A load distribution method, device, equipment and medium of a complex network

Abstract

The application is suitable for the technical field of complex network cascading failure, and provides a load distribution method, device, equipment and medium for a complex network. The method comprises the following steps: step 1, a plurality of network nodes are acquired, and a topology structure is constructed; step 2, if the sum of the capacity margins of all adjacent nodes of a fault node is less than or equal to the load of the fault node, the distribution parameters of the adjacent nodes are acquired based on the load of the fault node and the importance weight of the adjacent nodes; if the sum of the capacity margins of all adjacent nodes of the fault node is greater than the load of the fault node, the load of the fault node is proportionally distributed to the adjacent nodes of the fault node; step 3, the load of the fault node is distributed to the adjacent nodes according to the distribution parameters corresponding to the adjacent nodes, and when the load of an adjacent node is greater than the total capacity of the adjacent node after the load is distributed, the adjacent node is taken as the fault node in step 2 and step 2 is executed again. The method can improve the robustness of the complex network.

Description

Technical Field

[0001] This application relates to the field of complex network cascading fault technology, and in particular to a load distribution method, apparatus, device and medium for complex networks. Background Technology

[0002] As human society becomes increasingly networked, the connection between human society and complex network systems becomes closer. Simultaneously, there is an exchange of matter, energy, and information between the various components of the network and between the network's internal and external environments. Once external systems exert interference or the network's own systems malfunction, changes in the matter, energy, and information within the network can occur, potentially causing a component to fail. Due to the close connections or interactions between nodes or edges, this failure can easily propagate throughout the network, altering the network's connectivity and the reachability between nodes. In the real world, the failure of one or a few nodes in a network can trigger the failure of numerous nodes, even leading to a complete network collapse, resulting in severe economic losses. Once these large network systems experience cascading failures, they cannot function normally, significantly impacting people's lives and production, and potentially causing serious socio-economic losses. Therefore, mitigating the impact of cascading failures on complex networks has become an urgent problem to solve. Researching robustness improvement strategies for complex networks under cascading failures has significant theoretical and practical application value.

[0003] Research problems in network science originate from various real-world networks. Therefore, some concepts, methods, and theories derived from network science can be used to guide the analysis and design of real-world network performance. In recent years, an increasing number of scientists have studied the dynamic behavior of cascading failures in complex networks from the perspectives of modeling, analysis, and control. However, due to the mutual coupling and influence between the components within complex networks, as well as the complexity of the dynamic behavior, the study of cascading failure behavior remains a highly challenging and important direction in the field of complex networks. As the scale of complex network systems in the real world continues to expand, the types of disturbances they experience also become increasingly complex. These disturbances make the systems prone to collapse, highlighting the low robustness of complex networks. Summary of the Invention

[0004] This application provides a load distribution method, apparatus, device, and medium for complex networks, which can solve the problem of low robustness in complex networks.

[0005] In a first aspect, embodiments of this application provide a load distribution method for complex networks, the load distribution method comprising: Step 1: Obtain multiple network nodes in the target complex network and construct the topology of the target complex network; the multiple nodes in the topology correspond one-to-one with the multiple network nodes, and the edge between each pair of nodes represents the adjacency relationship between the two corresponding network nodes. Step 2: If the sum of the capacity margins of all neighboring nodes of the faulty node in the target complex network is less than or equal to the load of the faulty node, then for each neighboring node of the faulty node, the allocation parameters of the neighboring nodes are obtained based on the load of the faulty node and the importance weight of the neighboring nodes. Step 3: For each neighboring node of the faulty node, the load of the faulty node is distributed to the neighboring nodes according to the corresponding distribution parameters. When the load of the neighboring node after being distributed exceeds the total load capacity of the neighboring nodes, the neighboring node is returned as the faulty node in Step 2 and Step 2 is executed again.

[0006] Optional, also includes: If the sum of the capacity margins of all neighboring nodes of a faulty node in the target complex network is greater than the load of the faulty node, then the load of the faulty node will be distributed proportionally to all neighboring nodes of the faulty node.

[0007] Optionally, the load of the failed node can be proportionally distributed to all its neighboring nodes, including: Through the formula:

[0008] Calculate the first The load distributed to each adjacent node ; in, Indicates the faulty node The current load, Indicates the first The current load of each adjacent node. Indicates the first The total load capacity of the adjacent nodes. , Indicates the first Initial load of adjacent nodes, This represents the capacity threshold parameter. Indicates a faulty node in the topology. The set of adjacent nodes of the corresponding node. , This represents the total number of network nodes in the target complex network; The first The load distributed to each adjacent node Assigned to the 1 neighboring node.

