Social network key node identification method based on double-population interaction

Abstract

The invention discloses a social network key node identification method based on double-population interaction, which comprises the following steps of: 1, constructing double populations, respectively generating a main population and an auxiliary population based on an original network space and a reduced search space, and completing initialization; 2, carrying out double-population evolution, respectively carrying out genetic manipulation on the main population and the auxiliary population obtained in the step 1, generating filial generations through crossover variation, and forming a new population according to a corresponding population updating method; 3, double-population interaction: when the double populations are evolved to a certain number of iterations to meet interaction conditions, the influence strategy and the expansion strategy are alternately executed, and information interaction between the main population and the auxiliary population is realized; and 4, individual selection: sorting the individuals in the main population and the auxiliary population based on an objective function value, and selecting an optimal individual as a key node combination for output. According to the method, the key node combination can be quickly and effectively identified in the large-scale social network, and a high-quality selection scheme is provided for decision makers within reasonable time.

Description

Technical Field

[0001] The present invention relates to the field of key node identification in social networks, and in particular to a method for identifying key nodes in social networks based on dual population interactions. Background Art

[0002] As an important part of modern society, social networks play a vital role in people's daily lives and the construction of social relationships. In this context, it is particularly important to identify key node combinations in social networks. As key hubs for information dissemination, these key nodes have a great impact on the connectivity of social networks and play a decisive role in the spread or control of information. They show important practical significance in actual situations such as advertising marketing, disease control, and public opinion analysis. However, with the continuous expansion of the network scale, the search space for solving the key node problem is growing exponentially. How to find high-quality key node combinations within a reasonable time has become a major challenge. At present, the key node identification methods in social networks are mainly divided into the following two categories:

[0003] The first category: considers the exact method of solving the quality of key nodes. From the perspective of ensuring the theoretical optimal solution of the key node combination identified in the social network, the exact method usually derives mathematical formulas based on the integer linear programming model and applies it to the social network to find the exact global optimal key node combination in the entire search space. Common algorithms include dynamic programming, branch and cut algorithms, and other polynomial time algorithms. Although these exact models can find the best solution in small networks, they have considerable computational complexity on large social networks due to the existence of a large number of constraints.

[0004] The second category: approximate methods that consider the efficiency of solving key nodes. From the perspective of improving the efficiency of identifying key node combinations in social networks, approximate methods hope to strike a balance between solution quality and solution efficiency, and approximately obtain the optimal key node combination. In social networks, they mainly include greedy algorithms based on centrality indicators, heuristic algorithms based on local search, and population-based algorithms. Although these methods have improved the efficiency of identifying key node combinations, they may fall into local optimality during the search, and the effect of identified key nodes in social networks usually has a certain loss of accuracy. The identification of key node combinations on larger social networks is still subject to certain limitations, and there is still room for improvement in the efficiency and effect of solving. Summary of the invention

[0005] In view of some deficiencies in the prior art, the present invention provides a method for identifying key nodes in a social network based on dual-population interaction. The method utilizes the co-evolution of a main population generated by the original network and an auxiliary population generated by the reduced network, and exchanges information through a dual-population interaction mechanism consisting of an influence strategy and an expansion strategy. The method effectively identifies the key node combination that has the greatest impact on the connectivity of the social network, and provides decision makers with high-quality selection options within a reasonable time, thereby meeting the needs of solving practical problems.

[0006] In one aspect of the present invention, the present invention proposes a method for identifying key nodes in a social network based on dual population interaction. According to an embodiment of the present invention, the method comprises the following steps:

[0007] The social network is modeled as a graph G = (V, E), where the node set V (|V| = N) and the edge set E (|E| = M) represent the users in the social network and the connections between any two users, respectively, where N represents the number of nodes in the network and M represents the number of edges in the network;

[0008] Step 1: Dual population construction: generate the main population and auxiliary population based on the original network space and the reduced search space respectively to complete initialization;

[0009] Step 2: Dual population evolution: genetic operations are performed on the main population and auxiliary population obtained in step 1 respectively, offspring are generated through crossover mutation, and a new population is formed according to the corresponding population update method;

[0010] Step 3: Dual population interaction: When the dual populations evolve to a certain number of iterations and meet the interaction conditions, the influence strategy and the expansion strategy are executed alternately to realize the information interaction between the main population and the auxiliary population.

