in the solution individuality of the Advanced group species selected by expression
rthe set of all nodes of r class is not belonged in the solution individuality of the Advanced group species selected by expression;
(3e) judge whether the value of count flag e equals 200, if so, then obtains the fitness of Advanced group species, perform step (4), otherwise, the value of count flag e is added 1, performs step (3b);
(4) the outside population of initialization:
(4a) solution of deleting all repetitions in Advanced group species is individual;
(4b) from the remaining solution individuality of Advanced group species, the solution choosing all non-dominant is individual, forms initial outside population;
(5) according to the following formula, the reference point of initialization Advanced group species:
z＝(z
1,z
2)
Wherein, z represents the reference point of Advanced group species, z
1represent all in Advanced group species and separate the minimum value that individual imbalance bears the number of fillet, z
2represent all minimum value of separating the number of the individual positive fillet of imbalance in Advanced group species;
(6) Population Regeneration:
(6a) all neighborhoods separating individuality in Advanced group species are set;
(6b) initial value of iteration count mark iteration is set to 1;
(6c) individual execution genetic manipulation is separated to each in Advanced group species, upgrade Advanced group species;
(6d) reference point of Advanced group species is upgraded;
(6e) outside population is upgraded;
(6f) all neighborhoods separating individual correspondence in Advanced group species are upgraded;
(6g) judge whether the value of iteration count mark iteration equals 200, if so, then complete and upgrade Advanced group species operation, perform step (7), otherwise, the value of iteration count mark iteration is added 1, performs step (6c);
(7) the outside population of Local Search:
(7a) initial value of count flag sl is set to 1;
(7b) with the value of count flag sl for sequence number, the solution choosing the outside population corresponding with this sequence number is individual;
(7c) according to the value of each gene position of the solution individuality of selected outside population, the number of the class comprised in this solution individuality and the node set corresponding with each class is determined;
(7d) from the solution individuality of selected outside population, a class is chosen arbitrarily;
(7e) from the solution individuality of selected outside population, find out all classes only having positive fillet between selected class, obtain the set of the adjacent class of selected class;
(7f) from the set of the adjacent class of selected class, find out the class that the number of positive fillet between selected class is maximum, and such and selected class are merged;
(7g) judge whether the value of count flag sl equals the number of the solution individuality in outside population, if so, then obtains outside population, otherwise, the value of count flag sl is added 1, performs step (7b);
(8) optimum network equalize structure is determined:
(8a) number imbalance individual for each solution of outside population being born fillet is added with the number of the positive fillet of imbalance, and each obtaining outside population separates the degree of unbalancedness of individuality;
(8b) from the solution individuality of outside population, the solution individuality that the value of degree of unbalancedness is minimum is chosen, using the network equalize structure of individual for selected solution corresponding network structure as optimum.
The present invention compared with prior art tool has the following advantages:
First, because the present invention adopts positive abutment points real number coding method to carry out initialization to Advanced group species, undirected for complexity symbolic network is divided into multiple class, overcomes the deficiency of the polarization phenomena existed in prior art, the more realistic demand of network equalize structure that the present invention is obtained.
The second, the imbalance being the solution individuality of Advanced group species due to the fitness adopted in the present invention bears the number of fillet and the number of the positive fillet of imbalance, the unbalancedness direct correlation of both and network structure; In addition, present invention employs the local search approach for equilibrium problem, arbitrarily a class is selected, by the solution individuality of outside population and there is between selected class the class of number of maximum positive fillet and selected class merges from the solution individuality of outside population.The present invention is by above two operations, reduce the unbalancedness of the individual corresponding network structure of solution in outside population, overcome the network of prior art for topological structure complexity, the deficiency that the network structure unbalancedness of gained is high, makes the present invention more effectively can search out the balanced structure of complicated undirected symbolic network.
3rd, because the present invention adopts the method for Population Regeneration, each obtaining in outside population separates the cluster result of individual corresponding a kind of network, overcome in prior art and can only obtain single cluster result, when the cost of network equalize conversion changes, the deficiency of the demand finding optimum cluster result can not be met, the network clustering under making the present invention can adapt to heterogeneous networks balance switching cost.
Accompanying drawing explanation
Fig. 1 is process flow diagram of the present invention;
Fig. 2 is the balanced structure comparison diagram that the present invention and prior art Meme-SB divide network G GS;
Fig. 3 is the cluster result distribution plan of the present invention to network ecoli, yeast.
Embodiment
Below in conjunction with accompanying drawing, the present invention will be further described.
With reference to Fig. 1, the concrete steps that the present invention realizes are described in further detail.
Step 1. reads in the data set of the undirected symbolic network of target.
Step 2. initialization Advanced group species.
Adopt positive abutment points real number coding method, generate and separate individual initial Advanced group species containing 200, each solution individuality is made up of m gene position, and m equals number of network node.
