A method for maximizing social network influence based on discrete spider monkey optimization

Abstract

This paper discloses an influence maximization method based on discrete spider monkey optimization. This method constructs a fitness function using the EDV value as the optimization objective. The spider monkey population is iteratively optimized, primarily through a leadership phase involving local and global leaders, a learning phase for the local and global leaders, and a decision phase for the local and global leaders, to iteratively search for the optimal set of seed nodes. While ensuring the accuracy of the selected seed node set, the method can be efficiently expanded to large-scale and high-density social networks, demonstrating its effectiveness, efficiency, and robustness in solving the influence maximization problem.

Description

Technical Field

[0001] The present invention belongs to the technical field of information dissemination in social networks, and in particular relates to an influence maximization method based on discrete spider monkey optimization. Background Art

[0002] The rapid development of the internet has made online social networks (such as Weibo and Facebook) essential platforms for people to access and exchange information. Due to their core characteristics of immediacy, openness, multimedia integration, and explosive dissemination, the popularity of online social networks has posed a series of opportunities and challenges. On the one hand, a growing number of businesses are targeting high-influence online users for online product marketing, thereby enhancing brand effectiveness. On the other hand, the rapid and widespread spread of false and counterintuitive statements on social networks can easily cause social panic and instability. To control the spread of this malicious propaganda, the government and relevant departments are directing high-influence online users to promote positive and truthful information.

[0003] Under limited budgets, businesses and government agencies alike focus on selecting a small number of the most influential user nodes to maximize the spread of product and positive information within the network. This practical need raises a new problem: how to select a specified set of the most influential seed nodes as the initial disseminators of information, thereby achieving the greatest possible reach within the social network. Researchers have defined this as the influence maximization problem and proposed various solutions, among which greedy and heuristic algorithms have proven to be effective. However, with increasingly complex, diverse, and large-scale social networks, greedy algorithms with high time complexity and heuristic algorithms that rely heavily on network structure are no longer suitable. Summary of the Invention

[0004] The purpose of the present invention is to provide an influence maximization method based on discrete spider monkey optimization to solve the technical problem that the influence maximization method in the prior art cannot be effectively and efficiently applied to diverse large-scale social networks.

[0005] In order to achieve the above object, the present invention adopts the following technical solutions:

[0006] An influence maximization method based on discrete spider monkey optimization includes the following steps:

[0007] Step 1: According to the information propagation rule of the independent cascade model, the calculation of the EDV value is selected as the optimization target and the fitness function is constructed;

[0008] Step 2: Based on the characteristics of the influence maximization problem, a discrete spider monkey individual representation function is constructed and the node replacement strategy in the spider monkey individual update is optimized;

[0009] Step 3: According to the calculation characteristics of EDV values, construct an EDV-based spider monkey individual initialization method;

[0010] Step 4: Select the calculation of EDV value as the fitness function of the optimization target, and calculate the fitness function value of a single spider monkey individual in the initialized spider monkey population;

[0011] Step 5: Iterative optimization process of spider monkey population:

[0012] The individual with the maximum value in the group is called the local leader LL of the group, and the individual with the maximum value among all individuals is called the global leader GL of the population;

[0013] Step 5.1: Local leader leadership phase: Based on the local leader LL of the group and another random spider monkey in the same group , update each individual in the spider monkey population;

[0014] Step 5.2: Global leader leadership phase: Based on the global leader GL of the population and another random spider monkey in the same group Update every individual in the spider monkey population;

[0015] Step 5.3: Local leader learning phase: Update the local leader LL of each group based on the current best individual in the group;

[0016] Step 5.4: Global leader learning phase: Update the global leader GL of the spider monkey population based on the best individual among all the current local leaders LL in the spider monkey population;

[0017] Step 5.5: Local leader decision phase: Based on the number of unupdated times corresponding to each local leader LL, decide whether to redirect all spider monkey individuals in the group based on two different rules, intercepting and retaining the global optimal individual information;

[0018] Step 5.6: Global leader decision phase: According to the number of unupdated global leaders GL in the spider monkey population and the number of current groups, the population is divided into groups or reorganized groups;

[0019] After the specified number of iterations T, the global leader GL in the spider monkey population is returned and used as the target solution.