[0011] Step 4: Individual selection: sort the individuals in the main population and auxiliary population based on the objective function value, and select the best individual as the key node combination output.

[0012] In addition, the key node identification method based on dual population interaction according to the above embodiment of the present invention may also have the following additional technical features:

[0013] In some embodiments of the present invention, in step 1, the dual population construction specifically includes the following steps:

[0014] Step 1.1, based on the network topology information, reduce the original network G, use the betweenness centrality index to score each node in the original network and sort them in descending order, select the first r×N nodes to form the reduced network G', where N is the number of network nodes and r is the reduction factor;

[0015] Betweenness centrality index BC iIt is used to measure the importance of node i in the network. The calculation formula is:

[0016]

[0017] In the formula, N represents the number of nodes in the network, n st represents the number of shortest paths between nodes s and t, n st (i) represents the number of shortest paths between nodes s and t passing through node i;

[0018] Step 1.2: Define the number of key nodes as K, the population size as popsize, and use binary coding to represent each individual S in the population. i ={s1,s2,…,s j ,…,s N},s j Indicates whether the jth node in the social network is selected as a key node, s j =1 means the node is selected as a key node, s j =0 means the node is a normal node;

[0019] Step 1.3: Based on the original network space G, generate the main population P by random initialization m ;

[0020] Step 1.4: Based on the reduced search space G', generate the auxiliary population P using random initialization a .

[0021] In some embodiments of the present invention, in step 2, the dual population evolution specifically includes the following steps:

[0022] Step 2.1, define the maximum number of evaluations as maxcalls, and the initial number of iterations as gen=0;

[0023] Step 2.2: Evaluate each individual S in the dual population, calculate the objective function value of the key node combination represented by the individuals in the main population and the auxiliary population in the corresponding network, and calculate the network connectivity value F(S) caused by S using the following formula:

[0024]

[0025] In the formula, G - represents the remaining network after removing the critical node set, |C i | represents the size of the i-th connected component in the residual network;

[0026] Step 2.3, perform genetic operations on the main population and the auxiliary population to produce offspring;

[0027] Step 2.4: Update the main population and auxiliary population respectively. For the main population, sort the individuals according to the objective function value, and keep the top popsize individuals as the new main population. For the auxiliary population, sort the individuals according to the mixed score of the objective function value and individual diversity, and keep the top popsize individuals as the new auxiliary population. For each individual S i , whose individual diversity D(S i ) is calculated as follows:

[0028]

[0029] In the formula, S j represents other individuals in the auxiliary population, the denominator |S i ∨S j | represents the total number of key nodes in two individuals, the numerator Represents the number of key nodes common to two individuals;

[0030] Step 2.5, assign gen+1 to gen, and repeat the above steps until the number of evaluation calls reaches the maximum number of evaluation calls maxcalls, thereby obtaining the final main population and auxiliary population.

[0031] In some embodiments of the present invention, step 2.3 is specifically as follows:

[0032] Step 2.3.1: Use the binary tournament selection method to select the main population P m Select individuals as parents to form a mating pool MP m ; Using binary tournament selection method from auxiliary population P a Select individuals as parents to form a mating pool MP a ;

[0033] Step 2.3.2: Use the main population mating pool MP m and auxiliary population mating pool MP a The individuals in the crossover operation are carried out separately. For the two selected individuals X1 and X2, the new individuals retain the same key node SC=X1∩X2 after the crossover, and then c Select nodes from the remaining critical nodes RC = (X1∪X2)\SC of the two individuals until the size of the critical node set reaches K;

[0034] Step 2.3.3: Use the individuals obtained after the crossover of the main population and the auxiliary population to perform mutation operations to obtain the corresponding sub-populations. The key nodes in the individuals after the crossover are expressed as p m The probability of mutation into any common node completes the generation of sub-population.