The concrete steps of positive abutment points real number coding method are as follows:
1st step, chooses arbitrarily the gene position of the solution individuality of an initial Advanced group species, the value of this gene position is set to the label with the class belonging to this gene position map network node.
2nd step, repeats the 1st step, until the value of m gene position of the solution individuality of initial Advanced group species is all determined.
3rd step, choose arbitrarily the gene position of the solution individuality of an initial Advanced group species, find out the positive adjacent node collection of the network node corresponding with it, random selecting node is concentrated, using the allele value of the value of the gene position corresponding with selected node as the solution genes of individuals position of selected initial Advanced group species from this positive adjacent node.
4th step, repeats the 3rd step, until m gene position of the solution individuality of initial Advanced group species all determines affiliated allele value.
5th step, judges that m gene position in initial Advanced group species has all determined whether the number of the solution individuality of affiliated allele value equals 200, if so, then obtains initial Advanced group species, otherwise, perform the 1st step.
Step 3., according to following step, calculates the fitness of Advanced group species.
1st step, is set to 1 by the initial value of count flag e.
2nd step, with the value of count flag e for sequence number, the solution choosing the Advanced group species corresponding with this sequence number is individual.
3rd step, according to the following formula, the imbalance of the solution individuality of the Advanced group species selected by calculating bears the number of fillet:
Wherein, f
1(X) imbalance of the solution individuality of the Advanced group species selected by expression bears the number of fillet, X represents that the solution of selected Advanced group species is individual, Σ represents sum operation, k represents the number of the class comprised in the solution individuality of selected Advanced group species, the value of k is determined by the solution individuality of selected Advanced group species, N (C
r, C
r) Advanced group species selected by expression solution individuality in belong to r class all nodes between the number of negative fillet, C
rthe set of all nodes of r class is belonged in the solution individuality of the Advanced group species selected by expression.
4th step, according to the following formula, the number of the positive fillet of imbalance of the solution individuality of the Advanced group species selected by calculating:
Wherein, f
2(X) number of the positive fillet of imbalance of the solution individuality of the Advanced group species selected by expression, X represents that the solution of selected Advanced group species is individual, Σ represents sum operation, k represents the number of the class comprised in the solution individuality of selected Advanced group species, the value of k is determined by the solution individuality of selected Advanced group species, P (C
r, O
r) Advanced group species selected by expression solution individuality in belong in all nodes of r class and other classes between node positive fillet number, C
rthe set of all nodes of r class is belonged to, O in the solution individuality of the Advanced group species selected by expression
rthe set of all nodes of r class is not belonged in the solution individuality of the Advanced group species selected by expression.
5th step, judges whether the value of count flag e equals 200, if so, then obtains the fitness of Advanced group species, performs step 4, otherwise, the value of count flag e is added 1, performs the 2nd step.
Step 4. according to following step, the outside population of initialization.
The solution of deleting all repetitions in Advanced group species is individual; From the remaining solution individuality of Advanced group species, the solution choosing all non-dominant is individual, forms initial outside population.
Step 5. according to the following formula, the reference point of initialization Advanced group species:
z＝(z
1,z
2)
Wherein, z represents the reference point of Advanced group species, z
1represent all in Advanced group species and separate the minimum value that individual imbalance bears the number of fillet, z
2represent all minimum value of separating the number of the individual positive fillet of imbalance in Advanced group species.
Step 6. according to following step, Population Regeneration.
1st step, arrange and allly in Advanced group species separate individual neighborhood, concrete operations are, individually arrange a corresponding weight vectors for each in Advanced group species is separated; From Advanced group species, select y to separate individual, the span of y is [1,200], and the weight vectors of the solution individuality of the Advanced group species selected by calculating and all of Advanced group species separate the Euclidean distance between individual weight vectors; The value of the weight vectors of the solution individuality of selected Advanced group species and all of Advanced group species being separated the Euclidean distance between individual weight vectors arranges by ascending order, the weight vectors of solution individuality and all of Advanced group species of the Advanced group species selected by after ascending order arrangement are separated the value of the Euclidean distance between individual weight vectors, choose the individual neighborhood as the solution individuality of selected Advanced group species of solution of Advanced group species corresponding to front 20 values.
2nd step, is set to 1 by the initial value of iteration count mark iteration.
