A social network key node identification method based on double population interaction

Abstract

The application discloses a social network key node identification method based on double population interaction, which comprises the following steps: 1, double population construction, based on the original network space and the reduced search space, the main population and the auxiliary population are generated respectively to complete initialization; 2, double population evolution, the main population and the auxiliary population obtained in step 1 are respectively subjected to genetic operation, offspring is generated through crossover and mutation, and a new population is formed according to the corresponding population updating method; 3, double population interaction, when the double population evolution reaches a certain iteration number and meets the interaction condition, the influence strategy and the expansion strategy are alternately executed to realize the information interaction of the main population and the auxiliary population; 4, individual selection, the individuals in the main population and the auxiliary population are sorted based on the target function value, and the optimal individual is selected as the key node combination output. The application can quickly and effectively identify the key node combination in a large-scale social network, and provide a high-quality selection scheme for decision makers within a reasonable time.

Description

Technical Field

[0001] This invention relates to the field of key node identification in social networks, specifically a method for key node identification in social networks based on dual-population interaction. Background Technology

[0002] Social networks, as a crucial component of modern society, play a vital role in people's daily lives and the construction of social relationships. In this context, identifying key node combinations within social networks is particularly important. These key nodes, as crucial hubs for information dissemination, significantly impact the connectivity of social networks and play a decisive role in the spread or control of information, demonstrating significant practical importance in areas such as advertising, disease control, and public opinion analysis. However, with the continuous expansion of network scale, the search space for solving the key node problem grows exponentially, making it a major challenge to find high-quality key node combinations within a reasonable timeframe. Currently, key node identification methods in social networks mainly fall into two categories:

[0003] The first category considers precise methods for determining the quality of key nodes. From the perspective of ensuring the theoretically optimal solution for the combination of key nodes identified in a social network, precise methods typically derive mathematical formulas based on integer linear programming models and apply them to the social network to find the precise globally optimal combination of key nodes across the entire search space. Common algorithms include dynamic programming, branch and cut algorithms, and other polynomial-time algorithms. While these precise models can find optimal solutions in small networks, they have considerable computational complexity on large social networks due to numerous constraints.

[0004] The second category considers approximate methods for improving the efficiency of identifying key node combinations in social networks. From the perspective of improving the efficiency of identifying key node combinations in social networks, approximate methods aim to achieve a balance between solution quality and efficiency, approximating the optimal key node combination. In social networks, these mainly include greedy algorithms based on centrality metrics, heuristic algorithms based on local search, and population-based algorithms. While these methods improve the efficiency of identifying key node combinations, they may get stuck in local optima during the search, resulting in a certain loss of accuracy in identifying key nodes in social networks. Identifying key node combinations in larger social networks remains limited, and there is still room for improvement in both efficiency and effectiveness. Summary of the Invention

[0005] This invention addresses some shortcomings in existing technologies by providing a method for identifying key nodes in social networks based on dual-population interaction. It utilizes the co-evolution of the primary population generated from the original network and the auxiliary population generated from the reduced network, and exchanges information through a dual-population interaction mechanism consisting of influence and expansion strategies. This effectively identifies key node combinations that have the greatest impact on social network connectivity, providing decision-makers with high-quality options within a reasonable timeframe, thereby meeting the needs of solving practical problems.

[0006] In one aspect of the present invention, a method for identifying key nodes in a social network based on dual-population interaction is proposed. According to an embodiment of the present invention, the method includes 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 users in the social network and the connections between any two users, respectively. N represents the number of nodes in the network, and M represents the number of edges in the network.

[0008] Step 1: Constructing a dual population: Generate a primary population and an auxiliary population based on the original network space and the reduced search space, respectively, to complete the initialization;

[0009] Step 2: Two-population evolution. Genetic operations are performed on the main population and auxiliary population obtained in Step 1. Offspring are generated through crossover and mutation, and a new population is formed according to the corresponding population update method.

[0010] Step 3: Two-population interaction. When the two 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 information interaction between the main population and the auxiliary population.