[0009] Optionally, based on the load of the failed node and the importance weights of neighboring nodes, the allocation parameters of neighboring nodes are obtained, including: Based on the load of the faulty node and the importance weights of the adjacent nodes, an objective function is constructed for the load allocation optimization problem of adjacent nodes. An optimization model is constructed based on the objective function and constraints of the load allocation optimization problem, and the Lagrange augmented function of the optimization model is obtained. An iterative algorithm is designed based on the Lagrange augmented function to obtain the allocation parameters of adjacent nodes.

[0010] Optionally, the objective function of the load balancing optimization problem is:

[0011] in, Indicates a faulty node in the topology. The set of adjacent nodes of the corresponding node. For step function, when Greater than hour, ,when Less than hour, After L1 norm regularization, it can be expressed as , Indicates the first The total load capacity of the adjacent nodes. Indicates the first The probability of failure of each adjacent node. , Indicates the first The remaining capacity after the load is distributed to each adjacent node. Indicates assignment to the first The load of each adjacent node Indicates the first The current load of each adjacent node Indicates the first The total load capacity of the adjacent nodes. , Indicates the first The importance weights of each adjacent node, when hour, , ,when hour, .

[0012] Optionally, the optimized model is: Through the formula:

[0013]

[0014] in, , , Indicates the faulty node The remaining capacity vector after all adjacent network nodes have been loaded. Indicates the faulty node The current load after all adjacent network nodes have been assigned load, , Indicates a faulty node in the topology. The set of adjacent nodes of the corresponding node. , This represents the total number of network nodes in the target complex network. Indicates an indicator function, when hour, ,when hour, , Indicates the faulty node The total load capacity matrix of all adjacent nodes. This represents a parameter matrix where the elements are either 1 or 0. This represents a parameter matrix where the elements are 0 or -1. Representing vectors Importance weight matrix:

[0015]

[0016] in, This represents the total load capacity of the first adjacent node. This represents the total load capacity of the second adjacent node. Indicates the first The total load capacity of the adjacent nodes. Represents a set The total number of elements in Indicates the faulty node capacity, , This represents the weighted parameters of the 0th network node. This represents the weighted parameters of the first network node. Indicates the first Weighted parameters of each network node, This represents the importance weight of the 0th network node. This represents the importance weight of the first network node. Indicates the first The importance weight of each network node. Represents the 1-norm; The Lagrange augmented function of the optimization model is:

[0017] in, This represents the value of the Lagrange augmented function. Represents the dual variable. This represents the matrix transpose operation. The coefficient representing the penalty term. This represents the square of the vector's magnitude.

[0018] Optionally, an iterative algorithm is designed based on the Lagrange augmented function to obtain the assignment parameters of adjacent nodes, including: The parameters in the Lagrange augmented function are iterated using an iterative formula, with the iteration count incremented by 1. The iterative formula is as follows:

[0019]

[0020]

[0021] in, Indicates the first Faulty node during the next iteration The remaining capacity matrix after all adjacent nodes have been assigned loads. Indicates the first During the next iteration The value, Indicates the first During the next iteration The value, Represents the importance weight matrix, The coefficient representing the penalty term. Represents the identity matrix. This represents a parameter matrix where the elements are either 1 or 0. This represents a parameter matrix where the elements are 0 or -1. , Represents a mapping function; Through the formula:

[0022] Calculate the remaining capacity difference ; Determine the difference in remaining capacity Is it less than or equal to the preset difference in remaining capacity? If the remaining capacity difference If the remaining capacity difference is less than or equal to the preset difference, the weighted parameters are updated using the weighted parameter update formula, and the update count is incremented by 1. The weighted parameter update formula is:

[0023] in, Indicates the first During the nth iteration The remaining capacity after the load is distributed to each adjacent node. Indicates the first The first update The values ​​of the weighted parameters of the neighboring nodes, Represents a constant. , Indicates a faulty node in the topology. The set of adjacent nodes of the corresponding node. , This represents the total number of network nodes in the target complex network; judge Is it less than ;in, Indicates the first The first update The values ​​of the weighted parameters of the adjacent nodes; like Less than Then As the first The allocation parameters for each adjacent node; like Greater than or equal to Returns the steps of iterating over the parameters in the Lagrange augmented function using the iterative formula; If the remaining capacity difference If the difference exceeds the preset remaining capacity, return to the steps of iterating the parameters in the Lagrange augmented function using the iterative formula.

[0024] Optionally, the load of the failed node is distributed to neighboring nodes according to the allocation parameters corresponding to the neighboring nodes, including: Through the formula:

[0025] Calculate the allocation to the first Load of adjacent nodes ; in, Indicates the first The allocation parameters for each adjacent node. Indicates the first The total load capacity of the adjacent nodes. Indicates the first The current load of each adjacent node; According to the allocation to the Load of adjacent nodes , for the first The load is distributed among adjacent nodes.