3rd step, individual execution genetic manipulation is separated to each in Advanced group species, upgrade Advanced group species, genetic manipulation comprises interlace operation and mutation operation, interlace operation refers to, each solution for Advanced group species is individual, from outside population, choose arbitrarily one separates individual, from the solution individuality of selected outside population, the value of a random selecting gene position, from the solution individuality of selected outside population, the value finding out gene position equals all gene position of the value of selected gene position, obtain the position collection of gene position to be updated in the solution individuality of selected Advanced group species, by the value of gene position of answering with the position set pair of gene position to be updated in the solution individuality of selected Advanced group species, replace with the value of the gene position of institute's random selecting in the solution individuality of selected outside population, the offspring individual of the solution individuality of the Advanced group species selected by generation, mutation operation refers to, generate a random number rand, the span of rand is [0,1], if rand is less than mutation probability 0.1, each gene position in the offspring individual of the solution individuality of the Advanced group species selected by interlace operation is produced, find out the positive adjacent node collection of the network node corresponding with this gene position, the label choosing the maximum class of occurrence number is concentrated, using the value of such label as corresponding gene position in the offspring individual of the solution individuality of the Advanced group species selected by interlace operation generation from this positive adjacent node.
4th step, upgrade the reference point of Advanced group species, concrete operations are, value with reference to the 1st element of point replaces with all imbalances of separating individuality in Advanced group species and bears the minimum value of the number of fillet, and the value with reference to the 2nd element of point replaces with all minimum value of separating the number of the individual positive fillet of imbalance in Advanced group species.
5th step, upgrades outside population, and concrete operations are, the solution choosing all non-dominant of Advanced group species is individual, is merged in outside population by the solution individuality of all non-dominant of selected Advanced group species, obtains interim outside population; The solution choosing all non-dominant of interim outside population is individual, as outside population.
6th step, upgrade the individual corresponding neighborhood of each solution in Advanced group species, concrete operations are, select y to separate individual from Advanced group species, the span of y is [1,200], from the neighborhood of the solution individuality of selected Advanced group species, choose a and separate individual, the value scope of a is [1,20], according to the following formula, Chebyshev's value of the solution individuality of the new Advanced group species selected by calculating:
g
1＝max{λ
1|f
1(X)-z
1|,λ
2|f
2(X)-z
2|}
Wherein, g
1chebyshev's value of the solution individuality of the Advanced group species selected by expression, max represents that maximizing operates, λ
1represent with in the neighborhood of the solution individuality from Advanced group species selected by the imbalance of solution individuality bear weight corresponding to the number of fillet, f
1(X) imbalance of the solution individuality of the Advanced group species selected by expression bears the number of fillet, and X represents that the solution of selected Advanced group species is individual, z
1represent all in Advanced group species and separate the minimum value that individual imbalance bears the number of fillet, λ
2represent the weight corresponding with the number of the positive fillet of imbalance of solution individuality selected in the neighborhood of the solution individuality from selected Advanced group species, f
2(X) number of the positive fillet of imbalance of the solution individuality of the Advanced group species selected by expression, z
2represent all minimum value of separating the individual positive fillet number of imbalance in Advanced group species, || represent and ask absolute value operation, according to the following formula, calculate and choose the individual Chebyshev's value of solution from the neighborhood of the solution individuality of selected Advanced group species:
g
2＝max{λ
1|f
1(W)-z
1|,λ
2|f
2(W)-z
2|}
Wherein, g
2represent Chebyshev's value of the solution individuality chosen from the neighborhood of the solution individuality of selected Advanced group species, max represents that maximizing operates, λ
1to represent and the imbalance of the solution individuality chosen in the neighborhood of the solution individuality from selected Advanced group species bears weight corresponding to the number of fillet, f
1(W) represent that the imbalance of solution individuality selected from the neighborhood of the solution individuality of selected Advanced group species bears the number of fillet, W represents that solution selected from the neighborhood of the solution individuality of selected Advanced group species is individual, z
1represent all in Advanced group species and separate the minimum value that individual imbalance bears the number of fillet, λ
2represent the weight corresponding with the number of the positive fillet of imbalance of solution individuality selected in the neighborhood of the solution individuality from selected Advanced group species, f
2(W) number of the positive fillet of imbalance of the solution individuality chosen from the neighborhood of the solution individuality of selected Advanced group species is represented, z
2represent all minimum value of separating the individual positive fillet number of imbalance in Advanced group species, || represent and ask absolute value operation; If Chebyshev's value of the solution individuality of selected Advanced group species is less than Chebyshev's value of the solution individuality chosen from the neighborhood of the solution individuality of selected Advanced group species, then the solution solution chosen in the neighborhood of the solution individuality from selected Advanced group species individuality being replaced with selected Advanced group species is individual.
7th step, judges whether the value of iteration count mark iteration equals 200, if so, then completes and upgrades Advanced group species operation, perform step 7, otherwise, the value of iteration count mark iteration is added 1, performs the 3rd step;
Step 7. according to following step, the outside population of Local Search.