[0020] In the above technical solution, in step 1, the calculation of the EDV value is selected as the optimization target, and the fitness function formula constructed is expressed as follows:

[0021] In the formula, S represents the seed node set, k represents the size of the seed node set, represents the union of the out-degree neighbor nodes of all nodes in the set S, E represents the set of all edges in the social network, It represents the probability of information propagation on the edge (u, v) in the network, that is, the possibility of information being transmitted from node u to node v.

[0022] In the above technical solution, in step 2, the discrete spider monkey individual representation function is a k-dimensional non-repeating integer vector, which is expressed as follows: Where N represents the size of the spider monkey population, k represents the size of the seed node set, (j=1,2,...,k) represents the node id in a given social network.

[0023] In the above technical solution, in step 2, the node replacement strategy in the spider monkey individual update includes a single-node greedy replacement strategy and a full-node greedy replacement strategy.

[0024] In the above technical solution, in step 3, the individual initialization method based on EDV specifically includes the following steps:

[0025] Step 3.1: Calculate the EDV value of each node in the network and select the first k nodes with the largest EDV value as the initial vector ;

[0026] Step 3.2: Replace with any node in the node set V with a probability of 0.5 For each node in, get the first initialized individual ;

[0027] Step 3.3: Repeat step 3.2 until the initialization of N spider monkey individuals is completed.

[0028] In the above technical solution, the step 5.1 local leader leadership phase specifically includes the following steps: based on the local leader LL of the group to which it belongs and another randomly selected spider monkey in the same group For each spider monkey Perform individual vector updates;

[0029] For each individual , first use The function randomly generates a probability between 0 and 1. If the generated probability is greater than the given interference rate pr, the node search space is calculated using the following formula : Where LL represents individual Local leader of the group to which they belong, and are two random values ​​uniformly distributed between 0 and 1, used to refer to the proportion of selected nodes, symbol " " indicates the difference operation between two sets, and the symbol " " indicates that two sets are unioned; according to the above formula, Considered as an updated individual The required node search space is then used to complete the individual update based on the node replacement strategy in the spider monkey individual update in step 2;

[0030] The step 5.2 global leader leadership phase specifically includes the following steps:

[0031] Based on the global leader GL of the population and another randomly selected spider monkey from the same group For each spider monkey Perform individual vector updates;

[0032] For each individual , first calculate according to the following formula The probability of being updated at this stage ; In the formula Represents an individual The corresponding fitness value, express The fitness value of the best individual in the group; then, use The function randomly generates a probability between 0 and 1. If the generated probability is less than or equal to , then the node search space is calculated using the following formula : Where GL represents the global leader of the spider monkey population; according to the above formula, Considered as an updated individual The required node search space is then used to complete the individual update based on the node replacement strategy in the spider monkey individual update in step 2.

[0033] In the above technical solution, the step 5.3 local leader learning phase specifically includes the following steps: first, recalculate the fitness function values ​​of all individuals, and identify the individual with the maximum value in each group based on the calculated values. ; then compare And the fitness function value of the corresponding group local leader LL, if the former is greater, the local leader of the current group is updated to , and reset the number of unupdated times of the current local leader is 0; otherwise, keep the local leader LL unchanged, and Increase 1; the step 5.4 global leader learning phase specifically includes the following steps: first, identify the individual with the maximum fitness value from all local leaders LL , then compare and the fitness function value of the global leader GL. If the former is greater, the global leader of the current spider monkey population is updated to , and reset the number of unupdated times of the global leader is 0, otherwise, keep GL unchanged and Add 1.

[0034] In the above technical solution, the step 5.5 local leader decision-making stage specifically includes the following steps:

[0035] Determine the corresponding Has the given local leader not been updated for a certain number of times? If so, redirect all spider monkeys in the group. Determine the current redirected individual. Is it the global leader GL? If so, skip the redirection update operation for the individual to retain the optimal individual information; if not, use The function randomly generates a probability between 0 and 1, compares the generated probability with the given interference rate pr, and redirects the individual , get a new individual .