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

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

[0013] In some embodiments of the present invention, step 1, the construction of the two populations specifically includes the following steps:

[0014] Step 1.1: Reduce the original network G based on the network topology information. 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 iThe formula used to measure the importance of node i in the network is as follows:

[0016]

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

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

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

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

[0021] In some embodiments of the present invention, 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 two populations, calculate the objective function value of the key node combination represented by the individual in the corresponding network for both the main population and the auxiliary population, and calculate the network connectivity value F(S) caused by S using the following formula:

[0024]

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

[0026] Step 2.3: Perform genetic operations on the main population and auxiliary population respectively to produce offspring;

[0027] Step 2.4: Perform population updates for the main population and the auxiliary population separately. For the main population, sort individuals according to their objective function values ​​and retain the top popsize individuals as the new main population. For the auxiliary population, sort individuals according to the mixed score of objective function value and individual diversity, retain the top popsize individuals as the new auxiliary population. For each individual S... i Its individual diversity D(S) i The calculation is as follows:

[0028]

[0029] In the formula, S j The denominator |S represents the other individuals in the auxiliary population. i ∨S j | represents the total number of key nodes in two individuals, numerator The number of key nodes shared by 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), thus 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 from the main population P m Individuals are selected as parents to form a mating pool (MP). m Using a binary tournament selection method to select from the auxiliary population P a Individuals are selected as parents to form a mating pool (MP). a ;

[0033] Step 2.3.2: Utilize the main population mating pool MP respectively m and auxiliary population mating pool MP a Individuals in the dataset undergo their respective crossover operations. For two selected individuals X1 and X2, the new individual retains the same key node SC = X1∩X2 after crossover, and then proceeds with a crossover operation with probability p. c Select nodes from the remaining key nodes RC=(X1∪X2)\SC of the two individuals until the size of the key node set reaches K;

[0034] Step 2.3.3: Perform mutation operations on the individuals obtained after crossover of the main population and the auxiliary population to obtain the corresponding subpopulations. The key nodes in the individuals after crossover are denoted by p. m The probability of mutation is used to generate any ordinary node, thus completing the generation of the subpopulation.

[0035] In some embodiments of the present invention, in step 2.4, the auxiliary population update strategy uses a hybrid score (Score(S) that considers both the objective function value and individual diversity). i The calculation formula for ) is 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 ) for individual S i The resulting network connectivity value, D(S) i ) for individual S i The individual diversity value in the auxiliary population, θ t This represents the adaptive adjustment parameter, and its specific calculation is as follows:

[0038]

[0039] In the formula, N' t This represents the size of the reduced network used by the auxiliary population in the t-th iteration.

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

[0041] Step 3.1: Determine whether the two-population interaction condition is met based on the current population evolution iteration number gen. When the two-population evolution iteration number is every iter generation, i.e. gen%iter==0, the two-population interaction condition is met, and the influence strategy and expansion strategy are executed alternately.

[0042] Step 3.2: Implement the influencing strategy;

[0043] Step 3.3: Execute the expansion strategy.

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

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

[0046] Step 3.2.1: Apply the objective function value to the auxiliary population P. a Sort the data and map it to the original network space;

[0047] Step 3.2.2: Select the top-ranked individuals in the 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 betweenness centrality in LC, and add this node to the key node set of the current individual;

[0049] Step 3.2.4: Remove all critical nodes from the network for the current individual, calculate the connectivity index value for reconnecting these critical nodes to the network, select the critical node with the minimum value and delete it from the individual, thus completing the improvement and enhancement of the selected individual. The connectivity index value ConSize(v) is calculated using the following formula:

[0050]

[0051] In the formula, N c (v) represents the set of connected components that are connected to the critical node v when it is restored to the remaining network;

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

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

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

[0055] Step 3.3.1: Based on the objective function value, adjust the population P of the main population. m Sort the data and calculate the weighted frequency information Fre for each node. v The calculation formula is as follows:

[0056]

[0057] In the formula, ind i This represents the i-th individual in the main population after sorting. If v is a key node in this individual, the value of occurrence 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] 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 based on their importance values ​​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 the top half of the individuals with the highest objective function values, and calculate the selection value (SV) of the key nodes in each individual using the node selection index. c And the selection value SV of the newly added node e The node selection criteria are calculated as follows when modifying the other half of the individual:

[0063]

[0064] In the formula, rand∈(0,1] represents a random value, ensuring diversity of choices for the SV of key nodes. c The calculation, where nodes represent the set of key nodes, and the SV of newly added nodes. e The calculation is performed, where nodes represent the set of newly added nodes;

[0065] Step 3.3.5: Swap 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 Update.