1st step, is set to 1 by the initial value of count flag sl;
2nd step, with the value of count flag sl for sequence number, the solution choosing the outside population corresponding with this sequence number is individual;
3rd step, according to the value of each gene position of the solution individuality of selected outside population, determines the number of the class comprised in this solution individuality and the node set corresponding with each class;
4th step, from the solution individuality of selected outside population, chooses arbitrarily a class;
5th step, from the solution individuality of selected outside population, finds out all classes only having positive fillet between selected class, obtains the set of the adjacent class of selected class;
6th step, from the set of the adjacent class of selected class, chooses the maximum class of the number of positive fillet between selected class and selected class merges;
7th step, judges whether the value of count flag sl equals the number of the solution individuality in outside population, if so, then obtains outside population, otherwise, the value of count flag sl is added 1, performs the 2nd step.
Step 8. determines optimum network equalize structure.
Be added with the number of the positive fillet of imbalance by the number that imbalance individual for each solution of outside population bears fillet, each obtaining outside population separates the degree of unbalancedness of individuality; From the solution individuality of outside population, choose the solution individuality that the value of degree of unbalancedness is minimum, using the network equalize structure of individual for selected solution corresponding network structure as optimum.
Effect of the present invention can be described further by following emulation experiment.
1. simulated conditions
The emulation experiment of the present invention and prior art Meme-SB is under Intel (R) Core (TM) i5-2450MCPU2.50GHzWindows7 system, and MatlabR2012b operation platform completes.
2. emulation experiment content
Choose real world network SPP, Ecoli, yeast respectively as experimental subjects.Optimum configurations of the present invention is as follows, and separating individual number in Advanced group species is 200, and maximum iteration time is 200, and crossover probability is 1, and mutation probability is 0.1, and separating individual number in neighborhood is 20.Prior art Meme-SB optimum configurations is as follows, and separating individual number in Advanced group species is 500, and population maximum iteration time is 50, and crossover probability is 0.9, and mutation probability is 0.1.The present invention and prior art Meme-SB have carried out 30 independent experiments respectively to experimental subjects.The positive fillet number of imbalance in using network to divide and imbalance bear fillet number sum, and weigh the quality of balance of the live network division that emulation detects, its value is less, show that the network partition structure obtained is close to balance.
Fig. 2 is the balanced structure comparison diagram that the present invention and prior art Meme-SB divide network G GS, wherein Fig. 2 (a) represents that, by the balanced structure of the network G GS of gained of the present invention, Fig. 2 (b) represents the balanced structure by the network G GS of prior art Meme-SB gained.Comprising 16 nodes in GGS network, is KOTUN, GAVEV, GAMA, NAGAD, SEUVE, UHETO, NAGAM, NOTOH, KOHIK, OVE, ALIKA, ASARO, GAHUK, MASIL, UKUDZ, GEHAM respectively.In each subgraph, the node that shape is identical, belongs to same class respectively, and the solid line between node represents the positive fillet between node, and the dotted line between node represents the negative fillet between node.From Fig. 2 (a), network G GS is divided into three classes by the present invention, its interior joint KOTUN, GAVEV, GAMA, NAGAD belong to a class, represent with ellipse, node SEUVE, UHETO, NAGAM, NOTOH, KOHIK belong to a class, represent by circle, and node OVE, ALIKA, ASARO, GAHUK, MASIL, UKUDZ, GEHAM belong to a class, represent with rhombus, the solid line of 2 overstrikings to represent in this network structure that one co-exists in 2 unbalanced positive fillets; From Fig. 2 (b), network G GS is divided into two classes by prior art Meme-SB, its interior joint KOTUN, GAVEV, GAMA, NAGAD belong to a class, represent by circle, node SEUVE, UHETO, NAGAM, NOTOH, KOHIK, OVE, ALIKA, ASARO, GAHUK, MASIL, UKUDZ, GEHAM belong to a class, represent with rhombus, the dotted line of 7 overstrikings to represent in this network structure that one co-exists in 7 unbalanced negative fillets; It can thus be appreciated that the balanced structure balance of the network G GS of gained of the present invention is better.In addition, the actual division of network G GS is consistent with the result of gained of the present invention, and therefore acquired results of the present invention more tallies with the actual situation.
Fig. 3 (a) is the cluster result distribution plan of the present invention to network Yeast, and Fig. 3 (b) is the cluster result distribution plan of the present invention to network Ecoli.Wherein, horizontal ordinate f
1represent the number of uneven negative fillet, ordinate f
2represent the number of uneven positive fillet.Each point in each subgraph, represents a kind of cluster result of network.As shown in Figure 3, the present invention can obtain multiple cluster results of each network, thus when the cost of network equalize conversion changes, can find optimum cluster result.
Table 1 is that the present invention and prior art prior art Meme-SB are to network Eoli, Yeast cluster result quality of balance comparison sheet.Data in table be after independent 30 experiments the present invention and prior art Meme-SB to the mean value of the number of the uneven fillet of network Eoli, Yeast cluster result.
