Network construction and optimization method and device, electronic equipment and storage medium

Abstract

The invention discloses a network construction and optimization method and device, electronic equipment and a storage medium, and relates to the technical field of computer application, and the method comprises the steps: determining an evaluation index of a network; the evaluation indexes comprise robustness evaluation indexes of the network and robust influence evaluation indexes of key nodes in the network; performing random reconnection on the network according to the evaluation index to obtain an initial population; and updating the initial population based on an improved multi-objective evolutionary algorithm to construct a target network structure. From the perspective of the structure of the network and the robust influence performance of the key nodes of the network, a network structure and an initial population with robust stability and robust influence maximization are randomly constructed; in combination with the two evaluation indexes, the candidate network structure can be effectively evaluated and optimized through the improved multi-objective evolutionary algorithm. According to the method, wider solution distribution and more excellent solution sets can be found through the improved multi-objective evolutionary algorithm, and the method has the advantage of high availability.

Description

Technical Field

[0001] The present application relates to the field of computer application technology, and in particular to a network construction and optimization method, device, electronic device and storage medium. Background Art

[0002] Most complex systems in nature and society can be abstractly described by specific complex networks, such as transportation networks, social networks, and the Internet. Individuals in the above networks can be represented as nodes, and certain relationships between network individuals represent the connections between nodes. However, in real life scenarios, the construction of networks often presents random and disordered characteristics. Although the above construction method has certain conveniences, it also hides many crises. Summary of the invention

[0003] The main purpose of the embodiments of the present application is to propose a network construction and optimization method, device, electronic device and storage medium to effectively address the many problems and challenges faced in real network applications.

[0004] To achieve the above objectives, an embodiment of the present application provides a network construction and optimization method, which includes the following steps:

[0005] Determining evaluation indicators of the network; wherein the evaluation indicators include robustness evaluation indicators of the network and robust influence evaluation indicators of key nodes in the network;

[0006] Randomly reconnect the network according to the evaluation index to obtain an initial population;

[0007] The initial population is updated based on an improved multi-objective evolutionary algorithm to construct a target network structure.

[0008] In some embodiments, determining the evaluation index of the network includes the following steps:

[0009] Determining the robustness evaluation index of the network when a node attack occurs on the network;

[0010] Determine the robust influence evaluation index of the key node in the network when node damage occurs in the network and a cascading failure occurs in the network.

[0011] In some embodiments, determining the robustness evaluation index of the network when a node attack occurs in the network comprises the following steps:

[0012] Determining the robustness evaluation index of the network when a node attack occurs to the network according to a first calculation formula;

[0013] The first calculation formula is:

[0014]

[0015] Among them, R represents the robustness evaluation index, N represents the number of nodes in the network, e represents the maximum limit of network damage, e is greater than or equal to 1, q represents the number of removed nodes, and s(q) represents the maximum connectivity ratio of the network after removing q nodes.

[0016] In some embodiments, determining the robust influence evaluation index of the key node in the network when node damage occurs in the network and a cascading failure occurs in the network comprises the following steps:

[0017] Determining, according to a second calculation formula, the robust influence evaluation index of the key node in the network when a node is damaged and a cascading failure occurs in the network;

[0018] The second calculation formula is:

[0019]

[0020] Among them, RIM cf represents the robust influence evaluation index, N overload represents the number of times the network overload event occurs, t represents the number of times the cascading failure occurs, represents the influence evaluation value of the key node;

[0021] The calculation formula of the influence evaluation value of the key node is:

[0022]

[0023] in, represents the sum of the influence ranges of each node in the set S of key nodes whose distance is 1; The overlapping influence of the nodes in the set S of the key nodes within the distance 1, the set C s represents the neighboring nodes within a distance of 1 of node s, p(c,s) represents the propagation probability between the activated node s and the node to be activated c, Represents the direct neighbor node of node c; represents the overlapping influence of the newly activated node c and the set S of key nodes; d represents the direct neighbor node of the first-order neighbor node c of the set S of key nodes.

[0024] In some embodiments, the updating of the initial population based on the improved multi-objective evolutionary algorithm to construct a target network structure comprises the following steps:

[0025] Executing the improved multi-objective evolutionary algorithm to update the initial population, so as to construct the target network structure;

[0026] Executing the improved multi-objective evolutionary algorithm comprises the following steps:

[0027] Calculating the fitness value of each individual in the initial population;

[0028] According to the fitness value, each of the individuals in the initial population is subjected to non-dominated sorting, crowding distance calculation, and an elite preservation selection operator to obtain a parent population;

[0029] Execute a crossover operator and a mutation operator on the parent population to obtain an initial child population;

[0030] Executing a non-similarity search operator on the initial offspring population so as to make each of the individuals in the initial offspring population learn a network structure with the largest difference in network feature values, thereby obtaining an optimized offspring population;

[0031] Mixing the parent population and the optimized offspring population to obtain an initial mixed population;

[0032] According to the fitness value, each of the individuals in the initial mixed population is subjected to non-dominated sorting, crowding distance calculation, and an elite preservation selection operator is adopted to obtain an optimized mixed population;

[0033] The optimized mixed population is used as the current initial population, and the step of calculating the fitness value of each individual in the initial population is returned until a preset end condition is reached, and the network structure of the non-dominated individuals in the current optimized mixed population is output as the target network structure.