[0035] In some embodiments of the present invention, in step 2.4, the auxiliary population update strategy uses a mixed score Score (S) that considers both the objective function value and the individual diversity. i ) is calculated as follows:

[0036] Score(S i )=θ t ×rank(F(S i ))+(1-θ t )×rank(D(S i ))

[0037] In the formula, rank represents the ranking obtained by sorting the corresponding values, F(S i ) is individual S i The resulting network connectivity value, D(S i ) is individual S i The individual diversity value in the auxiliary population, θ t Represents the adaptive adjustment parameter, which is calculated as follows:

[0038]

[0039] Where N' t Represents the size of the reduced network used by the auxiliary population at the tth iteration.

[0040] In some embodiments of the present invention, in step 3, the interaction mode of the two populations specifically includes the following steps:

[0041] Step 3.1, judging whether the dual-population interaction condition is met according to the current population evolution iteration number gen, when the dual-population evolution iteration number is iter generations apart, that is, gen%iter==0, the dual-population interaction condition is met, and the influence strategy and the expansion strategy are executed alternately;

[0042] Step 3.2: Execute the influence strategy;

[0043] Step 3.3: Execute the expansion strategy.

[0044] In some embodiments of the present invention, in step 3.2, the influencing strategy is as follows:

[0045] When Flag == 1, the influence strategy is executed to transfer the elite individuals of the auxiliary population to the main population to quickly locate excellent candidate nodes, thereby guiding the main population to evolve quickly in a better direction;

[0046] Step 3.2.1: According to the objective function value, the auxiliary population P a Sort them and map them to the original network space;

[0047] Step 3.2.2, select the individuals in the top enum after mapping for improvement;

[0048] Step 3.2.3, for each selected individual, find the largest connected component LC of the remaining network after removing its key node combination, find the node a with the largest LC betweenness centrality, and add this node to the key node set of the current individual;

[0049] Step 3.2.4, remove all key nodes of the current individual from the network, calculate the connection index value of its key nodes to reconnect to the network, select the key node with the smallest value and delete it from the individual, complete the improvement and promotion of the selected individual, and the connection index value ConSize(v) is calculated as follows:

[0050]

[0051] Where N c (v) represents the set of connected components connected to the critical node v when it is assumed to be restored to the remaining network;

[0052] Step 3.2.5: Pass the improved individual set to the main population and update the main population P using environmental selection m , set the flag of the next use strategy to 0.

[0053] In some embodiments of the present invention, in step 3.3, the expansion strategy is as follows:

[0054] When Flag == 0, the expansion strategy is executed, using the global statistical information of the main population to help the auxiliary population expand the search space;

[0055] Step 3.3.1: According to the objective function value, the main population P m Sort and calculate the weighted frequency information Fre of each node v , and its calculation formula is as follows:

[0056]

[0057] In the formula, ind i Represents the i-th individual in the main population after sorting. If v is a key node in this individual, the value of occur is 1, otherwise it is 0;

[0058] Step 3.3.2: Calculate the importance index of node v. The calculation formula is as follows:

[0059] Importance v =rank(BC v )+rank(Fre v )

[0060] Among them, the rank value represents the ranking obtained by sorting the corresponding values;

[0061] Step 3.3.3, select the top e×N nodes from the original network according to the node importance value, and add them to the reduced network to form a new reduced network G', where e is the expansion factor;

[0062] Step 3.3.4: Map the auxiliary population to the new reduction network, retain half of the individuals with the highest objective function value, and use the node selection index to calculate the selection value SV of the key nodes in the individuals c And the selection value SV of the newly added node e Modify the other half of the individuals, and the node selection index is calculated as follows:

[0063]

[0064] In the formula, rand∈(0,1] represents a random value to ensure the diversity of selection. For the SV of key nodes c , nodes represents the set of key nodes, and the SV of the newly added node e , nodes represents the set of newly added nodes;

[0065] Step 3.3.5: Exchange the key node with the smallest selection value in the individual with the node with the largest selection value in the newly added node set, modify the original individual into a new adapted individual, and complete the auxiliary population P. a Updates.

