CN105160580A - Symbol network structure balance of multi-objective particle swarm optimization based on decomposition - Google Patents

Abstract

The invention discloses a method of solving a symbol network structural balance problem by particle swarm optimization based on decomposition, which is used for mainly solving problems existing in the prior art during complex symbol network structure processing procedures. The method comprises the following steps of (1) determining an objective function; (2) constructing an initial solution population; (3) sequentially using a particle swarm optimization algorithm to update individual speeds and positions; (4) using offspring individuals to update the solution population; (5) using neighborhood information to update neighbor populations; (6) judging whether to terminate: if the iteration times can satisfy preset times, then executing the step (7), otherwise, moving back to the step (3); (8) according to acquired network division, selecting a community with minimum imbalance variables and changing imbalance edges to make a network reach a balance state. By means of the method, more accurate symbol network division more according with facts can be achieved An optimum network structure is further acquired. Imbalance edges are changed to make imbalanced networks reach a balance state.

Description

Based on the symbolic network constitutional balance of the multi-objective particle swarm optimization decomposed

Technical field

The invention belongs to complex symbol network field, the knowledge that the structure relating to complex symbol network tends to balance, specifically a kind of symbolic network constitutional balance of the multi-objective particle swarm optimization method based on decomposing, can be used for the research of the constitutional balance to complex network.

Background technology

Network is made up of node and line, represents all multi-objects and connect each other.Mathematically, network is a kind of figure, it is generally acknowledged and specially refers to weighted graph.Network is except mathematical definition, and also have concrete physical meaning, namely network is abstract model out from the practical problems of certain identical type.In computer realm, network is information transmission, reception, shared virtual platform, by it the informational linkage of each point, face, body to together, thus realize sharing of these resources.Network is that human development history carrys out most important invention, improves the development of science and technology and human society.Network can be checked by word read, picture, audio-visual broadcasting, download the Software tools such as transmission, game, chat and bring the life and fine enjoyment extremely enriched from aspects such as word, picture, sound, videos.

In our life, network is ubiquitous.At present the part to complex system study to the research of network.The rise of the fast development of areas of information technology and complex network research, the investigation and application for network brings new opportunities and challenges.On the one hand, along with the development of areas of information technology, the digitalized network data of ubiquitous network application and magnanimity provide abundant research formation to researcher, along with the development of science and technology, and portable electric appts ubiquity.People are by some social platform, and e.g., Facebook, microblogging, the facility that the social networks such as micro-letter provide sets up oneself social circle.Community network is the example of a good large-scale social system.Connection in community network between obstructed user creates complicated, multifaceted social relationships.Complex network research is just penetrating into numerous different fields such as mathematics and sciences, life science and engineering discipline, has become an extremely important challenge subjects in scientific research cybertimes to the understanding of science that is quantitative and qualitative features of complex network.

In recent years, people create very large interest to complex network, because many complication systems can be modeled as complex network, comprise contract network, WWW and neural network etc., and these researchs are probably understood complication system to us and brought new understanding.In order to understand and utilize the information of community network, researcher has found a lot of unique character of network, worldlet, uncalibrated visual servo etc., and have studied the architectural characteristic of a lot of method from different angle research networks.The research of community structure is caused to the extensive concern of scholar.Although proposed a lot of Community Clustering method, major part all can only process without symbolic network.But a lot of complication system all can only be modeled as the network having positive and negative connection, i.e. symbolic network in life.People more and more recognize, go to study these networks aligning confirm that knowing this kind of complication system has great importance with the application design on it based on symbol attribute.Such as, utilize the symbol attribute on limit to go analysis, understand and predict that the topological structure of these complex networks, function, dynamic behavior have very important theory significance, and to personalized recommendation, attitude prediction, user feature analysis and cluster etc., there is important using value.