[0034] In some embodiments, performing a crossover operator and a mutation operator on the parent population to obtain an initial child population includes the following steps:

[0035] Executing the crossover operator on the parent population comprises the following steps:

[0036] Randomly select two individuals in the parent population to perform crossover, and perform edge connection swapping on two pairs of edges that are different in the network structures of the two randomly selected individuals;

[0037] If the degree distribution of the two individuals after the crossover is different from that of the original network, the crossover operator is re-executed;

[0038] Executing the mutation operator on the parent population includes the following steps:

[0039] The mutation operator is executed on each of the individuals in the parent population with a preset probability to introduce topological reconnection into the individuals, thereby adjusting the structure of the network.

[0040] In some embodiments, the method further comprises the following steps:

[0041] The optimized mixed population and the corresponding network structure of each generation in the process of executing the improved multi-objective evolutionary algorithm are recorded; wherein the fitness value is recorded and displayed in a dynamic form.

[0042] To achieve the above-mentioned purpose, another aspect of the embodiment of the present application provides a network construction and optimization device, the device comprising:

[0043] An indicator determination unit, used to determine an evaluation indicator of the network; wherein the evaluation indicator includes a robustness evaluation indicator of the network and a robust influence evaluation indicator of a key node in the network;

[0044] A network construction unit, used for randomly reconnecting the network according to the evaluation index to obtain an initial population;

[0045] The network optimization unit is used to update the initial population based on an improved multi-objective evolutionary algorithm to construct a target network structure.

[0046] To achieve the above objective, another aspect of an embodiment of the present application provides an electronic device, the electronic device comprising a memory and a processor, the memory storing a computer program, and the processor implementing the above method when executing the computer program.

[0047] To achieve the above objective, another aspect of an embodiment of the present application provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and the computer program implements the above method when executed by a processor.

[0048] The embodiments of the present application include at least the following beneficial effects:

[0049] This application can determine the evaluation index of the network; wherein, the evaluation index includes the robustness evaluation index of the network and the robust influence evaluation index of the key nodes in the network; the network is randomly reconnected according to the evaluation index to obtain the initial population; the initial population is updated based on the improved multi-objective evolutionary algorithm to construct the target network structure. First, from the perspective of the network's own structure and the robust influence performance of the key nodes of the network, this application randomly constructs a network structure with robust stability and maximized robust influence, and an initial population; combining the two evaluation indicators, the improved multi-objective evolutionary algorithm can be used to effectively evaluate and optimize the candidate network structure. Secondly, this application can find a wider distribution of solutions and a better set of solutions through the improved multi-objective evolutionary algorithm, which has the advantage of high availability. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings required for use in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0051] Figure 1 A flowchart of a network construction and optimization method provided in an embodiment of the present application;

[0052] Figure 2 A reference flow chart based on an improved multi-objective evolutionary algorithm provided in an embodiment of the present application;

[0053] Figure 3 A schematic diagram of the structure of a network construction and optimization device provided in an embodiment of the present application;

[0054] Figure 4 A schematic diagram of the hardware structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0055] In order to make the purpose, technical solutions and advantages of the present application clearer, the present application is further described in detail below in conjunction with the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present application and are not intended to limit the present application. When the following description refers to the drawings, unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with the embodiments of the present application. They are only examples of devices and methods consistent with some aspects of the embodiments of the present application as detailed in the attached claims.

[0056] It is understood that the terms "first", "second", etc. used in this application can be used to describe various concepts in this article, but unless otherwise specified, these concepts are not limited by these terms. These terms are only used to distinguish one concept from another concept. For example, without departing from the scope of the embodiment of the present application, the first information may also be referred to as the second information, and similarly, the second information may also be referred to as the first information. Depending on the context, the words "if" and "if" as used herein can be interpreted as "at the time of" or "when" or "in response to determination".

[0057] The terms "at least one", "multiple", "each", "any", etc. used in this application, at least one includes one, two or more, multiple includes two or more, each refers to each of the corresponding multiple, and any refers to any one of the multiple.

[0058] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as those commonly understood by those skilled in the art to which this application belongs. The terms used herein are only for the purpose of describing the embodiments of this application and are not intended to limit this application.

