Social network opinion maximization method, system and device and medium

Abstract

The invention provides a social network opinion maximization method, a social network opinion maximization system, a social network opinion maximization device and a medium, and the method comprises the steps: carrying out the modeling of a social network, and constructing an optimization problem which takes the maximization of a network average final opinion value and the minimization of the total selection cost of a seed node as double targets based on a modeling result; the core requirement of realizing optimal propagation under limited resources in practical application is met; by constructing a multi-objective evolutionary optimization framework, on one hand, population basic diversity can be guaranteed, a certain type of nodes are prevented from being excessively focused in an initial stage, on the other hand, an initial population has global coverage and also contains community propagation dominant genes, a high-quality foundation is laid for follow-up evolutionary optimization, and the population quality is improved. The problem that traditional sampling communities are insufficient in coverage or uneven in transmission force is solved; when the population is iteratively optimized, on the premise that the opinion propagation effect is not seriously reduced, seed node selection cost is greatly reduced, and the defect of an evolutionary operator in local cost fine adjustment is overcome.

Description

Technical Field

[0001] This invention belongs to the field of social network information processing technology, and specifically relates to a method, system, device and medium for maximizing opinions on social networks. Background Technology

[0002] Current mainstream methods for maximizing opinions mainly fall into two categories: one is static screening methods based on greedy strategies, such as the classic K-center and degree-centrality algorithms; the other is random search methods based on simple evolutionary algorithms. These latter methods suffer from the core flaw of focusing solely on maximizing opinions without considering other factors in practical applications, such as the cost of seed node selection and resource constraints. Furthermore, they lack depth in utilizing community information, failing to meet the needs of real-world social network scenarios. Social networks inherently possess community characteristics, and the influence of node propagation is significantly limited by community boundaries. Cross-community propagation is far more difficult than intra-community propagation due to differences in user interests and low interaction frequency. Existing methods that consider community often merely use communities as node grouping labels, failing to deeply explore the synergistic value between high-propagation-capable nodes within a community and cross-community bridge nodes. By evenly distributing seed nodes across communities while neglecting the priority selection of community bridge nodes, opinions struggle to break through community barriers. Over-focusing on high-propagation-capable nodes within a single community results in seed nodes being concentrated in a few communities, creating propagation blind spots.

[0003] Therefore, this application anticipates a method that can ensure seed nodes maximize opinions while minimizing costs, achieving a synergistic balance between propagation effect and resource investment. Summary of the Invention

[0004] In order to overcome the shortcomings of existing technologies in terms of the depth of community information utilization, which makes it difficult to meet the needs of actual social network scenarios, and the problem that they only consider a single optimization goal while ignoring the cost required to maximize opinions, this invention provides a method, system, device and medium for maximizing opinions in social networks.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] In a first aspect, embodiments of this disclosure provide a method for maximizing opinions on a social network, comprising the following steps:

[0007] Step S1: Model the social network and construct an optimization problem with the dual objectives of maximizing the average final opinion value of the network and minimizing the total cost of seed node selection based on the modeling results;

[0008] Step S2: Construct a multi-objective evolutionary optimization framework, which includes: a population initialization method based on a hybrid strategy, constructing an evolutionary operator for the optimization problem, and an iterative optimization mechanism that combines cost optimization local search.

[0009] Step S3: Use the non-dominated sorting genetic algorithm NSGA-II framework, combined with the multi-objective evolutionary optimization framework, to iteratively optimize the population, output a set of Pareto optimal solutions, and use them as the optimal seed node scheme containing multiple opinion-cost balances.

[0010] Furthermore, in step S1, when modeling the social network, the social network is abstracted as an undirected graph. :

[0011] ;

[0012] In the formula, Let be a set of nodes, representing users in a social network. Each node corresponds to an individual with independent interactive and opinion-expressing capabilities. The total number of nodes is . ; Let be a set of edges, representing the interaction relationships between nodes. If nodes have at least one valid interaction within a set time window, then an edge exists. The existence of an edge determines the potential path for opinion propagation.

[0013] Set the adjacency matrix For the set of edges Mathematical mapping, adjacency matrix The matrix dimension is If an edge exists, then ,otherwise 0;

[0014] Define binary decision variable vector :

[0015] ;

[0016] In the formula, Represents a node Selected as a seed node This indicates that the item was not selected; all items were selected. Given seed nodes, obtain the seed node set. for:

[0017] ;

[0018] Based on the Friedkin-Johnsen opinion propagation model, if Then the inherent opinion Fixed to 1, otherwise Random initialization;

[0019] By solving linear systems The balanced opinion vector is obtained. In the formula, It is a diagonal matrix representing the node degree; The identity matrix is ​​denoted by s; the inherent opinion vector s is composed of the inherent opinions of all nodes. A column vector formed by arranging nodes in order.

