CN114218502A - Social network key member detection method based on sparse evolution algorithm - Google Patents

Abstract

The invention discloses a social network key member detection method based on a sparse evolution algorithm, which is characterized by comprising the following steps of 1, constructing a target function; step 2, calculating scores of all members in the social network and initializing a state population; step 3, taking the state in the state population as a parent according to the designed genetic operator, generating a new state and adding the new state into an offspring state population; and 4, combining the offspring state population with the previous generation state population, deleting repeated states, sequencing without domination, calculating crowding distances among members and the like, and selecting the states with the same number as the original state population in a reverse sequence to serve as a new state population until a group of social networks consisting of key members and non-key members is obtained. The method and the device can reduce the time for identifying the key members in the large-scale complex social network and improve the accuracy for identifying the key members.

Description

Social network key member detection method based on sparse evolution algorithm

Technical Field

The invention belongs to the field of social network key member detection, and particularly relates to a social network key member detection method based on a sparse evolution algorithm.

Background

A social network is a social structure formed by a plurality of nodes such as individuals or organizations, and represents various social relationships. The social network has the four characteristics of rapidness, spreading, equality, self-organization and the like. Because of these characteristics, such networks have an influence on aspects of real society. From a member classification perspective, identifying members with higher reputation and impact in a social network is very important in designing marketing strategies. Locating a product may have a tremendous impact on society if the strategy is properly targeted to the most influential and recognized member of the community in place. However, if some public opinion and other information is also spread rapidly by virtue of social networking features, uncontrollable consequences are often produced. Therefore, how to identify key members in a large-scale complex social network becomes especially important.

Currently, there are mainly accurate methods and approximate methods for detecting key members of social networks. The accurate method provides a mathematical formula capable of solving key members of the social network by using integer linear programming, and the mathematical formula is used for solving. This approach can consume a large amount of computation when the size of the social network is too large or the complexity is too high, rendering the approach ineffective. Approximation methods include greedy algorithms and evolutionary algorithms. Greedy algorithms have been proposed to find key sites in a reasonable time, the key members of the selection always being the best choice currently viewed, but this cannot be considered overall optimal. The evolutionary algorithm is a popular method at present, and has better effect than the former two methods in the aspect of solving the large-scale social network. However, in a huge social network, the number of key members is small, that is, the key members are sparse, and the current evolutionary algorithm does not consider the situation, so that the time consumed for identifying the key members is increased, and the identification accuracy is also reduced.

Disclosure of Invention

The invention aims to overcome the defects in the prior art, and provides a social network key member detection method based on a sparse evolution algorithm, so that the time for identifying key members in a large-scale complex social network can be reduced, and the accuracy of identifying key members can be improved, thereby laying a foundation for constructing the social network of key member information.

In order to achieve the purpose, the invention adopts the following technical scheme:

the invention discloses a social network key member detection method based on a sparse evolution algorithm, which is characterized by being applied to a social network G consisting of D members and | E | relationship links, and recording a state set of whether all members in the social network G are key members as S ═ S { (S) } in a state set of whether all members in the social network G are key members₁,s₂,...,s_i,...,s_N}，s_iAn ith status indicating whether all members in the social network G are key members, N indicating the total number of statuses of all members, each status consisting of a key member and a non-key member; and s_i＝{v_i1,v_i2,...,v_ij,....,v_iD}，v_ijIndicates the i-th state s_iThe next jth member v_jWhether it is a key member, if v _ij1 denotes the i-th state s_iThe next jth member v_jIs a key member if v _ij0 denotes the i-th state s_iThe next jth member v_jIs not a key member, j is more than or equal to 1 and less than or equal to D; the r-th member v_rAnd h member v_hWhether or not to link the link is marked as e_rhA relationship link refers to a member v_rAnd member v_hA direct relationship or an indirect relationship of (a); if e _rh1 denotes the r-th member v_rAnd h member v_hThere is a direct relationship or an indirect relationship between them; if e _rh0 denotes the r-th member v_rAnd h member v_hThere is no direct relationship or indirect relationship between the two, and the method for detecting the key members of the social network comprises the following steps:

step one, constructing an objective function:

step 1.1, constructing a function COST of the number of key members by using the formula (1):