[0059] Before describing the embodiments of the present application in detail, some related technologies involved in the embodiments of the present application are first described as follows:

[0060] This application focuses on the field of computer application technology and is committed to proposing a new way of network construction. In this way, by carrying out targeted adjustment operations on the network structure and cleverly guiding two specific evaluation indicators to continuously optimize, the goal of continuously optimizing the structure of the network throughout the process of population evolution is achieved. In particular, this application focuses on the key nodes in the network. When these key nodes encounter network node attacks, it is necessary to ensure that they can always maintain good robustness and have a strong level of influence.

[0061] Based on the above-mentioned goals, this application innovatively proposes a method based on a multi-objective evolutionary algorithm. The core of this method is to effectively solve the stability problems faced in the process of adjusting and building the network structure, while achieving the goal of maximizing the robust influence of key nodes, thereby providing strong technical support for creating a better-performing and more adaptable network architecture.

[0062] Most complex systems in nature and society can be abstractly described by specific complex networks, such as transportation networks, social networks, and the Internet. The members of these systems are represented as nodes, and certain relationships between system members represent the connections between nodes.

[0063] In real life, the construction of a network may be random and disordered, which may cause potential crises in the structure of the network, especially when the network may fail due to internal and external reasons, which will affect the normal function of the network. How to evaluate this impact and take these impacts into consideration during the process of network construction and network structure adjustment is the starting point of our invention. The network structure not only affects the integrity of the overall function of the network. Due to the interaction between network nodes, the interaction of key nodes in a small range can spread to the entire network, which is called the influence characteristic of the network. This characteristic can help business marketing in social networks and help infrastructure networks radiate the entire area under reasonable layout. In complex networks, the essence of the problem of maximizing influence is to select a small number of influential nodes and maximize the scope of influence propagation.

[0064] In complex application environments, network systems are inevitably affected by external interference and malicious attacks. These interferences and damages vary in degree, which may only cause minor disturbances or may destroy the network structure and greatly damage the function of the network system. Current methods for solving the problem of maximizing influence rarely consider the situation where the network structure is damaged. Because during the information propagation process, the network structure changes dynamically and is closely related to the network performance. This means that changes in the network structure will further affect the influence propagation process of key nodes. Therefore, given that how to select key nodes with robustness and influence in dynamic networks is crucial to ensuring network stability and performance, the problem of maximizing robust influence deserves further study.

[0065] Current research on the problem of robust influence maximization mainly focuses on uncertain factors such as system parameters such as influence propagation probability and probability model. However, these studies ignore the impact of network structure damage on the influence propagation performance of key nodes. In real-world problems and challenges, cascading failures are a common and destructive form of network failure propagation. It means that after a small number of nodes fail, the network load they originally borne is distributed to the surrounding nodes. Since the surrounding nodes cannot bear these additional loads, they will also fail one after another, causing a chain reaction to spread to the entire network. Considering that the existing ways of building networks are mostly random, which may not be enough to consider these key information, we propose a network construction scheme with a robust structure and stable propagation of network key node information.

[0066] In today's era, complex systems exist widely in various fields of nature and society, such as transportation networks, social networks, and the Internet. These complex systems can be effectively abstracted and described through specific complex networks. In such complex network models, members within the system are usually abstracted as nodes, and the various relationships between members are correspondingly represented as connections between nodes.

[0067] However, in real-life scenarios, the construction of the network often presents random and disordered characteristics. Although this construction method has certain conveniences, it also hides many crises. Specifically, whether it is due to hidden faults within the network itself or various interference factors from the outside, it is very likely to cause the nodes or connection edges in the network to fail, which will have a serious impact on the normal functioning of the network. In this context, how to accurately evaluate these impacts and fully take these influencing factors into consideration during network construction and subsequent network structure adjustments has become the core starting point of this application.

[0068] In fact, the network structure has a crucial impact on the integrity of the overall network function. On the one hand, due to the interaction between network nodes, the interaction between key nodes in a relatively small range may gradually spread to the entire network through the connection relationship between nodes. This feature is the so-called network influence feature. This feature has important value in practical applications. For example, in social networks, it can provide a powerful communication boost for commercial marketing activities; in infrastructure networks, with the help of reasonable layout planning, the influence of the network can be effectively radiated to the entire region.

[0069] On the other hand, in the application environment of complex networks, network systems will inevitably be subject to various interferences and malicious attacks from the outside. The degree of these interferences and attacks varies greatly. The light ones may only cause slight disturbances to the network, while the heavy ones may directly destroy the structure of the network, thus greatly damaging the original functions of the network system.

[0070] At present, most of the existing research methods on how to maximize influence focus on the uncertainty factors of system parameters, such as influence propagation probability and probability model. Although these studies provide a useful perspective for understanding the influence propagation mechanism to a certain extent, they generally ignore a key factor, that is, the impact of network structure destruction on the influence propagation performance of key nodes. In the actual information propagation process, the network structure is not static, but in dynamic change, and there is a very close relationship between this dynamic change and network performance. In other words, any change in the network structure will further affect the influence propagation process of key nodes. Among the many problems and challenges faced in reality, cascading failures are a very common and destructive form of network failure propagation. Specifically, when a small number of nodes in the network fail, the network load originally borne by these nodes will be distributed to the nodes around them. However, due to the limited carrying capacity of the surrounding nodes themselves, they cannot bear these additional loads, so they will also fail one after another.

