CN115510288A - Network node searching method and system based on multi-factor evolutionary algorithm - Google Patents
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Abstract
The invention discloses a network node searching method and a system based on a multi-factor evolutionary algorithm, wherein the method comprises the following steps: constructing a robust influence evaluation index function of the seed node set under attack; evaluating the seed node set according to the robust influence evaluation index function to obtain individual attributes of the seed node set; and based on the robust influence evaluation index function of the seed node set, updating the individual attributes of the seed node set through a multi-factor evolution algorithm to obtain an optimal seed node set. By using the method and the device, the convergence speed of the individual performance of the seed node set can be improved under the condition of simultaneously considering node attack and link attack, so that an information transmission task is well completed. The network node searching method and system based on the multi-factor evolutionary algorithm can be widely applied to the technical field of computer application.
Description
Technical Field
The invention relates to the technical field of computer application, in particular to a network node searching method and system based on a multi-factor evolutionary algorithm.
Background
In the field of complex networks, the problem of influence maximization is one of important research directions. The problem of maximizing the influence is to find out a small part of important nodes with strong propagation performance from the network. These important nodes can propagate information to a greater extent than other nodes, the influence can rapidly spread to most other nodes in the network, in fact, the application of maximizing the influence is ubiquitous, for example, in recent years, the popularization and the rise of the internet, a social network platform has become an important component in human society, the network marketing is an efficient way for merchants to promote commodities due to the efficient information propagation function and the characteristics of a large number of users, but obviously, due to the restriction of factors such as funds, the merchants cannot promote their products for each user, in fact, some important and more influential "seed" users often exist in the social network, the merchants can select these users as promotion objects through some analysis means, the cost is reduced as much as possible to achieve the purpose of maximizing marketing, for example, in the traffic network, some traffic jam caused by unexpected events at intersections, the streets adjacent to the intersections are also very likely to be blocked, the traffic route interruption in the urban area is broken, the decision-making miners can achieve the purpose of maximizing the traffic paralysis in a large scale, the important nodes can be mined, the city operation points and the effective traffic protection points can be paid attention to the important traffic guidance and the important points, and the important points can be studied in a life;
based on the problem of influence maximization, people have increasingly strong interest in the topic of robustness. In the field of complex networks, robustness generally refers to the capability of a network to tolerate internal faults and resist external interference, and existing research proves that the interaction behavior in the network is also influenced by the change of the network structure. Therefore, the evaluation and optimization methods corresponding to the seeds and the network have a very critical position in the previous research, but in the practical application at the present stage, the network system is greatly damaged by the attack from the nodes or the links, and for the problem of maximizing the robust influence, the existing technologies are mostly limited to consider the single condition of the link attack or the node attack, and the group information is not well considered in the search process, and the disadvantages are also obvious: first, there may be low convergence, easily getting trapped in a locally optimal solution; second, the seeds from a single optimization are only applicable in a single kind of attack situation.
Disclosure of Invention
In order to solve the technical problems, the invention aims to provide a network node searching method and a network node searching system based on a multi-factor evolutionary algorithm, which can improve the convergence speed of the individual performance of a seed node set under the condition of simultaneously considering node attack and link attack so as to well complete an information transmission task.
The first technical scheme adopted by the invention is as follows: the network node searching method based on the multi-factor evolutionary algorithm comprises the following steps:
constructing a robust influence evaluation index function of the seed node set under attack;
evaluating the seed node set according to the robust influence evaluation index function to obtain the individual attributes of the seed node set;
and based on the robust influence evaluation index function of the seed node set, updating the individual attributes of the seed node set through a multi-factor evolution algorithm to obtain an optimal seed node set.
Further, the robust influence evaluation index function of the seed node set under the attack comprises the robust influence evaluation index function of the seed node set under the node attack and the robust influence evaluation index function of the seed node set under the link attack.
Further, the robust influence evaluation index function of the seed set under node attack and the robust influence evaluation index function of the seed set under link attack are as follows:
in the above formula, the first and second carbon atoms are,
the robust influence evaluation index function of the seed node set under node attack is represented, S represents the seed node set, N represents the number of nodes of the current network,
representing the 2-hop influence propagation value of the set of seed nodes on the network after removing the Q nodes,
a robust impact evaluation index function representing the set of seed nodes under link attack, M representing the total number of links of the current network,
and representing the 2-hop influence propagation value of the seed node set on the network after the P link is removed.