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

[0067] Step 4.1: Obtain the final auxiliary population P a Map it to the original cyberspace 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 values;

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

[0070] Compared with existing technologies, the beneficial effects of this invention are reflected in:

[0071] 1. Compared with precise methods that consider solving the quality of key nodes, this invention utilizes the co-evolution of an auxiliary population generated from the reduced network and a main population generated from the original network, which can quickly identify high-quality combinations of key nodes on large-scale networks and improve the efficiency of key node identification.

[0072] 2. Compared with approximate methods that consider the efficiency of solving key nodes, this invention proposes an effective dual-population interaction mechanism that uses influence strategies and expansion strategies to conduct information interaction between the two populations, achieving a good balance between efficiency and effectiveness in identifying key node sets in social networks. Attached Figure Description

[0073] Figure 1 This is a flowchart of a method for identifying key nodes in a social network based on dual-population interaction, as described in an embodiment of the present invention.

[0074] Figure 2 This is a schematic diagram of the dual-population interaction mechanism proposed in this embodiment of the invention;

[0075] Figure 3 This is a schematic diagram of the local search strategy based on large components used in the influence strategy proposed in this embodiment of the invention, where (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 the key nodes of the improved individual being {v1, v3}. Detailed Implementation

[0076] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0077] like Figure 1 As shown, a method for identifying key nodes in a social network based on dual-population interaction is performed according to 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 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: Construct a dual population. Generate a primary population and an auxiliary population based on the original network space and the reduced search space, respectively, to complete the initialization.

[0080] Step 1.1: Reduce the original network G based on the network topology information. 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, set to 0.05.

[0081] Betweenness centrality index BC i The formula for measuring the importance of node i in the network is:

[0082]

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

[0084] Step 1.2: Define the number of key nodes as K, the population size as popsize, and use binary encoding to represent individuals S in the main population and individuals S' in the auxiliary population. Each individual S... i ={s1,s2,…,s j ,…,s N}, s j This indicates whether the j-th node in the social network has been selected as a key node, s j =1 indicates that the node is selected as a key node, s j =0 indicates that the node is a normal node;

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

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

[0087] Step 2: Two-population evolution. Genetic operations are performed on the main population and auxiliary population obtained in Step 1. Offspring are generated through crossover and mutation, and a new population is 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 two populations, calculate the objective function value of the key node combination represented by the individual in the corresponding network for both the main population and the auxiliary population, and calculate the network connectivity value F(S) caused by S using the following formula:

[0090]

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

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

[0093] Step 2.3.1: Use the binary tournament selection method to select from the main population P m Individuals are selected as parents to form a mating pool (MP). m Using a binary tournament selection method to select from the auxiliary population P a Individuals are selected as parents to form a mating pool (MP). a ;

[0094] Step 2.3.2: Utilize the main population mating pool MP respectively m and auxiliary population mating pool MP a Individuals in the dataset undergo their respective crossover operations. For two selected individuals X1 and X2, the new individual retains the same key node SC = X1∩X2 after crossover, and then proceeds with a crossover operation with probability p. c Select nodes from the remaining key nodes RC=(X1∪X2)\SC of the two individuals until the size of the key node set reaches K;

[0095] Step 2.3.3: Perform mutation operations on the individuals obtained after crossover of the main population and the auxiliary population to obtain the corresponding subpopulations. The key nodes in the individuals after crossover are denoted by p. m The probability of mutation is used to generate any ordinary node, thus completing the generation of the subpopulation.

