Influence maximization method based on discrete spider monkey optimization

Abstract

The invention discloses a discrete spider monkey optimization-based influence maximization method, which is characterized in that a fitness function is constructed by taking an EDV value as an optimization target, and a spider monkey population iterative optimization process mainly comprises a leader stage of a local leader and a global leader; an optimal seed node set is iteratively searched through the steps of local leader and global leader learning stage, local leader and global leader decision-making stage and the like. On the premise that the precision of the selected seed node set is guaranteed, the method can be efficiently expanded to a large-scale and high-density social network, and the effectiveness, high efficiency and high robustness of the method in solving the problem of influence maximization are shown.

Description

Technical Field

[0001] The present invention belongs to the technical field of social network information dissemination, and particularly 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) an important platform for people to obtain and exchange information. Due to core features such as immediacy, openness, multimedia integration, and fission-like dissemination, the popularity of online social networks has brought a series of opportunities and challenges. On the one hand, more and more merchants market products online by selecting a part of highly influential network users, thereby enhancing the brand effect.

[0003] Under the limitation of a limited budget, whether for merchants or departments, they focus on selecting a small number of the most influential user nodes to maximize the dissemination of product information and positive information in the network. For this actual demand, a new problem has emerged: how to select a specified-size set of the most influential seed nodes as the initial disseminators of information to achieve the maximum influence dissemination range of this information in the social network. Researchers have defined it as the influence maximization problem and proposed various solutions. Among them, the greedy algorithm and heuristic algorithm perform excellently in solving the influence maximization problem. However, in the face of increasingly complex, diverse, and larger-scale social networks, the greedy algorithm with high time complexity and the heuristic algorithm that highly depends on the network structure are no longer applicable. 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 methods in the prior art cannot be effectively and efficiently applied to diverse large-scale social networks.

[0005] To achieve the above purpose, the present invention adopts the following technical solutions: An influence maximization method based on discrete spider monkey optimization, comprising the following steps: Step 1: According to the information dissemination rule of the independent cascade model, select the calculation of the EDV value as the optimization objective and construct a fitness function; Step 2: According to the characteristics of the influence maximization problem, construct a discrete spider monkey individual representation function and optimize the node replacement strategy in the update of spider monkey individuals; Step 3: According to the calculation characteristics of the EDV value, construct an initialization method for spider monkey individuals based on EDV; Step 4: Select the fitness function with the calculation of the EDV value as the optimization objective and calculate the fitness function value of each spider monkey individual in the initialized spider monkey population; Step 5: Spider Monkey Population Iterative Optimization Process: 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: Update each individual in the spider monkey population according to the local leader LL of the group and another random spider monkey in the same group ; Step 5.2: Global Leader Leadership Phase: Update each individual in the spider monkey population according to the global leader GL of the population and another random spider monkey in the same group ; Step 5.3: Local Leader Learning Phase: Update the local leader LL of each group according to the current optimal individual in the group; Step 5.4: Global Leader Learning Phase: Update the global leader GL of the spider monkey population according to the optimal individual among all the current local leaders LL in the spider monkey population; Step 5.5: Local Leader Decision Phase: Decide whether to redirect all spider monkey individuals in the affiliated group based on two different rules according to the number of unupdated times corresponding to each local leader LL, intercept and retain the global optimal individual information; Step 5.6: Global Leader Decision Phase: Make a decision on grouping or reorganizing the population according to the number of unupdated times of the global leader GL in the spider monkey population and the number of current groups; After a specified number of iterations T, return the global leader GL in the spider monkey population and use it as the target solution.

[0006] In the above technical solution, in step 1, the calculation of the EDV value is selected as the optimization objective, and the constructed fitness function formula is expressed as follows: In the formula, S represents the set of seed nodes, k represents the size of the set of seed nodes, 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 propagation probability of information on the edge (u, v) in the network, that is, the possibility of information being transmitted from node u to node v.

[0007] 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: In the formula, N represents the size of the spider monkey population, k represents the size of the set of seed nodes, (j = 1, 2,..., k) represents the node id in the given social network.