As shown in Table 1, the cluster result of the present invention to network Eoli, Yeast is better than the cluster result of prior art Meme-SB to network Eoli, Yeast.
In sum, the present invention adopts the complex network balance clustering method based on multiple-objection optimization, multiple cluster results of complicated undirected symbolic network can be obtained, thus when the cost of network equalize conversion changes, optimum cluster result can be found; The present invention is with weak level theory for instructing, and acquired results overcomes the polarization phenomena that prior art exists; Invention introduces the local search approach based on equilibrium problem, more effectively can search for the balanced structure of complicated undirected symbolic network.
Claims (7)
1., based on a complex network balance clustering method for multiple-objection optimization, comprise the steps:
(1) data set of the undirected symbolic network of target is read in;
(2) initialization Advanced group species:
Adopt positive abutment points real number coding method, generate and separate individual initial Advanced group species containing 200, each solution individuality is made up of m gene position, and m equals number of network node;
(3) fitness of Advanced group species is calculated:
(3a) initial value of count flag e is set to 1;
(3b) with the value of count flag e for sequence number, the solution choosing the Advanced group species corresponding with this sequence number is individual;
(3c) imbalance of the solution individuality of the Advanced group species according to the following formula, selected by calculating bears the number of fillet:
Wherein, f
1(X) imbalance of the solution individuality of the Advanced group species selected by expression bears the number of fillet, X represents that the solution of selected Advanced group species is individual, Σ represents sum operation, k represents the number of the class comprised in the solution individuality of selected Advanced group species, the value of k is determined by the solution individuality of selected Advanced group species, N (C
r, C
r) Advanced group species selected by expression solution individuality in belong to r class all nodes between the number of negative fillet, C
rthe set of all nodes of r class is belonged in the solution individuality of the Advanced group species selected by expression;
(3d) number of the positive fillet of imbalance of according to the following formula, selected in calculation procedure (3b) solution individuality:
Wherein, f
2(X) number of the positive fillet of imbalance of the solution individuality of the Advanced group species selected by expression, X represents that the solution of selected Advanced group species is individual, Σ represents sum operation, k represents the number of the class comprised in the solution individuality of selected Advanced group species, the value of k is determined by the solution individuality of selected Advanced group species, P (C
r, O
r) Advanced group species selected by expression solution individuality in belong in all nodes of r class and other classes between node positive fillet number, C
rthe set of all nodes of r class is belonged to, O in the solution individuality of the Advanced group species selected by expression
rthe set of all nodes of r class is not belonged in the solution individuality of the Advanced group species selected by expression;
(3e) judge whether the value of count flag e equals 200, if so, then obtains the fitness of Advanced group species, perform step (4), otherwise, the value of count flag e is added 1, performs step (3b);
(4) the outside population of initialization:
(4a) solution of deleting all repetitions in Advanced group species is individual;
(4b) from the remaining solution individuality of Advanced group species, the solution choosing all non-dominant is individual, forms initial outside population;
(5) according to the following formula, the reference point of initialization Advanced group species:
z＝(z
1,z
2)
Wherein, z represents the reference point of Advanced group species, z
1represent all in Advanced group species and separate the minimum value that individual imbalance bears the number of fillet, z
2represent all minimum value of separating the number of the individual positive fillet of imbalance in Advanced group species;
(6) Population Regeneration:
(6a) all neighborhoods separating individuality in Advanced group species are set;
(6b) initial value of iteration count mark iteration is set to 1;
(6c) individual execution genetic manipulation is separated to each in Advanced group species, upgrade Advanced group species;
(6d) reference point of Advanced group species is upgraded;
(6e) outside population is upgraded;
(6f) all neighborhoods separating individual correspondence in Advanced group species are upgraded;
(6g) judge whether the value of iteration count mark iteration equals 200, if so, then complete and upgrade Advanced group species operation, perform step (7), otherwise, the value of iteration count mark iteration is added 1, performs step (6c);
(7) the outside population of Local Search:
(7a) initial value of count flag sl is set to 1;
(7b) with the value of count flag sl for sequence number, the solution choosing the outside population corresponding with this sequence number is individual;
(7c) according to the value of each gene position of the solution individuality of selected outside population, the number of the class comprised in this solution individuality and the node set corresponding with each class is determined;
(7d) from the solution individuality of selected outside population, a class is chosen arbitrarily;
(7e) from the solution individuality of selected outside population, find out all classes only having positive fillet between selected class, obtain the set of the adjacent class of selected class;
(7f) from the set of the adjacent class of selected class, find out the class that the number of positive fillet between selected class is maximum, and such and selected class are merged;
(7g) judge whether the value of count flag sl equals the number of the solution individuality in outside population, if so, then obtains outside population, otherwise, the value of count flag sl is added 1, performs step (7b);
(8) optimum network equalize structure is determined:
(8a) number imbalance individual for each solution of outside population being born fillet is added with the number of the positive fillet of imbalance, and each obtaining outside population separates the degree of unbalancedness of individuality;
(8b) from the solution individuality of outside population, the solution individuality that the value of degree of unbalancedness is minimum is chosen, using the network equalize structure of individual for selected solution corresponding network structure as optimum.