Symbolic network refers to that limit has the network of plus or minus symbol attribute, wherein positive limit and the marginal relation representing positive relation and passiveness respectively.Specifically, the positive relationships such as the positive limit in symbolic network can represent friend, trusts, likes, support, use positive sign "+" mark, and are marginally generally used for representing the passive relations such as enemy, distrust, disagreeable, opposition, use negative sign "-" mark.At society, biological and message area, all there are antagonistic relations in a lot of complication system, such as, in social field, there is friend and enemy's relation between men; In international relations, there are cooperation and hostile relations; In biological field, exist between neuron and promote and the relation of suppression; In message area, user can express other users and trust or distrust attitude, mark friend or enemy's relation on social network sites or Social Media, can also vote for or oppose keeper's nomination of a user.In addition, in on-line communities, also there are close and antagonistic relations in User Perspective.Except the above-mentioned situation with clear and definite positive and negative relation identity, the positive-negative relationship also having some complication systems is implicit.The hyperlink comprised as page in WWW both may represent the approval to the hyperlink target page, and also may be oppose, these needs be judged by the semanteme analyzing two pages.These complication systems can abstractly be described for symbolic network.

In symbolic network field, most basic theory is that constitutional balance is theoretical, is proposed as far back as nineteen forty-six by Heider, and the prelude of symbolic network research had both been pulled open in the proposition of this theory, had also laid solid theoretical foundation for it.This theory is used to process the potential dynamic development trend of network.Originally equilibrium relation is mapped in triangle, sees accompanying drawing 1, and positive and negative frontier juncture system represents friend and enemy respectively, and equilibrium state meets principle, and the friend of friend is friend, and the enemy of friend is enemy, and the friend of enemy is enemy, and the enemy of enemy is friend.This theory is constantly improved and development after proposition, and due to the complicacy of social relationships, there are polarization phenomena when being applied on it by triangle balanced, famous scholar Davis studies network equalize to whole network system based on clustering method afterwards.Namely first carry out cluster to network, the connection between class between node is marginal entirely, and the connection between class interior knot is entirely for the network on positive limit is balancing network.

At sociology, computer science, psychology also has other any fields that can be described to symbolic network, and constitutional balance theory all show theory significance and the social value of its existence.Although the research of this theory also exists a lot of difficulty, due to its interesting property and importance, attract the famous scholar of every field.

The realistic meaning that the research of symbolic network constitutional balance has it important, Figure of description 2 have studied the active development of international relations, and finally tends to balance.This figure is to the development of the alliance of participating country during we show both the World War I.These relationship modelings are become symbolic network, and we just can predict the final relation between various countries, thus avoid a lot of catastrophic war.

Symbolic network constitutional balance problem can be modeled as optimization problem, and in a lot of situation, this problem is a np hard problem.Therefore, process problems with evolution algorithm and just seem particularly necessary.In some applications, network structure equilibrium problem needs to consider many factors, therefore, solves network structure equilibrium problem even more ideal by conflicting multiple goal.Several multi-objective Evolutionary Algorithm with solving network clustering is had to you can well imagine out.But they are all with solving without symbolic network, even if with solving symbolic network, result is also undesirable.Stable and effective network structure can not be detected, and the complexity of some algorithm is high and search capability is more weak.

Summary of the invention

The object of the invention is to the deficiency for prior art, propose a kind of new model and propose a kind of algorithm based on decomposed particles group optimization newly for solving the relevant issues of symbolic network constitutional balance.

First the relation of symbolic network community and symbolic network structure is introduced: symbolic network structure is-symbol topology of networks, it is a global concept, and community, it is the module that the concept of this entirety of symbolic network is divided, whole communities is exactly that to be added together be exactly the structure of whole network, that is, community is that the one of network structure represents form.Community has some similar features, contacts the set of people's (thing) closely, and the community in the present invention is that the node that some in whole macroreticular has a similar features is divided in a plate, and each plate is a community.