[0036] In the above technical solution, step 5.6, the global leader decision-making stage, specifically includes the following steps:

[0037] Determine the number of times the global leader has not been updated Has the given global leader's unupdated times limit GLL been exceeded? If so, the population is grouped or reorganized, and Reset to 0. If the current number of groups g exceeds the given maximum number of groups MG, all spider monkey individuals are reorganized into 1 group. Otherwise, all spider monkey individuals are divided into (g+1) groups. After T rounds of iterative optimization, the global leader GL is obtained. All nodes contained in the global leader GL are the selected optimal seed node set. In the above technical solution, in step 5, before the iterative optimization of the spider monkey population, the number of groups of the population is initialized to 1.

[0038] Compared with existing technologies, the present invention offers significant advantages: It uses the expected diffusion value (EDV) as the optimization objective and iteratively searches for the optimal set of seed nodes through a series of steps, including a leadership phase involving local and global leaders, a learning phase involving local and global leaders, and a decision phase involving local and global leaders. The proposed method has the following features: First, its EDV-based population initialization method accelerates convergence to the optimal solution. Second, the method considers the update direction of individual spider monkeys from multiple perspectives, including the local leader, the global leader, random members of the same group, and neighboring nodes with high values. Furthermore, the spider monkey optimization method's unique grouping and reorganization mechanism increases the diversity of group members, further enhancing the diversity of the solution search directions. Third, the method's alternating use of a two-node greedy replacement strategy and an interception and retention method to prevent information decay among optimal individuals accelerates the overall convergence of the algorithm.

[0039] Experimental results show that, under the premise that the accuracy of the selected seed node set is guaranteed, the method of the present invention can be efficiently expanded to large-scale and high-density social networks, demonstrating the effectiveness, efficiency and high robustness of the method of the present invention in solving the problem of maximizing influence. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 1 is a flow chart of the influence maximization method for discrete spider monkey optimization of the present invention;

[0041] Figure 2 This is a schematic diagram of the spider monkey population initialization method based on EDV;

[0042] Figure 3 This is a schematic diagram of a single-node greedy replacement strategy;

[0043] Figure 4 This is a schematic diagram of the method of redirecting a spider monkey individual during the local leader decision-making stage;

[0044] Figure 5 This is a schematic diagram of the greedy replacement strategy of all nodes;

[0045] FIG6 (a) is a comparison diagram of the EDV value of the method of the present invention and three swarm intelligence algorithms in the ego-Facebook network;

[0046] FIG6( b ) is a comparison diagram of the EDV value of the method of the present invention and three swarm intelligence algorithms in the wiki-Vote network;

[0047] FIG6 (c) is a comparison result of the method of the present invention and three swarm intelligence algorithms on EDV value in the feather-lastfm-social network;

[0048] FIG6 (d) is a comparison diagram of the EDV value of the method of the present invention and three swarm intelligence algorithms in the feather-deezer-social network;

[0049] FIG7 (a) is a comparison result of the running time of the method of the present invention and three swarm intelligence algorithms in the ego-Facebook network;

[0050] FIG7( b ) is a graph showing the comparison of the running time of the method of the present invention and three swarm intelligence algorithms in the Wiki-Vote network;

[0051] FIG7 (c) is a comparison result of the running time of the method of the present invention and three swarm intelligence algorithms in the feather-lastfm-social network;

[0052] FIG7( d ) is a graph showing the comparison of the running time of the method of the present invention and three swarm intelligence algorithms in the feather-deezer-social network;

[0053] FIG8 (a) is a comparison diagram of the influence propagation range of the method of the present invention and four traditional algorithms in the ego-Facebook network;

[0054] FIG8( b ) is a comparison diagram of the influence propagation range of the method of the present invention and four traditional algorithms in the Wiki-Vote network;

[0055] FIG8 (c) is a comparison diagram of the influence propagation range of the method of the present invention and four traditional algorithms in the feather-lastfm-social network;

[0056] FIG8( d ) is a graph showing the comparison of the influence propagation range of the method of the present invention and four traditional algorithms in the feather-deezer-social network;

[0057] Figure 9 This is a comparison chart of the running time between the method of the present invention and four traditional algorithms. DETAILED DESCRIPTION

[0058] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.