Further, the step of evaluating the seed node set according to the robust influence evaluation index function to obtain individual attributes of the seed node set specifically includes:
evaluating the seed node set according to the robust influence evaluation index function to obtain corresponding seed node set factor cost;
sequencing the seed node sets according to the factor cost of the seed node sets to obtain corresponding factor levels of the seed node sets;
performing reciprocal summation on the factor levels of the seed node set to obtain a fitness scalar of the seed node set;
and giving an index to the seeds with the optimal levels in the factor levels of the seed node set to obtain the skill factors of the seed node set.
Further, the multi-factor evolution algorithm comprises an initialization operator, a crossover operator, a mutation operator, a learning operator and a selection operator, the robust influence evaluation index function based on the seed node set is updated through the multi-factor evolution algorithm to the individual attributes of the seed node set, and the optimal seed node set is obtained, and the method specifically comprises the following steps:
initializing the seed node set by executing an initialization operator to obtain an initial population;
performing individual cross treatment on the initial population by executing a cross operator according to the skill factor of the seed node set to generate a temporary population;
according to the fitness scalar of the seed node set, the initial population and the temporary population are adjusted through executing a mutation operator to obtain an adjusted initial population and an adjusted temporary population;
optimizing the adjusted initial population and the adjusted temporary population by executing a learning operator according to the seed node set skill factor to obtain an optimized initial population and an optimized temporary population;
according to the factor level of the seed node set, the skill factor of the seed node set and the fitness scalar of the seed node set, carrying out individual selection on the optimized initial population and the optimized temporary population through a selection operator to obtain optimized population individuals;
and (4) circularly updating the individual attributes of the seed node set until a preset condition is met, and outputting the optimal seed node set.
Further, after the crossing operator and the mutation operator are performed on the initial population and the temporary population, the method further comprises the step of correcting the initial population and the temporary population, and the specific process is as follows:
traversing and checking the seed node sets in the initial population and the temporary population;
and checking that repeated gene nodes appear in the seed node set, correcting the seed node set, and randomly selecting one node in the initial network to replace the repeated node in the individual until no repeated gene nodes exist in the seed node set.
Further, the learning operator is a task-oriented learning operator, and the step of performing optimization processing on the adjusted initial population and the adjusted temporary population by executing the learning operator according to the seed node set skill factor to obtain an optimized initial population and an optimized temporary population specifically includes:
grouping the adjusted initial population and the adjusted temporary population according to different skill factors of the seed node set;
the seed node sets in the group are learned according to the robust influence evaluation index function to obtain the learned seed node sets;
and comparing the factor cost of the learned seed node set with the factor cost of the original seed node set, judging that the factor cost of the learned seed node set is superior to the factor cost of the original seed node set, and replacing the original seed node set with the learned seed node set to obtain an optimized initial population and an optimized temporary population.
Further, the learning operator is a gene-oriented learning operator, and the step of performing optimization processing on the adjusted initial population and the adjusted temporary population by executing the learning operator according to the seed node set skill factor to obtain an optimized initial population and an optimized temporary population specifically includes:
grouping the adjusted initial population and the adjusted temporary population according to different skill factors of the seed node set;
selecting a seed node set with the optimal factor level of the seed node sets in the group;
the optimal seed node set in the group is learned according to the robust influence evaluation index function to obtain a learned optimal seed node set;
and comparing the factor cost of the learned optimal seed node set with the factor cost of the original seed node set, judging that the factor cost of the learned optimal seed node set is superior to the factor cost of the original seed node set, and replacing the original seed node set with the learned optimal seed node set to obtain an optimized initial population and an optimized temporary population.
The second technical scheme adopted by the invention is as follows: the network node searching system based on the multi-factor evolutionary algorithm comprises the following steps:
the construction module is used for constructing a robust influence evaluation index function of the seed node set under attack;
the evaluation module is used for evaluating the seed node set according to the robust influence evaluation index function to obtain the individual attributes of the seed node set;
and the optimization module is used for evaluating an index function based on the robust influence of the seed node set and updating the individual attributes of the seed node set through a multi-factor evolution algorithm to obtain an optimal seed node set.