[0020] Furthermore, when the optimization problem is obtained in step S1, the following steps are included:

[0021] Based on the binary decision variable vector and the balanced opinion vector Obtain the average final opinion value :

[0022] ;

[0023] In the formula, It is the i-th component of the equilibrium opinion vector z, corresponding to the equilibrium opinion value of the i-th node in the network;

[0024] Total cost of seed node selection based on PageRank :

[0025] ;

[0026] In the formula, Represents seed node The PageRank value is used to reflect the seed node. Global influence on social networks;

[0027] Based on average final opinion value and the total cost of seed node selection Construct an optimization problem with the dual objectives of maximizing the average final opinion value of the network and minimizing the total cost of seed node selection:

[0028] ;

[0029] In the formula, This indicates a constraint.

[0030] Furthermore, the population initialization method based on the hybrid strategy in step S2 is as follows:

[0031] The initial population was divided into two parts, each of which accounted for half of the population size;

[0032] The first part adopts a random sampling strategy, selecting nodes as seed nodes completely randomly.

[0033] The second part employs a roulette wheel sampling strategy based on the Community Spreader Ranking (CSR) metric. A probability distribution is constructed based on the CSR values ​​of nodes, prioritizing nodes with high CSR values ​​as seed nodes. The Community Spreader Ranking (CSR) metric is represented as follows:

[0034] ;

[0035] In the formula, For nodes The degree, Represents a node Connected community collections Indicates community For nodes The contribution of community diversity Indicates community The proportion of the scale, Indicates community Internal density, It is used to comprehensively reflect the cross-community propagation potential of nodes in the network structure.

[0036] Furthermore, step S2, which involves constructing an evolutionary operator for the optimization problem and an iterative optimization mechanism incorporating cost-optimized local search, includes:

[0037] A uniform crossover operator is used to generate offspring individuals;

[0038] A bit-flipping mutation operator is used, with a preset mutation probability;

[0039] Construct and execute a two-hop neighbor cost optimization local search operator. The execution process includes:

[0040] Step A1: For each seed node in the current individual, select the set of two-hop neighbor nodes of each seed node as candidate nodes. The two-hop neighbor nodes include the direct neighbors of the seed node and the neighbors of the direct neighbors, and exclude the seed node itself.

[0041] Step A2: For each candidate node, simulate the opinion propagation process after replacing the candidate node with the current seed node, and calculate the average final opinion value after the replacement. Total cost ;

[0042] Step A3: Set the opinion effect protection threshold and cost optimization threshold If the following conditions are met:

[0043] ≤ ,and ;

[0044] Then the candidate node is included in the valid candidate set, where The average final opinion value before the replacement; Select the total cost for the seed node before replacement; otherwise, do not include it in the valid candidate set.

[0045] Step A4: From the valid candidate set corresponding to each seed node, select the one that maximizes the total cost. The candidate node with the largest reduction is selected as the optimal replacement node, and the replacement iteration optimization is performed.

[0046] Furthermore, the execution probability of the two-hop neighbor cost optimization local search operator is preset to 0.6, and the opinion effect protection threshold is... The preset cost optimization threshold is 20%. The default setting is 40%.

[0047] Furthermore, in step S3, when outputting a set of Pareto optimal solutions, the following steps are included:

[0048] A dual-objective stratification of the population is performed by non-dominantly ranking the population according to the effect of opinion propagation and the total cost. Individuals in the same stratum do not dominate each other, and individuals are divided into multiple non-dominant strata.

[0049] Calculate the crowding degree of individuals within the same non-dominated hierarchy, and prioritize retaining sparsely distributed individuals;

[0050] A binary tournament selection strategy based on non-dominated hierarchy and crowding degree is adopted. Each time, two individuals are randomly selected from the current parent population, and the non-dominated hierarchy of the two individuals is compared. If the non-dominated hierarchy of the two individuals is different, the individual with the better non-dominated hierarchy is selected; if the non-dominated hierarchy of the two individuals is the same, the individual with higher crowding degree is selected. This selection process is repeated until n individuals are selected as the parent population for crossover and mutation operations.