COST＝|v_ij＝1| (1)

in the formula (1, | v _ij1| represents the number of key members in the social network G;

step 1.2, constructing a function PWC about the number of different pairs of members connected by relationship links on the social network G by using the formula (2):

in formula (2), V' represents a set of all members except the key member in the social network G;

step 1.3, constructing a total objective function f by using the formula (3):

f＝min(COST,PWC) (3)

calculating scores of all members in the social network and initializing a state population;

step 2.1, calculating the scores of all members in the social network:

step 2.1.1, let N states of the state population Q, define the state population as Q ═ Q₁,Q₂,...,Q_i,...Q_N}，Q_iRepresenting the ith state in the social network G, and enabling the number N of the states in the social network G to be the same as the number D of the members; forming a D multiplied by D matrix by the states of all members in the state population Q;

step 2.1.2, setting diagonal elements of the matrix of DxD as 1, and setting other elements as 0;

step 2.1.3, according to the total objective function f, carrying out non-dominant sorting on each state in the state population Q, and taking the non-dominant front edge number of the ith state as the SCORE SCORE of the ith member_i；

Step 2.2, initializing the state population:

step 2.2.1, let N states of the state population P, define the state population as P ═ P₁,p₂,...,p_i,...p_N}，p_iRepresents the ith state in social network G; setting all states in the state population P as 0 vectors;

step 2.2.2, initializing i to 1;

step 2.2.3, defining a variable z and initializing z to be 1;

step 2.2.4, randomly selecting two members v from the social network G for the z-th time_rAnd member v_hAnd judging the member v_rSCORE of (SCORE)_rWhether or not less than member v_hSCORE of (SCORE)_hIf yes, the member v in the ith state is selected_rSetting as a key member; otherwise, the member v in the ith state_hSetting as a key member;

step 2.2.5, assigning z +1 to z, repeating step 2.2.4 for several times to obtain the final ith state p_iAnd is used as the ith initial state of the state population P;

step 2.2.6, assigning i +1 to i, judging whether i is greater than N, and if so, indicating that N initial states of the state population P are obtained; otherwise, returning to the step 2.2.3 for sequential execution;

step three, taking the state in the state population P as a parent according to the designed genetic operator, generating a new state and adding the new state into an offspring state population;

step 3.1, initializing parameters:

defining and initializing the current evaluation time t as 1 and the maximum evaluation time t_max(ii) a Let the t generation offspring state population R^tIs an empty set;

taking N initial states of the state population P as the t generation state population P^t；

Step 3.2, carrying out comparison on the t generation state population P according to the total objective function f^tPerforming non-dominant sorting, and calculating the congestion distance of each state of the sorted non-dominant front edges, so as to perform descending sorting on each state according to the congestion distance, and finally obtaining a plurality of non-dominant front edges after descending sorting;

3.3, using the binary brocade according to the descending non-dominant front edges and the crowding distance thereofBidding competition method from t generation state population P^t2N states are selected as the t generation parent generation state population;

and 3.4, generating a filial generation state population according to the new genetic operator:

step 3.4.0, defining a variable n, and initializing n to be 1;

step 3.4.1, randomly selecting a pair of parent states p from the nth time in the tth generation parent state population_αAnd p_βAnd generates an nth sub-generation state

State the nth sub generation

Initial value and parent state p of_αSet to be the same, and then set the parent state p_αAnd p_βDeleting from the parent generation state population of the t generation; alpha, beta ∈ [1,2N ]]；

Step 3.4.2, generating the t random number rand_tIf rand_tIf < 0.5, then according to

Of two key members v 'are randomly selected'_rAnd key member v'_hAnd judging the key member v'_rSCORE of SCORE'_rWhether is greater than key member v'_hSCORE of SCORE'_hIf yes, the child state is set

V 'of'_rSetting as a non-critical member; otherwise, the child state is set

V 'of'_hSetting as a non-critical member;

if rand_tNot less than 0.5, according to

As a result of the state of (c), two key members v ″' are randomly selected_rAnd key member v ″)_hAnd judging the key member v ″)_rSCORE of (SCORE)_rWhether or not it is less than key member v_hSCORE of (SCORE)_hIf yes, the offspring state is set