The method and the system have the beneficial effects that: the method aims to search the solving space of each task in parallel by constructing a robust influence evaluation index function as an optimization task of the seed node set, optimizes the individual attributes of the seed node set through a multi-factor evolution algorithm, designs the algorithm by taking diversity attention as a principle, and ensures population diversity as much as possible, so that the obtained seed node set can obtain a better influence propagation effect in the network damage process.
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FIG. 1 is a flow chart of steps of a network node finding method based on a multi-factor evolutionary algorithm of the present invention;
FIG. 2 is a block diagram of the network node searching system based on the multi-factor evolutionary algorithm.
Detailed Description
The invention is described in further detail below with reference to the figures and the specific embodiments. The step numbers in the following embodiments are provided only for convenience of illustration, the order between the steps is not limited at all, and the execution order of each step in the embodiments can be adapted according to the understanding of those skilled in the art.
Referring to fig. 1, the invention provides a network node searching method based on a multi-factor evolutionary algorithm, which comprises the following steps:
s1, constructing a robust influence evaluation index function of a seed node set under attack;
s11, the robust influence evaluation index function of the seed node set under node attack is as follows:
in the above formula, the first and second carbon atoms are,
the robust influence evaluation index function of the seed node set under node attack is represented, S represents the seed node set, N represents the number of nodes of the current network,
representing a 2-hop influence propagation value of the seed node set on the network after the Q node is removed;
s12, the robust influence evaluation index function of the seed node set under the link attack is as follows:
in the above formula, the first and second carbon atoms are,
a robust impact evaluation index function representing the set of seed nodes under link attack, M representing the total number of links of the current network,
representing a 2-hop influence propagation value of the seed node set on the network after the P link is removed;
s2, evaluating the seed node set according to the robust influence evaluation index function to obtain individual attributes of the seed node set;
in particular, a complex network represents nodes as entities in the network, and edges connecting the nodes represent information channels between the entities, and image maximization in the complex network is a basic problem for understanding information propagation in a real system, and attempts to activate candidate seed nodes composed of a small part of nodes in the network, so that the propagation effect of information influence is maximized.
S21, defining factor cost in individual attribute of the seed node set;
in particular, use is made of
And
for the current individual p i Evaluating, wherein the individual is a seed node set, and the corresponding value is the task T of the individual 1 And T 2 A factor cost of above, the task T 1 Namely a robust influence evaluation index of the seed node set under node attack, wherein the task T is 2 Namely, the robust influence evaluation index of the seed node set under the link attack is obtained, and the factor costs of different tasks are recorded as
And
s22, defining factor levels in individual attributes of the seed node set;
in particular, the individual p i At task T 1 And T 2 Factor of
And
the rank of the individual in the population is defined, and the rank is determined after the factor cost of each individual is arranged from small to large.
S23, defining a fitness scalar in individual attributes of the seed node set;
in particular, the individual p i Is a fitness scalar psi i Defined as the sum of the reciprocal of the factor level of the individual at each task, i.e.
S24, defining a technical factor in the individual attribute of the seed node set;
in particular, the individual p i Skill factor τ of i For the individual, i.e. the index of the task that performs the best among all tasks, i.e. the index of the task
Wherein j is equal to {1,2, …, K }, and when the ranks of the individual on all the tasks are the same, the individual is assigned as a random good task index.
And S3, based on the robust influence evaluation index function of the seed node set, updating the individual attributes of the seed node set through a multi-factor evolution algorithm to obtain the optimal seed node set.
Specifically, two evaluation indexes, namely a robust influence evaluation index of the seed node set under node attack and a robust influence evaluation index of the seed node set under link attack, are simultaneously used as optimization tasks, and influence of seed selection is improved to the maximum extent based on a multi-factor evolution algorithm.
S31, executing an initialization operator;
specifically, the initialization operator uses three strategies of Degree priority, clustering priority and PageRank priority to initialize the first 1/3, the middle 1/3 and the remaining 1/3 of the population according to the principle of 'individual diversity', namely, a roulette method is used for selecting a given number of nodes as genes of the individuals and generating an initial population according to three structural properties of Degree, clustering and PageRank of the nodes in the network. The basic idea of the roulette method is that the selection probability of each node is proportional to the fitness value (here, degree, clustering and PageRank) of the node; and finally, updating the attribute information of all individuals.