2. the complex network balance clustering method based on multiple-objection optimization according to claim 1, is characterized in that, described in step (2), the step of positive abutment points real number coding method is as follows:
1st step, chooses arbitrarily the gene position of the solution individuality of an initial Advanced group species, the value of this gene position is set to the label with the class belonging to this gene position map network node;
2nd step, repeats the 1st step, until the value of m gene position of the solution individuality of initial Advanced group species is all determined;
3rd step, choose arbitrarily the gene position of the solution individuality of an initial Advanced group species, find out the positive adjacent node collection of the network node corresponding with it, random selecting node is concentrated, using the allele value of the value of the gene position corresponding with selected node as the solution genes of individuals position of selected initial Advanced group species from this positive adjacent node;
4th step, repeats the 3rd step, until m gene position of the solution individuality of initial Advanced group species all determines affiliated allele value;
5th step, judges that m gene position in initial Advanced group species has all determined whether the number of the solution individuality of affiliated allele value equals 200, if so, then obtains initial Advanced group species, otherwise, perform the 1st step.
3. the complex network balance clustering method based on multiple-objection optimization according to claim 1, is characterized in that, the step arranging the neighborhood that all solutions are individual in Advanced group species described in step (6a) is as follows:
1st step, individual arranges a corresponding weight vectors for each in Advanced group species is separated;
2nd step, chooses arbitrarily one and separates individual from Advanced group species, calculates the selected all Euclidean distances separated between individual weight vectors separating individual weight vectors and Advanced group species;
3rd step, arranges the value of the Euclidean distance between weight vectors individual for selected solution and all weight vectors separating individuality of Advanced group species by ascending order;
4th step, separate the value of the Euclidean distance between individual weight vectors and all weight vectors separating individuality of Advanced group species selected by after ascending order arrangement, choose the individual neighborhood as the solution individuality of selected Advanced group species of solution of Advanced group species corresponding to front 20 values;
5th step, repeats the 2nd step, the 3rd step, the 4th step, until obtain all neighborhoods separating individuality in Advanced group species.
4. the complex network balance clustering method based on multiple-objection optimization according to claim 1, is characterized in that, separate individual execution genetic manipulation to each in Advanced group species described in step (6c), the step upgrading Advanced group species is as follows:
1st step, is set to 1 by the initial value of count flag sl;
2nd step, with the value of count flag sl for sequence number, the solution choosing the Advanced group species corresponding with this sequence number is individual;
3rd step, chooses arbitrarily one and separates individual from outside population;
4th step, from the solution individuality of selected outside population, the value of a random selecting gene position;
5th step, from the solution individuality of selected outside population, the value finding out gene position equals all gene position of the value of selected gene position, obtains the position collection of gene position to be updated in the solution individuality of selected Advanced group species;
6th step, interlace operation is carried out to the solution individuality of selected Advanced group species, obtain the offspring individual of the solution individuality of the selected Advanced group species that interlace operation produces, described interlace operation refers to, by the value of gene position of answering with the position set pair of gene position to be updated in the solution individuality of selected Advanced group species, replace with the value of the gene position of institute's random selecting from the solution individuality of selected outside population;
7th step, the span generating random number rand, a rand is [0,1], if rand is less than mutation probability 0.1, then performs the 8th step, otherwise, perform the 10th step;
8th step, the offspring individual of the solution individuality of the Advanced group species selected by producing interlace operation carries out mutation operation, obtain the offspring individual of the solution individuality of the selected Advanced group species that mutation operation produces, described mutation operation refers to, each gene position in the offspring individual of the solution individuality of the Advanced group species selected by interlace operation is produced, find out the positive adjacent node collection of the network node corresponding with this gene position, the label choosing the maximum class of occurrence number is concentrated from this positive adjacent node, using the value of such label as corresponding gene position in the offspring individual of the solution individuality of the Advanced group species selected by interlace operation generation,
9th step, replaces with the offspring individual of the solution individuality of the Advanced group species selected by mutation operation generation by the solution of selected Advanced group species individuality;
10th step, judges whether the value of count flag sl equals 200, if so, then obtains upgrading Advanced group species, otherwise, the value of count flag sl is added 1, performs the 2nd step.