[0071] Taking into account that the existing network structure often fails to fully consider the above-mentioned key information during the construction process, based on this, the present application proposes a network construction solution that aims to build a network with structural robustness and can ensure the stable propagation of information of key network nodes, in order to effectively deal with the many problems and challenges faced in real network applications.

[0072] Therefore, the embodiments of the present application provide a network construction and optimization method, device, electronic device and storage medium. The technical solution of the present application includes: determining the evaluation index of the network; wherein the evaluation index includes the robustness evaluation index of the network and the robust influence evaluation index of the key nodes in the network; randomly reconnecting the network according to the evaluation index to obtain the initial population; updating the initial population based on the improved multi-objective evolutionary algorithm to construct the target network structure. First, from the perspective of the network's own structure and the robust influence performance of the key nodes of the network, the present application randomly constructs a network structure with robust stability and maximized robust influence, and an initial population; combining the two evaluation indicators, the improved multi-objective evolutionary algorithm can be used to effectively evaluate and optimize the candidate network structure. Secondly, the present application can find a wider distribution of solutions and a better set of solutions through the improved multi-objective evolutionary algorithm, which has the advantage of high availability.

[0073] The embodiments of the present application provide a network construction and optimization method, device, electronic device and storage medium, which relate to the field of computer application technology. The network construction and optimization method, device, electronic device and storage medium provided in the embodiments of the present application can be applied to a terminal, can also be applied to a server, and can also be software running in a terminal or a server. In some embodiments, the terminal can be a smart phone, a tablet computer, a laptop computer, a desktop computer, a smart speaker, a smart watch, and a car terminal, etc., but is not limited to this; the server side can be configured as an independent physical server, or a server cluster or distributed system composed of multiple physical servers, and can also be configured to provide cloud services, cloud databases, cloud computing, cloud functions, cloud storage, network services, cloud communications, middleware services, domain name services, security services, CDN, and big data and artificial intelligence platforms and other basic cloud computing services. The server can also be a node server in a blockchain network; the software can be an application that implements a network construction and optimization method, etc., but is not limited to the above forms.

[0074] The present application can be used in many general or special computer system environments or configurations. For example: personal computers, server computers, handheld or portable devices, tablet devices, multiprocessor systems, microprocessor-based systems, set-top boxes, programmable consumer electronics, network PCs, minicomputers, mainframe computers, distributed computing environments including any of the above systems or devices, etc. The present application can be described in the general context of computer-executable instructions executed by a computer, such as program modules. Generally, program modules include routines, programs, objects, components, data structures, etc. that perform specific tasks or implement specific abstract data types. The present application can also be practiced in distributed computing environments, in which tasks are performed by remote processing devices connected through a communication network. In a distributed computing environment, program modules can be located in local and remote computer storage media including storage devices.

[0075] Reference Figure 1 The embodiment of the present application provides a network construction and optimization method, which may include but is not limited to S100 to S120, as follows:

[0076] S100: Determine evaluation indicators of the network; wherein the evaluation indicators include robustness evaluation indicators of the network and robust influence evaluation indicators of key nodes in the network.

[0077] It should be noted that the selection of each key node can be determined according to actual application needs as a node with maximum degree distribution, a node with maximum betweenness centrality, or a community center node, etc. Among them, each key node can be pre-selected.

[0078] Furthermore, S100 may include S101-S102:

[0079] S101: Determine the robustness evaluation index of the network when a node attack occurs in the network.

[0080] More specifically, S101 may include:

[0081] Determining the robustness evaluation index of the network when a node attack occurs to the network according to a first calculation formula;

[0082] The first calculation formula is:

[0083]

[0084] Among them, R represents the robustness evaluation index, N represents the number of nodes in the network, e represents the maximum limit of network damage, e is greater than or equal to 1, q represents the number of removed nodes, and s(q) represents the maximum connectivity ratio of the network after removing q nodes.

[0085] S102: Determine the robust influence evaluation index of the key node in the network when node damage occurs in the network and a cascading failure occurs in the network.

[0086] More specifically, S102 may include:

[0087] Determining, according to a second calculation formula, the robust influence evaluation index of the key node in the network when a node is damaged and a cascading failure occurs in the network;

[0088] The second calculation formula is:

[0089]

[0090] Among them, RIM cf represents the robust influence evaluation index, N overload represents the number of times the network overload event occurs, t represents the number of times the cascading failure occurs, represents the influence evaluation value of the key node;

[0091] The calculation formula of the influence evaluation value of the key node is:

[0092]

[0093] in, represents the sum of the influence ranges of each node in the set S of key nodes whose distance is 1; The overlapping influence of the nodes in the set S of the key nodes within the distance 1, the set C s represents the neighboring nodes within a distance of 1 of node s, p(c,s) represents the propagation probability between the activated node s and the node to be activated c, Represents the direct neighbor node of node c; represents the overlapping influence of the newly activated node c and the set S of key nodes; d represents the direct neighbor node of the first-order neighbor node c of the set S of key nodes, and d is not included in the set S of key nodes.