[0051] The parent population is optimized for local search using a uniform crossover operator, a position-flipping mutation operator, and a two-hop neighbor cost to generate a child population. The child populations are then merged into a temporary population of size 2n.

[0052] The new generation of parent population is selected again by non-dominated sorting and crowding calculation. The process is iterated until the preset number of iterations is reached, and a set of Pareto optimal solutions is obtained, which are used as the optimal seed node scheme containing multiple opinion-cost balances.

[0053] In a second aspect, embodiments of this disclosure provide a system for maximizing opinions on a social network, comprising:

[0054] The initialization unit is configured to: model the social network and, based on the modeling results, construct an optimization problem with the dual objectives of maximizing the average final opinion value of the network and minimizing the total cost of seed node selection;

[0055] The optimization unit is configured to: construct a multi-objective evolutionary optimization framework, which includes: a population initialization method based on a hybrid strategy, construct an evolutionary operator for the optimization problem, and an iterative optimization mechanism that combines cost-optimized local search;

[0056] The output unit is configured to iteratively optimize the population using the non-dominated sorting genetic algorithm NSGA-II framework, combined with the multi-objective evolutionary optimization framework, to output a set of Pareto optimal solutions, which serve as the optimal seed node scheme containing multiple opinion-cost balances.

[0057] In a third aspect, embodiments of this disclosure provide an electronic device, characterized in that the electronic device comprises:

[0058] At least one processor; and,

[0059] The memory is communicatively connected to the at least one processor; wherein,

[0060] The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method for maximizing social network opinions.

[0061] In a fourth aspect, embodiments of this disclosure provide a non-transitory computer-readable storage medium, characterized in that the non-transitory computer-readable storage medium stores computer instructions for causing the computer to perform the method of maximizing opinions on the social network.

[0062] Compared with the prior art, the present invention has the following beneficial technical effects:

[0063] This invention provides a method, system, device, and medium for maximizing opinions in a social network. The method models the social network and, based on the modeling results, constructs an optimization problem with two objectives: maximizing the average final opinion value and minimizing the total cost of seed node selection. This addresses the shortcomings of traditional methods that only pursue opinion propagation effects while neglecting resource input, achieving a synergistic balance between effect and cost. This better aligns with the core requirement of achieving optimal propagation with limited resources in practical applications. By constructing a multi-objective evolutionary optimization framework, on the one hand, it ensures basic population diversity, avoiding excessive focus on a certain type of node in the initial stage; on the other hand, it ensures that the initial population has both global coverage and contains genes with community propagation advantages, laying a high-quality foundation for subsequent evolutionary optimization and solving the problems of insufficient community coverage or uneven propagation power in traditional sampling. During iterative optimization of the population, the cost of seed node selection is significantly reduced without a severe decline in opinion propagation effects, compensating for the shortcomings of evolutionary operators in fine-tuning local costs and further improving the practicality of Pareto optimal solutions, achieving a synergistic balance between propagation effects and resource input. Attached Figure Description

[0064] Figure 1 A flowchart illustrating a method for maximizing social network opinions according to an embodiment of this disclosure is shown;

[0065] Figure 2 The diagram shows a comparison of the results of the proposed method and the greedy algorithm when the number of seed nodes Seed_Num is 10 in this embodiment of the present disclosure.

[0066] Figure 3 The diagram shows a comparison of the results of the method proposed in this application and the greedy algorithm when the number of seed nodes Seed_Num is 15, according to an embodiment of this disclosure.

[0067] Figure 4 The diagram shows a comparison of the results of the method proposed in this application and the greedy algorithm when the number of seed nodes Seed_Num is 20, according to an embodiment of this disclosure.

[0068] Figure 5 A diagram of an apparatus for maximizing opinions on a social network, according to an embodiment of the present disclosure, is shown. Detailed Implementation

[0069] The embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0070] This disclosure addresses the shortcomings of existing opinion maximization techniques in terms of the depth of community information utilization, making it difficult to meet the needs of real-world social network scenarios, and the problem that they only consider a single optimization objective while ignoring the costs required to achieve opinion maximization. The disclosure provides a method flow 100 for maximizing opinions in social networks, including the following steps:

[0071] In step S101, the social network is modeled, and an optimization problem with dual objectives of maximizing the average final opinion value of the network and minimizing the total cost of seed node selection is constructed based on the modeling results.

