CN111488991A - Communication community detection method of cuckoo algorithm combined with genetic and discrete difference - Google Patents

Communication community detection method of cuckoo algorithm combined with genetic and discrete difference Download PDF

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CN111488991A
CN111488991A CN202010102799.0A CN202010102799A CN111488991A CN 111488991 A CN111488991 A CN 111488991A CN 202010102799 A CN202010102799 A CN 202010102799A CN 111488991 A CN111488991 A CN 111488991A
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周井泉
许杰
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Nanjing University of Posts and Telecommunications
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Abstract

The invention discloses a communication community detection method of cuckoo algorithm combining heredity and discrete difference, which comprises the steps of converting a telephone communication network to be detected into an adjacent matrix form of nodes, coding bird nests by adopting a track-based coding mode, calculating corresponding objective functions, sequencing, storing high-quality bird nests into an external storage gene library, then, the bird nest is updated for the first time by adopting a method of random walk and combining a high-quality gene genetic strategy, the bird nest with the optimal objective function is compared and replaced, and then, locally searching the updated bird nest, updating the bird nest for the second time by adopting a method of combining Levy flight and a discrete difference strategy, comparing again, selecting an optimal solution, and decoding the bird nest to obtain optimal community division.

Description

Communication community detection method of cuckoo algorithm combined with genetic and discrete difference
Technical Field
The invention relates to a communication community detection method of a cuckoo algorithm by combining genetic inheritance and a discrete difference strategy, belonging to the technical field of communication network community analysis.
Background
Many real-world systems can be represented as complex networks such as computer networks, power systems, social networks, biological networks, transportation networks. Nodes in a complex network are partitioned according to rules, and such a partition is called a community. Is characterized in that: the nodes in the same community have higher connectivity, and the connectivity of the nodes among the communities is lower. The nodes in the community have many same attributes, so the community structure of the complex network is very important for researching the network characteristics, which is helpful for analyzing the intrinsic rules and topological structure characteristics of the complex network, and in addition, the research result of the community structure of the complex network has been applied to multiple aspects such as terrorist organization identification, protein function detection, customer relationship clustering, and the like.
The complex network community detection is a popular research project, a plurality of community detection algorithms emerge during the period, the main body is divided into a GN algorithm based on a graph decomposition method, such as a Kernighan-L in algorithm, a hierarchical clustering-based algorithm main body is subdivided into a splitting algorithm and a clustering algorithm, a classical algorithm in the splitting algorithm is a GN algorithm, a representative algorithm in the clustering algorithm is a Fast Newman algorithm and a CNM algorithm, a random Walk-based method, such as a Walk Trap algorithm, an optimization-based algorithm, a partitioning result is obtained by optimizing a community evaluation function based on the optimization algorithm, an intelligent evolution community discovery algorithm is divided into multi-objective optimization and single-target optimization, the single-target optimization is generally optimized for the modularity, Newman and the like use a standard degree Q as an index of network partitioning quality, the basic idea of modularity optimization is to maximize the degree by iteration valley, the occurrence of a simulated annealing algorithm is optimized for the early degree, a binary optimization based on the community discovery algorithm based on the simulated annealing algorithm, a module degree Q is an index of the modular network partitioning quality, a modular optimization based on the theoretical optimization algorithm, a high-based on a BGGA algorithm, a high-based on a genetic algorithm, a high-based on a BGga search algorithm, a high-based on a high-probability algorithm is developed for optimizing a new algorithm, a high-based on a cluster algorithm for a cluster search algorithm for a cluster algorithm for optimizing a cluster algorithm for a cluster search algorithm for a cluster algorithm for a high-based on a cluster algorithm for which is developed algorithm for a cluster optimization algorithm for a cluster search algorithm for a cluster optimization for a cluster search algorithm for a cluster optimization for a cluster.