[0096] Step 2.4: Perform population updates for the main population and the auxiliary population separately. For the main population, sort individuals based on their objective function values ​​and retain the top popsize individuals as the new main population. For the auxiliary population, to reduce accuracy loss caused by reduction space, the auxiliary population update considers both the objective function value and individual diversity. Sort individuals based on the combined score of both, and retain the top popsize individuals as the new auxiliary population. For each individual S... i Its individual diversity D(S) i The calculation is as follows:

[0097]

[0098] Among them, S j The denominator represents the 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 shared by the two individuals.

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

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

[0101] Where rank represents the ranking obtained by sorting the corresponding values, F(S) i The individual S is calculated using formula (2). i The resulting network connectivity value, D(S) i The individual S is calculated using formula (3). i The individual diversity value in the auxiliary population, θ t This represents the adaptive adjustment parameter, and its specific calculation is as follows:

[0102]

[0103] Among them, N' t This represents the size of the reduced network used by the auxiliary population in the t-th 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 evaluation calls maxcalls, thereby obtaining the final main population and auxiliary population;

[0105] Step 3, two-population interaction, the specific process of which is as follows: Figure 2 As shown, 'elite' represents the elite individual selected from the auxiliary population. m Let m represent the m-th elite individual. In the influence individual module, 'elite' represents the auxiliary population elite individual improved through local search based on large components. When the two populations evolve to a certain number of iterations and the interaction conditions are met, the influence strategy and the expansion strategy are executed alternately to achieve information interaction between the main population and the auxiliary population.

[0106] Step 3.1: Determine whether the two-population interaction condition is met based on the current population evolution iteration number gen. When the two-population evolution iteration number is every iter generation, i.e. gen%iter==0, the two-population interaction condition is met. Alternately execute the influence strategy and the expansion strategy, set the interval number iter to 5, and set the flag of the strategy to 1.

[0107] Step 3.2, Influence Strategy

[0108] When Flag == 1, the influence strategy is executed, and the elite individual 'elite' of the auxiliary population is modified through a local search based on large components and passed 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: Adjust the auxiliary population P based on the objective function value. a Sort the data and map it to the original network space;

[0110] Step 3.2.2: Select the top-ranked enum individuals after mapping and improve upon it based on local search of large components;

[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 betweenness centrality in LC, and add this node to the key node set of the current individual;

[0112] Step 3.2.4: Remove all critical nodes from the network for the current individual, calculate the connectivity index value for reconnecting these critical nodes to the network, select the critical node with the minimum value and delete it from the individual, thus completing the improvement and enhancement of the selected individual. The connectivity index value ConSize(v) is calculated using the following formula:

[0113]

[0114] Where, N c (v) represents the set of connected components that are connected to the critical node v when it is restored to the remaining network;

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

[0116] For example Figure 3 As shown in Figure (a), the current network situation is as follows. Assuming the current individual's chosen key node combination is {v2, v3}, the remaining network situation is as follows: The largest connected component C1 in the remaining network is found, as shown in Figure (b). C1 has a size of 6. The node v1 with the highest betweenness centrality in C1 is added to the key node set, as shown in Figure (c). For key nodes v2 and v3, their connection index values ​​in the network are restored to 3 and 6, respectively. Therefore, node v2 with a smaller connection value is removed from the key nodes. The improved individual's key nodes are {v1, v3}, as shown in Figure (d).

[0117] Step 3.3, Extension Strategy

[0118] When Flag == 0, the expansion strategy is executed, which uses 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: Based on the objective function value, adjust the population P of the main population. m Sort the data and calculate the weighted frequency information Fre for each node. v The calculation formula is as follows:

[0120]

[0121] Among them, ind i This represents the i-th individual in the main population after sorting. If v is a key node in this individual, the value of occurrence 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] 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 based on their importance values ​​and add them to the reduced network to form a new reduced network G', where e is the expansion factor, set to 0.05;

[0126] Step 3.3.4: Map the auxiliary population to the new reduction network, retain the top half of the individuals with the highest objective function values, and calculate the selection value (SV) of the key nodes in each individual using the node selection index. c And the selection value SV of the newly added node e To modify the other half of the individual, the node selection criteria are calculated as follows:

[0127]

[0128] Where rand∈(0,1] represents a random value to ensure diversity of choices, for the SV of key nodes c The calculation, where nodes represent the set of key nodes, and the SV of newly added nodes. e The calculation is performed, where nodes represent the set of newly added nodes;

[0129] Step 3.3.5: Swap 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 Update.