Member v "of (1)_rSetting as a key member; otherwise, the child state is set

Member v "of (1)_hSetting as a key member;

step 3.4.3 of generating a t-th random number rand'_tIf rand'_t< 0.5, then in the offspring state

Of two Key members v'_rAnd Key Member v'_h(ii) a And judging key member v'_rSCORE of SCORE'_rWhether greater than key member v'_hSCORE of SCORE'_hIf so, it will be in the child state

V 'of'_rSetting as a non-critical member; otherwise, it will be in the child state

V 'of'_hSetting as a non-critical member;

if rand'_tGreater than or equal to 0.5, in the filial generation state

Randomly selecting two non-key members

And non-critical members

And determining non-key members

Is scored by

Whether less than a non-critical member

Is scored by

If so, it will be in the child state

Members of (1)

Setting as a key member; otherwise, it will be in the child state

Members of (1)

Setting as a key member; thereby generating new offspring states

Step 3.4.4 New offspring State to be generated

Adding into the filial generation state population R^tPerforming the following steps;

step 3.5, after n +1 is assigned to n, judging n>Whether N is true or not, if so, the method indicates that the t generation filial generation state population R of N sub generation states is obtained^t(ii) a Otherwise, return to stepStep 3.4.1 is carried out sequentially;

step four, circularly iterating to obtain a group of social networks G' consisting of key members and non-key members;

step 4.1, the filial generation state population R of the t generation^tAnd the t generation status population P^tMerging to obtain the state population RP with the size of 2N^tAnd carrying out deduplication processing on the merged 2N states to obtain a state population RP after deduplication of the t generation^′t；

Step 4.2, removing the state population RP 'of the t generation'^tPerforming non-dominant sorting, and calculating the congestion distance of each state of the sorted non-dominant front edge, so as to sort each state in a descending order according to the congestion distance, and finally obtaining all the sorted states;

step 4.3, selecting the state of N before ranking in all the sorted states as the t +1 generation state population P^t+1；

Step 4.4, after t +1 is assigned to t, judging that t is more than t_maxIf yes, the t-th step is executed_maxGeneration status population

The key members and non-key members represented by the respective states in the social network G' are formed, otherwise, the step 3.2 is returned to and executed.

Compared with the prior art, the invention has the beneficial effects that:

1. according to the method, the problem of detecting the key members in the social network is converted into a multi-objective optimization problem, whether the members in the social network are key or not is digitalized by a binary representation method, whether the members are key or not can be represented more conveniently, the initialized state can well keep the sparsity of the key members through a state initialization strategy, and the time for identifying the key members in the social network is reduced to a certain extent.

2. The member score is calculated according to the relationship link of the non-key node after the key node is removed, so that the contribution degree of each member in the social network can be effectively measured. In addition, the binary tournament method is used, so that the conversion of the members between the key state and the non-key state is more random and fair, and the accuracy of identifying the key members in the social network is improved.

3. According to the invention, whether the member is a key member or not is determined by calculating the score of the member, and the member with high score is more likely to become the key member, so that the average probability that half of the members are key members and half of the members are not key members is overcome, the sparsity of the key members in the optimization process is controlled, and the probability of accurately identifying the key members in a large-scale complex social network is improved.

Drawings

FIG. 1 is a flow chart of the algorithm of the present invention;

FIG. 2a is a simplified social network structure diagram illustrating an example of the present invention;

FIG. 2b is a diagram illustrating an exemplary process of initializing a state population and generating state children from a state parent according to the present invention.