[0059] like Figure 1 As shown, a method for maximizing influence based on discrete spider monkey optimization includes the following steps:

[0060] Step 1: According to the information propagation rule of the independent cascade model, the calculation of the EDV value is selected as the optimization target and the fitness function is constructed;

[0061] Step 2: Based on the characteristics of the influence maximization problem, a discrete spider monkey individual representation function is constructed and the node replacement strategy in the spider monkey individual update is optimized;

[0062] Step 3: According to the calculation characteristics of EDV values, construct an EDV-based spider monkey individual initialization method;

[0063] Step 4: Select the calculation of EDV value as the fitness function of the optimization target, and calculate the fitness function value of a single spider monkey individual in the initialized spider monkey population;

[0064] Step 5: Iterative optimization process of spider monkey population:

[0065] The individual with the maximum value in the group is called the local leader LL of the group, and the individual with the maximum value among all individuals is called the global leader GL of the population;

[0066] Step 5.1: Local leader leadership phase: Based on the local leader LL of the group and another random spider monkey in the same group , update each individual in the spider monkey population;

[0067] Step 5.2: Global leader leadership phase: Based on the global leader GL of the population and another random spider monkey in the same group Update every individual in the spider monkey population;

[0068] Step 5.3: Local leader learning phase: Update the local leader LL of each group based on the current best individual in the group;

[0069] Step 5.4: Global leader learning phase: Update the global leader GL of the spider monkey population based on the best individual among all the current local leaders LL in the spider monkey population;

[0070] Step 5.5: Local leader decision phase: Based on the number of unupdated times corresponding to each local leader LL, decide whether to redirect all spider monkey individuals in the group based on two different rules, intercepting and retaining the global optimal individual information;

[0071] Step 5.6: Global leader decision phase: According to the number of unupdated global leaders GL in the spider monkey population and the number of current groups, the population is divided into groups or reorganized.

[0072] After the specified number of iterations T, the global leader GL in the spider monkey population is returned and used as the target solution.

[0073] This embodiment will introduce the details of each step in detail according to the order of the steps of the above method.

[0074] In step 1, the independent cascade model is a classic information propagation model, often used to describe the propagation rules of information in social networks. It has the following characteristics: in social networks, the initially activated set of seed nodes is activated first; each newly activated node has only one chance to try to activate its unactivated neighbor nodes with an independent probability preset for each edge at the next moment after its activation (for example, if multiple neighbor nodes of node v are activated at the same time, its probability of being activated is 1 minus the probability of all unsuccessful activations); this process is iterated round by round until the propagation stops when no new nodes are activated.

[0075] Based on the independent cascade model, the EDV (Expected Diffusion Value) value is used to quantify the influence spread of a given seed node set. This method analyzes the combined influence spread capabilities of the node set's first-order neighbors. When the probability of information diffusion is low, the calculated EDV value can accurately estimate the influence spread of a given node set.

[0076] In step 1, the calculation of the EDV value is selected as the optimization target, and the fitness function formula constructed is expressed as follows: In the formula, S represents the seed node set, k represents the size of the seed node set, represents the union of the out-degree neighbor nodes of all nodes in the set S, E represents the set of all edges in the social network, It represents the probability of information propagation on the edge (u, v) in the network, that is, the possibility of information being transmitted from node u to node v.

[0077] In step 2, the discrete spider monkey individual representation function is a k-dimensional non-repeating integer vector, which is expressed as follows: Where N represents the size of the spider monkey population, k represents the size of the seed node set, (j=1,2,...,k) represents the node id in a given social network.

[0078] The node replacement strategy in step 2 includes a single node greedy replacement strategy and a full node greedy replacement strategy. The difference between these two node replacement strategies is as follows: When the single node greedy replacement strategy only needs to greedily replace the individual according to the given node search space X A random node in the, and the full node greedy replacement strategy needs to greedily replace the individual according to the given node search space X The alternating use of these two node replacement strategies effectively balances the convergence speed and running time of the proposed algorithm.

[0079] In a specific embodiment: given the target seed node set size k, the spider monkey population size N and the social network G = (V, E), the spider monkey population is initialized based on the calculation of the EDV value. ,like Figure 2 shown.