S32, executing a crossover operator;
specifically, the crossover operator divides the population into different groups according to the different skill factors, and the individuals in each group mate with each other, but have a certain probability (1- (MaxGen-Gen)/MaxGen) to mate with the individuals in other groups. The operator follows a 'gene diversity' principle, three different intersection strategies of uniform intersection, two-point intersection and single-point intersection are selected according to probability to improve population diversity, an individual needs to be subjected to traversal inspection after the intersection operator is executed, if repeated gene nodes appear in the individual after the inspection, correction operation is executed, and the correction operation is as follows: randomly selecting a node in an initial network to replace a repeated node in an individual until no repeated node exists in the individual, executing a crossover operator combining three strategies of uniform crossover, two-point crossover and single-point crossover on an initial population, expanding the population scale, generating a temporary population with the same number as that of an original population, wherein the initial network is given artificially, and finally updating the attribute information of all the individuals;
specifically, in the first evolution, the initial population is the population generated by the initialization operator, the temporary population is the population generated by the crossover operator and plays a role in expanding the number of individuals, the mutation operator and the learning operator in the middle process the initial population and the temporary population, and the final selection operator selects the most excellent series of individuals (the size of the initial population) from the initial population and the temporary population to be inherited into the next evolution, and the inherited individuals form the initial population again after the next evolution (i.e. the second evolution to the nth evolution), and the step of generating the temporary population is repeatedly performed, wherein the temporary population is generated after the initial population is processed by the crossover operator, and the temporary population plays a role in expanding the number of the population.
S33, executing mutation operators;
specifically, variance calculationAnd the children dynamically adjust the variation probability according to the individual fitness scalar according to the principle of probability diversity. For each individual in the population, the mutation operator is represented by p m X β (β =1 — fitness scalar of the individual/sum of fitness scalars of all individuals in the population) is performed, an operator randomly selects one gene node in the individual, the gene node is replaced by a random node in the network, similarly, traversal inspection needs to be performed on the individual after the mutation operator is performed, if the same node appears in the individual after inspection, the correction operation mentioned in step S32 is performed, the mutation operator is performed on the initial population and the temporary population, genetic information is enriched, population diversity is increased, and a local optimal solution is eliminated.
S34, executing a learning operator facing to the task;
specifically, the task-oriented learning operator groups the population according to the difference of individual skill factors, the individuals in the group learn for the corresponding task, and the operator follows the "learning space diversity principle", that is, randomly determines the learning space according to the probability. The learning spaces here are: the method comprises the steps of collecting 2-hop neighbors of current nodes and a Random node collection (a certain number of nodes are randomly selected from a network and account for 10% of the network scale), then, learning the nodes in a learning space by individuals in a population, namely, randomly replacing each node in the individuals with the node in the learning space, accepting replacement operation if the replaced individuals have better factor cost compared with original individuals without replacement, finally, updating attribute information of all the individuals, executing task-oriented learning operators on an initial population and a temporary population, and learning excellent individuals on different tasks in a targeted manner, so that the performance of each individual in the population is rapidly improved, and the convergence speed is accelerated.
S35, executing a learning operator facing to genes;
specifically, firstly, the gene-oriented learning operator divides the population into two groups according to different individual skill factors, two excellent individuals, namely two optimal individuals, are selected from each group according to the factor levels of the individuals, a gene pool is created to store the gene nodes of the individuals, in order to reduce the calculation cost, the genes of the excellent individuals are not all put into the gene pool, but are randomly sampled and put into the gene pool, and finally the number of the stored genes in the gene pool is 0.1 times the number of the current network nodes. The random sampling operation here is to randomly select a given number of nodes from all gene nodes of these excellent individuals. Then, each individual in the population learns the nodes in the gene pool according to the probability; the learning operation is the same as step S34, that is, the nodes are randomly replaced with the nodes in the search space, if the replaced individuals have a better factor cost than the original individuals without replacement, the replacement operation is accepted, finally, the attribute information of all the individuals is updated, and a gene-oriented learning operator is executed on the original population and the temporary population, the operator selects a certain number of excellent gene nodes from the excellent individuals in the population and forms a gene pool, and other individuals in the population learn the excellent genes from the gene pool, so as to further improve the performance of the individuals in the population and accelerate convergence;
the further task-oriented learning is fundamentally different from the gene-oriented learning in that the task-oriented learning is that an individual learns about individuals who perform well on different tasks, and the gene-oriented learning is that a gene of the excellent individuals in a population is learned.