[0066] In some embodiments of the present invention, in step 4, the selection of individuals specifically includes the following steps:

[0067] Step 4.1: The final auxiliary population P a Map it into the original network space and evaluate it;

[0068] Step 4.2: Merge the main population P m and auxiliary population P a , and sort them according to the objective function value;

[0069] Step 4.3: Select the first-ranked individual as the optimal key node combination and output it.

[0070] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0071] 1. Compared with the precise method of considering the quality of key nodes, the present invention utilizes the auxiliary population generated by the reduced network and the main population generated by the original network to co-evolve, which can quickly identify high-quality key node combinations on large-scale networks and improve the efficiency of key node identification;

[0072] 2. Compared with the approximate method that considers the efficiency of solving key nodes, the present invention proposes an effective dual-population interaction mechanism, which uses influence strategy and expansion strategy to conduct information interaction between the two populations, and achieves a good balance between the efficiency and effect of identifying the key node set of social networks. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 This is a flow chart of a method for identifying key nodes in a social network based on dual population interaction in an embodiment of the present invention;

[0074] Figure 2 A schematic diagram of a dual-population interaction mechanism proposed in an embodiment of the present invention;

[0075] Figure 3 Schematic diagram of the large component-based local search strategy used by the influence strategy proposed in the embodiment of the present invention, wherein (a) represents the current network situation, (b) represents the largest connected branch C1 in the remaining network, (c) represents adding the node v1 with the largest betweenness centrality in C1 to the key node set, and (d) represents that the key nodes of the improved individual are {v1, v3}. DETAILED DESCRIPTION

[0076] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0077] like Figure 1 As shown in FIG. 1 , a method for identifying key nodes in a social network based on dual population interaction is performed in the following steps:

[0078] The social network is modeled as a graph G = (V, E), where the node set V (|V| = N) and the edge set E (|E| = M) represent the users in the social network and the connections between any two users, respectively; where N represents the number of nodes in the network, and M represents the number of edges in the network.

[0079] Step 1: Dual population construction: generate the main population and auxiliary population based on the original network space and the reduced search space respectively to complete the initialization.

[0080] Step 1.1, based on the network topology information, the original network G is reduced, each node in the original network is scored using the betweenness centrality index and sorted in descending order, and the first r×N nodes are selected to form the reduced network G', where N is the number of network nodes and r is the reduction factor, which is set to 0.05;

[0081] Betweenness centrality index BC i It can measure the importance of node i in the network, and its calculation formula is:

[0082]

[0083] Where N represents the number of nodes in the network, n st represents the number of shortest paths between nodes s and t, n st (i) represents the number of shortest paths between nodes s and t passing through node i;

[0084] Step 1.2, define the number of key nodes as K, the population size as popsize, and use binary coding to represent the individuals S in the population and the individuals S' in the auxiliary population. Each individual S i ={s1,s2,…,s j ,…,s N},s j Indicates whether the jth node in the social network is selected as a key node, s j =1 means the node is selected as a key node, s j =0 means the node is a normal node;

[0085] Step 1.3: Based on the original network space G, generate the main population P by random initialization m ;

[0086] Step 1.4: Based on the reduced search space G', generate the auxiliary population P using random initialization a .

[0087] Step 2: Dual population evolution: genetic operations are performed on the main population and auxiliary population obtained in step 1 respectively, offspring are generated through crossover mutation, and new populations are formed according to the corresponding population update method.

[0088] Step 2.1: Define the maximum number of evaluations as maxcalls and the initial number of iterations as gen=0.

[0089] Step 2.2: Evaluate each individual S in the dual population, calculate the objective function value of the key node combination represented by the individuals in the main population and the auxiliary population in the corresponding network, and calculate the network connectivity value F(S) caused by S using the following formula:

[0090]

[0091] Among them, G - represents the remaining network after removing the critical node set, |C i| represents the size of the i-th connected component in the remaining network, C represents the set of components in the remaining network that are still connected through edges after removing the key node set, and C i represents the i-th connected component in the residual network.

[0092] Step 2.3: Perform genetic operations on the main population and auxiliary population to produce offspring.