Technical scheme of the present invention is: complex network structures equilibrium problem is regarded as two target problems, these two objective functions form by based on the k-mean value function of core and ratio function, be defined as SKKM respectively, SRC utilizes the multi-objective particle swarm optimization method based on decomposing to optimize two objective functions simultaneously, and introduce neighborhood local searching strategy, search for better network clustering structure, obtain PF face, each point on PF face represents a solution, and each solution represents a kind of classification.Choose from classification again and change the minimum classification reaching balance of limit number.Implementation step is as follows:

Step 1, for the concept that symbolic network community divides, builds new objective function, and make the positive limit density in symbolic network community large, the positive limit density between community is little;

Step 2, according to the ultimate principle that particle is optimized, uses particle group optimizing strategy, carrys out the objective function that Optimization Steps 1 builds, and obtains multiple different symbolic network community and divides;

Step 3, chooses a kind of symbolic network community division result making the positive limit number sum between the marginal number of inside, community and community minimum from multiple different symbolic network community divides;

Step 4, divides the symbolic network community chosen, changes the symbol attribute on uneven limit.Change positive limit into by the marginal of inside, symbolic network community, the positive limit between community changes into marginal, thus obtains final balancing network.

Particle swarm optimization algorithm in the present invention is a kind of random search algorithm based on group collaboration grown up by simulation flock of birds foraging behavior.It is the one of Swarm Intelligence Algorithm, simulation flock of birds predation, and bevy is at random search food, and only with one piece of food in this region, where all birds all do not know food.But they know how far current position also has from food.The optimal strategy of food is found to be search for the peripheral region of the current bird nearest from food.Particle swarm optimization algorithm model is simple, and seldom occurs hypothesis in process problem process, does not need requirement problem to have good mathematical property, such as, can fall, concavity and convexity etc.Particle swarm optimization algorithm obtains great achievement in solution continuous problem, based on this, devises Discrete Particle Swarm Optimization Algorithm herein.To improve the accuracy of network clustering, realize the correct division to complex network.The present invention compared with prior art tool has the following advantages:

The first, the present invention regards the clustering problem of complex symbol network as a multi-objective problem, utilizes and optimizes two objective functions based on particle group optimizing method simultaneously.The method is simple, and parameter need be adjusted less, and overcoming prior art needs to formulate class number size in advance.

The second, present invention employs discrete particle cluster optimization, redesign some models in particle group optimizing process.

3rd, present invention employs real number coding method and particle is encoded, in decode procedure, automatically determine community

Classification number.

4th, invention introduces new strategy and carry out process symbol network structure equilibrium problem.

Accompanying drawing explanation

Fig. 1 is constitutional balance framework;

Fig. 2 is the development of the World War I each allied power relation, describes the realistic meaning of network structure balance;

Fig. 3 is the concrete framework that the present invention deals with problems;

Fig. 4 is the comparison diagram in PF face after the present invention and existing method divide several representative network community.

Embodiment

Specific implementation step of the present invention is as follows:

Step 1, the adjacency matrix A of input aiming symbol network establishing target function: the adjacency matrix A of the positive-negative relationship composition symbolic network in (1a) symbolic network between each node, it is defined as follows:

$A=\left[\begin{array}{cccc}{A}_{11}& A_{12}& ...& A_{1n}\\ A_{21}& A_{22}& ...& A_{2n}\\ \begin{array}{c}\·\\ \·\\ \·\end{array}& \begin{array}{c}\·\\ \·\\ \·\end{array}& A_{ij}& \begin{array}{c}\·\\ \·\\ \·\end{array}\\ A_{n1}& A_{n2}& ...& A_{nn}\end{array}\right]---1)$

Wherein A _ijrepresent the connection of node i and j, the elements A of adjacency matrix _ij∈-1,0 ,+1}, as i ≠ j, represent that node i with j is just being connected, A _ij=-1 represents that node is negative connection, and A _ij=0 represents node i, and j is without connecting; As i=j, A _ij=0, n represents the node number of symbolic network;

(1b) according to the community's concept dividing symbolic network, establishing target function is as follows:

$\min =\left\{\begin{array}{c}SKKM=-{\Σ}_{i=1}^k\frac{L^{+}(V_i,V_i)-L^{-}(V_i,V_i)}{\left|V_i\right|}\\ SRC=-{\Σ}_{i=1}^k\frac{L^{+}(V_i,\stackrel{\‾}{V_i})-L^{-}(V_i,\stackrel{\‾}{V_i})}{\left|V_i\right|}\end{array}\right\}---2)$