[0094] S110: Randomly reconnect the network according to the evaluation index to obtain an initial population.

[0095] Exemplarily, this embodiment may execute an initialization operator to guide and randomly generate an initial population through evaluation indicators, thereby improving the diversity of the initial population and laying a foundation for subsequent population evolution.

[0096] S120: updating the initial population based on an improved multi-objective evolutionary algorithm to construct a target network structure.

[0097] Further, S120 may include:

[0098] Executing the improved multi-objective evolutionary algorithm to update the initial population, so as to construct the target network structure;

[0099] Executing the improved multi-objective evolutionary algorithm includes the following steps S121 to S127:

[0100] S121: Calculate the fitness value of each individual in the initial population;

[0101] S122: performing non-dominated sorting, crowding distance calculation and elite preservation selection operator on each of the individuals in the initial population according to the fitness value to obtain a parent population;

[0102] S123: Execute a crossover operator and a mutation operator on the parent population to obtain an initial child population;

[0103] S124: Execute a non-similarity search operator on the initial offspring population, so as to make each of the individuals in the initial offspring population learn a network structure with the largest difference in network feature values, thereby obtaining an optimized offspring population;

[0104] S125: Mixing the parent population and the optimized offspring population to obtain an initial mixed population;

[0105] S126: performing non-dominated sorting, crowding distance calculation and elite preservation selection operator on each of the individuals in the initial mixed population according to the fitness value to obtain an optimized mixed population;

[0106] S127: Taking the optimized mixed population as the current initial population, returning to the step of calculating the fitness value of each individual in the initial population until a preset end condition is reached, and outputting the network structure of the non-dominated individuals in the current optimized mixed population as the target network structure.

[0107] Furthermore, S123 may include S1231-S1232:

[0108] S1231: Executing the crossover operator on the parent population includes the following steps:

[0109] Randomly select two individuals in the parent population to perform crossover, and perform edge connection swapping on two pairs of edges that are different in the network structures of the two randomly selected individuals;

[0110] If the degree distribution of the two individuals after the crossover is different from that of the original network, the crossover operator is re-executed.

[0111] S1232: Executing the mutation operator on the parent population includes the following steps:

[0112] The mutation operator is executed on each of the individuals in the parent population with a preset probability to introduce topological reconnection into the individuals, thereby adjusting the structure of the network.

[0113] As an optional implementation, S120 may further include:

[0114] S128: Recording the optimized mixed population and the corresponding network structure of each generation in the process of executing the improved multi-objective evolutionary algorithm; wherein the fitness value is recorded and displayed in a dynamic form.

[0115] Next, the solution of the embodiment of the present application will be introduced and explained in detail with reference to specific application examples.

[0116] This embodiment aims to address the shortcomings of the prior art. This embodiment is a method for constructing a complex network with stable structural characteristics and stable information propagation based on a multi-objective optimization algorithm. When the network is subject to external interference and attack, the maximum connected component of the network remains maximum, and the comprehensive performance evaluation indicators of the robustness and influence of key nodes maintain good performance.

[0117] This embodiment uses a multi-objective evolutionary algorithm to solve the problem of building a network with a stable network structure and maximizing the spread of stable influence. The specific feature is that according to the propagation of cascading failures in the network structure, the structural characteristics of the network are effectively jointly optimized, and the above characteristics are comprehensively used to construct a network structure with a stable structure and robust influence.

[0118] Specifically, this embodiment may include the following technical solutions:

[0119] (1) When a node attack occurs on the network, determine the network robustness evaluation index:

[0120] (1a) When a node attack occurs on the network, the maximum connectivity characteristics of the network are evaluated;

[0121] (1b) According to the first calculation formula The most connected components of the network after each node is damaged are normalized and summed to obtain the robustness level of the network when facing node attacks.

[0122] (2) When a node is damaged in the network, the robust influence evaluation index of the key nodes in the network is evaluated considering the cascading failure of the network:

[0123] (2a) Simulate t cascading failures on the current network and randomly select the failed node each time.

[0124] (2b) Simulate the cascading fault propagation process on the current network and re-evaluate the influence of the critical node set S at the end of each fault propagation until t cascading faults occur and the network completely collapses;

[0125] (2c) According to the second calculation formula The influence of the key node set S after each cascading failure is summed and normalized to obtain the robust influence level of the key node set S.