Detailed Description

In the embodiment, the social network key member detection method based on the sparse evolutionary algorithm is characterized in that a state initialization strategy is used for initializing a state, the score of a member is calculated through the number of key nodes and the relation link calculation of non-key nodes after the key nodes are removed, and whether the member is a key member is judged through unequal probability on the basis of the score, so that the sparsity of the key member can be well maintained, the time for identifying the key member is accelerated to a certain extent, and the accuracy for identifying the key member is improved. In particular, the present invention relates to a method for producing,

the method for detecting key members of the social network is applied to the social network G consisting of D members and | E | relationship links, and the state set of whether all the members in the social network G are key members is recorded as S ═ S₁,s₂,...,s_i,...,s_N}，s_iStatus of i representing whether all members in social network G are key members, N representing the total number of statuses of all members, perSeed states consist of critical members and non-critical members; and s_i＝{v_i1,v_i2,...,v_ij,....,v_iD}，v_ijIndicates the i-th state s_iThe next jth member v_jWhether it is a key member, if v_ij1 denotes the i-th state s_iThe next jth member v_jIs a key member if v_ij0 denotes the i-th state s_iThe next jth member v_jIs not a key member, j is more than or equal to 1 and less than or equal to D; the r-th member v_rAnd h member v_hWhether or not to link the link is marked as e_rhA relationship link refers to a member v_rAnd member v_hA direct relationship or an indirect relationship of (a); if e_rh1 denotes the r-th member v_rAnd h member v_hThere is a direct relationship or an indirect relationship between them; if e_rh0 denotes the r-th member v_rAnd h member v_hThere is no direct or indirect relationship between them; as shown in fig. 2a, a network structure diagram containing 8 members and relationship links therebetween is shown, and each edge represents that there is a direct or indirect relationship between the members.

In this embodiment, referring to fig. 1, the method for detecting key members in a social network is performed according to the following steps:

step one, constructing an objective function:

step 1.1, constructing a function COST of the number of key members by using the formula (1):

COST＝|v_ij＝1| (1)

in the formula (1, | v _ij1| represents the number of key members in the social network;

step 1.2, constructing a function PWC about the number of different pairs of members connected by relationship links on the social network G by using the formula (2):

in formula (2), V' represents a set of all members except the key member in the social network G;

step 1.3, constructing a total objective function f by using the formula (3):

f＝min(COST,PWC) (3)

calculating scores of all members in the social network and initializing a state population;

step 2.1, calculating the scores of all members in the social network:

step 2.1.1, let N states exist in the state population P, and define the state population as Q ═ Q₁,Q₂,...,Q_i,...Q_N}，Q_iRepresenting the ith state in the social network G, and enabling the number N of the states in the social network G to be the same as the number D of the members; forming a D multiplied by D matrix by the states of all members in the state population Q;

step 2.1.2, setting diagonal elements of the matrix of DxD as 1, and setting other elements as 0; for example, in fig. 2a, 8 members in the social network form an 8 × 8 matrix, and as shown in table 1, the status population Q with the initialization size of 8 and the number of members of 8, the diagonal element is 1, and the other elements are 0, which means that there is only one key member in each status, and the key members are determined by the status order. Therefore, the contribution degree of the member in the social network can be accurately measured.

TABLE 1 binary State population

	Member 1	Member 2	Member 3	Member 4	Member 5	Member 6	Member 7	Member 8
									State 1	1	0	0	0	0	0	0	0
State 2	0	1	0	0	0	0	0	0
									State 3	0	0	1	0	0	0	0	0
State 4	0	0	0	1	0	0	0	0
									State 5	0	0	0	0	1	0	0	0
State 6	0	0	0	0	0	1	0	0
									State 7	0	0	0	0	0	0	1	0
State 8	0	0	0	0	0	0	0	1

Step 2.1.3, according to the total objective function f, carrying out non-dominant sorting on each state in the state population Q, and taking the non-dominant front edge number of the ith state as the SCORE SCORE of the ith member_i(ii) a The smaller the number of key members and the number of relationship link connected pairs after the key member is removed indicates the greater the probability that the key member will eventually be identified as a key member at that state. As shown in fig. 2a, the COST of the first state in the state population Q is 1,

the second state COST is 1,

COST of all members {1,1,1,1,1,1, 1},

the non-dominated sorting leads to smaller ranks and ranks of the same value on the same front face, resulting in states 2 < state 5 < state 7 < state 3 < state 1-state 4-state 6-state 8. The results of the non-dominated sorting after the objective function values were calculated are shown in table 2. The pareto front for state 1 is 5, with only member 1 in state 1, then the score for member 1 is 5. By analogy, the scores of all the members can be obtained. The scores for all members are shown in table 3.