[0008] 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.

[0009] In the above technical solution, 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 values as the initial vectors ; Step 3.2: Replace each node in with any node in the node set V with a probability of 0.5 to obtain the first initialized individual ; Step 3.3: Repeat step 3.2 until the initialization of N spider monkey individuals is completed.

[0010] In the above technical solution, in the local leader leadership stage of step 5.1, it specifically includes the following steps: Based on the local leader LL of the affiliated group and another randomly selected spider monkey in the same group Update the individual vectors of each spider monkey ; For each individual , first use the function to randomly generate a probability between 0 and 1. If the generated probability is greater than the given interference rate pr, then calculate the node search space using the following formula : where LL represents the local leader of the group to which the individual belongs, and are two random values uniformly distributed between 0 and 1, used to represent the proportion of the selected nodes. The symbol " " represents the difference set operation between two sets, and the symbol " " represents the union set operation between two sets; the obtained according to the above formula is regarded as the node search space required to update the individual , and then complete the individual update based on the node replacement strategy in the spider monkey individual update in step 2; The global leader leadership stage of step 5.2 specifically includes the following steps: Based on the global leader GL of the population and another randomly selected spider monkey in the same group Update the individual vectors of each spider monkey ; For each individual , first calculate using the following formula, which is the probability of being updated in this stage ; In the formula represents an individual corresponding fitness value, represents the fitness value of the optimal individual in the group to which it belongs; then, use function to randomly generate a probability between 0 and 1. If the generated probability is less than or equal to , then calculate the node search space using the following formula: In the formula, GL represents the global leader of the spider monkey population; the obtained according to the above formula is regarded as the node search space required to update the individual , and then the individual update is completed based on the node replacement strategy in step 2 of the spider monkey individual update.

[0011] In the above technical solution, in the local leader learning stage of step 5.3, it 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 according to the calculated values ; then compare with the fitness function value of the local leader LL of the corresponding group. If the former value is larger, then update the local leader of the current group to , and reset the number of times the current local leader has not been updated to 0; otherwise, keep the local leader LL unchanged, and increment by 1; in the global leader learning stage of step 5.4, it specifically includes the following steps: First, identify the individual with the maximum fitness value from all local leaders LL , then compare with the fitness function value of the global leader GL. If the former value is larger, then update the global leader of the current spider monkey population to , and reset the number of times the global leader has not been updated to 0, otherwise, keep GL unchanged, and increment by 1.

[0012] In the above technical solution, in the local leader decision-making stage of step 5.5, it specifically includes the following steps: Judge whether the corresponding to each group has exceeded the given limit value LLL of the number of times the local leader has not been updated; if so, perform a redirection operation on all spider monkey individuals in the group; judge whether the current individual to be redirected is the global leader GL; if so, skip the redirection update operation on this 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 to obtain a new individual .

[0013] In the above technical solution, in the step 5.6 global leader decision-making stage, the following steps are specifically included: Judge the number of times the global leader has not been updated Whether it has exceeded the given global leader non-update times limit value GLL; if so, make a decision on grouping or recombination of the population, and reset to 0. If the current group number g exceeds the given maximum group number MG, then recombine all spider monkey individuals into 1 group, otherwise divide all spider monkey individuals into (g + 1) groups; after the T-round iterative optimization is completed, obtain the global leader GL, and all the nodes included in the global leader GL are the selected optimal seed node set. In the above technical solution, in the step 5, before the spider monkey population is iteratively optimized, the group number of the initialized population is 1.

[0014] Compared with the prior art, the beneficial effects of the present invention are as follows: The present invention takes the EDV (Expected Diffusion Value, the expected value of the propagation range size) value as the optimization goal, and mainly iteratively searches for the optimal seed node set through steps such as the leadership stage of the local leader and the global leader, the learning stage of the local leader and the global leader, and the decision-making stage of the local leader and the global leader. The constructed method includes the following characteristics: First, the initialization population method based on EDV of this algorithm accelerates the convergence of the optimal solution. Second, this method considers the update directions of spider monkey individuals from multiple perspectives, including local leaders, global leaders, random members in the same group, and neighbor nodes with high values. In addition, the unique grouping and recombination mechanism of the spider monkey optimization method improves the diversity of group members, further increasing the diversity of the solution search directions of this method. Third, the two node greedy replacement strategies used alternately in this method and the interception and retention method introduced to prevent the attenuation of the optimal individual information improve the convergence speed of the overall algorithm.