[0126] (3)Reference Figure 2 , based on the improved multi-objective evolutionary algorithm, network structure candidates with stable network structure and good robustness influence are selected.

[0127] (3a) Execute the initialization operator to construct the initial population through indicator guidance and random generation to ensure that the initial population has a certain diversity and lay the foundation for subsequent evolution. Specifically, perform the initialization operation: reconnect the network structure with random network topology. At the same time, the initialization operation with preference can improve the quality of candidate individuals and accelerate the convergence speed.

[0128] (3b) Evaluate the fitness of individuals in the population: Calculate the fitness value of each individual in the population according to the pre-defined evaluation method, including the robustness evaluation index R and the robust influence evaluation index RIM cf To quantify the non-dominated order of individuals.

[0129] (3c) Perform non-dominated sorting and calculate the non-dominance of individuals based on the crowding distance. Use the elite preservation selection operator to better preserve high-quality genes during the inheritance process to obtain the parent population. Specifically, this embodiment can perform non-dominated sorting and crowding calculation, and select the parent population of the initial population size to perform subsequent evolutionary operations. In the selection process, the elite preservation strategy is implemented. According to the non-dominance of individuals, individuals with non-dominance are more likely to be selected, and the optimal solution is used to further explore the solution space.

[0130] (3d) Execute the crossover operator and the mutation operator to generate the initial offspring population and enrich the population genes to increase the search range of the optimal solution.

[0131] Specifically, crossover and mutation operations are performed: each population member may perform crossover and mutation operations. When selecting two individuals for crossover, two individuals in the population are randomly selected, and two pairs of edge connections with differences in the network structure of these two individuals are found, and the edge connections are exchanged. If the degree distribution of the individual after the crossover is different from that of the original network, the crossover operation needs to be performed again to ensure that the adjustment of the network structure does not change the degree of the network nodes.

[0132] Perform mutation operation: Each individual executes the mutation operator with a certain probability, introducing topological reconnection to the individual to adjust the structure of the network.

[0133] (3e) Execute the non-similarity search operator to identify and learn the network structures with high or low similarity in a targeted manner. By optimizing the evolutionary direction of the population, the optimized offspring population is obtained, thereby improving the convergence speed of the algorithm and the optimization accuracy of the solution. Specifically, the search operation is performed: for each individual, the non-similarity search operator is executed with a preset probability, and the selected individual will select a network structure with the largest difference in network feature value from the global network for learning.

[0134] (3f) Mixed population update and non-dominated frontier update: The optimized offspring population is mixed with the parent population to obtain the initial mixed population. On this basis, the non-dominated sorting and crowding distance calculation are performed again to obtain the optimized mixed population: the non-dominated frontier update operator is used to update and save the non-dominated individuals in the initial mixed population to achieve continuous optimization of the high-quality solution.

[0135] (3g) Repeat steps (3b) to (3g) until a predetermined maximum number of evolutionary generations is reached, and output the non-dominated individuals of the final optimized mixed population. The network structure of the above non-dominated individuals is the optimal target network structure.

[0136] (3h) Output results: Output the network structure of the non-dominated frontier and record the optimized mixed population and the corresponding network structure of each generation in the evolution process. Among them, the fitness value is recorded and displayed in a dynamic form to facilitate the observation of the entire evolution process.

[0137] Reference Figure 3 The embodiment of the present application also provides a network construction and optimization device, which can implement the above-mentioned network construction and optimization method, and the device includes:

[0138] An indicator determination unit, used to determine an evaluation indicator of the network; wherein the evaluation indicator includes a robustness evaluation indicator of the network and a robust influence evaluation indicator of a key node in the network;

[0139] A network construction unit, used for randomly reconnecting the network according to the evaluation index to obtain an initial population;

[0140] The network optimization unit is used to update the initial population based on an improved multi-objective evolutionary algorithm to construct a target network structure.

[0141] It can be understood that the contents of the above method embodiments are all applicable to the present device embodiments, the functions specifically implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0142] The embodiment of the present application also provides an electronic device, the electronic device includes a memory and a processor, the memory stores a computer program, and the processor implements the above-mentioned network construction and optimization method when executing the computer program. The electronic device can be any intelligent terminal including a tablet computer, a car computer, etc.

[0143] It can be understood that the contents of the above method embodiments are all applicable to the present device embodiments, the functions specifically implemented by the present device embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0144] See also Figure 4 , Figure 4 The hardware structure of an electronic device of another embodiment is illustrated, and the electronic device includes:

[0145] The processor 401 may be implemented by a general-purpose CPU (Central Processing Unit), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of the present application;

[0146] The memory 402 can be implemented in the form of a read-only memory (ROM), a static storage device, a dynamic storage device, or a random access memory (RAM). The memory 402 can store an operating system and other application programs. When the technical solution provided in the embodiment of this specification is implemented by software or firmware, the relevant program code is stored in the memory 402, and the processor 401 calls and executes a network construction and optimization method of the embodiment of this application;

[0147] Input / output interface 403, used to implement information input and output;

[0148] Communication interface 404, used to realize communication interaction between the device and other devices, which can be realized by wired mode (such as USB, network cable, etc.) or wireless mode (such as mobile network, WIFI, Bluetooth, etc.);

[0149] Bus 405 , which transmits information between various components of the device (e.g., processor 401 , memory 402 , input / output interface 403 , and communication interface 404 );

[0150] The processor 401 , the memory 402 , the input / output interface 403 and the communication interface 404 are connected to each other in communication within the device via the bus 405 .