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

[0131] Step 4.1: Obtain the final auxiliary population P a Map it to the original cyberspace 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 values;

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

[0134] The above description is merely an example and illustration of the present invention. Those skilled in the art can make various modifications or additions to the specific embodiments described, or use similar methods to replace them, as long as they do not deviate from the structure of the present invention or exceed the scope defined in the claims, all of which should 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, Includes the following steps: Modeling social networks as graphs Let V be the set of nodes and E be the set of edges, representing users in the social network and the connections between any two users, respectively, where |V|=N and |E|=M. M represents the number of nodes in the network, and M represents the number of edges in the network; Step 1: Constructing a dual population: Generate a primary population and an auxiliary population based on the original network space and the reduced search space, respectively, to complete the initialization; Step 2: Two-population evolution. Genetic operations are performed on the main population and auxiliary population obtained in Step 1. Offspring are generated through crossover and mutation, and a new population is formed according to the corresponding population update method. Step 3: Two-population interaction. When the two 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 information interaction between the main population and the auxiliary population. The influencing strategies are as follows: when At that time, the influence strategy is implemented to transmit the elite individuals of the auxiliary population to the main population in order to quickly locate excellent candidate nodes, thereby guiding the main population to evolve rapidly in a better direction; Step 3.2.1: Adjust the auxiliary population based on the objective function value. Sort the data and map it to the original network space; Step 3.2.2: Select the top-ranked items after mapping. Improvements are made to individuals; Step 3.2.3: For each selected individual, find the largest connected component of the remaining network after removing its key node combination. ,turn up The node with the highest intermediary centrality And add this node to the current individual's key node set; Step 3.2.4: Remove all critical nodes from the network for the current individual, calculate the connectivity index value for reconnecting these critical nodes to the network, select the critical node with the minimum value and delete it from the individual, thus completing the improvement and enhancement of the selected individual. (Connectivity index value...) The calculation formula is as follows: ， In the formula, Indicates the assumption of a critical node The set of connected components that are connected to the remaining network when it is restored; Step 3.2.5: Transfer the improved set of individuals to the main population, and use environmental selection to update the main population. The next time the strategy will be used will be marked. Set to 0; Step 4: Individual selection. Based on the objective function value, individuals in the main population and auxiliary population are sorted, and the optimal individual is selected as the key node combination output. The expansion strategy is as follows: when At that time, an expansion strategy is implemented, using global statistical information from the main population to help the auxiliary population expand the search space; Step 3.3.1: Adjust the main population based on the objective function value. Sort the data and calculate the weighted frequency information for each node. The calculation formula is as follows: ， In the formula, For population size, Indicates the th order in the main population after sorting. Individual, if It is the key node in this individual. The value is 1 if it is 1, otherwise it is 0. Step 3.3.2, Calculate the nodes The importance indicator is calculated using the following formula: ， in, The value represents the ranking obtained by sorting the corresponding values; Step 3.3.3: Select the top-ranked nodes from the original network based on their importance values. Each node is added to the reduced network to form a new reduced network. ,in For expansion factor; Step 3.3.4: Map the auxiliary population to the new reduction network, retain the top half of the individuals with the highest objective function values, and calculate the selection values ​​of key nodes in each individual using the node selection index. and the selection value of newly added nodes The node selection criteria are calculated as follows when modifying the other half of the individual: ， In the formula, Representing random values ​​ensures diversity of choices, especially for key nodes. The calculation, This represents the set of key nodes, and for newly added nodes... The calculation, This represents the set of newly added nodes; Step 3.3.5: Swap 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, modifying the original individual into a new adapted individual, thus completing the auxiliary population. Update.