However, in a communication network, the searching efficiency of the traditional cuckoo algorithm is low, and the traditional cuckoo algorithm is easy to fall into local optimization.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects in the prior art, the invention provides a communication community detection method of a cuckoo algorithm combining heredity and discrete difference. On the first hand, a method of combining random walk and genetic strategy is adopted for updating the position of the bird nest, so that the diversity and the global property of the bird nest can be ensured; in the second aspect, aiming at the defects that the convergence speed of the cuckoo algorithm is low and the search result is inaccurate, the elite search is added, and the quality of the population can be improved and the search speed is accelerated by adopting a method of combining the Levy flight and the discrete difference strategy.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the technical scheme that:
a communication community detection method combining genetic and discrete difference cuckoo algorithm converts a telephone communication network to be detected into an adjacent matrix form of nodes, codes bird nests by adopting a track-based coding mode, calculates corresponding objective functions, sorts, stores high-quality bird nests into an external storage gene library, updates the bird nests for the first time by adopting a method of random walk and combining a high-quality gene genetic strategy, compares and replaces the bird nests with the optimal objective functions, then carries out local search on the updated bird nests, updates the bird nests for the second time by adopting a method combining Levis flight and a discrete difference strategy, selects an optimal solution after comparison again, decodes the bird nests to obtain optimal community division, and specifically comprises the following steps:
step 1, obtaining communication network information, wherein the communication network information comprises each telephone and call records among the telephones.
And 2, converting the communication network into a form of an adjacent matrix of nodes, wherein each different telephone is regarded as a node, and a call record between two telephones is regarded as an edge. And carrying out bird nest coding on the communication network by adopting a track-based coding mode, wherein the bird nest is regarded as a solution, and the modularity Q value is taken as an objective function. The coding mode has the advantages that the division number of communities does not need to be known first, each bird nest is used as a community division result, and x is solved for the ith nestiIs denoted by xi＝(xi1,xi2,xi3,xi4,…xinN represents the number of nodes in the network and is also the dimension of the bird nest, and when coding, the neighbor nodes of the node j are found out according to the adjacent matrix A of the network, and x isijMay randomly select one of the neighbor nodes of node j, such as xijK, it means that there is an edge between the j node and the k node.
Step 3, in order to make the solving efficiency faster and the convergence faster, defining a concept of an external storage bank R, selecting a bird nest with a large target function value from the gene bank, sorting the Q values of the target function, and then storing the first s Q values into the external storage bank, wherein R ═ { R ═ R { (R) }1,r2,r3,…rsThe value x of each dimension of the bird nest in the elite library is calculatedijAs a gene.
Step 4, updating the position of the bird nest: in order to ensure the diversity and the flexibility of bird nests, the bird nest search is carried out by adopting a method of global random walk and combining a high-quality gene genetic strategy in an elite library R, and the bird nest with the optimal objective function is correspondingly updated.
Bird nest from t1Time t2The change in position change at a time can be expressed as:
Figure RE-GDA0002557713670000021
wherein n represents the number of nodes in the network and the nodes in the bird nest
Figure RE-GDA0002557713670000022
With probability p1Global random walk derived, probability
Figure RE-GDA0002557713670000023
djIn degrees of node j. The random walk process enables the position of the bird nest to be updated quickly, and the flexibility of understanding is guaranteed to a certain extent.
Then adopting a strategy of high-quality genetic inheritance to convert x in the bird nestijRegarded as a gene, with a probability pcAnd pgPreservation of elite gene (r)m) And global optimal solution (gbest) gene, x in bird nestijThe updating method is as follows:
Figure RE-GDA0002557713670000031
rmj＝R(round*(rand×s))
wherein x isijDenotes the jth node, k, in the ith bird's nest1Is a neighbor node in the global random walk process, rmjFor a value corresponding to the jth node of a bird's nest in the gene library, gbestjRepresents the value corresponding to the jth node of the optimal bird nest, round represents the nearest rounding, pcRepresenting the probability of a gene, p, of an elite bird nest in the inherited gene librarygThe probability of the gene inheriting the optimal nest is shown, R (round × s) is the probability of randomly picking the nest in the elite library, round is the rounding, and s is the size of the nest in the elite.
Replacement updating process: calculating an objective function of a new bird nest position, comparing the maximum objective function with the objective function of the original corresponding position, if Q (x'i)>Q(xi) Then x isi←x′iMixing Q (x)i) Finding out the maximum value in the range, comparing with the global optimal gbest, if best>gbest, then gbest ← best, where Q (x'i) Representing the modularity of the bird's nest i' after its position has been updated, Q (x)i) Representing the modularity, x, of the original nest iiDenotes the ith bird nest, x'iRepresenting the updated bird nest i', best representing the originalAnd a bird nest corresponding to the maximum modularity in the elite library exists, and the gbest represents the bird nest with the maximum modularity in the bird nest after the position is updated.