TABLE 2 results after non-dominated sorting of population states

	State 1	State 2	State 3	State 4	State 5	State 6	State 7	State 8
									Pareto frontier	5	1	4	5	2	5	3	5

Score of the members of Table 3

	Member 1	Member 2	Member 3	Member 4	Member 5	Member 6	Member 7	Member 8
									Membership score	5	1	4	5	2	5	3	5

Step 2.2, initializing the state population:

step 2.2.1, let N states of the state population P, define the state population as P ═ P₁,p₂,...,p_i,...p_N}，p_iRepresents the ith state in social network G; setting all states in the state population P as 0 vectors; table 4 shows the status population P with a size of 10. The 0 vector indicates that there are no key members in the current state.

TABLE 4 State population size 10

	Member 1	Member 2	Member 3	Member 4	Member 5	Member 6	Member 7	Member 8
									State 1	0	0	0	0	0	0	0	0
State 2	0	0	0	0	0	0	0	0
									State 3	0	0	0	0	0	0	0	0
State 4	0	0	0	0	0	0	0	0
									State 5	0	0	0	0	0	0	0	0
State 6	0	0	0	0	0	0	0	0
									State 7	0	0	0	0	0	0	0	0
State 8	0	0	0	0	0	0	0	0
									State 9	0	0	0	0	0	0	0	0
State 10	0	0	0	0	0	0	0	0

Step 2.2.2, initializing i to 1;

step 2.2.3, defining a variable z and initializing z to be 1;

step 2.2.4, randomly selecting two members v from the social network G for the z-th time_rAnd member v_hAnd judging the member v_rSCORE of (SCORE)_rWhether or not less than member v_hSCORE of (SCORE)_hIf yes, the member v in the ith state is selected_rSetting as a key member; otherwise, the member v in the ith state is set_hSetting as a key member; as in fig. 2b, assuming i is 1 and z is 1, two members v are randomly selected₁And member v₅According to Table 3, Member v₁Is not less than member v₅Is given a score of 1, then member v in the 1 st state₅Can be set as a key member, i.e. v₁₅＝1。

Step 2.2.5, assigning z +1 to z, repeating step 2.2.4 for several times to obtain the final ith state p_iAnd is used as the ith initial state of the state population P; assuming that i is 1, the 1 st initial state in the state population P is shown in table 5.

TABLE 5 initial state 1 in State population P

	Member 1	Member 2	Member 3	Member 4	Member 5	Member 6	Member 7	Member 8
									State 1	0	1	0	0	1	1	0	0

Step 2.2.6, assigning i +1 to i, judging whether i is greater than N, and if so, indicating that N initial states of the state population P are obtained; otherwise, returning to the step 2.2.3 for sequential execution; table 6 shows the N initial states in the state population P.

Table 6 initial status of status population.

	Member 1	Member 2	Member 3	Member 4	Member 5	Member 6	Member 7	Member 8
									State 1	0	1	0	0	1	1	0	0
State 2	1	1	1	0	1	0	1	0
									State 3	0	1	0	0	1	0	0	0
State 4	0	0	0	1	1	1	0	0
									State 5	0	1	1	0	0	0	1	0
State 6	0	0	0	1	0	1	0	0
									State 7	0	1	0	1	1	1	1	0
State 8	0	1	0	1	0	1	0	0
									State 9	1	0	1	0	0	0	1	0
State 10	0	1	0	1	0	1	0	1

Step three, taking the state in the state population P as a parent according to the designed genetic operator, generating a new state and adding the new state into an offspring state population;

step 3.1, initializing parameters:

defining and initializing the current evaluation time t as 1 and the maximum evaluation time t_max(ii) a Let the t generation offspring state population R^tIs an empty set;

taking N initial states of the state population P as the t generation state population P^t；