5. the complex network balance clustering method based on multiple-objection optimization according to claim 1, it is characterized in that, the step upgrading the reference point of Advanced group species described in step (6d) is as follows:
1st step, the value with reference to the 1st element of point replaces with all imbalances of separating individuality in Advanced group species and bears the minimum value of the number of fillet;
2nd step, the value with reference to the 2nd element of point replaces with all minimum value of separating the number of the individual positive fillet of imbalance in Advanced group species.
6. the complex network balance clustering method based on multiple-objection optimization according to claim 1, it is characterized in that, the step upgrading outside population described in step (6e) is as follows:
1st step, the solution choosing all non-dominant of Advanced group species is individual;
2nd step, is merged into the solution individuality of all non-dominant of selected Advanced group species in outside population, obtains interim outside population;
3rd step, the solution choosing all non-dominant of interim outside population is individual, as outside population.
7. the complex network balance clustering method based on multiple-objection optimization according to claim 1, is characterized in that, the step upgrading the individual corresponding neighborhood of all solutions in Advanced group species described in step (6f) is as follows:
1st step, is set to 1 by the initial value of count flag sl;
2nd step, with the value of count flag sl for sequence number, the solution choosing the Advanced group species corresponding with this sequence number is individual;
3rd step, from the neighborhood of the solution individuality of selected Advanced group species, chooses arbitrarily one and separates individual;
4th step, according to the following formula, Chebyshev's value of the solution individuality of the new Advanced group species selected by calculating:
g
1＝max{λ
1|f
1(X)-z
1|,λ
2|f
2(X)-z
2|}
Wherein, g
1chebyshev's value of the solution individuality of the Advanced group species selected by expression, max represents that maximizing operates, λ
1represent with in the neighborhood of the solution individuality from Advanced group species selected by the imbalance of solution individuality bear weight corresponding to the number of fillet, f
1(X) imbalance of the solution individuality of the Advanced group species selected by expression bears the number of fillet, and X represents that the solution of selected Advanced group species is individual, z
1represent all in Advanced group species and separate the minimum value that individual imbalance bears the number of fillet, λ
2represent the weight corresponding with the number of the positive fillet of imbalance of solution individuality selected in the neighborhood of the solution individuality from selected Advanced group species, f
2(X) number of the positive fillet of imbalance of the solution individuality of the Advanced group species selected by expression, z
2represent all minimum value of separating the individual positive fillet number of imbalance in Advanced group species, || represent absolute value operation;
5th step, according to the following formula, calculates the Chebyshev's value chosen from the neighborhood of the solution individuality of selected Advanced group species and separate individuality:
g
2＝max{λ
1|f
1(W)-z
1|,λ
2|f
2(W)-z
2|}
Wherein, g
2represent Chebyshev's value of the solution individuality chosen from the neighborhood of the solution individuality of selected Advanced group species, max represents that maximizing operates, λ
1to represent and the imbalance of the solution individuality chosen in the neighborhood of the solution individuality from selected Advanced group species bears weight corresponding to the number of fillet, f
1(W) represent that the imbalance of solution individuality selected from the neighborhood of the solution individuality of selected Advanced group species bears the number of fillet, W represents that solution selected from the neighborhood of the solution individuality of selected Advanced group species is individual, z
1represent all in Advanced group species and separate the minimum value that individual imbalance bears the number of fillet, λ
2represent the weight corresponding with the number of the positive fillet of imbalance of solution individuality selected in the neighborhood of the solution individuality from selected Advanced group species, f
2(W) number of the positive fillet of imbalance of the solution individuality chosen from the neighborhood of the solution individuality of selected Advanced group species is represented, z
2represent all minimum value of separating the individual positive fillet number of imbalance in Advanced group species, || represent absolute value operation;
6th step, if Chebyshev's value of the solution individuality of selected Advanced group species is less than Chebyshev's value of the solution individuality chosen from the neighborhood of the solution individuality of selected Advanced group species, then the solution solution chosen in the neighborhood of the solution individuality from selected Advanced group species individuality being replaced with selected Advanced group species is individual;
7th step, repeats the 3rd step, the 4th step, the 5th step, the 6th step, until the solution individuality in the neighborhood of the solution individuality of selected new Advanced group species is all finished;