[0080] The individual initialization method based on EDV in step 3 is described as follows:

[0081] Step 3.1: Calculate the EDV value of each node in the network and select the first k nodes with the largest EDV value as the initial vector ;

[0082] Step 3.2: Replace with any node in the node set V with a probability of 0.5 For each node in, get the first initialized individual ;

[0083] Step 3.3: Repeat step 3.2 until the initialization of N spider monkey individuals is completed.

[0084] Step 4: Select the EDV value calculation as the fitness function for the optimization objective, and calculate the fitness function value of each spider monkey individual in the initialized spider monkey population. The individual with the maximum value in each group is called the local leader LL of that group, and the individual with the maximum value among all individuals is called the global leader GL of the population. Therefore, when the number of groups is 1, LL is equal to GL. That is, in step 5, before the iterative optimization of the spider monkey population, the number of groups in the initial population is 1.

[0085] Initialize the number of times each group's local leader is not updated 0, the global leader of the initialized population has not been updated is 0.

[0086] Given the number of optimization iterations T, the initialized spider monkey population is subjected to T rounds of evolution. The specific steps of each round of evolution are as follows: Step 5.1, enter the local leader leadership phase, based on the LL of the group to which it belongs and another random spider monkey in the same group Update each individual in the spider monkey population. LL guides the individual to optimize towards the local optimal direction, while Further increase the diversity of solutions.

[0087] Step 5.1.1, for each individual , first use The function randomly generates a probability between 0 and 1. If the generated probability is greater than the given interference rate pr, the node search space is calculated using the following formula : Where LL represents individual Local leader of the group to which they belong; and are two random values ​​uniformly distributed between 0 and 1, used to refer to the proportion of selected nodes. The symbol " " indicates that two sets are subjected to a difference operation, while the symbol " "Indicates the union operation of two sets.

[0088] Step 5.1.2, the As an updated individual The required node search space is then used to complete the individual update based on the single-node greedy replacement strategy, such as Figure 3 .

[0089] The detailed steps are as follows: First, randomly select an integer r in [0, k-1]. Second, Randomly select a node to replace the individual The rth node in the equation gets the new solution vector Then, judge Is the fitness value better than If yes, keep , and then continue to select replacement nodes. Until the new solution obtained after replacement does not improve the fitness value, the node replacement process ends and the updated new individual is obtained .

[0090] Step 5.2, enter the global leader leadership stage, based on the GL of the population and another random spider monkey in the same group Update each individual in the spider monkey population. GL guides the individual to optimize towards the global optimal direction, while Further increase the diversity of solutions.

[0091] Step 5.2.1, for each individual , first calculate according to the following formula The probability of being updated at this stage The larger the calculated probability, the more likely the individual is to be updated. When an individual no longer has further opportunities for improvement in its group, it will tend to explore new solutions towards the global optimal direction.

[0092] In the formula Represents an individual The corresponding fitness value, express The fitness value of the best individual in the group.

[0093] Step 5.2.2, use The function randomly generates a probability between 0 and 1. If the generated probability is less than or equal to , then the node search space is calculated using the following formula : Where GL represents the global leader of the spider monkey population.

[0094] Step 5.2.3, the As an updated individual The required node search space is then used to complete the individual update based on the single-node greedy replacement strategy mentioned in step 5.1.2.

[0095] Recalculate the fitness function value of each spider monkey.

[0096] Step 5.3, enter the local leader learning phase, and update the local leader LL of each group based on the current best individual in the group. First, identify the individual with the largest fitness value in each group. Then compare and the fitness function value of the corresponding group local leader LL. If the former is greater, the local leader LL of the current group is updated to , and reset the number of unupdated times of the current local leader is 0. Otherwise, keep LL unchanged and Add 1.

[0097] Step 5.4, enter the global leader learning phase, and update the GL of the spider monkey population based on the best individual among all the current local leaders in the spider monkey population. First, identify the individual with the largest fitness value from all LLs. , then compare and the fitness function value of the global leader GL. If the former is greater, the global leader of the current spider monkey population is updated to , and reset the number of unupdated times of the global leader is 0. Otherwise, keep GL unchanged and Add 1.