Step 3.2, carrying out comparison on the t generation state population P according to the total objective function f^tPerforming non-dominant sorting, and calculating the congestion distance of each state of the sorted non-dominant front edges, so as to perform descending sorting on each state according to the congestion distance, and finally obtaining a plurality of non-dominant front edges after descending sorting;

step 3.3, according to the descending non-dominant front edges and the crowding distance thereof, using a binary tournament method to carry out the state population P from the t generation^t2N states are selected as the t generation parent generation state population;

and 3.4, generating a filial generation state population according to the new genetic operator:

step 3.4.0, defining a variable n, and initializing n to be 1;

step 3.4.1, randomly selecting a pair of parent states p from the nth time in the tth generation parent state population_αAnd p_βAnd generates the nth sub-generationStatus of state

State the nth sub generation

Initial value and parent state p of_αSet to be the same, and then set the parent state p_αAnd p_βDeleting from the parent generation state population of the t generation; alpha, beta ∈ [1,2N ]]；

Step 3.4.2, generating the t random number rand_tIf rand_tIf < 0.5, then according to

Of two key members v 'are randomly selected'_rAnd key member v'_hAnd judging the key member v'_rSCORE of SCORE'_rWhether is greater than key member v'_hSCORE of SCORE'_hIf yes, the child state is set

V 'of'_rSetting as a non-critical member; otherwise, the child state is set

V 'of'_hSetting as a non-critical member; as shown in FIG. 2b, p_α＝{0，1，0，0，1，1，0，0}，p_βN-th sub-generation state {1, 0, 1, 0, 0, 0, 1, 0}

From which two key members v are randomly selected₂And v₅From Table 3, key member v is known₂Has a score of 1, key member v₅Has a score of 2, key member v₂Score of (a) to a key member v₅Small, therefore, child state

Member v of (1)₅Is set as a non-critical member and,

if rand_tNot less than 0.5, according to

As a result of the state of (c), two key members v ″' are randomly selected_rAnd key member v ″)_hAnd judging the key member v ″)_rSCORE of (SCORE)_rWhether or not it is less than key member v_hSCORE of (SCORE)_hIf yes, the offspring state is set

Member v "of (1)_rSetting as a key member; otherwise, the child state is set

Member v "of (1)_hSetting as a key member;

step 3.4.3 of generating a t-th random number rand'_tIf rand'_t< 0.5, then in the offspring state

Of two Key members v'_rAnd Key Member v'_h(ii) a And judging key member v'_rSCORE of SCORE'_rWhether greater than key member v'_hSCORE of SCORE'_hIf so, it will be in the child state

V 'of'_rSetting as a non-critical member; otherwise, it will be in the child state

V 'of'_hSetting as a non-critical member;

if rand'_tGreater than or equal to 0.5, in the filial generation state

Randomly selecting two non-key members

And non-critical members

And determining non-key members

Is scored by

Whether less than a non-critical member

Is scored by

If so, it will be in the child state

Members of (1)

Setting as a key member; otherwise, it will be in the child state

Members of (1)

Setting as a key member; thereby generating new offspring states

As shown in figure 2b of the drawings,

random selection of non-critical members v₃And v₇Non-critical Member v₃Is 4, non-critical member v₇Is 3, non-critical member v₃Is scored against non-critical member v₇Is high, and thus, the offspring status

Member v of (1)₇Is set as a key member and is set as a key member,

step 3.4.4 New offspring State to be generated

Adding into the filial generation state population R^tPerforming the following steps;

step 3.5, after n +1 is assigned to n, judging n>Whether N is true or not, if so, the method indicates that the t generation filial generation state population R of N sub generation states is obtained^t(ii) a Otherwise, returning to the step 3.4.1 for sequential execution;

step four, carrying out filial generation state population R of the t generation^tAnd t generation state population P^tCombining, deleting repeated states, sequencing without domination, calculating crowding distance and the like, and selecting states with the same number as the original state population in a reverse sequence to serve as a new state population until a group of social networks consisting of key members and non-key members is obtained;

step 4.1, the filial generation state population R of the t generation^tAnd the t generation status population P^tMerging to obtain the state population RP with the size of 2N^tAnd carrying out deduplication processing on the merged 2N states to remove the states of completely same key members in the 2N state populations to obtain the state population RP 'subjected to deduplication in the t generation'^t；

Step 4.2, removing the state population RP 'of the t generation'^tPerforming non-dominant sorting, and calculating congestion distance of each state of the sorted non-dominant front edge so as to followThe congestion distance carries out descending sorting on each state, and all the sorted states are finally obtained;

step 4.3, selecting the state of N before ranking in all the sorted states as the t +1 generation state population P^t+1；

Step 4.4, after t +1 is assigned to t, judging that t is more than t_maxIf yes, the t-th step is executed_maxGeneration status population

And (3) the social network G' consisting of the key members and the non-key members represented by the states, and otherwise, returning to the step 3.2 for execution.