8th step, judges whether the value of count flag sl equals 200, if so, then completes and upgrades all operations of separating individual corresponding neighborhood in Advanced group species, otherwise, the value of count flag sl is added 1, performs the 2nd step.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510512727.2A CN105160404A (en) | 2015-08-19 | 2015-08-19 | Complex network balance clustering method based on multi-objective optimization |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201510512727.2A CN105160404A (en) | 2015-08-19 | 2015-08-19 | Complex network balance clustering method based on multi-objective optimization |
Publications (1)
| Publication Number | Publication Date |
|---|---|
| CN105160404A true CN105160404A (en) | 2015-12-16 |
Family
ID=54801255
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201510512727.2A Pending CN105160404A (en) | 2015-08-19 | 2015-08-19 | Complex network balance clustering method based on multi-objective optimization |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN105160404A (en) |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105868480A (en) * | 2016-04-05 | 2016-08-17 | 南京航空航天大学 | Quick multi-objective optimization design method for two-finger robot gripper |
Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2004006137A1 (en) * | 2002-07-02 | 2004-01-15 | British Telecommunications Public Limited Company | Optimisation method and apparatus |
| CN103745258A (en) * | 2013-09-12 | 2014-04-23 | 北京工业大学 | Minimal spanning tree-based clustering genetic algorithm complex web community mining method |
| CN104200272A (en) * | 2014-08-28 | 2014-12-10 | 北京工业大学 | Complex network community mining method based on improved genetic algorithm |
-
2015
- 2015-08-19 CN CN201510512727.2A patent/CN105160404A/en active Pending
Patent Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2004006137A1 (en) * | 2002-07-02 | 2004-01-15 | British Telecommunications Public Limited Company | Optimisation method and apparatus |
| CN103745258A (en) * | 2013-09-12 | 2014-04-23 | 北京工业大学 | Minimal spanning tree-based clustering genetic algorithm complex web community mining method |
| CN104200272A (en) * | 2014-08-28 | 2014-12-10 | 北京工业大学 | Complex network community mining method based on improved genetic algorithm |
Non-Patent Citations (3)
| Title |
|---|
| YIXIANG SUN: "Fast computing global structural balance in signed networks based on memetic algorithm", 《PHYSICAL A STATISTICAL MECHANICS & ITS APPLICATIONS》 * |
| 李峻金: "一种新的复杂网络聚类算法", 《计算机应用研究》 * |
| 陆楠等: "基于遗传理论的复杂网络模糊聚类算法", 《计算机与信息技术》 * |
Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN105868480A (en) * | 2016-04-05 | 2016-08-17 | 南京航空航天大学 | Quick multi-objective optimization design method for two-finger robot gripper |
| CN105868480B (en) * | 2016-04-05 | 2019-08-16 | 南京航空航天大学 | A kind of two refer to the fast multi-target optimum design method of robot gripper |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN102413029B (en) | Method for partitioning communities in complex dynamic network by virtue of multi-objective local search based on decomposition | |
| CN109886588A (en) | A method of flexible job shop scheduling is solved based on whale algorithm is improved | |
| CN109840154B (en) | Task dependency-based computing migration method in mobile cloud environment | |
| CN108882256B (en) | Method and device for optimizing coverage of wireless sensor network node | |
| CN112013829A (en) | Multi-UAV/UGV (unmanned aerial vehicle/user generated Unit) cooperative long-term operation path planning method based on multi-objective optimization | |
| CN114386694A (en) | Drug molecule property prediction method, device and equipment based on comparative learning | |
| CN103473482B (en) | Based on the prediction method for three-dimensional structure of protein that differential evolution and conformational space are annealed | |
| CN101482876B (en) | Weight-based link multi-attribute entity recognition method | |
| CN109447264B (en) | Virtual machine placement genetic optimization method based on VHAM-R model in cloud computing environment | |
| CN106651000B (en) | Black-start partitioning method based on semi-supervised spectral clustering | |
| CN102708327A (en) | Network community discovery method based on spectrum optimization | |
| Cai et al. | Self-organizing neighborhood-based differential evolution for global optimization | |
| CN105512755A (en) | Decomposition-based multi-objective distribution estimation optimization method | |
| CN110851247B (en) | Cost optimization scheduling method for cloud workflow with constraint | |
| CN102496033B (en) | Image SIFT feature matching method based on MR computation framework | |
| CN114358414A (en) | Adaptive parallel community endowment service point site selection optimization method and system | |
| CN116647459A (en) | Multi-agent co-evolution topological robustness optimization method for Internet of things | |
| Lamiable et al. | An algorithmic game-theory approach for coarse-grain prediction of RNA 3D structure | |
| CN103714384A (en) | Integrated circuit floor planning method based on moving modal sequence and Memetic algorithm | |
| CN105160404A (en) | Complex network balance clustering method based on multi-objective optimization | |
| CN109888817A (en) | Position deployment and method for planning capacity are carried out to photovoltaic plant and data center | |
| CN112395822B (en) | Time delay driven non-Manhattan structure Steiner minimum tree construction method | |
| CN105205534A (en) | Ternary FPRM circuit area and power consumption optimum polarity searching method | |
| CN111412795A (en) | Test point setting scheme generation method and device | |
| CN116595120A (en) | Automatic map surface element annotation configuration method based on genetic algorithm |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| RJ01 | Rejection of invention patent application after publication |
Application publication date: 20151216 |
|
| RJ01 | Rejection of invention patent application after publication |