Wherein $L^{+}(V_i,V_j)={\&Sigma;}_{i\&Element;V_i,j\&Element;V_j}{A}_{ij},(A_{ij}>0),L^{-}(V_i,V_j)={\&Sigma;}_{i\&Element;V_i,j\&Element;V_j}\left|A_{ij}\right|,(A_{ij}<0).$

V _irepresent community of i-th, community, L ⁺(V _i, V _j) represent positive limit number between community i and community j, L ^-(V _i, V _j) represent marginal number between community i and community j.K is community's number, | V _i| be the node number of i-th community, do not comprise other communities in k community of i community, i ∈ V _irepresent that i is the node in community i, j ∈ V _jrepresent that j is the node in community j.

Step 2, concrete optimisation strategy

Performing step is as follows:

(2a) initialization:

2a1) construct initialization population, adopt real number coding method initialization population, P={x ₁, x ₂..., x _popwherein x _i=i;

2a2) initialization speed V={v ₁, v ₂..., v _n, v _i=0;

2a3) the uniform weight vectors of Computation distribution;

2a4) initialization Pbest={pbest ₁, pbest ₂..., pbest _n, pbest _i=x _i;

2a5) initialized reference point k is the number of objective function,

$z_i^{*}=\left\{{\mathrm{minf}}_i\left(x\right)\right|x\&Element;\mathrm{\&Omega;}\};$

2a6) the neighbours of each subproblem of initialization.The neighbor adjacency problem n={n of each subproblem is calculated according to Euclidean distance ₁, n ₂... n _niche.

(2b) t=0 is established;

2b1) circulate:

To i=1,2 ..., pop

2b11) from particle neighbours Stochastic choice particle as gbest;

2b12) speed upgrades, and calculates the speed of i-th particle in current population

2b13) location updating, calculates the position of i-th particle in current population

If 2b2) t < maxgen*pm, perform Perturbed algorithms, see reference document ComplexNetworkClusteringbyMultiobjectiveDiscreteParticle SwarmOptimizationBasedonDecomposition wherein, maxgen is maximum iteration time, pm ∈ (0,1) is disturbing operator;

2b3) calculate corresponding fitness function;

2b4) more new neighbor solution: for each particle i neighbor particle j (j=1,2 ... niche), if $g^{\mathrm{te}}\left(X_i^{t+1}\right|{\mathrm{\&omega;}}_j,Z^{*})\&le;g^{\mathrm{te}}\left(X_i^t\right|{\mathrm{\&omega;}}_j,Z^{*}),$ So $X_i^t=X_i^{t+1},F\left(X_i^t\right)=F\left(X_i^{t+1}\right);$

2b5) upgrade reference point: upgrade pbest _i, upgrading, is that the concept that pbest Pareto is arranged upgrades, if new solution domination, then upgrades it for new solution; If arrange the solution that new pbest produces, the value keeping pbest original is constant; If both mutual non-pbest dominations, then more corresponding functional value, that functional value is less is pbest.

Step 3, obtains multiple different symbolic network community by carried model and divides, therefrom choose a kind of community division method closest to network equalize, then change the symbol attribute on uneven limit, and then obtain final balancing network.

Specific Principles 3a) chosen is: choosing from multiple different symbolic network community divides is the minimum a kind of symbolic network community division result of positive limit number sum between the negative parameter of inside, community and community

$H\left(s\right)=\underset{i,j}{\&Sigma;}(1-J_{ij}(s_i{s}_j\left)\right)/2$

Wherein J _ijfor adjacency matrix, s _i, s _jrepresent the label of node i and node j respectively, s _i=s _jtime, s _is _j=1; Otherwise s _is _j=-1.

3b) according to the community selected, the symbol attribute on change symbolic network limit, the positive limit between community changes into marginal, and marginal in community changes positive limit into, obtains final balancing network.

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

1. simulated conditions

This example, under Intel (R) Core (TM) 2DuoCPU2.33GHzWindowsXP system, on VC++6.0 operation platform, completes the emulation experiment of the present invention and NSGA-II method.