And 5, in order to prevent the situation of trapping into local optimization, improve the searching accuracy and the population quality, enable the algorithm searching to be more accurate and accelerate convergence, adopting a method combining Levy flight and a discrete difference strategy to take the updated elite library R nest as an initial solution set, updating the position of the nest again, calculating a target function Q, and finding out a high-quality solution to replace the solution into the updated elite library R after comparison.
Step 51: the traditional Levy flight mode is not suitable for discrete position updating, cosine mapping is carried out on random step length, and the random step length is expressed as a value of each dimension in a bird nest
Figure RE-GDA0002557713670000032
Thus finding the step length of the bird nest
Figure RE-GDA0002557713670000033
The method for calculating the step length in the flight of Levy is
Figure RE-GDA0002557713670000034
Wherein x isiAs a solution to the current bird's nest, xgbestIs the solution of the optimal bird nest,
Figure RE-GDA0002557713670000035
the step size is represented as a function of time,
Figure RE-GDA0002557713670000036
represents a constant, here taken to be 1.
Step 52: calculating the contribution degree of the neighbor node corresponding to each node: the concept of contribution degree is introduced here and used as a condition for replacing the position of the bird nest, and the calculation method of the contribution degree of the neighbor node a of the node j comprises the following steps: and selecting all the nodes in the j dimension, finding out the objective function value corresponding to the node a, and solving the corresponding average value. And judging, if the neighbor node is in the jth dimension, obtaining the contribution value by adopting the method, and if the neighbor node is not in the jth dimension, selecting the obtained minimum contribution value to be assigned to the node.
Step 53: updating the position of the bird nest, comparing the obtained step value after cosine mapping change with the preference search probability Pa, and if the step length is larger than the preference search probability Pa
Figure RE-GDA0002557713670000041
Is not greater than paAnd the value of the dimension corresponding to the current bird nest is not changed. If step size
Figure RE-GDA0002557713670000047
Is greater than paCalculating the contribution degree of the corresponding neighbor of each node, then adding the contribution degrees of all the neighbor nodes to sum up to obtain the probability p of each neighbor node being selected2Selecting neighbor node k according to the nearest principle2(ii) a The formula for updating bird's nest in local search is as follows
Figure RE-GDA0002557713670000042
Wherein,
Figure RE-GDA0002557713670000043
represents the selection of node j in bird nest i after the t +1 th iteration,
Figure RE-GDA0002557713670000044
represents the step length corresponding to each jth node of the ith bird nest
Figure RE-GDA0002557713670000045
Mapped value, k, whose value is cosine mapped2Representing the neighbor nodes of node j.
And 6, repeating the step 4, solving the objective function value of the updated elite library R again, comparing the objective function value with the optimal bird nest, and carrying out related replacement work.
And 7, terminating judgment: firstly, t is t +1, whether the value of the target function reaches a convergence condition is judged, if the convergence condition of the target function is met, whether the convergence condition Q '-Q is less than or equal to is judged, Q' is the current target function, Q is the last target function and represents the target convergence precision, if the convergence condition is met, the step 8 is switched to, and if the convergence condition is not met, the termination condition is considered: t > iter, iter represents the iteration times, t represents the algorithm operation times, if not, the step 3 is switched to, otherwise, the step 8 is switched to.
And 8, outputting an optimal solution: and exiting the iterative process, decoding the optimal bird nest gbest and obtaining community division.
Preferably: the method for calculating the contribution degree of the neighbor node a of the node j in the step 52 comprises the following steps:
step 52-1: all the nodes in the j dimension are selected first.
Step 52-2: and the calculation node a corresponds to an objective function value, and an average value is obtained.
Step 52-3: and judging, if the neighbor node is in the jth dimension, calculating the contribution value by adopting the method in the step 52-2, and if the neighbor node is not in the jth dimension, selecting the obtained minimum contribution value to be assigned to the node.