[0015] Experimental results show that: on the premise that the accuracy of the selected seed node set is guaranteed, the method of the present invention can be efficiently extended 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 influence maximization problem. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Figure 1 is a schematic flow chart of the method for maximizing influence by discrete spider monkey optimization of the present invention; Figure 2 is a schematic diagram of the initialization method of the spider monkey population based on EDV; Figure 3 It is a schematic diagram of the single-node greedy replacement strategy; Figure 4 It is a schematic diagram of the method for redirecting an individual spider monkey in the local leader decision-making stage; Figure 5 It is a schematic diagram of the full-node greedy replacement strategy; Figure 6(a) is a comparison result graph of the method of the present invention and three swarm intelligence algorithms for the EDV value in the ego-Facebook network; Figure 6(b) is a comparison result graph of the method of the present invention and three swarm intelligence algorithms for the EDV value in the wiki-Vote network; Figure 6(c) is a comparison result graph of the method of the present invention and three swarm intelligence algorithms for the EDV value in the feather-lastfm-social network; Figure 6(d) is a comparison result graph of the method of the present invention and three swarm intelligence algorithms for the EDV value in the feather-deezer-social network; Figure 7(a) is a comparison result graph of the method of the present invention and three swarm intelligence algorithms for the running time in the ego-Facebook network; Figure 7(b) is a comparison result graph of the method of the present invention and three swarm intelligence algorithms for the running time in the wiki-Vote network; Figure 7(c) is a comparison result graph of the method of the present invention and three swarm intelligence algorithms for the running time in the feather-lastfm-social network; Figure 7(d) is a comparison result graph of the method of the present invention and three swarm intelligence algorithms for the running time in the feather-deezer-social network; Figure 8(a) is a comparison result graph of the method of the present invention and four traditional algorithms for the influence propagation range in the ego-Facebook network; Figure 8(b) is a comparison result graph of the method of the present invention and four traditional algorithms for the influence propagation range in the wiki-Vote network; Figure 8(c) is a comparison result graph of the method of the present invention and four traditional algorithms for the influence propagation range in the feather-lastfm-social network; Figure 8(d) is a comparison result graph of the method of the present invention and four traditional algorithms for the influence propagation range in the feather-deezer-social network; Figure 9 It is a comparison result graph of the method of the present invention and four traditional algorithms in terms of running time. Detailed implementation manners

[0017] The present invention will be described in detail below with reference to the accompanying drawings and specific implementation manners.

[0018] As Figure 1 shown, an influence maximization method based on discrete spider monkey optimization includes the following steps: Step 1: According to the information propagation rule of the independent cascade model, select the calculation of the EDV value as the optimization objective, and construct a fitness function; Step 2: According to the characteristics of the influence maximization problem, construct a discrete spider monkey individual representation function and optimize the node substitution strategy in the update of spider monkey individuals; Step 3: According to the calculation characteristics of the EDV value, construct an initialization method of spider monkey individuals based on EDV; Step 4: Select the fitness function with the calculation of the EDV value as the optimization objective, and calculate the fitness function value of each individual spider monkey in the initialized spider monkey population; Step 5: Iterative optimization process of the 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 leading stage: According to 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 leading stage: According to the global leader GL of the population and another random spider monkey in the same group update each individual in the spider monkey population; Step 5.3: Local leader learning stage: Update the local leader LL of each group according to the current optimal individual in the group; Step 5.4: Global leader learning stage: Update the global leader GL of the spider monkey population according to the optimal individual among the current local leaders LL in the spider monkey population; Step 5.5: Local leader decision-making stage: According to the number of times of non-update corresponding to each local leader LL, decide whether to redirect all spider monkey individuals in the affiliated group based on two different rules, intercept and retain the global optimal individual information; Step 5.6: Global leader decision-making stage: According to the number of times of non-update of the global leader GL in the spider monkey population and the number of current groups, make a decision on grouping or recombination of the population; After a specified number of iterations T, return the global leader GL in the spider monkey population and use it as the target solution.