[0093] Step 2.3.1: Use the binary tournament selection method to select the main population P m Select individuals as parents to form a mating pool MP m ; Using binary tournament selection method from auxiliary population P a Select individuals as parents to form a mating pool MP a ;

[0094] Step 2.3.2: Use the main population mating pool MP m and auxiliary population mating pool MP a The individuals in the crossover operation are carried out separately. For the two selected individuals X1 and X2, the new individuals retain the same key node SC=X1∩X2 after the crossover, and then c Select nodes from the remaining critical nodes RC = (X1∪X2)\SC of the two individuals until the size of the critical node set reaches K;

[0095] Step 2.3.3: Use the individuals obtained after the crossover of the main population and the auxiliary population to perform mutation operations to obtain the corresponding sub-populations. The key nodes in the individuals after the crossover are expressed as p m The probability of mutation into any common node completes the generation of sub-population.

[0096] Step 2.4: Update the main population and the auxiliary population respectively. For the main population, sort the individuals according to the objective function value, and keep the top popsize individuals as the new main population. For the auxiliary population, in order to reduce the precision loss caused by the reduction space, consider the objective function value while also considering the individual diversity when updating the auxiliary population, sort them according to the mixed score of the two, and keep the top popsize individuals as the new auxiliary population. For each individual S i , whose individual diversity D(S i ) is calculated as follows:

[0097]

[0098] Among them, S j represents other individuals in the auxiliary population, the denominator represents the total number of key nodes in the two individuals, and the numerator represents the number of key nodes common to the two individuals.

[0099] The auxiliary population update strategy uses a mixed score Score (S) that considers both the objective function value and individual diversity. i ) is calculated as follows:

[0100] Score(S i )=θ t ×rank(F(S i ))+(1-θ t )×rank(D(S i )) (4)

[0101] Among them, rank represents the ranking obtained by sorting the corresponding values, F(S i ) is the individual S calculated by formula (2) i The resulting network connectivity value, D(S i ) is the individual S calculated by formula (3) i The individual diversity value in the auxiliary population, θ t Represents the adaptive adjustment parameter, which is calculated as follows:

[0102]

[0103] Among them, N' t represents the size of the reduced network used by the auxiliary population at the tth iteration;

[0104] Step 2.5, assign gen+1 to gen, and repeat the above steps until the number of evaluation calls reaches the maximum number of evaluations maxcalls, thereby obtaining the final main population and auxiliary population;

[0105] Step 3: Two-population interaction. The specific process is as follows: Figure 2 As shown, elite' represents the elite individuals selected from the auxiliary population, elite' m Represents the mth elite individual, and elite' in the influence individual module represents the elite individual of the auxiliary population after being improved by local search based on large components. When the two populations evolve to a certain number of iterations to meet the interaction conditions, the influence strategy and the expansion strategy are executed alternately to realize the information interaction between the main population and the auxiliary population.

[0106] Step 3.1, judge whether the dual population interaction condition is met according to the current population evolution iteration number gen. When the dual population evolution iteration number is every iter generation, that is, gen%iter==0, the dual population interaction condition is met, and the influence strategy and the expansion strategy are executed alternately. The interval number iter is set to 5, and the flag Flag of the use strategy is set to 1;

[0107] Step 3.2: Influencing strategy

[0108] When Flag == 1, the influence strategy is executed to modify the elite individual elite' of the auxiliary population through a local search based on large components and pass it to the main population to quickly locate excellent candidate nodes, thereby guiding the main population to evolve quickly in a better direction;

[0109] Step 3.2.1: According to the objective function value, the auxiliary population P a Sort them and map them to the original network space;

[0110] Step 3.2.2, select the individuals of the top enum after mapping, and improve them based on the local search of the large component;

[0111] Step 3.2.3, for each selected individual elite' m , find the largest connected component LC of the remaining network after removing its key node combination, find the node a with the largest LC betweenness centrality, and add this node to the key node set of the current individual;

[0112] Step 3.2.4, remove all key nodes of the current individual from the network, calculate the connection index value of its key nodes to reconnect to the network, select the key node with the smallest value and delete it from the individual, complete the improvement and promotion of the selected individual, and the connection index value ConSize(v) is calculated as follows:

[0113]

[0114] Among them, N c (v) represents the set of connected components connected to the critical node v when it is assumed to be restored to the remaining network;

[0115] Step 3.2.5: Pass the improved individual set elite' to the main population and update the main population P using environmental selection m , set the flag of the next use strategy to 0;

[0116] For example Figure 3 As shown in Figure (a), Figure (a) shows the current network situation. Assuming that the key node combination selected by the current individual is {v2, v3}, the current remaining network situation, find the largest connected branch C1 in the remaining network as shown in Figure (b), the size of C1 is 6, and add the node v1 with the largest betweenness centrality in C1 to the key node set, as shown in Figure (c). For key nodes v2 and v3, restore them to the connection index values ​​in the network of 3 and 6 respectively. Therefore, delete the node v2 with a smaller connection value from the key nodes, and the key nodes of the improved individual are {v1, v3}, as shown in Figure (d).

[0117] Step 3.3: Extending the strategy

[0118] When Flag==0, the expansion strategy is executed, using the global statistical information of the main population to help the auxiliary population expand the search space and reduce the accuracy loss of the auxiliary population in the reduced space;

[0119] Step 3.3.1: According to the objective function value, the main population P m Sort and calculate the weighted frequency information Fre of each node v , and its calculation formula is as follows:

[0120]

[0121] Among them, ind i Represents the i-th individual in the main population after sorting. If v is a key node in this individual, the value of occur is 1, otherwise it is 0;

[0122] Step 3.3.2: Calculate the importance index of node v according to formula (1) and formula (7). The calculation formula is as follows:

[0123] Importance v =rank(BC v )+rank(Fre v ) (8)

[0124] Among them, the rank value represents the ranking obtained by sorting the corresponding values;

[0125] Step 3.3.3, select the top e×N nodes from the original network according to the node importance value, and add them to the reduced network to form a new reduced network G', where e is the expansion factor, which is set to 0.05;

[0126] Step 3.3.4: Map the auxiliary population to the new reduction network, retain half of the individuals with the highest objective function value, and use the node selection index to calculate the selection value SV of the key nodes in the individuals c And the selection value SV of the newly added node e To modify the other half of the individuals, the node selection index is calculated as follows:

[0127]

[0128] Among them, rand∈(0,1] represents a random value to ensure the diversity of selection. For the SV of key nodes, c , nodes represents the set of key nodes, and the SV of the newly added node e , nodes represents the set of newly added nodes;

[0129] Step 3.3.5: Exchange the key node with the smallest selection value in the individual with the node with the largest selection value in the newly added node set, modify the original individual into a new adapted individual, and complete the auxiliary population P. a Updates.

[0130] Step 4: Individual selection: sort the individuals in the main population and auxiliary population based on the objective function value, and select the best individual as the key node combination output.

[0131] Step 4.1: The final auxiliary population P a Map it into the original network space and evaluate it;

[0132] Step 4.2: Merge the main population P m and auxiliary population P a , and sort them according to the objective function value;

[0133] Step 4.3: Select the first-ranked individual as the optimal key node combination and output it.

[0134] The above contents are merely examples and explanations of the present invention. Those skilled in the art may make various modifications or additions to the specific embodiments described or replace them in a similar manner. As long as they do not deviate from the structure of the present invention or exceed the scope defined by the claims, they shall all fall within the protection scope of the present invention.

Claims

1. A method for identifying key nodes in a social network based on dual population interaction, characterized in that: The following steps are involved: The social network is modeled as a graph G = (V, E), where the node set V (|V| = N) and the edge set E (|E| = M) represent the users in the social network and the connections between any two users, respectively, where N represents the number of nodes in the network and M represents the number of edges in the network; Step 1: Dual population construction: generate the main population and auxiliary population based on the original network space and the reduced search space respectively to complete initialization; Step 2: Dual population evolution: genetic operations are performed on the main population and auxiliary population obtained in step 1 respectively, offspring are generated through crossover mutation, and a new population is formed according to the corresponding population update method; Step 3: Dual population interaction: When the dual populations evolve to a certain number of iterations and meet the interaction conditions, the influence strategy and the expansion strategy are executed alternately to realize the information interaction between the main population and the auxiliary population. Step 4: Individual selection: sort the individuals in the main population and auxiliary population based on the objective function value, and select the best individual as the key node combination output.