[0072] Specifically, in step S101, when modeling the social network, the social network is abstracted as an undirected graph. :

[0073] ;

[0074] In the formula, Let be a set of nodes, representing users in a social network. Each node corresponds to an individual with independent interactive and opinion-expressing capabilities. The total number of nodes is . ; Let be a set of edges, representing the interaction relationships between nodes. If nodes have at least one valid interaction within a set time window, then an edge exists. The existence of edges determines the potential path for opinion propagation.

[0075] The undirected graph It provides a mathematical expression for network topology, accurately depicting the core characteristics of nodes and interactions in social networks, and offering a basic model support for subsequent optimization.

[0076] Set the adjacency matrix For the set of edges Mathematical mapping, adjacency matrix The matrix dimension is If an edge exists, then ,otherwise 0;

[0077] Define binary decision variable vector :

[0078] ;

[0079] In the formula, Represents a node Selected as a seed node This indicates that the item was not selected; all items were selected. Given seed nodes, obtain the seed node set. for:

[0080] ;

[0081] Based on the Friedkin-Johnsen opinion propagation model, if Then the inherent opinion Fixed to 1, otherwise Random initialization is used. It's important to note that the Friedkin-Johnsen discrete combinatorial optimization problem of "choosing which nodes to select as initial opinion holders, i.e., seeds" is connected to the continuous output of "the final state of public opinion across the entire network" through a linear system. This allows the evolutionary algorithm to quantitatively and reproducibly evaluate the propagation effect of each seed selection scheme.

[0082] By solving linear systems The balanced opinion vector is obtained. In the formula, It is a diagonal matrix representing the node degree; The identity matrix is ​​denoted by s; the inherent opinion vector s is composed of the inherent opinions of all nodes. A column vector formed by arranging nodes in order.

[0083] Furthermore, when the optimization problem is obtained in step S101, the following steps are included:

[0084] Based on the binary decision variable vector and the balanced opinion vector Obtain the average final opinion value :

[0085] ;

[0086] In the formula, It is the i-th component of the equilibrium opinion vector z, corresponding to the equilibrium opinion value of the i-th node in the network;

[0087] Total cost of seed node selection based on PageRank :

[0088] ;

[0089] In the formula, Represents seed node The PageRank value is used to reflect the seed node. Global influence on social networks;

[0090] Based on average final opinion value and the total cost of seed node selection Construct an optimization problem with the dual objectives of maximizing the average final opinion value of the network and minimizing the total cost of seed node selection:

[0091] ;

[0092] In the formula, and Both are optimization goals. The constraints in the above formula are represented by .

[0093] Next, proceed to step S102.

[0094] In step S102, a multi-objective evolutionary optimization framework is constructed, which includes: a population initialization method based on a hybrid strategy, an evolutionary operator for the optimization problem, and an iterative optimization mechanism that combines cost-optimized local search.

[0095] Specifically, the population initialization method based on the hybrid strategy in step S102 is as follows:

[0096] The initial population was divided into two parts, each of which accounted for half of the population size;

[0097] The first part adopts a random sampling strategy, selecting nodes as seed nodes completely randomly.

[0098] The second part employs a roulette wheel sampling strategy based on the Community Spreader Ranking (CSR) metric. A probability distribution is constructed based on the CSR values ​​of nodes, prioritizing nodes with high CSR values ​​as seed nodes. The Community Spreader Ranking (CSR) metric is represented as follows:

[0099] ;

[0100] In the formula, For nodes The degree, Represents a node Connected community collections Indicates community For nodes The contribution of community diversity Indicates community The proportion of the scale, Indicates community Internal density, It is used to comprehensively reflect the cross-community propagation potential of nodes in the network structure.

[0101] In other words, in this embodiment, a two-part sampling strategy is used to generate the initial population during the initialization of the evolutionary population. Each part accounts for 1 / 2 of the population, which takes into account both the needs of community coverage and randomness, avoids the initial population from getting trapped in local optima, and provides a high-quality foundation for subsequent evolution.

[0102] The first part involves random sampling, where nodes are randomly selected as seeds to cover nodes of different types and communities in the network, ensuring basic diversity in the population and avoiding excessive focus on a particular type of node in the initial stage.

[0103] The second part involves roulette wheel sampling based on the Community Spreader Ranking (CSR) metric. A probability distribution is constructed based on CSR, and nodes are selected using a roulette wheel algorithm. Nodes with high propagation potential within the community are prioritized, injecting a community-based propagation advantage into the population and ensuring that the initial population contains nodes capable of efficiently driving propagation within the community. Nodes with higher CSR values ​​typically possess stronger cross-community propagation capabilities, serving as a crucial basis for selecting efficient seed nodes.