Preferably: neighbor node k of node j in step 532The selection probability of (2) is as follows:
step 53-1: and calculating the contribution values of all the neighbor nodes.
Step 53-2: summing all the contribution values to obtain a sum value sGeneral assembly。
Step 53-3: k is a radical of2Is selected probability of
Figure RE-GDA0002557713670000046
And n is the number of the neighbor nodes.
Preferably: the gene bank R is stored externally.
Compared with the prior art, the invention has the following beneficial effects:
1. by combining global random walk and high-quality gene genetic strategies, the diversity of the population in the iterative process of the algorithm is ensured, and the algorithm is prevented from falling into local optimum.
2. According to the Laevir flight and the discrete differential evolution of the local search, the convergence speed and the search efficiency of the algorithm are improved, and meanwhile, the accuracy of the algorithm in the iteration process is improved.
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FIG. 1 is a block diagram of the present invention.
FIG. 2 is a flow chart of the present invention.
FIG. 3 shows the simulation partitioning result of the present invention in a real network.
FIG. 4 shows the simulation partitioning result and the optimal Q value in the real network according to the present invention.
Detailed Description
The present invention is further illustrated by the following description in conjunction with the accompanying drawings and the specific embodiments, it is to be understood that these examples are given solely for the purpose of illustration and are not intended as a definition of the limits of the invention, since various equivalent modifications will occur to those skilled in the art upon reading the present invention and fall within the limits of the appended claims.
A communication community detection method of a cuckoo algorithm combining inheritance and discrete difference is disclosed, as shown in figures 1 and 2, in life, people make calls every day, and many call records are recorded every day, in order to improve the search accuracy of a communication complex network community structure, based on a cuckoo search algorithm framework, a network is firstly converted into an adjacent matrix, then a nest is initialized, a related objective function is calculated, the position of the nest is updated through global random walk and a high-quality genetic strategy is combined, the diversity and flexibility of the nest are ensured, meanwhile, the quality of a population is improved and the accuracy of an optimal solution is searched by applying an elite search method combining Levis flight and a discrete difference strategy, the population diversity is high, the algorithm efficiency is high, and the community division is more accurate, and the method comprises the following steps:
step 1, initializing parameters: the population scale l; a static network G; preference search probability pa(ii) a Iteration termination times iter, and target convergence accuracy.
Step 2, initializing bird nests: writing an adjacent matrix A of nodes according to a network G, coding a bird nest by adopting a track-based coding mode according to the adjacent matrix A of the nodes, initializing the bird nest by adopting an identifier-based formula, solving a corresponding objective function value Q, and calculating the objective function value according to the sizeAnd (6) sorting. The initialization mode adopts an initialization mechanism based on identifier transmission: after bird nest coding, initializing by adopting an identifier-based transfer mechanism, firstly randomly selecting a node j in the bird nest, assuming that the node j has k neighbor nodes, wherein the neighbor node set is A (j), and the neighbor node identifier set is S (j) { x }1,x2,...,xk-initialisation of each node identifier in the network is dependent on the identifiers in its neighbour set;
if the identifiers of all nodes in the neighbor set of the node j are different, one neighbor identifier is randomly selected to cover the original xi(ii) a If the neighbor set of node j has the same identifier, the identifier with the largest proportion is selected to cover the original xi。
And 3, establishing an external storage gene library R, and storing the bird nests with the first s large objective function values into the external storage gene library R.
Step 4, updating the position of the bird nest; in order to ensure the flexibility and diversity of bird nests, a global random walk mode and a high-quality gene genetic strategy mode are combined. The specific update formula is:
Figure RE-GDA0002557713670000061
rmj＝R(round*(rand×s))
wherein k is1Is a neighbor node in the random walk process, rmjRound means rounding, gbest, for the value corresponding to the jth node of a bird's nest in the gene libraryjRepresenting the value corresponding to the jth node of the optimal bird's nest.
Calculating an objective function of a new bird nest position, comparing the maximum objective function with the objective function of the original corresponding position, if Q (x'i)>Q(xi) Then x isi←x′iMixing Q (x)i) Finding out the maximum value in the range, comparing with the global optimal gbest, if best>gbest, gbest ← best.