2. According to claim 1, a method for identifying key nodes in a social network based on dual population interaction is characterized in that: In step 1, the dual population construction specifically includes the following steps: Step 1.1, based on the network topology information, reduce the original network G, use the betweenness centrality index to score each node in the original network and sort them in descending order, select the first r×N nodes to form the reduced network G', where N is the number of network nodes and r is the reduction factor; Betweenness Centrality Index BC i It is used to measure the importance of node i in the network. The calculation formula is: In the formula, N represents the number of nodes in the network, n st represents the number of shortest paths between nodes s and t, n st (i) represents the number of shortest paths between nodes s and t passing through node i; Step 1.2: Define the number of key nodes as K, the population size as popsize, and use binary coding to represent each individual S in the population. i ={s1,s2,…,s j ,…,s N },s j Indicates whether the jth node in the social network is selected as a key node, s j =1 means the node is selected as a key node, s j =0 means the node is a normal node; Step 1.3: Based on the original network space G, generate the main population P by random initialization m ; Step 1.4: Based on the reduced search space G', generate the auxiliary population P using random initialization a .

3. The method for identifying key nodes in a social network based on dual population interaction according to claim 2, characterized in that: In step 2, the dual population evolution specifically includes the following steps: Step 2.1, define the maximum number of evaluations as maxcalls, and the initial number of iterations as gen=0; Step 2.2: Evaluate each individual S in the dual population, calculate the objective function value of the key node combination represented by the individuals in the main population and the auxiliary population in the corresponding network, and calculate the network connectivity value F(S) caused by S using the following formula: In the formula, G - represents the remaining network after removing the critical node set, |C i | represents the size of the i-th connected component in the residual network; Step 2.3, perform genetic operations on the main population and the auxiliary population to produce offspring; Step 2.4: Update the main population and auxiliary population respectively. For the main population, sort the individuals according to the objective function value, and keep the top popsize individuals as the new main population. For the auxiliary population, sort the individuals according to the mixed score of the objective function value and individual diversity, and keep the top popsize individuals as the new auxiliary population. For each individual S i , whose individual diversity D(S i ) is calculated as follows: In the formula, S j represents other individuals in the auxiliary population, the denominator |S i ∨S j | represents the total number of key nodes in two individuals, the numerator Represents the number of key nodes common to two individuals; Step 2.5, assign gen+1 to gen, and repeat the above steps until the number of evaluation calls reaches the maximum number of evaluation calls maxcalls, thereby obtaining the final main population and auxiliary population.

4. The method for identifying key nodes in a social network based on dual population interaction according to claim 3, characterized in that: The step 2.3 is as follows: Step 2.3.1: Use the binary tournament selection method to select the main population P m Select individuals as parents to form a mating pool MP m ; Using binary tournament selection method from auxiliary population P a Select individuals as parents to form a mating pool MP a ; Step 2.3.2: Use the main population mating pool MP m and auxiliary population mating pool MP a The individuals in the crossover operation are carried out separately. For the two selected individuals X1 and X2, the new individuals retain the same key node SC=X1∩X2 after the crossover, and then c Select nodes from the remaining critical nodes RC = (X1∪X2)\SC of the two individuals until the size of the critical node set reaches K; Step 2.3.3: Use the individuals obtained after the crossover of the main population and the auxiliary population to perform mutation operations to obtain the corresponding sub-populations. The key nodes in the individuals after the crossover are expressed as p m The probability of mutation into any common node completes the generation of sub-population.