[0026] Secondly, embodiments of this application provide a load distribution apparatus for complex networks, comprising: The construction module is used to perform step 1: obtain multiple network nodes in the target complex network and construct the topology of the target complex network; the multiple nodes in the topology correspond one-to-one with the multiple network nodes, and the edge between each two nodes represents the adjacency relationship between the corresponding two network nodes; The acquisition module is used to execute step 2: If the sum of the capacity margins of all neighboring nodes of the faulty node in the target complex network is less than or equal to the load of the faulty node, then for each neighboring node of the faulty node, the allocation parameters of the neighboring nodes are acquired based on the load of the faulty node and the importance weight of the neighboring nodes. The allocation module is used to execute step 3: for each adjacent node of the faulty node, the load of the faulty node is allocated to the adjacent nodes according to the allocation parameters of the adjacent nodes. When the load of the adjacent node after being allocated is greater than the total load capacity of the adjacent nodes, the adjacent node is regarded as the faulty node in step 2 and the acquisition module is triggered to execute step 2.

[0027] Thirdly, embodiments of this application provide a terminal device, including a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the computer program, it implements the aforementioned load distribution method for complex networks.

[0028] Fourthly, embodiments of this application provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned load distribution method for complex networks.

[0029] The above-mentioned solution in this application has the following beneficial effects: In the embodiments of this application, by acquiring multiple network nodes in the target complex network and constructing the topology of the target complex network, if the sum of the capacity margins of all adjacent nodes of the faulty node in the target complex network is less than or equal to the load of the faulty node, then for each adjacent node of the faulty node, allocation parameters of the adjacent nodes are obtained based on the load of the faulty node and the importance weight of the adjacent nodes. Finally, for each adjacent node of the faulty node, the load of the faulty node is allocated to the adjacent nodes according to the corresponding allocation parameters. When the load of an adjacent node after being allocated is greater than the total load capacity of the adjacent nodes, the adjacent node is regarded as the faulty node, and its load is allocated. The method of obtaining the allocation parameters of the adjacent nodes based on the load of the faulty node and the importance weight of the adjacent nodes, and then allocating the load based on the allocation parameters, can improve the rationality of load allocation to adjacent nodes, reduce the possibility of adjacent nodes failing due to excessive load allocation, reduce the scale of network node failures in complex networks, and effectively improve the robustness of complex networks.

[0030] Other beneficial effects of this application will be described in detail in the following detailed description section. Attached Figure Description

[0031] To more clearly illustrate the technical solutions in the embodiments of this application, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0032] Figure 1 A flowchart illustrating a load distribution method for a complex network according to an embodiment of this application; Figure 2 A schematic diagram of a topology provided in an embodiment of this application; Figure 3 A detailed flowchart of a load distribution method for complex networks provided in an embodiment of this application; Figure 4 Robustness curves in scale-free networks provided in one embodiment of this application; Figure 5 Robustness curves in small-world networks provided as an embodiment of this application; Figure 6 A robustness curve in a random network provided in an embodiment of this application; Figure 7 A schematic diagram of the structure of a load distribution device for a complex network provided in an embodiment of this application; Figure 8This is a schematic diagram of the structure of a terminal device provided in an embodiment of this application. Detailed Implementation

[0033] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0034] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0035] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0036] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0037] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0038] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0039] To address the low robustness of existing complex networks, this application provides a load allocation method for complex networks. This method involves acquiring multiple network nodes in a target complex network and constructing its topology. If the sum of the capacity margins of all adjacent nodes of a faulty node is less than or equal to the load of the faulty node, then for each adjacent node of the faulty node, allocation parameters are obtained based on the faulty node's load and the importance weights of the adjacent nodes. Finally, for each adjacent node of the faulty node, its load is allocated to the adjacent nodes according to these allocation parameters. When the load of an adjacent node after being allocated exceeds its total capacity, the adjacent node is designated as the faulty node, and its load is allocated accordingly. The method of obtaining allocation parameters based on the faulty node's load and the importance weights of the adjacent nodes, and then allocating load based on these parameters, improves the rationality of load allocation to adjacent nodes, reduces the possibility of adjacent nodes failing due to excessive load allocation, decreases the scale of network node failures in complex networks, and effectively improves the robustness of complex networks.

[0040] The following is an exemplary description of the load distribution method for complex networks in this application.

[0041] like Figure 1 As shown, the load distribution method for complex networks in this application includes the following steps: Step 1: Obtain multiple network nodes in the target complex network and construct the topology of the target complex network.