And step 5, searching for elite: in order to accelerate the convergence rate of the algorithm and improve the accuracy of the algorithm, a local search algorithm combining Levis flight and a difference strategy is adopted, the traditional Levis flight method is suitable for a continuous function, and the discretization problem comprises the following specific steps:
step 51: step length of bird nest
Figure RE-GDA0002557713670000066
The method for calculating the step length in the flight of Levy is
Figure RE-GDA0002557713670000062
xiAs a solution to the current bird's nest, xgbestA solution for an optimal bird nest;
step 52: the method for calculating the contribution degree of the neighbor node a of the node j is specifically realized as follows:
step 52-1: firstly, selecting all nodes in the j dimension;
step 52-2: calculating the objective function value corresponding to the node a, and calculating the average value;
step 52-3: judging, if the neighbor node is in the jth dimension, obtaining a contribution value by adopting the method, and if the neighbor node is not in the jth dimension, selecting the obtained minimum contribution value to be assigned to the node;
step 53: the position of the bird nest is updated, the above mentioned
Figure RE-GDA0002557713670000067
Searching probability p with preference after cosine mapping change of valueaMake a comparison if
Figure RE-GDA0002557713670000063
The mapping value is not greater than paThe current value is not changed, if
Figure RE-GDA0002557713670000064
The mapped value is greater than paThen select its neighbor node k according to the principle of proximity2Carry out the replacement, k2The selection probability is specifically as follows
Step 53-1: calculating the contribution values of all the neighbor nodes according to the method for calculating the contribution values in the step 2;
step 53-2: summing all the contribution values to obtain a sum value sGeneral assembly；
Step 53-3: k is a radical of2Is selected probability of
Figure RE-GDA0002557713670000065
n is the number of neighbor nodes;
the bird nest position updating method comprises the following steps:
Figure RE-GDA0002557713670000071
step 6, repeating the step 4, solving the objective function value of the newly generated bird nest again, comparing the objective function value with the optimal bird nest, and carrying out related replacement work;
and step 7, termination judgment: firstly, t is t +1, then, whether a convergence condition Q '-Q ≤ Q' is met is judged to be the current target function, Q is the last target function, if the convergence condition is met, the process goes to the step 8, and if the convergence condition is not met, the termination condition is considered: t > iter, if not, turning to the step 3, otherwise, turning to the step 8;
and 8, outputting an optimal solution: and exiting the iterative process and decoding the optimal bird nest gbest.
As shown in fig. 3 and 4, the partitioning result and the modularity Q value in the Karate real dataset of the present invention are obtained, and the real partitioning of the Karate network is to partition the network into two communities, namely community 1: { 012345671011121316171921 }, community 2: { 891411820222324252627282930313233 }, the present invention subdivides the network into four communities, community 1: { 01237111213171921 }, community 2: { 4561016 }, community 3: { 89141518202226293032 }, community 4: {23242527283133}.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (4)

1. A communication community detection method combining genetic and discrete differential cuckoo algorithm is characterized by comprising the following steps:
step 1, obtaining communication network information, wherein the communication network information comprises each telephone and call records among the telephones;
step 2, converting the communication network into an adjacent matrix form of nodes, wherein each different telephone is regarded as a node, and a call record between two telephones is regarded as an edge; the method comprises the steps that a track-based coding mode is adopted to carry out bird nest coding on a communication network, a bird nest is regarded as a solution, and a modularity Q value is taken as a target function;
step 3, establishing an elite library R: sequencing the modularity Q values obtained by calculation, and storing the first s modularity Q values in an elitism library R;
step 4, updating the position of the bird nest: searching the bird nest by adopting a method of global random walk and combining a high-quality gene genetic strategy in an elite library R, and correspondingly updating the bird nest with the optimal target function;
bird nest from t1Time t2The change in position at a time is expressed as:
Figure FDA0002387442030000011
wherein n represents the number of nodes in the network and the nodes in the bird nest
Figure FDA0002387442030000012
With probability p1Global random walk derived, probability
Figure FDA0002387442030000013
djDegree of node j;
then adopting a strategy of high-quality genetic inheritance to convert x in the bird nestijRegarded as a gene, x in the nestijThe updating method is as follows:
Figure FDA0002387442030000014
rmj＝R(round*(rand×s))
wherein x isijRepresents the j-th node, k, in the bird's nest i1Is a neighbor node in the global random walk process, rmjFor selecting the value corresponding to the jth node of the bird nest in the gene library, gbestjRepresenting the value of the jth node corresponding to the optimal bird nest, round representing the nearest rounding, pcRepresenting the probability of a gene, p, of an elite bird nest in the inherited gene librarygRepresenting the probability of inheriting the genes of the optimal bird nest, R (round × s)) representing the probability of randomly extracting the bird nest in the elite library, round representing the nearest rounding, and s representing the scale of the elite library;
replacement updating process: calculating an objective function of a new bird nest position, comparing the maximum objective function with the objective function of the original corresponding position, if Q (x'i)＞Q(xi) Then x isi←x′iMixing Q (x)i) Finding the maximum value, comparing with global optimal gbest, and if best > gbest, then mixing gbest ← best, where Q (x'i) Representing the modularity size, Q (x), of the bird's nest i' after the current update positioni) Representing the modularity, x, of the original nest iiI, x 'representing original bird nest'iRepresenting a bird nest i' after the updating position, best representing a bird nest corresponding to the maximum modularity in the original elite library, and gbest representing a bird nest corresponding to the maximum modularity after the updating position;
step 5, adopting a method combining Levy flight and discrete difference strategies to take the updated elite library R nest as an initial solution set, updating the position of the nest again, calculating a target function Q, and finding out a high-quality solution to replace the solution into the updated elite library R after comparison;
step 51: step length of bird nest
Figure FDA0002387442030000021
The method for calculating the step length in the flight of Levy is
Figure FDA0002387442030000022
Wherein x isiAs a solution to the current bird's nest, xgbestIs the solution of the optimal bird nest,
Figure FDA0002387442030000023
the step size is represented as a function of time,
Figure FDA0002387442030000024
is a constant;
step 52: calculating the contribution degree of a neighbor node corresponding to each node;
step 53: and (3) updating the position of the bird nest:
Figure FDA0002387442030000025
wherein,
Figure FDA0002387442030000026
representing the selection of the jth node after t +1 iterations of the bird nest i,
Figure FDA0002387442030000027
representing the step size in bird nest i
Figure FDA0002387442030000028
Value, k, corresponding to the value at the jth node position2A neighbor node representing node j;
step 6, solving the objective function value again for the updated elite library R, comparing the objective function value with the optimal bird nest, and carrying out related replacement work;
and 7, terminating judgment: judging whether a convergence condition Q ' -Q ' is less than or equal to, wherein Q ' is a current target function, Q is a last target function and represents target convergence precision, if the convergence condition is met, turning to the step 8, and if the convergence condition is not met, seeing a termination condition: t is greater than iter, iter represents the iteration times, t represents the operation times of the algorithm, if not, the step 3 is switched to, otherwise, the step 8 is switched to;
and 8, outputting an optimal solution: and exiting the iterative process, decoding the optimal bird nest gbest and obtaining community division.
2. The method for detecting communication communities based on the genetic and discrete differential cuckoo algorithm as claimed in claim 1, wherein: the method for calculating the contribution degree of the neighbor node a of the node j in the step 52 comprises the following steps:
step 52-1: firstly, selecting all nodes in the j dimension;
step 52-2: calculating the objective function value corresponding to the node a, and calculating the average value;
step 52-3: and judging, if the neighbor node is in the jth dimension, calculating the contribution value by adopting the method in the step 52-2, and if the neighbor node is not in the jth dimension, selecting the obtained minimum contribution value to be assigned to the node.
3. The method for detecting communication communities based on the genetic and discrete differential cuckoo algorithm as claimed in claim 2, wherein: neighbor node k of node j in step 532The selection probability of (2) is as follows:
step 53-1: calculating contribution values of all neighbor nodes;
step 53-2: summing all the contribution values to obtain a sum value sGeneral assembly；
Step 53-3: k is a radical of2Is selected probability of
Figure FDA0002387442030000029
And n is the number of the neighbor nodes.
4. The method for detecting communication communities based on the genetic and discrete differential cuckoo algorithm as claimed in claim 1, wherein: the gene bank R is stored externally.
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