Claims (1)

1. A social network key member detection method based on a sparse evolution algorithm is characterized by being applied to a social network G formed by D members and | E | relationship links, and recording a state set of whether all members in the social network G are key members as S ═ S₁,s₂,...,s_i,...,s_N}，s_iAn ith status indicating whether all members in the social network G are key members, N indicating the total number of statuses of all members, each status consisting of a key member and a non-key member; and s_i＝{v_i1,v_i2,...,v_ij,....,v_iD}，v_ijIndicates the i-th state s_iThe next jth member v_jWhether it is a key member, if v_ij1 denotes the i-th state s_iThe next jth member v_jIs a key member if v_ij0 denotes the i-th state s_iThe next jth member v_jIs not a key member, j is more than or equal to 1 and less than or equal to D; the r-th member v_rAnd h member v_hWhether or not to link the link is marked as e_rhA relationship link refers to a member v_rAnd member v_hA direct relationship or an indirect relationship of (a); if e_rh1 denotes the r-th member v_rAnd h member v_hThere is a direct relationship or an indirect relationship between them; if e_rh0 denotes the r-th member v_rAnd h member v_hThere is no direct relationship or indirect relationship between the two, and the method for detecting the key members of the social network comprises the following steps:

step one, constructing an objective function:

step 1.1, constructing a function COST of the number of key members by using the formula (1):

COST＝|v_ij＝1| (1)

in the formula (1, | v_ij1| represents the number of key members in the social network G;

step 1.2, constructing a function PWC about the number of different pairs of members connected by relationship links on the social network G by using the formula (2):

in formula (2), V' represents a set of all members except the key member in the social network G;

step 1.3, constructing a total objective function f by using the formula (3):

f＝min(COST,PWC) (3)

calculating scores of all members in the social network and initializing a state population;

step 2.1, calculating the scores of all members in the social network:

step 2.1.1, let N states of the state population Q, define the state population as Q ═ Q₁,Q₂,...,Q_i,...Q_N}，Q_iRepresenting the ith state in the social network G, and enabling the number N of the states in the social network G to be the same as the number D of the members; forming a D multiplied by D matrix by the states of all members in the state population Q;

step 2.1.2, setting diagonal elements of the matrix of DxD as 1, and setting other elements as 0;

step 2.1.3, according to the total objective function f, carrying out non-dominant sorting on each state in the state population Q, and taking the non-dominant front edge number of the ith state as the SCORE SCORE of the ith member_i；

Step 2.2, initializing the state population:

step 2.2.1, let N states of the state population P, define the state population as P ═ P₁,p₂,...,p_i,...p_N}，p_iRepresents the ith state in social network G; setting all states in the state population P as 0 vectors;

step 2.2.2, initializing i to 1;

step 2.2.3, defining a variable z and initializing z to be 1;

step 2.2.4, randomly selecting two members v from the social network G for the z-th time_rAnd member v_hAnd judging the member v_rSCORE of (SCORE)_rWhether or not less than member v_hSCORE of (SCORE)_hIf yes, the member v in the ith state is selected_rSetting as a key member; otherwise, the member v in the ith state_hSetting as a key member;

step 2.2.5, assigning z +1 to z, repeating step 2.2.4 for several times to obtain the final ith state p_iAnd is used as the ith initial state of the state population P;

step 2.2.6, assigning i +1 to i, judging whether i is greater than N, and if so, indicating that N initial states of the state population P are obtained; otherwise, returning to the step 2.2.3 for sequential execution;

step three, taking the state in the state population P as a parent according to the designed genetic operator, generating a new state and adding the new state into an offspring state population;

step 3.1, initializing parameters:

defining and initializing the current evaluation time t as 1 and the maximum evaluation time t_max(ii) a Let the t generation offspring state population R^tIs an empty set;

taking N initial states of the state population P as the t generation state population P^t；