[0104] Furthermore, the construction of the evolutionary operator for the optimization problem in step S102, and the iterative optimization mechanism combining cost-optimized local search, include:

[0105] The offspring individuals are generated using a uniform crossover operator; the seed position state is randomly inherited from the two parents with equal probability for each position of the offspring individual. This method does not rely on community structure, introduces more perturbation, and helps maintain the global diversity of the population.

[0106] A mutation operator with bit flipping is adopted, and the mutation probability is preset to 0.2. The local exploration of the population is achieved by randomly flipping the gene position state, which improves the flexibility of the algorithm to find the best.

[0107] To further reduce the cost of seed node selection while ensuring the basic stability of opinion dissemination, the probability of triggering a local search for each individual in the population is considered. This is achieved by precisely selecting two-hop neighbor nodes to optimize both the dissemination effect and cost.

[0108] Specifically, a two-hop neighbor cost optimization local search operator is constructed and executed, and the execution process includes:

[0109] Step A1: For each seed node in the current individual, select the set of two-hop neighbor nodes of each seed node as candidate nodes. The two-hop neighbor nodes include the direct neighbors of the seed node and the neighbors of the direct neighbors, and exclude the seed node itself.

[0110] Step A2: For each candidate node, simulate the opinion propagation process after replacing the candidate node with the current seed node using the FJ propagation model, and calculate the average final opinion value after the replacement. Total cost ;

[0111] Step A3: Set the opinion effect protection threshold and cost optimization threshold If the following conditions are met:

[0112] ≤ ,and ;

[0113] Then the candidate node is included in the valid candidate set, where The average final opinion value before the replacement; Select the total cost for the seed node before replacement; if the protection threshold for any opinion effect is not met. and cost optimization threshold If the candidate node either leads to a significant reduction in the effectiveness of opinion propagation or fails to achieve significant cost optimization, it will not be included in the effective candidate set.

[0114] Step A4: From the valid candidate set corresponding to each seed node, select the one that maximizes the total cost. The candidate node with the largest reduction is selected as the optimal replacement node, and the replacement iteration optimization is performed.

[0115] Specifically, the execution probability of the two-hop neighbor cost optimization local search operator is preset to 0.6, and the opinion effect protection threshold is... The preset cost optimization threshold is 20%. The default value is 40%, and these thresholds are adjustable parameters.

[0116] The two-hop neighbor cost optimization local search operator achieves significant optimization of seed node selection cost under the premise of strictly controlling the attenuation range of opinion propagation effect, making the final output seed node scheme more in line with the needs of achieving optimal propagation under limited resources in practical applications.

[0117] Next, proceed to step S103.

[0118] In step S103, the non-dominated sorting genetic algorithm NSGA-II framework is used in conjunction with the multi-objective evolutionary optimization framework to iteratively optimize the population, outputting a set of Pareto optimal solutions, which serve as the optimal seed node scheme containing multiple opinion-cost balances.

[0119] Specifically, in step S103, when outputting a set of Pareto optimal solutions, the following steps are included:

[0120] A dual-objective stratification of the population is performed by non-dominantly ranking the population according to the effect of opinion propagation and the total cost. Individuals in the same stratum do not dominate each other, and individuals are divided into multiple non-dominant strata.

[0121] Calculate the crowding degree of individuals within the same non-dominated hierarchy, and prioritize retaining sparsely distributed individuals;

[0122] A binary tournament selection strategy based on non-dominated hierarchy and crowding degree is adopted. Each time, two individuals are randomly selected from the current parent population, and the non-dominated hierarchy of the two individuals is compared. If the non-dominated hierarchy of the two individuals is different, the individual with the better non-dominated hierarchy is selected; if the non-dominated hierarchy of the two individuals is the same, the individual with higher crowding degree is selected. This selection process is repeated until n individuals are selected as the parent population for crossover and mutation operations.

[0123] The parent population is optimized for local search using a uniform crossover operator, a position-flipping mutation operator, and a two-hop neighbor cost to generate a child population. The child populations are then merged into a temporary population of size 2n.

[0124] The new generation of parent population is selected again by non-dominated sorting and crowding calculation. The process is iterated until the preset number of iterations is reached, and a set of Pareto optimal solutions is obtained, which are used as the optimal seed node scheme containing multiple opinion-cost balances.