[0019] In this embodiment, the details of each step will be introduced in detail according to the step sequence of the above method.

[0020] In step 1, the independent cascade model is a classic information propagation model, which is often used to describe the propagation rules of information in social networks and has the following characteristics: in a social network, the initially activated set of seed nodes is first activated; at the next moment when each newly activated node is activated, it has only one chance to try to activate its unactivated neighbor nodes with a preset independent probability for each edge (for example, if multiple neighbor nodes of node v are activated simultaneously, the probability of its activation is 1 minus the probability of all unsuccessful activations); this process iterates round by round until the propagation stops when no new nodes are activated.

[0021] Based on the independent cascade model, the EDV (Expected Diffusion Value, the expected value of the propagation range size) value is used to quantify the influence propagation range of a given set of seed nodes. This method analyzes the comprehensive influence propagation ability of the first-order neighbors of the node set. When the information propagation probability is small, the calculated EDV value can accurately estimate the influence propagation range of the given node set.

[0022] In step 1, the calculation of the EDV value is selected as the optimization objective, and the constructed fitness function formula is expressed as follows: In the formula, S represents the set of seed nodes, k represents the size of the set of seed nodes, represents the union of the out-degree neighbor nodes of all nodes in set S, E represents the set of all edges in the social network, represents the propagation probability of information on the edge (u, v) in the network, that is, the possibility of information being transmitted from node u to node v.

[0023] In step 2, the discrete spider monkey individual representation function is a k-dimensional non-repeating integer vector, which is expressed as follows: In the formula, N represents the size of the spider monkey population, k represents the size of the set of seed nodes, (j = 1, 2,..., k) represents the node id in the given social network.

[0024] The node replacement strategies in step 2 include the single-node greedy replacement strategy and the full-node greedy replacement strategy. The differences between these two node replacement strategies are as follows: when updating a certain spider monkey individual , the single-node greedy replacement strategy only needs to greedily replace a random node in the individual according to the given node search space X, while the full-node greedy replacement strategy needs to greedily replace all nodes in 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.

[0025] 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.

[0026] The individual initialization method based on EDV in step 3 is described as follows: 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.

[0027] 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.

[0028] 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.

[0029] 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.

[0030] 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 affiliated group; and are two random values uniformly distributed between 0 and 1, used to represent the proportion of selected nodes. The symbol " " represents the difference operation between two sets, and the symbol " " represents the union operation between two sets.

[0031] Step 5.1.2, regard the obtained in Step 5.1.1 as the node search space required for updating the individual , and then complete the individual update according to the single-node greedy replacement strategy, as Figure 3 .

[0032] The detailed steps are as follows: First, randomly select an integer r in [0, k - 1]. Second, randomly select a node from to replace the r-th node in the individual , to obtain a new solution vector . Then, judge whether the fitness value of is better than the fitness value of . If so, retain , and 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.

[0033] Step 5.2, enter the global leader leading stage, and update each individual in the spider monkey population based on the GL of the population and another random spider monkey in the same group . GL guides the individual to optimize in the direction of the global optimum, while further increases the diversity of the solution.

[0034] Step 5.2.1, for each individual , first calculate the probability of being updated in this stage according to the following formula . The larger the calculated probability, the more likely the individual is to be updated. When the individual no longer has the opportunity to further improve in its affiliated group, it will tend to explore new solutions in the direction of the global optimum.

[0035] In the formula represents the fitness value corresponding to the individual , and represents the fitness value of the optimal individual in the group where

[0036] Step 5.2.2, use the function to randomly generate a probability between 0 and 1. If the generated probability is less than or equal to , the node search space is calculated using the following formula : In the formula, GL represents the global leader of the spider monkey population.