5. The method for identifying key nodes in a social network based on dual population interaction according to claim 4, characterized in that: In step 2.4, the auxiliary population update strategy uses a mixed score Scpre(S i ) is calculated as follows: Score(S i )=θ t ×rank(F(S i ))+(1-θ t )×rank(D(S i )) In the formula, rank represents the ranking obtained by sorting the corresponding values, F(S i ) is individual S i The resulting network connectivity value, D(S i ) is individual S i The individual diversity value in the auxiliary population, θ t Represents the adaptive adjustment parameter, which is calculated as follows: Where N' t Represents the size of the reduced network used by the auxiliary population at the tth iteration.

6. The method for identifying key nodes in a social network based on dual population interaction according to claim 5, characterized in that: In step 3, the interaction mode of the two populations specifically includes the following steps: Step 3.1, judging whether the dual-population interaction condition is met according to the current population evolution iteration number gen, when the dual-population evolution iteration number is iter generations apart, that is, gen%iter==0, the dual-population interaction condition is met, and the influence strategy and the expansion strategy are executed alternately; Step 3.2: Execute the influence strategy; Step 3.3: Execute the expansion strategy.

7. The method for identifying key nodes in a social network based on dual population interaction according to claim 6, characterized in that: In step 3.2, the impact strategy is as follows: When Flag == 1, the influence strategy is executed to transfer the elite individuals of the auxiliary population to the main population to quickly locate excellent candidate nodes, thereby guiding the main population to evolve quickly in a better direction; Step 3.2.1: According to the objective function value, the auxiliary population P a Sort them and map them to the original network space; Step 3.2.2, select the individuals in the top enum after mapping for improvement; Step 3.2.3, for each selected individual, find the largest connected component LC of the remaining network after removing its key node combination, find the node a with the largest LC betweenness centrality, and add this node to the key node set of the current individual; Step 3.2.4, remove all key nodes of the current individual from the network, calculate the connection index value of its key nodes to reconnect to the network, select the key node with the smallest value and delete it from the individual, complete the improvement and promotion of the selected individual, and the connection index value ConSize(v) is calculated as follows: Where N c (v) represents the set of connected components connected to the critical node v when it is assumed to be restored to the remaining network; Step 3.2.5: Pass the improved individual set to the main population and update the main population P using environmental selection m , set the flag of the next use strategy to 0.

8. The method for identifying key nodes in a social network based on dual population interaction according to claim 7, characterized in that: In step 3.3, the expansion strategy is as follows: When Flag == 0, the expansion strategy is executed, using the global statistical information of the main population to help the auxiliary population expand the search space; Step 3.3.1: According to the objective function value, the main population P m Sort and calculate the weighted frequency information Fre of each node v , and its calculation formula is as follows: In the formula, ind i Represents the i-th individual in the main population after sorting. If v is a key node in this individual, the value of occur is 1, otherwise it is 0; Step 3.3.2: Calculate the importance index of node v. The calculation formula is as follows: Importance v =rank(BC v )+rank(Fre v ) Among them, the rand value represents the ranking obtained by sorting the corresponding values; Step 3.3.3, select the top e×N nodes from the original network according to the node importance value, and add them to the reduced network to form a new reduced network G', where e is the expansion factor; Step 3.3.4: Map the auxiliary population to the new reduction network, retain half of the individuals with the highest objective function value, and use the node selection index to calculate the selection value SV of the key nodes in the individuals c And the selection value SV of the newly added node e Modify the other half of the individuals, and the node selection index is calculated as follows: In the formula, rand∈(0,1] represents a random value to ensure the diversity of selection. For the SV of key nodes c , nodes represents the set of key nodes, and the SV of the newly added node e , nodes represents the set of newly added nodes; Step 3.3.5: Exchange the key node with the smallest selection value in the individual with the node with the largest selection value in the newly added node set, modify the original individual into a new adapted individual, and complete the auxiliary population P. a Updates.

9. The method for identifying key nodes in a social network based on dual population interaction according to claim 8, characterized in that: In step 4, the selection of individuals specifically includes the following steps: Step 4.1: The final auxiliary population P a Map it into the original network space and evaluate it; Step 4.2: Merge the main population P m and auxiliary population P a , and sort them according to the objective function value; Step 4.3: Select the first-ranked individual as the optimal key node combination and output it.

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