[0125] Figure 2 , Figure 3 and Figure 4 The graphs show a comparison of the results obtained using the proposed method and the greedy algorithm on public social network datasets with seed nodes (Seed_Num) of 10, 15, and 20. The horizontal axis represents the reciprocal of the average final opinion value (Opinion), and the vertical axis represents the cost (Cost). As can be seen from the graphs, purple dots (This method) represent the results of the current method, forming the Pareto front. Red crosses (Greedy cost) represent the results of the "Greedy cost method," showing a low cost but a large reciprocal of the opinion effect, indicating a poor actual opinion value. Green crosses (Greedy opinion) represent the results of the "Greedy opinion method," showing a small reciprocal of the opinion effect, indicating a good actual opinion value, but a high cost. In summary, the Pareto optimal solution set of this invention is evenly distributed and has a wide coverage in the opinion-cost two-dimensional space, providing richer choices for different resource budget scenarios.

[0126] A second embodiment of the present invention also provides a system for maximizing opinions on a social network, comprising:

[0127] The initialization unit is configured to: model the social network and, based on the modeling results, construct an optimization problem with the dual objectives of maximizing the average final opinion value of the network and minimizing the total cost of seed node selection;

[0128] The optimization unit is configured to: construct a multi-objective evolutionary optimization framework, which includes: a population initialization method based on a hybrid strategy, construct an evolutionary operator for the optimization problem, and an iterative optimization mechanism that combines cost-optimized local search;

[0129] The output unit is configured to iteratively optimize the population using the non-dominated sorting genetic algorithm NSGA-II framework, combined with the multi-objective evolutionary optimization framework, to output a set of Pareto optimal solutions, which serve as the optimal seed node scheme containing multiple opinion-cost balances.

[0130] The third embodiment of the present invention also provides an electronic device, the electronic device comprising:

[0131] At least one processor; and,

[0132] The memory is communicatively connected to the at least one processor; wherein,

[0133] The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method for maximizing social network opinions in any of the foregoing embodiments.

[0134] The fourth embodiment of the present invention also provides a non-transitory computer-readable storage medium storing computer instructions for causing the computer to perform the method for maximizing social network opinions as described in any of the preceding embodiments.

[0135] The fifth embodiment of the present invention also provides a computer program product, which includes a computing program stored on a non-transitory computer-readable storage medium. The computer program includes program instructions that, when executed by a computer, cause the computer to perform the method of maximizing social network opinions of any of the foregoing embodiments.

[0136] Figure 5 The illustration shows a method or device 1000 implementing an embodiment of the present invention. In some embodiments, more or fewer devices may be included than illustrated. In some embodiments, it may be implemented using a single or multiple devices. In some embodiments, it may be implemented using cloud-based or distributed devices.

[0137] like Figure 5 As shown, device 1000 includes a processor 1001 for performing various appropriate operations and processes based on programs and / or data stored in read-only memory (ROM) 1002 or programs and / or data loaded from storage portion 1008 into random access memory (RAM) 1003. Processor 1001 may be a multi-core processor or may contain multiple processors. In some embodiments, processor 1001 may include a general-purpose main processor and one or more special coprocessors, such as a central processing unit (CPU), graphics processing unit (GPU), neural network processor (NPU), digital signal processor (DSP), etc. Various programs and data required for the operation of device 1000 are also stored in RAM 1003. Processor 1001, ROM 1002, and RAM 1003 are interconnected via bus 1004. Input / output (I / O) interface 1005 is also connected to bus 1004.

[0138] The processor and memory described above are used together to execute programs stored in the memory. When the program is executed by a computer, it can implement the methods, steps, or functions described in the above embodiments.

[0139] The following components are connected to I / O interface 1005: an input section 1006 including a keyboard, mouse, touchscreen, etc.; an output section 1007 including a cathode ray tube (CRT), liquid crystal display (LCD), etc., and speakers, etc.; a storage section 1008 including a hard disk, etc.; and a communication section 1009 including a network interface card such as a LAN card, modem, etc. The communication section 1009 performs communication processing via a network such as the Internet. A drive 1010 is also connected to I / O interface 1005 as needed. A removable medium 1011, such as a disk, optical disk, magneto-optical disk, semiconductor memory, etc., is installed on drive 1010 as needed so that computer programs read from it can be installed into storage section 1008 as needed. Figure 5 The diagram only shows a portion of the components and does not imply that the device 1000 only includes... Figure 5 The components shown.