[0037] Step 5.2.3, use the obtained in Step 5.2.2 as the node search space required for updating the individual , and then complete the individual update based on the single-node greedy replacement strategy mentioned in Step 5.1.2.

[0038] Recalculate the fitness function value of each spider monkey.

[0039] Step 5.3, enter the local leader learning stage. According to the current optimal individual in the group, update the local leader LL of each group. First, identify the individual with the maximum fitness value in each group . Then compare with the fitness function value of the corresponding group local leader LL. If the former value is larger, update the local leader LL of the current group to , and reset the number of times the current local leader has not been updated to 0. Otherwise, keep LL unchanged, and increment by 1.

[0040] Step 5.4, enter the global leader learning stage. According to the optimal individual among all the current local leaders in the spider monkey population, update the GL of the spider monkey population. First, identify the individual with the maximum fitness value from all the LLs , and then compare with the fitness function value of the global leader GL. If the former value is larger, update the global leader of the current spider monkey population to , and reset the number of times the global leader has not been updated to 0. Otherwise, keep GL unchanged, and increment by 1.

[0041] Step 5.5, enter the local leader decision stage. Determine whether the corresponding to each group has exceeded the given local leader non-update times limit value LLL. If so, perform a redirection operation on all the spider monkey individuals in the group. To avoid the attenuation of the optimal individual information of the spider monkey population, intercept the global optimal individual before updating each spider monkey to be redirected, and skip the redirection update for this individual. The method of redirecting a certain spider monkey individual in the local leader decision stage is as shown in Figure 4 , and specifically includes the following steps: Step 5.5.1, determine the current individual to be redirected Whether it is the global leader GL.

[0042] Step 5.5.2: If yes, skip the redirection update operation for the individual, thereby retaining the optimal individual information.

[0043] 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 .

[0044] Strategy 1: If the generated probability is less than pr, redirect based on GL and the LL of the group to which it belongs.

[0045] 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.

[0046] 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.

[0047] Strategy 2: If the generated probability is greater than pr, then Select the top k nodes with the highest degree values among all the out-degree neighbor nodes of the included nodes as the new individuals.

[0048] Step 5.6, enter the global leader decision-making stage, and judge the number of times the global leader has not been updated Whether it has exceeded the given global leader non-update count limit value GLL. If so, make a decision on grouping or restructuring the population, and set Reset to 0. If the current number of groups g exceeds the given maximum number of groups MG, reorganize all spider monkey individuals into 1 group, otherwise divide all spider monkey individuals into (g + 1) groups. Since the number of groups has changed, finally, the number of times the local leaders of all current groups have not been updated also needs to be set to 0.

[0049] After the T-round iterative optimization is completed, the global leader GL is obtained, and the entire algorithm ends. All the nodes included in GL are the optimal seed node set selected by the algorithm of the present invention.

[0050] In order to analyze the feasibility and effectiveness of the present invention, the following experiments were conducted.

[0051] There are 4 data sets in this experiment, all of which belong to the public data sets of Stanford University. Each data set is extracted from a real social network, and the detailed data information is shown in Table 1: Table 1: Statistical table of the characteristics of 4 experimental data sets

[0052] The comparative algorithms used in this experiment include three swarm intelligence optimization algorithms, namely the discrete particle swarm optimization algorithm (DPSO), the discrete shuffled frog leaping algorithm (DSFLA), and the discrete harrier hawk optimization algorithm (DHHO); it also includes four traditional influence maximization algorithms, namely the greedy algorithm CELF, the heuristic algorithm DEGREE, PMIA, and the IMRank algorithm.

[0053] After parameter sensitivity analysis, the following settings are made for the relevant parameters in the present invention: the spider monkey population size N = 20, the interference rate pr = 0.1, the local leader non-update count limit value LLL = 3, the global leader non-update count limit value GLL = 5, the maximum number of groups MG = 5, and the number of iterations T = 100.