[0098] Step 5.5, enter the local leader decision stage, determine the corresponding Has the given local leader's unupdated times limit LLL been exceeded? If so, redirect all spider monkey individuals in the group. To avoid the attenuation of the optimal individual information of the spider monkey population, the global optimal individual is intercepted before the update operation is performed on each spider monkey to be redirected, and the redirection update of this individual is skipped. The method of redirecting a spider monkey individual in the local leader decision stage is as follows: Figure 4 As shown, the specific steps include:

[0099] Step 5.5.1, determine the current redirection individual Whether it is the global leader GL.

[0100] Step 5.5.2: If yes, skip the redirection update operation for the individual, thereby retaining the optimal individual information.

[0101] Step 5.5.3, if not, use The function randomly generates a probability between 0 and 1. Comparing the generated probability with the given interference rate pr, the individual is redirected with the following two strategies , get a new individual .

[0102] Strategy 1: If the generated probability is less than pr, redirect based on GL and the LL of the group to which it belongs.

[0103] First, get the spider monkey according to the following formula Node search space . Where GL represents the global leader of the spider monkey population, and LL represents the individual Local leader of the group to which they belong, and are two random values ​​uniformly distributed between 0 and 1, used to refer to the proportion of selected nodes. The symbol " "Indicates the difference operation between two sets.

[0104] Will get As an updated individual The required node search space is then used to complete the individual update based on the full-node greedy replacement strategy, such as Figure 5 The detailed steps are as follows: (1) For Each node in A node is randomly selected to replace the node. (2) If the new vector obtained after replacement The fitness function value ratio If the Updated to , and enter the (3)Otherwise, continue from Randomly select a node to replace the node and find a better value. If no better vector solution is obtained for the nodes in (4)Repeat steps (1) to (3) until the individual All nodes in the update.

[0105] Strategy 2: If the generated probability is greater than pr, then The first k nodes with the highest degree values ​​among all the out-degree neighbor nodes of the contained nodes are selected as new individuals.

[0106] Step 5.6: Enter the global leader decision phase and determine the number of times the global leader has not been updated. Has the given global leader not updated the number of times limit GLL been exceeded? If so, the population is grouped or reorganized, and Reset to 0. If the current number of groups g exceeds the given maximum number of groups MG, all spider monkey individuals are reorganized into 1 group. Otherwise, all spider monkey individuals are divided into (g+1) groups. Since the number of groups has changed, the number of times the local leader of all current groups has not been updated must be set to 0.

[0107] After T rounds of iterative optimization, the global leader GL is obtained and the entire algorithm ends. All nodes included in GL are the optimal seed node set selected by the algorithm of the present invention.

[0108] In order to analyze the feasibility and effectiveness of the present invention, the following experiments were conducted.

[0109] In this experiment, there are four datasets, all of which are public datasets from Stanford University. Each dataset is extracted from a real social network. The detailed data information is shown in Table 1:

[0110] Table 1: Feature statistics of 4 experimental datasets

[0111]

[0112] The comparison algorithms used in this experiment include three swarm intelligence optimization algorithms, namely, discrete particle swarm optimization algorithm (DPSO), discrete hybrid frog leaping algorithm (DSFLA) and discrete Harry Hawk optimization algorithm (DHHO); and also include four traditional influence maximization algorithms, namely, greedy algorithm CELF, heuristic algorithm DEGREE, PMIA and IMRank algorithm.

[0113] After parameter sensitivity analysis, the relevant parameters in the present invention are set as follows: spider monkey population size N=20, interference rate pr=0.1, local leader unupdated number limit LLL=3, global leader unupdated number limit GLL=5, maximum group number MG=5, and number of iterations T=100.