Step 3.2, carrying out comparison on the t generation state population P according to the total objective function f^tPerforming non-dominant sorting, and calculating the congestion distance of each state of the sorted non-dominant front edges, so as to perform descending sorting on each state according to the congestion distance, and finally obtaining a plurality of non-dominant front edges after descending sorting;

step 3.3, according to the descending non-dominant front edges and the crowding distance thereof, using a binary tournament method to carry out the state population P from the t generation^t2N states are selected as the t generation parent generation state population;

and 3.4, generating a filial generation state population according to the new genetic operator:

step 3.4.0, defining a variable n, and initializing n to be 1;

step 3.4.1, randomly selecting a pair of parent states p from the nth time in the tth generation parent state population_αAnd p_βAnd generates an nth sub-generation state

State the nth sub generation

Initial value and parent state p of_αSet to be the same, and then set the parent state p_αAnd p_βDeleting from the parent generation state population of the t generation; alpha, beta ∈ [1,2N ]]；

Step 3.4.2, generating the t random number rand_tIf rand_tIf < 0.5, then according to

Of two key members v 'are randomly selected'_rAnd key member v'_hAnd judging the key member v'_rSCORE of SCORE'_rWhether is greater than key member v'_hSCORE of SCORE'_hIf yes, the child state is set

V 'of'_rSetting as a non-critical member; otherwise, the child state is set

V 'of'_hSetting as a non-critical member;

if rand_tNot less than 0.5, according to

As a result of the state of (c), two key members v ″' are randomly selected_rAnd key member v ″)_hAnd judging the key member v ″)_rSCORE of (SCORE)_rWhether or not it is less than key member v_hSCORE of (SCORE)_hIf yes, the offspring state is set

Member v "of (1)_rSetting as a key member; otherwise, the child state is set

Member v "of (1)_hSetting as a key member;

step 3.4.3 of generating a t-th random number rand'_tIf rand'_t< 0.5, then in the offspring state

Of two Key members v'_rAnd Key Member v'_h(ii) a And judging key member v'_rSCORE of SCORE'_rWhether greater than key member v'_hSCORE of SCORE'_hIf so, it will be in the child state

V 'of'_rSetting as a non-critical member; otherwise, it will be in the child state

V 'of'_hSetting as a non-critical member;

if rand'_tGreater than or equal to 0.5, in the filial generation state

Randomly selecting two non-key members

And non-critical members

And determining non-key members

Is scored by

Whether less than a non-critical member

Is scored by

If so, it will be in the child state

Members of (1)

Setting as a key member; otherwise, it will be in the child state

Members of (1)

Setting as a key member; thereby generating new offspring states

Step 3.4.4 New offspring State to be generated

Adding into the filial generation state population R^tPerforming the following steps;

step 3.5, after n +1 is assigned to n, judging n>Whether N is true or not, if so, the method indicates that the t generation filial generation state population R of N sub generation states is obtained^t(ii) a Otherwise, returning to the step 3.4.1 for sequential execution;

step four, circularly iterating to obtain a group of social networks G' consisting of key members and non-key members;

step 4.1, the filial generation state population R of the t generation^tAnd the t generation status population P^tMerging to obtain the state population RP with the size of 2N^tAnd performing deduplication processing on the merged 2N states to obtain a state population RP 'after deduplication of the t generation'^t；

Step 4.2, removing the state population RP 'of the t generation'^tPerforming non-dominant sorting, and calculating the congestion distance of each state of the sorted non-dominant front edge, so as to sort each state in a descending order according to the congestion distance, and finally obtaining all the sorted states;

step 4.3, selecting the state of N before ranking in all the sorted states as the t +1 generation state population P^t+1；

Step 4.4, after t +1 is assigned to t, judging that t is more than t_maxIf yes, the t-th step is executed_maxGeneration status population

The key members and non-key members represented by the respective states in the social network G' are formed, otherwise, the step 3.2 is returned to and executed.

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