[0140] The systems, devices, modules, or units described in the above embodiments can be implemented by a computer or its associated components. The computer may be, for example, a mobile terminal, smartphone, personal computer, laptop computer, in-vehicle human-machine interface device, personal digital assistant, media player, navigation device, game console, tablet computer, wearable device, smart TV, Internet of Things system, smart home, industrial computer, server, or a combination thereof.

[0141] Although not shown, in this embodiment of the invention, a computer-readable storage medium is provided having a computer program / instructions stored thereon that, when executed by a processor, implements the method for maximizing social network opinions as described in the embodiments.

[0142] Storage media in embodiments of the present invention include articles that are permanent and non-permanent, removable and non-removable, capable of storing information by any method or technology. Examples of storage media include, but are not limited to, phase-change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, CD-ROM, digital versatile optical disc (DVD) or other optical storage, magnetic tape, magnetic magnetic disk storage or other magnetic storage devices, or any other non-transfer medium that can be used to store information accessible by a computing device.

[0143] Although not shown, embodiments of the present invention also provide a computer program product, including: a computer program / instructions that, when executed by a processor, implement the method for maximizing social network opinions as described in the embodiments.

[0144] The methods, programs, systems, apparatuses, etc., in embodiments of the present invention can be executed or implemented in one or more networked computers, or practiced in a distributed computing environment. In the embodiments of this specification, in these distributed computing environments, tasks can be performed by remote processing devices connected via a communication network.

Claims

1. A method for maximizing opinions on a social network, characterized in that, Includes the following steps: Step S1: Model the social network and construct an optimization problem with the dual objectives of maximizing the average final opinion value of the network and minimizing the total cost of seed node selection based on the modeling results; Step S2: Construct a multi-objective evolutionary optimization framework, which includes: a population initialization method based on a hybrid strategy, constructing an evolutionary operator for the optimization problem, and an iterative optimization mechanism that combines cost optimization local search. Step S3: Use the non-dominated sorting genetic algorithm NSGA-II framework, combined with the multi-objective evolutionary optimization framework, to iteratively optimize the population, output a set of Pareto optimal solutions, and use them as the optimal seed node scheme containing multiple opinion-cost balances.

2. The method for maximizing opinions on social networks according to claim 1, characterized in that, In step S1, when modeling the social network, the social network is abstracted as an undirected graph. : ； In the formula, Let be a set of nodes, representing users in a social network. Each node corresponds to an individual with independent interactive and opinion-expressing capabilities. The total number of nodes is . ; Let be a set of edges, representing the interaction relationships between nodes. If nodes have at least one valid interaction within a set time window, then an edge exists. The existence of an edge determines the potential path for opinion propagation. Set the adjacency matrix For the set of edges Mathematical mapping, adjacency matrix The matrix dimension is If an edge exists, then ,otherwise 0; Define binary decision variable vector : ； In the formula, Represents a node Selected as a seed node This indicates that the item was not selected; a total of [number] items were selected. Given seed nodes, obtain the seed node set. for: ； Based on the Friedkin-Johnsen opinion propagation model, if then the inherent opinion Fixed at 1, otherwise Random initialization; By solving linear systems The balanced opinion vector is obtained. In the formula, It is a diagonal matrix representing the node degree; The identity matrix is ​​denoted by s; the inherent opinion vector s is composed of the inherent opinions of all nodes. A column vector formed by arranging nodes in order.

3. The method for maximizing opinions on social networks according to claim 2, characterized in that, When the optimization problem is obtained in step S1, the following steps are included: Based on the binary decision variable vector and the balanced opinion vector Obtain the average final opinion value : ； In the formula, It is the i-th component of the equilibrium opinion vector z, corresponding to the equilibrium opinion value of the i-th node in the network; Total cost of seed node selection based on PageRank : ； In the formula, Represents seed node The PageRank value is used to reflect the seed node. Global influence on social networks; Based on average final opinion value and the total cost of seed node selection Construct an optimization problem with the dual objectives of maximizing the average final opinion value of the network and minimizing the total cost of seed node selection: ； In the formula, This indicates a constraint condition.

4. The method for maximizing opinions on social networks according to claim 1, characterized in that, The population initialization method based on the hybrid strategy in step S2 is as follows: The initial population was divided into two parts, each of which accounted for half of the population size; The first part adopts a random sampling strategy, selecting nodes as seed nodes completely randomly. The second part adopts a roulette wheel sampling strategy based on the Community Speaker Ranking (CSR) index. A probability distribution is constructed based on the CSR value of the nodes, and nodes with high CSR values ​​are selected as seed nodes. The Community Communicator Ranking (CSR) indicator is represented as follows: ； In the formula, For nodes The degree, Represents a node Connected community collections Indicates community For nodes The contribution of community diversity Indicates community The proportion of the scale, Indicates community Internal density, It is used to comprehensively reflect the cross-community propagation potential of nodes in the network structure.