[0151] An embodiment of the present application also provides a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the above-mentioned network construction and optimization method is implemented.

[0152] It can be understood that the contents of the above method embodiments are all applicable to the present storage medium embodiments, the functions specifically implemented by the present storage medium embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0153] The memory, as a non-transient computer-readable storage medium, can be used to store non-transient software programs and non-transient computer executable programs. In addition, the memory may include a high-speed random access memory, and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some embodiments, the memory may optionally include a memory remotely disposed relative to the processor, and these remote memories may be connected to the processor via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0154] The embodiments described in the embodiments of the present application are intended to more clearly illustrate the technical solutions of the embodiments of the present application and do not constitute a limitation on the technical solutions provided in the embodiments of the present application. Those skilled in the art will appreciate that with the evolution of technology and the emergence of new application scenarios, the technical solutions provided in the embodiments of the present application are also applicable to similar technical problems.

[0155] Those skilled in the art will appreciate that the technical solutions shown in the figures do not constitute a limitation on the embodiments of the present application, and may include more or fewer steps than shown in the figures, or a combination of certain steps, or different steps.

[0156] The device embodiments described above are merely illustrative, and the units described as separate components may or may not be physically separated, that is, they may be located in one place or distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0157] Those skilled in the art will appreciate that all or some of the steps in the methods disclosed above, and the functional modules / units in the systems and devices may be implemented as software, firmware, hardware, or a suitable combination thereof.

[0158] The terms "first", "second", "third", "fourth", etc. (if any) in the specification of the present application and the above-mentioned drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence. It should be understood that the data used in this way can be interchangeable where appropriate, so that the embodiments of the present application described herein can be implemented in an order other than those illustrated or described herein. In addition, the terms "including" and "having" and any of their variations are intended to cover non-exclusive inclusions, for example, a process, method, system, product or device comprising a series of steps or units is not necessarily limited to those steps or units clearly listed, but may include other steps or units that are not clearly listed or inherent to these processes, methods, products or devices.

[0159] It should be understood that in the present application, "at least one (item)" means one or more, and "plurality" means two or more. "And / or" is used to describe the association relationship of associated objects, indicating that three relationships may exist. For example, "A and / or B" can mean: only A exists, only B exists, and A and B exist at the same time, where A and B can be singular or plural. The character " / " generally indicates that the objects associated before and after are in an "or" relationship. "At least one of the following" or similar expressions refers to any combination of these items, including any combination of single or plural items. For example, at least one of a, b or c can mean: a, b, c, "a and b", "a and c", "b and c", or "a and b and c", where a, b, c can be single or multiple.

[0160] In the several embodiments provided in the present application, it should be understood that the disclosed devices and methods can be implemented in other ways. For example, the device embodiments described above are only schematic. For example, the division of the above units is only a logical function division. There may be other division methods in actual implementation, such as multiple units or components can be combined or integrated into another system, or some features can be ignored or not executed. Another point is that the mutual coupling or direct coupling or communication connection shown or discussed can be through some interfaces, indirect coupling or communication connection of devices or units, which can be electrical, mechanical or other forms.

[0161] The units described above as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0162] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit. The above-mentioned integrated unit may be implemented in the form of hardware or in the form of software functional units.

[0163] If the integrated unit is implemented in the form of a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or all or part of the technical solution can be embodied in the form of a software product, and the computer software product is stored in a storage medium, including multiple instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of various embodiments of the present application. The aforementioned storage medium includes: U disk, mobile hard disk, read-only memory (Read-Only Memory, referred to as ROM), random access memory (Random Access Memory, referred to as RAM), disk or optical disk and other media that can store programs.

[0164] The preferred embodiments of the present invention are described above with reference to the accompanying drawings, but the scope of the rights of the present invention is not limited thereto. Any modification, equivalent substitution and improvement made by a person skilled in the art without departing from the scope and essence of the present invention should be within the scope of the rights of the present invention.

Claims

1. A network construction and optimization method, characterized in that: The method comprises the following steps: Determining evaluation indicators of the network; wherein the evaluation indicators include robustness evaluation indicators of the network and robust influence evaluation indicators of key nodes in the network; Randomly reconnect the network according to the evaluation index to obtain an initial population; The initial population is updated based on an improved multi-objective evolutionary algorithm to construct a target network structure.