[0054] The algorithm evaluation criteria used in this embodiment include the EDV value, running time, and influence propagation range, which are used to evaluate the global optimization ability, efficiency, and effectiveness of the algorithm in solving the influence maximization problem. In addition, experiments are conducted on four different types of data sets to evaluate the robustness of the algorithm. Due to different seed node set selection strategies, the comparison algorithms in this embodiment are divided into two categories and compared with the algorithm DSMO of the present invention respectively. 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 optimizing the EDV value and running time. The experimental results are shown in FIGS. 6(a), 6(b), 6(c), 6(d) and FIGS. 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 influence propagation range and running time. The experimental results are shown in FIGS. 8(a), 8(b), 8(c), 8(d) and Figure 9 . In the first type of experiment, each algorithm is executed 100 times, and the average value is taken as the experimental result. In the second type of experiment, based on the Monte Carlo simulation method of the independent cascade model, the influence propagation range of the seed node set selected by each algorithm is calculated. And in order to evaluate the accuracy of the results, the number of Monte Carlo simulations is set to 20,000.

[0055] Among the results of comparison with three swarm intelligence optimization algorithms on four different data sets, the algorithm of the present invention can obtain the optimal EDV value in a shorter time in all data sets, which indicates that the algorithm of the present invention effectively avoids local optimal solutions in solving the influence maximization problem and has good global optimization ability. Among the results of comparison with four traditional influence maximization algorithms on four different data sets, the algorithm of the present invention can achieve a larger influence propagation range in a shorter time in all data sets, which indicates the effectiveness, efficiency, and high robustness of the algorithm of the present invention in solving the influence maximization problem.

[0056] 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. An influence maximization method based on discrete spider monkey optimization, characterized in that It includes the following steps: Step 1: According to the information propagation rule of the independent cascade model, select the calculation of the EDV value as the optimization objective and construct a fitness function; Step 2: According to the characteristics of the influence maximization problem, construct a discrete spider monkey individual representation function and optimize the node replacement strategy in the update of spider monkey individuals; Step 3: According to the calculation characteristics of the EDV value, construct an EDV-based spider monkey individual initialization method; Step 4: Select the fitness function with the calculation of the EDV value as the optimization objective and calculate the fitness function value of each individual spider monkey in the initialized spider monkey population; Step 5: Iterative optimization process of the 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 stage: Update each individual in the spider monkey population according to the local leader LL of the group and another random spider monkey in the same group , where; Step 5.2: Global leader leadership stage: Update each individual in the spider monkey population according to the global leader GL of the population and another random spider monkey in the same group Update each individual in the spider monkey population; Step 5.3: Local leader learning stage: Update the local leader LL of each group according to the current optimal individual in the group; Step 5.4: Global leader learning stage: Update the global leader GL of the spider monkey population according to the optimal individual among all current local leaders LL in the spider monkey population; Step 5.5: Local leader decision-making stage: According to the number of times the corresponding local leader LL has not been updated, decide whether to redirect all spider monkey individuals in the affiliated group based on two different rules, intercept and retain the global optimal individual information; Step 5.6: Global leader decision-making stage: Make a decision on grouping or restructuring the population according to the number of times the global leader GL in the spider monkey population has not been updated and the current number of groups; After the specified number of iterations T, return the global leader GL in the spider monkey population and use it as the target solution.

2. The influence maximization method based on discrete spider monkey optimization according to claim 1, wherein In the above Step 1, when selecting the calculation of the EDV value as the optimization objective, the formula of the constructed fitness function is expressed as follows: In the formula, S represents the set of seed nodes, k represents the size of the set of seed nodes, denotes the union of the out-degree neighbor nodes of all nodes in the set S, and E represents the set of all edges in the social network, represents the propagation probability of information on the edge (u, v) in the network, that is, the possibility of information being transmitted from node u to node v.

3. The influence maximization method based on discrete spider monkey optimization according to claim 1, characterized in that In the said step 2, the individual representation function of the discrete spider monkey is a k-dimensional non-repeating integer vector, which is represented as follows: In the formula, N represents the size of the spider monkey population, and k represents the size of the seed node set. (j = 1, 2,..., k) represents the node id in the given social network.

4. The influence maximization method based on discrete spider monkey optimization according to claim 1, wherein In the above Step 2, the node replacement strategy in the update of spider monkey individuals includes a single-node greedy replacement strategy and a full-node greedy replacement strategy.