S36, executing a selection operator;
specifically, first, for an individual p in the current population i The selection operator checks the attribute information of all individuals in the current population and ranks the factors as
And
the two individuals of (2) are inherited to the next generation, wherein the factor level is determined according to the ranking of the factor cost in the attribute of the individual, so that the population is not degraded; then, the skill factor tau is respectively obtained by using a roulette method i =1 and skill factor τ i 1/3 of the initial population number of individuals selected from the individuals of =2Entering a next generation population; finally, selecting the individuals to enter the next generation by using a roulette method according to the difference of the fitness scalars of the remaining individuals in the population of the next generation; finally, updating attribute information of all individuals
S37, outputting the optimal solution of the seed node set;
specifically, the above steps are repeatedly executed until a set termination condition is met, where the termination condition is that N cycles are met (N is artificially set and generally set to be 150 or more), that is, N cycles are executed or more, an optimal seed node set is output, where the output optimal seed node set is an optimal individual selected from an initial population and a temporary population that have been evolved, that is, updated for multiple times, and finally an optimal solution that appears in an optimization process is output, where the optimal solution is the seed node set with the maximum robust influence performance calculated by the present algorithm, and even if the seed node set is subjected to external attack and interference, the seed node set still has a strong influence and can well complete an information propagation task, and the optimal solution is the seed node set with the maximum robust influence performance calculated by the present algorithm, and even if the seed node set is subjected to external attack and interference, the seed node set still has a strong influence and can well complete the information propagation task.
Referring to fig. 2, the network node searching system based on the multi-factor evolutionary algorithm includes:
the construction module is used for constructing a robust influence evaluation index function of the seed node set under attack;
the evaluation module is used for evaluating the seed node set according to the robust influence evaluation index function to obtain the individual attributes of the seed node set;
and the optimization module is used for evaluating an index function based on the robust influence of the seed node set and updating the individual attributes of the seed node set through a multi-factor evolution algorithm to obtain an optimal seed node set.
The contents in the above method embodiments are all applicable to the present system embodiment, the functions specifically implemented by the present system embodiment are the same as those in the above method embodiment, and the beneficial effects achieved by the present system embodiment are also the same as those achieved by the above method embodiment.
While the preferred embodiments of the present invention have been illustrated and described, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (9)
1. The network node searching method based on the multi-factor evolutionary algorithm is characterized by comprising the following steps of:
constructing a robust influence evaluation index function of the seed node set under attack;
evaluating the seed node set according to the robust influence evaluation index function to obtain individual attributes of the seed node set;
and based on the robust influence evaluation index function of the seed node set, updating the individual attributes of the seed node set through a multi-factor evolution algorithm to obtain an optimal seed node set.
2. The method as claimed in claim 1, wherein the robust influence evaluation index function of the seednode set under attack comprises a robust influence evaluation index function of the seednode set under attack and a robust influence evaluation index function of the seednode set under attack.
3. The method for searching network nodes based on the multi-factor evolutionary algorithm as claimed in claim 2, wherein the robust impact evaluation index function of the seed set under node attack and the robust impact evaluation index function of the seed set under link attack are as follows:
in the above formula, the first and second carbon atoms are,
the robust influence evaluation index function of the seed node set under node attack is represented, S represents the seed node set, N represents the number of nodes of the current network,
representing the 2-hop influence propagation value of the set of seed nodes on the network after removing the Q nodes,
a robust impact evaluation index function representing the set of seed nodes under link attack, M representing the total number of links of the current network,
representing a 2-hop influence propagation value of the set of seed nodes on the network after the P-link is removed.