2. emulation experiment content

Symbol community network, bio-networks and artificial network are chosen as experimental subjects.Optimum configurations is as follows, and Population Size is 100, and iterations is 100, and crossover probability is 0.9, and mutation probability is 0.1, and sub-Population Size M is set to 10.Use degree of unbalancedness HS size as criterion.The value of HS value is less, also just proves that this network structure more tends to balance.Following SN-DMOPSO represents the symbolic network balance of the multi-objective particle swarm optimization based on decomposing of the present invention, and SN-NSGA-II represents the symbolic network community structure balance of existing quick elite's multi-objective genetic algorithm, and both optimum configurations are identical.

The network data used in this emulation, has the social live network of symbol, has symbol bio-networks, and the artificial network of balance.Wherein, SPP and GGS network has symbol community network really, EGFR and Macrophage network has symbolic network, and Internation6 network is artificial balancing network, is used for further illustrating the validity of the model and algorithm that the present invention proposes.Parameter list 1:

Table 1

Network	Nodal point number	Limit number	Positive limit number	Marginal number
					SPP	10	45	18	27
GGS	16	58	29	29
					EGFR	329	779	515	264
Macrophage	678	1425	947	478
					Internation6	6	15	6	9

Network data emulates: employ two true community networks in this emulation, two bio-networks, an artificial balancing network, and totally five symbolic networks verify the validity of the model and algorithm that the present invention proposes.The present invention first carries out community's detection to symbolic network, then calculates the quality of balance of HS size computational grid structure according to classification results.

In this experiment, the experimental result of six symbolic networks is shown in Fig. 4, and in figure, red boxes mark represents the result of SN-DMOPSO method of the present invention, and Blue circles mark represents the result of existing SN-NSGA-II method.

Fig. 4 (a) represents symbolic network SPP, SN-DMOPSO method of the present invention and existing SN-NSGA-II method choose best PF face result figure once respectively after independent operating 30 times, as can be seen from Fig. 4 (a), SN-DMOPSO acquired results of the present invention arranges the result of SN-NSGA-II gained completely.Shown in Fig. 4 (b), (c), (d), result is similar to (a).

Table 2 represents that the present invention puts in corresponding classification on Fig. 4 PF face and chooses the point making HS value minimum, and table 2 lists three kinds of less situations of Hs.

Table 2

In a word, method of the present invention divides the community of symbolic network can obtain better result, and carries out the conversion of symbol attribute to unbalanced limit in community and between community further according to the result divided, and obtains final balancing network.

Claims (8)

1., based on a method for the solution symbolic network constitutional balance of the multi-objective particle swarm optimization decomposed, comprise the steps:

Step 1, establishing target function, make the positive limit density in symbolic network community large, the positive limit density between community is little;

Step 2, uses particle group optimizing strategy, the objective function that Optimization Steps 1 builds, and obtains multiple different symbolic network community and divides;

Step 3, chooses a kind of symbolic network community division result making the positive limit number sum between the marginal number of inside, community and community minimum from multiple different symbolic network community divides;

Step 4, divide the symbolic network community chosen, change the symbol attribute on uneven limit, change positive limit into by the marginal of inside, symbolic network community, the positive limit between community changes into marginal, thus obtains final balancing network.

2. the method for solution symbolic network constitutional balance according to claim 1, wherein, step 1 specifically comprises:

(1a) represent the positive-negative relationship in symbolic network between each node with the adjacency matrix A of symbolic network, the adjacency matrix A of described symbolic network, is defined as follows:

Wherein A _ijrepresent the connection of node i and j, the elements A of adjacency matrix _ij∈-1,0 ,+1}, and as i ≠ j, A _ij=1 represents that node i with j is just being connected, A _ij=-1 represents that node is negative connection, and A _ij=0 represents node i, and j is without connecting; As i=j, A _ij=0, n represents the node number of symbolic network;

(1b) establishing target function is as follows:

Wherein

V _irepresent community of i-th, community, L ⁺(V _i, V _j) represent positive limit number between community i and community j, L ^-(V _i, V _j) represent marginal number between community i and community j.K is community's number, | V _i| be the node number of i-th community, _ido not comprise other communities in k community of i community, i ∈ V _irepresent that i is the node in community i, j ∈ V _jrepresent that j is the node in community j.