5. A method for maximizing influence based on discrete spider monkey optimization according to claim 1, characterized in that, In the above 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 top k nodes with the largest EDV values as the initial vectors ; Step 3.2: Replace each node in with any node in the node set V with a probability of 0.5 to obtain the first initialized individual ; Step 3.3: Repeat Step 3.2 until the initialization of N spider monkey individuals is completed.

6. The influence maximization method based on discrete spider monkey optimization according to claim 1, characterized in that In the local leader leadership stage of step 5.1, it 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 function to randomly generate a probability between 0 and 1. If the generated probability is greater than the given interference rate pr, then calculate the node search space using the following formula : where LL represents an individual as the local leader of the group to which it belongs, and are two random values uniformly distributed between 0 and 1, used to represent the proportion of selected nodes. The symbol " " represents the difference operation between two sets, and the symbol " " represents the union operation between two sets; the obtained according to the above formula is regarded as the node search space required to update the individual and then the individual update is completed based on the node replacement strategy in Step 2 of the spider monkey individual update; The above Step 5.2 global leader leading stage specifically includes the following steps: Population-based global leader GL and another randomly selected spider monkey in the same group For each spider monkey Perform individual vector update; For each individual , first calculate the probability updated at this stage according to the following formula ; ; In the formula represents the fitness value of individual ; represents the fitness value of the optimal individual in the group to which it belongs; then, use the function to randomly generate a probability between 0 and 1. If the generated probability is less than or equal to , then calculate the node search space using the following formula where GL represents the global leader of the spider monkey population; the obtained according to the above formula is regarded as the node search space required to update individual , and then the individual update is completed based on the node replacement strategy in Step 2 of the spider monkey individual update.

7. The influence maximization method based on discrete spider monkey optimization according to claim 1, characterized in that, In the local leader learning stage of step 5.3, the following steps are specifically included: First, recalculate the fitness function values of all individuals, and identify the individual with the maximum value in each group according to the calculated values. ; Then compare with the fitness function value of the local leader LL of the corresponding group. If the former value is larger, update the local leader of the current group to , and reset the number of times the current local leader has not been updated to 0; Otherwise, keep the local leader LL unchanged, and increment by 1. In the global leader learning stage of step 5.4, it specifically includes the following steps: First, identify the individual with the maximum fitness value from all local leaders LL , and then compare with the fitness function value of the global leader GL. If the value of the former is greater, then update the global leader of the current spider monkey population to , and reset the number of times the global leader has not been updated to 0. Otherwise, keep GL unchanged and increment by 1.

8. A method for maximizing influence based on discrete spider monkey optimization according to claim 1, characterized in that The above Step 5.5 local leader decision-making stage specifically includes the following steps: Determine the corresponding for each group whether the given local leader non-update times limit value LLL has been exceeded; if so, perform a redirection operation on all spider monkey individuals in the group; Determine the currently redirected individual Whether it is the global leader GL; If so, skip the redirection update operation for this individual, so as to retain the optimal individual information; If not, then use function to randomly generate a probability between 0 and 1, compare the generated probability with the given interference rate pr, and redirect the individual to obtain a new individual .

9. The influence maximization method based on discrete spider monkey optimization according to claim 1, characterized in that The above Step 5.6 global leader decision-making stage specifically includes the following steps: Judge the number of times the global leader has not been updated Whether it has exceeded the given limit value GLL of the number of times the global leader has not been updated; if so, make a decision on grouping or recombination of the population, and set Reset to 0. If the current number of groups g exceeds the given maximum number of groups MG, recombine all spider monkey individuals into 1 group, otherwise divide all spider monkey individuals into (g + 1) groups; after the T-round iterative optimization ends, obtain the global leader GL, and all the nodes included in the global leader GL are the selected optimal seed node set.

10. The influence maximization method based on discrete spider monkey optimization according to claim 1, wherein, In the above Step 5, before the iterative optimization of the spider monkey population, the number of groups of the initialized population is 1.

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