5. The method for maximizing opinions on social networks according to claim 4, characterized in that, The construction of the evolutionary operator for the optimization problem in step S2, and the iterative optimization mechanism combining cost-optimized local search, include: A uniform crossover operator is used to generate offspring individuals; A bit-flipping mutation operator is used, with a preset mutation probability; Construct and execute a local search operator that optimizes two-hop neighbor cost. The execution process includes: Step A1: For each seed node in the current individual, select the set of two-hop neighbor nodes of each seed node as candidate nodes. The two-hop neighbor nodes include the direct neighbors of the seed node and the neighbors of the direct neighbors, and exclude the seed node itself. Step A2: For each candidate node, simulate the opinion propagation process after replacing the candidate node with the current seed node, and calculate the average final opinion value after the replacement. Total cost ; Step A3: Set the opinion effect protection threshold and cost optimization threshold If the following conditions are met: ≤ ,and ; Then the candidate node is included in the valid candidate set, where The average final opinion value before the replacement; Select the total cost for the seed node before replacement; otherwise, do not include it in the valid candidate set. Step A4: From the valid candidate set corresponding to each seed node, select the one that maximizes the total cost. The candidate node with the largest reduction is selected as the optimal replacement node, and the replacement iteration optimization is performed.

6. The method for maximizing opinions on a social network according to claim 5, characterized in that, The execution probability of the two-hop neighbor cost optimization local search operator is preset to 0.6, and the opinion effect protection threshold is... The preset cost optimization threshold is 20%. The default setting is 40%.

7. The method for maximizing opinions on social networks according to claim 1, characterized in that, In step S3, when outputting a set of Pareto optimal solutions, the following steps are included: A dual-objective stratification of the population is performed by non-dominantly ranking the population according to the effect of opinion propagation and the total cost. Individuals in the same stratum do not dominate each other, and individuals are divided into multiple non-dominant strata. Calculate the crowding degree of individuals within the same non-dominated hierarchy, and prioritize retaining sparsely distributed individuals; A binary tournament selection strategy based on non-dominated hierarchy and crowding degree is adopted. Each time, two individuals are randomly selected from the current parent population, and the non-dominated hierarchy of the two individuals is compared. If the non-dominated hierarchy of the two individuals is different, the individual with the better non-dominated hierarchy is selected; if the non-dominated hierarchy of the two individuals is the same, the individual with higher crowding degree is selected. This selection process is repeated until n individuals are selected as the parent population for crossover and mutation operations. The parent population is optimized for local search using a uniform crossover operator, a position-flipping mutation operator, and a two-hop neighbor cost to generate a child population. The child populations are then merged into a temporary population of size 2n. The new generation of parent population is selected again by non-dominated sorting and crowding calculation. The process is iterated until the preset number of iterations is reached, and a set of Pareto optimal solutions is obtained, which are used as the optimal seed node scheme containing multiple opinion-cost balances.

8. A system for maximizing opinions on a social network, characterized in that, The method for maximizing social network opinions according to any one of claims 1-7 includes: The initialization unit is configured to: model the social network and, based on the modeling results, construct an optimization problem with the dual objectives of maximizing the average final opinion value of the network and minimizing the total cost of seed node selection; The optimization unit is configured to: construct a multi-objective evolutionary optimization framework, which includes: a population initialization method based on a hybrid strategy, construct an evolutionary operator for the optimization problem, and an iterative optimization mechanism that combines cost-optimized local search; The output unit is configured to iteratively optimize the population using the non-dominated sorting genetic algorithm NSGA-II framework, combined with the multi-objective evolutionary optimization framework, to output a set of Pareto optimal solutions, which serve as the optimal seed node scheme containing multiple opinion-cost balances.

9. An electronic device, characterized in that, The electronic device includes: At least one processor; and, The memory is communicatively connected to the at least one processor; wherein, The memory stores instructions that can be executed by the at least one processor to enable the at least one processor to perform the method for maximizing social network opinions as described in any one of claims 1 to 7.

10. A non-transitory computer-readable storage medium, characterized in that, The non-transitory computer-readable storage medium stores computer instructions for causing the computer to perform the method of maximizing social network opinions as described in any one of claims 1 to 7.

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