[0114] The algorithm evaluation criteria used in this embodiment include EDV value, running time and influence propagation range, which are respectively used to evaluate the global optimization ability, efficiency and effectiveness of the algorithm in solving the influence maximization problem. In addition, experiments were conducted on four different types of data sets to evaluate the robustness of the algorithm. Due to different seed node set selection strategies, this embodiment divides the comparison algorithms into two categories and compares them with the algorithm DSMO of the present invention. The first category is the comparison of the algorithm of the present invention with three swarm intelligence optimization algorithms (i.e., DPSO, DSFLA, DHHO) in terms of optimized EDV value and running time. The experimental results are shown in Figures 6 (a), 6 (b), 6 (c), 6 (d) and Figures 7 (a), 7 (b), 7 (c), 7 (d); the second category is the comparison of the algorithm of the present invention with four traditional influence maximization algorithms (i.e., CELF, DEGREE, PMIA, IMRank) in terms of influence propagation range and running time. The experimental results are shown in Figures 8 (a), 8 (b), 8 (c), 8 (d), and Figure 9 In the first type of experiment, each algorithm was executed 100 times, and the average value was taken as the experimental result. In the second type of experiment, the Monte Carlo simulation method based on the independent cascade model was used to calculate the influence propagation range of the seed node set selected by each algorithm. In order to evaluate the accuracy of the results, the number of Monte Carlo simulations was set to 20,000.

[0115] In comparisons with three swarm intelligence optimization algorithms on four different datasets, the algorithm of the present invention was able to achieve the optimal EDV value in a relatively short time in all datasets, demonstrating that the algorithm of the present invention effectively avoids local optimal solutions in solving the influence maximization problem and has good global optimization capabilities. In comparisons with four traditional influence maximization algorithms on four different datasets, the algorithm of the present invention was able to achieve a larger influence propagation range in a relatively short time in all datasets, demonstrating the effectiveness, efficiency, and high robustness of the algorithm of the present invention in solving the influence maximization problem.

[0116] In summary, the DSMO algorithm of the present invention can effectively and efficiently handle the influence maximization problem in larger-scale and more complex social networks.

Claims

1. A method for maximizing social network influence based on discrete spider monkey optimization, characterized in that: The following steps are involved: Step 1: According to the information propagation rule of the independent cascade model, the calculation of the EDV value is selected as the optimization target and the fitness function is constructed; Step 2: Based on the characteristics of the influence maximization problem, a discrete spider monkey individual representation function is constructed and the node replacement strategy in the spider monkey individual update is optimized; Step 3: According to the calculation characteristics of EDV values, construct an EDV-based spider monkey individual initialization method; Step 4: Select the calculation of EDV value as the fitness function of the optimization target, and calculate the fitness function value of a single spider monkey individual in the initialized spider monkey population; Step 5: Iterative optimization process of spider monkey population: The individual with the maximum value in the group is called the local leader LL of the group, and the individual with the maximum value among all individuals is called the global leader GL of the population; Step 5.1: Local leader leadership phase: Based on the local leader LL of the group and another random spider monkey in the same group , update each individual in the spider monkey population; Step 5.2: Global leader leadership phase: Based on the global leader GL of the population and another random spider monkey in the same group Update every individual in the spider monkey population; Step 5.3: Local leader learning phase: Update the local leader LL of each group based on the current best individual in the group; Step 5.4: Global leader learning phase: Update the global leader GL of the spider monkey population based on the best individual among all the current local leaders LL in the spider monkey population; Step 5.5: Local leader decision phase: Based on the number of unupdated times corresponding to each local leader LL, decide whether to redirect all spider monkey individuals in the group based on two different rules, intercepting and retaining the global optimal individual information; Step 5.6: Global leader decision phase: According to the number of unupdated global leaders GL in the spider monkey population and the number of current groups, the population is divided into groups or reorganized groups; After the specified number of iterations T, the global leader GL in the spider monkey population is returned and used as the target solution; In step 1, the calculation of the EDV value is selected as the optimization target, and the fitness function formula constructed is expressed as follows: ; Where S represents the seed node set, k represents the size of the seed node set, represents the union of the out-degree neighbor nodes of all nodes in the set S, E represents the set of all edges in the social network, Represents the probability of information propagation on the edge (u, v) in the network, that is, the possibility of information being transmitted from node u to node v; In step 2, the discrete spider monkey individual representation function is a k-dimensional non-repeating integer vector, which is expressed as follows: ; Where N represents the size of the spider monkey population, k represents the size of the seed node set, represents a node in a given social network, j=1,2,...,k.

2. The method for maximizing social network influence based on discrete spider monkey optimization according to claim 1, characterized in that: In step 2, the node replacement strategy in the spider monkey individual update includes a single-node greedy replacement strategy and a full-node greedy replacement strategy.