2. A network construction and optimization method according to claim 1, characterized in that: Determining the evaluation index of the network includes the following steps: Determining the robustness evaluation index of the network when a node attack occurs on the network; Determine the robust influence evaluation index of the key node in the network when node damage occurs in the network and a cascading failure occurs in the network.

3. A network construction and optimization method according to claim 2, characterized in that: Determining the robustness evaluation index of the network when a node attack occurs in the network comprises the following steps: Determining the robustness evaluation index of the network when a node attack occurs to the network according to a first calculation formula; The first calculation formula is: Among them, R represents the robustness evaluation index, N represents the number of nodes in the network, e represents the maximum limit of network damage, e is greater than or equal to 1, q represents the number of removed nodes, and s(q) represents the maximum connectivity ratio of the network after removing q nodes.

4. A network construction and optimization method according to claim 2, characterized in that: Determining the robust influence evaluation index of the key node in the network when node damage occurs in the network and a cascading failure occurs in the network comprises the following steps: Determining, according to a second calculation formula, the robust influence evaluation index of the key node in the network when a node is damaged and a cascading failure occurs in the network; The second calculation formula is: Among them, RIM cf represents the robust influence evaluation index, N overload represents the number of times the network overload event occurs, t represents the number of times the cascading failure occurs, represents the influence evaluation value of the key node; The calculation formula of the influence evaluation value of the key node is: in, represents the sum of the influence ranges of each node in the set S of key nodes whose distance is 1; The overlapping influence of the nodes in the set S of the key nodes within the distance 1, the set C s represents the neighboring nodes within a distance of 1 of node s, p(c,s) represents the propagation probability between the activated node s and the node to be activated c, Represents the direct neighbor node of node c; represents the overlapping influence of the newly activated node c and the set S of key nodes; d represents the direct neighbor node of the first-order neighbor node c of the set S of key nodes.

5. A network construction and optimization method according to claim 1, characterized in that: The method of updating the initial population based on the improved multi-objective evolutionary algorithm to construct a target network structure includes the following steps: Executing the improved multi-objective evolutionary algorithm to update the initial population, so as to construct the target network structure; Executing the improved multi-objective evolutionary algorithm comprises the following steps: Calculating the fitness value of each individual in the initial population; According to the fitness value, each of the individuals in the initial population is subjected to non-dominated sorting, crowding distance calculation, and an elite preservation selection operator to obtain a parent population; Execute a crossover operator and a mutation operator on the parent population to obtain an initial child population; Executing a non-similarity search operator on the initial offspring population so as to make each of the individuals in the initial offspring population learn a network structure with the largest difference in network feature values, thereby obtaining an optimized offspring population; Mixing the parent population and the optimized offspring population to obtain an initial mixed population; According to the fitness value, each of the individuals in the initial mixed population is subjected to non-dominated sorting, crowding distance calculation, and an elite preservation selection operator is adopted to obtain an optimized mixed population; The optimized mixed population is used as the current initial population, and the step of calculating the fitness value of each individual in the initial population is returned until a preset end condition is reached, and the network structure of the non-dominated individuals in the current optimized mixed population is output as the target network structure.

6. A network construction and optimization method according to claim 5, characterized in that: The step of executing a crossover operator and a mutation operator on the parent population to obtain an initial child population includes the following steps: Executing the crossover operator on the parent population comprises the following steps: Randomly select two individuals in the parent population to perform crossover, and perform edge connection swapping on two pairs of edges that are different in the network structures of the two randomly selected individuals; If the degree distribution of the two individuals after the crossover is different from that of the original network, the crossover operator is re-executed; Executing the mutation operator on the parent population includes the following steps: The mutation operator is executed on each of the individuals in the parent population with a preset probability to introduce topological reconnection into the individuals, thereby adjusting the structure of the network.

7. A network construction and optimization method according to claim 5, characterized in that: The method further comprises the following steps: The optimized mixed population and the corresponding network structure of each generation in the process of executing the improved multi-objective evolutionary algorithm are recorded; wherein the fitness value is recorded and displayed in a dynamic form.

8. A network construction and optimization device, characterized in that: The device comprises: An indicator determination unit, used to determine an evaluation indicator of the network; wherein the evaluation indicator includes a robustness evaluation indicator of the network and a robust influence evaluation indicator of a key node in the network; A network construction unit, used for randomly reconnecting the network according to the evaluation index to obtain an initial population; The network optimization unit is used to update the initial population based on an improved multi-objective evolutionary algorithm to construct a target network structure.

9. An electronic device, characterized in that: The electronic device comprises a memory and a processor, the memory stores a computer program, and the processor implements the method according to any one of claims 1 to 7 when executing the computer program.

10. A computer-readable storage medium storing a computer program, characterized in that: When the computer program is executed by a processor, the method according to any one of claims 1 to 7 is implemented.

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