2. The method for identifying key nodes in a social network based on dual-population interaction according to claim 1, characterized in that, Step 1, the construction of the two populations, specifically includes the following steps: Step 1.1: Based on network topology information, analyze the original network. The process involves reduction, scoring each node in the original network using the betweenness centrality index and sorting them in descending order, then selecting the top nodes. The reduced network consists of nodes. ,in The number of network nodes. The reduction factor; Betweenness Centrality Index Used to measure nodes Its importance in the network is calculated using the following formula: ， In the formula, Indicates the number of nodes in the network. Represents a node and The number of shortest paths between them Represents a node and Between nodes The number of shortest paths; Step 1.2: Define the number of key nodes as... Population size is Each individual in the population is represented by a binary code. , Indicates the first in social networks Whether a node is selected as a key node. This indicates that the node has been selected as a key node. This indicates that the node is a regular node; Step 1.3, based on the original cyberspace The main population is generated using random initialization. ; Step 1.4: Based on the reduced search space Auxiliary population is generated using random initialization. .

3. The method for identifying key nodes in a social network based on dual-population interaction according to claim 2, characterized in that, Step 2, the dual-population evolution, specifically includes the following steps: Step 2.1: Define the maximum number of evaluations as... The initial number of iterations is ; Step 2.2: For each individual in the two populations To evaluate, the objective function values ​​of the key node combinations of individual representations in the corresponding networks for both the primary and secondary populations are calculated using the following formula. The resulting network connectivity value : ， In the formula, This represents the remaining network after removing the set of critical nodes. Indicates the number of remaining network nodes. Size of each connected component; Step 2.3: Perform genetic operations on the main population and auxiliary population respectively to produce offspring; Step 2.4: Perform population updates for both the main population and the auxiliary population. For the main population, sort the individuals according to their objective function values ​​and retain the top-ranked individuals. Each individual is designated as the new main population; for the auxiliary population, individuals are ranked according to a mixture of the objective function value and individual diversity score, and the top-ranked individuals are retained. Each individual serves as a new auxiliary population; for each individual Its individual diversity The calculation is as follows: ， In the formula, The denominator represents the other individuals in the auxiliary population. The numerator represents the total number of key nodes in two individuals. The number of key nodes shared by two individuals; Step 2.5, Assign to Repeat the above steps until the maximum number of evaluation calls is reached. This process continues until the final main population and auxiliary population are obtained.

4. The method for identifying key nodes in a social network based on dual-population interaction according to claim 3, characterized in that, Step 2.3 is as follows: Step 2.3.1: Use the binary tournament selection method to select from the main population Individuals are selected as parents to form a mating pool. ; Using a binary tournament selection method from the auxiliary population Individuals are selected as parents to form a mating pool. ; Step 2.3.2: Utilize the mating pools of the main populations respectively and auxiliary population mating pool Each individual in the set performs its own crossover operation; for two selected individuals... and After the crossover, the new individuals retain the same key nodes. Then with probability Remaining key nodes from the two individuals Select nodes until the size of the key node set reaches... ; Step 2.3.3: Perform mutation operations on the individuals obtained after crossover of the main population and the auxiliary population to obtain the corresponding subpopulations. The key nodes in the individuals after crossover are... The probability of mutation is used to generate any ordinary node, thus completing the generation of the subpopulation.

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 is used while considering a hybrid score that takes into account both the objective function value and individual diversity. The calculation formula is as follows: ， In the formula, This indicates the ranking obtained by sorting the corresponding values. , For individuals Individual diversity values ​​in the auxiliary population This represents the adaptive adjustment parameter, and its specific calculation is as follows: ， In the formula, Indicates the first The size of the reduced network used by the auxiliary population in the next 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 method between the two populations specifically includes the following steps: Step 3.1: Based on the current population's evolutionary iteration count To determine whether the interaction condition between the two populations is met, the number of evolutionary iterations between the two populations is determined at intervals of [number missing]. generation, that is 0, satisfying the two-population interaction condition, alternately execute the influence strategy and the expansion strategy; Step 3.2: Implement the influencing 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 1, characterized in that, Step 4, the selection of individuals specifically includes the following steps: Step 4.1: Obtain the final auxiliary population Map it to the original cyberspace and evaluate it; Step 4.2: Merge the main populations and auxiliary population And sort them according to the objective function values; Step 4.3: Select the top-ranked individual as the optimal key node combination and output it.

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