3. The method for maximizing social network influence based on discrete spider monkey optimization according to claim 1, characterized in that: In step 3, the individual initialization method based on EDV specifically includes the following steps: Step 3.1: Calculate the EDV value of each node in the network and select the first k nodes with the largest EDV value as the initial vector ; Step 3.2: Replace with any node in the node set V with a probability of 0.5 For each node in, get the first initialized individual ; Step 3.3: Repeat step 3.2 until the initialization of N spider monkey individuals is completed.

4. The method for maximizing social network influence based on discrete spider monkey optimization according to claim 1, characterized in that: The step 5.1 local leader leadership phase specifically includes the following steps: based on the local leader LL of the group to which it belongs and another randomly selected spider monkey in the same group For each spider monkey Perform individual vector update; for each individual , first use The function randomly generates a probability between 0 and 1. If the generated probability is greater than the given interference rate pr, the node search space is calculated using the following formula : ; In the formula, LL represents individual Local leader of the group to which they belong, and are two random values ​​uniformly distributed between 0 and 1, used to refer to the proportion of selected nodes, symbol " " indicates the difference operation between two sets, and the symbol " " indicates that two sets are unioned; according to the above formula, Considered as an updated individual The required node search space is then used to complete the individual update based on the node replacement strategy in the spider monkey individual update in step 2; The step 5.2 global leader leadership phase specifically includes the following steps: Based on the global leader GL of the population and another randomly selected spider monkey from the same group For each spider monkey Perform individual vector updates; For each individual , first calculate according to the following formula The probability of being updated at this stage ; Where, Represents an individual The corresponding fitness value, express The fitness value of the best individual in the group; then, use The function randomly generates a probability between 0 and 1. If the generated probability is less than or equal to , then the node search space is calculated using the following formula : ; Where GL represents the global leader of the spider monkey population; According to the above formula, Considered as an updated individual The required node search space is then used to complete the individual update based on the node replacement strategy in the spider monkey individual update in step 2.

5. The method for maximizing social network influence based on discrete spider monkey optimization according to claim 1, characterized in that: The step 5.3 local leader learning phase specifically includes the following steps: first, recalculate the fitness function values ​​of all individuals, and identify the individual with the maximum value in each group based on the calculated values. ; then compare And the fitness function value of the corresponding group local leader LL, if the former is greater, the local leader of the current group is updated to , and reset the number of unupdated times of the current local leader is 0; otherwise, keep the local leader LL unchanged, and Add 1; The step 5.4 global leader learning phase specifically includes the following steps: first, identify the individual with the maximum fitness value from all local leaders LL , then compare and the fitness function value of the global leader GL. If the former is greater, the global leader of the current spider monkey population is updated to , and reset the number of unupdated times of the global leader is 0, otherwise, keep GL unchanged and Add 1.

6. The method for maximizing social network influence based on discrete spider monkey optimization according to claim 1, characterized in that: The local leader decision-making stage in step 5.5 specifically includes the following steps: Determine the corresponding Whether the given local leader has exceeded the limit value LLL of the number of times it has not been updated; if so, redirect all spider monkey individuals in the group; Determine the current redirection individual Whether it is the global leader GL; If yes, skip the redirection update operation for the individual, thereby retaining the optimal individual information; If not, use The function randomly generates a probability between 0 and 1, compares the generated probability with the given interference rate pr, and redirects the individual , get a new individual .

7. The method for maximizing social network influence based on discrete spider monkey optimization according to claim 1, characterized in that: The global leader decision-making stage in step 5.6 specifically includes the following steps: Determine the number of times the global leader has not been updated Has the given global leader's unupdated times limit GLL been exceeded? If so, the population is grouped or reorganized, and Reset to 0. If the current number of groups g exceeds the given maximum number of groups MG, all spider monkey individuals are reorganized into 1 group. Otherwise, all spider monkey individuals are divided into (g+1) groups. After T rounds of iterative optimization, the global leader GL is obtained. All nodes contained in the global leader GL are the selected optimal seed node set.

8. The method for maximizing social network influence based on discrete spider monkey optimization according to claim 1, characterized in that: In step 5, before iterative optimization of the spider monkey population, the number of groups in the population is initialized to 1.

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