3. the method for solution symbolic network constitutional balance according to claim 2, wherein, step 2 comprises:

Chebyshev's mathematic decomposition method is utilized to be decomposed into N number of single goal subfunction two objective functions in step 1:

Wherein, x is the solution of function, f _ix () separates functional value corresponding to x, f _ithe maximal value of (x), λ _ithe weighting parameter that i-th objective function is corresponding, i ∈ (1,2);

Discrete particle cluster algorithm update mechanism comprises:

1) speed upgrades:

Wherein, be ω weight, c ₁and c ₂studying factors, r ₁, r ₂the random number that ∈ (0,1) is interval, it is xor operation; Function Y=sig (X), Y=(y ₁, y ₂..., y _n), X=(x ₁, x ₂..., x _n)

Wherein

2) location updating: produce reposition such as: wherein X ₂=(x ₂₁, x ₂₂... x _2n), X ₂each element upgrade by following principle:

Wherein Nbest _ibeing the current optimal location of i-th particle, is an integer, v _ithe speed of i-th particle, x _1irepresent the position under particle i current iteration number of times, x _2irepresent the position of particle i after once upgrading.Suppose that node i has neighbours to collect N={n ₁, n ₂..., n _k, so

If wherein i=j, so otherwise be 0.

4. the method for solution symbolic network balance according to claim 1, wherein, step 2 comprises:

(2a) initialization:

2a1) construct initialization population, adopt real number coding method initialization population, P={x ₁, x ₂..., x _popwherein x _i=i;

2a2) initialization speed V={v ₁, v ₂..., v _n, v _i=0;

2a3) the uniform weight vectors of Computation distribution;

2a4) initialization Pbest={pbest ₁, pbest ₂..., pbest _n, pbest _i=x _i;

2a5) initialized reference point k is the number of objective function,

2a6) the neighbours of each subproblem of initialization.The neighbor adjacency problem n={n of each subproblem is calculated according to Euclidean distance ₁, n ₂... n _niche;

(2b) t=0 is established;

2b1) circulate:

To i=1,2 ..., pop

2b11) from particle neighbours Stochastic choice particle as gbest;

2b12) speed upgrades, and calculates the speed of i-th particle in current population

2b13) location updating, calculates the position of i-th particle in current population

If 2b2) t < maxgen*pm, perform Perturbed algorithms, wherein, maxgen is maximum iteration time, and pm ∈ (0,1) is disturbing operator;

2b3) calculate corresponding fitness function;

2b4) more new neighbor solution: for each particle i neighbor particle j (j=1,2 ... niche), if so wherein, the position after the t time iteration of particle i, functional value corresponding to position after particle i the t time iteration;

2b5) upgrade reference point: upgrade pbest _i, upgrading, is that the concept that pbest Pareto is arranged upgrades, if new solution domination, then upgrades it for new solution; If arrange the solution that new pbest produces, the value keeping pbest original is constant; If both mutual non-dominant, then more corresponding functional value, that functional value is less is pbest.

5. the balance method of solution symbolic network according to claim 1, choosing from multiple different symbolic network community divides described in step 3 is that the minimum a kind of symbolic network community division result of positive limit number sum between the negative parameter of inside, community and community adopts following formula:

Wherein J _ijfor adjacency matrix, s _i, s _jrepresent the label of node i and node j respectively, s _i=s _jtime, s _is _j=1; Otherwise s _is _j=-1.

6. the method for solution symbolic network constitutional balance according to claim 1, wherein, given iterations maxgen=100, niche=10, pop=100.

7. the method for solution symbolic network constitutional balance according to claim 3, wherein, Studying factors c ₁and c ₂usually all 2 are got.

8. the method for solution symbolic network constitutional balance according to claim 3, wherein, weights omega gets 1.419.