4. The method for searching network nodes based on the multi-factor evolutionary algorithm as claimed in claim 3, wherein the step of evaluating the seed node set according to the robust influence evaluation index function to obtain the individual attributes of the seed node set specifically comprises:
evaluating the seed node set according to the robust influence evaluation index function to obtain corresponding seed node set factor cost;
sequencing the seed node sets according to the factor cost of the seed node sets to obtain the corresponding factor levels of the seed node sets;
performing reciprocal summation on the factor levels of the seed node set to obtain a fitness scalar of the seed node set;
and giving an index to the seeds with the optimal levels in the factor levels of the seed node set to obtain the skill factors of the seed node set.
5. The method for searching network nodes based on the multi-factor evolutionary algorithm as claimed in claim 4, wherein the multi-factor evolutionary algorithm comprises an initialization operator, a crossover operator, a mutation operator, a learning operator and a selection operator, the robust influence evaluation index function based on the seed node set is obtained by updating the individual attributes of the seed node set through the multi-factor evolutionary algorithm, and the method specifically comprises the following steps:
initializing the seed node set by executing an initialization operator to obtain an initial population;
performing individual cross processing on the initial population by executing a cross operator according to the seed node set skill factor to generate a temporary population;
according to the fitness scalar of the seed node set, the initial population and the temporary population are adjusted through executing a mutation operator to obtain an adjusted initial population and an adjusted temporary population;
according to the seed node set skill factors, optimizing the adjusted initial population and the adjusted temporary population through executing a learning operator to obtain an optimized initial population and an optimized temporary population;
according to the factor level of the seed node set, the skill factor of the seed node set and the fitness scalar of the seed node set, carrying out individual selection on the optimized initial population and the optimized temporary population through a selection operator to obtain optimized population individuals;
and (4) circularly updating the individual attributes of the seed node set until a preset condition is met, and outputting the optimal seed node set.
6. The method for searching network nodes based on the multi-factor evolutionary algorithm of claim 5, wherein the step of modifying the initial population and the temporary population after performing the crossover operator and the mutation operator on the initial population and the temporary population comprises the following specific steps:
traversing and checking the seed node sets in the initial population and the temporary population;
and checking that repeated gene nodes appear in the seed node set of the seed node set, correcting the seed node set, and randomly selecting one node in the initial network to replace the repeated nodes in the individual until no repeated gene nodes exist in the seed node set.
7. The method for searching network nodes based on the multi-factor evolutionary algorithm according to claim 5, wherein the learning operator is a task-oriented learning operator, and the step of performing optimization processing on the adjusted initial population and the adjusted temporary population by executing the learning operator according to the skill factor of the seed node set to obtain an optimized initial population and an optimized temporary population specifically comprises:
grouping the adjusted initial population and the adjusted temporary population according to different skill factors of the seed node set;
the seed node sets in the group can be learned according to the robust influence evaluation index function to obtain the learned seed node sets;
and comparing the factor cost of the learned seed node set with the factor cost of the original seed node set, judging that the factor cost of the learned seed node set is superior to the factor cost of the original seed node set, and replacing the original seed node set with the learned seed node set to obtain an optimized initial population and an optimized temporary population.
8. The method for searching network nodes based on the multi-factor evolutionary algorithm of claim 5, wherein the learning operator is a gene-oriented learning operator, and the step of performing optimization processing on the adjusted initial population and the adjusted temporary population by executing the learning operator according to the skill factor of the seed node set to obtain the optimized initial population and the optimized temporary population specifically comprises:
grouping the adjusted initial population and the adjusted temporary population according to different skill factors of the seed node set;
selecting a seed node set with the optimal factor level of the seed node sets in the group;
the optimal seed node set in the group can be learned according to the robust influence evaluation index function to obtain the learned optimal seed node set;
and comparing the factor cost of the learned optimal seed node set with the factor cost of the original seed node set, judging that the factor cost of the learned optimal seed node set is superior to the factor cost of the original seed node set, and replacing the original seed node set with the learned optimal seed node set to obtain an optimized initial population and an optimized temporary population.
9. The network node searching system based on the multi-factor evolutionary algorithm is characterized by comprising the following modules:
the construction module is used for constructing a robust influence evaluation index function of the seed node set under attack;
the evaluation module is used for evaluating the seed node set according to the robust influence evaluation index function to obtain the individual attributes of the seed node set;
and the optimization module is used for evaluating an index function based on the robust influence of the seed node set and updating the individual attributes of the seed node set through a multi-factor evolution algorithm to obtain an optimal seed node set.
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