[0042] The aforementioned complex network is a system composed of multiple interconnected computing devices or operating devices, such as a communication network. Network nodes can be computing devices or operating devices in the complex network, such as each communication device in the communication network. The aforementioned load refers to programs, tasks, etc., that occupy the capacity of the network nodes and are executed.

[0043] In the above topology, each node corresponds to a network node, and the edge between any two nodes represents the adjacency relationship between the two corresponding network nodes.

[0044] In some embodiments of this application, the topology of the target complex network can be constructed using computer software for data processing such as Matlab.

[0045] It should be noted that the aforementioned target complex network refers to a complex network in which network nodes fail and load distribution is required.

[0046] It is worth mentioning that obtaining the topology of the target complex network can describe the network nodes and the adjacency relationships between them, which facilitates the calculation in subsequent steps.

[0047] The above topology will be illustrated with a specific example below.

[0048] like Figure 2 As shown in the figure, the edges with arrows represent the connection relationships between nodes in the topology, the black circles represent nodes that are assigned load, the black circle in the center represents the faulty node, and the white circles represent the normally operating nodes.

[0049] Step 2: If the sum of the capacity margins of all neighboring nodes of the faulty node in the target complex network is less than or equal to the load of the faulty node, then for each neighboring node of the faulty node, the allocation parameters of the neighboring nodes are obtained based on the load of the faulty node and the importance weight of the neighboring nodes.

[0050] In some embodiments of this application, the steps of obtaining the allocation parameters of neighboring nodes include: constructing an objective function for the load allocation optimization problem of neighboring nodes based on the load of the faulty node and the importance weights of the neighboring nodes; constructing an optimization model based on the objective function and constraints of the load allocation optimization problem and obtaining the Lagrange augmented function of the optimization model; and designing an iterative algorithm based on the Lagrange augmented function to obtain the allocation parameters of neighboring nodes.

[0051] For example, the allocation parameters of adjacent nodes can be obtained based on the weighted L1 algorithm and the alternating direction multiplier method.

[0052] It should be noted that the aforementioned faulty nodes are network nodes in complex networks that have failed or been attacked and are therefore unable to continue operating. Before proceeding to step 2, it is necessary to determine whether the sum of the capacity margins of all neighboring nodes of the faulty node in the target complex network is less than or equal to the load of the faulty node. If the sum of the capacity margins of all neighboring nodes of the faulty node in the target complex network is less than or equal to the load of the faulty node, then proceed with the above steps; if the sum of the capacity margins of all neighboring nodes of the faulty node in the target complex network is greater than the load of the faulty node, then the load of the faulty node is proportionally distributed to all neighboring nodes of the faulty node, specifically: Through the formula:

[0053] Calculate the first The load distributed to each adjacent node ; in, Indicates the faulty node The current load, Indicates the first The current load of each adjacent node. Indicates the first The total load capacity of the adjacent nodes. , Indicates the first Initial load of adjacent nodes, This represents the capacity threshold parameter. This represents a faulty node in the topology. The set of adjacent nodes of the corresponding node. , This represents the total number of network nodes in the target complex network; The first The load distributed to each adjacent node Assigned to the There are 10 adjacent nodes.

[0054] For example, if a faulty node in a target complex network has three neighboring nodes, the faulty node has a load of 6, the total load capacity of each of the three neighboring nodes is 6, and each neighboring node is under load, and the sum of the remaining load capacities of all neighboring nodes of the faulty node is greater than 6, then the load allocated to each neighboring node is calculated according to the formula above. If the sum of the remaining load capacities of all neighboring nodes of the faulty node is less than 6, then for each neighboring node of the faulty node, based on the load of the faulty node and the importance weight of the neighboring nodes, the allocation parameters of the neighboring nodes are obtained, and subsequent calculations are performed to determine the load allocated to the neighboring nodes.

[0055] It is worth mentioning that by considering the load distribution under the two scenarios separately and using different methods to determine the load allocated to adjacent nodes, the rationality of load distribution to adjacent nodes under different circumstances can be improved. Furthermore, considering the load of the faulty node and the importance weight of the adjacent nodes can improve the accuracy of the obtained distribution parameters.

[0056] Step 3: For each neighboring node of the faulty node, the load of the faulty node is distributed to the neighboring nodes according to the corresponding distribution parameters. When the load of the neighboring node after being distributed exceeds the total load capacity of the neighboring nodes, the neighboring node is returned as the faulty node in Step 2 and Step 2 is executed again.

[0057] In some embodiments of this application, the step of allocating the load of the faulty node to neighboring nodes according to the allocation parameters corresponding to the neighboring nodes includes: The first step is through the formula:

[0058] Calculate the allocation to the first Load of adjacent nodes ; in, Indicates the first The allocation parameters for each adjacent node. Indicates the first The total load capacity of the adjacent nodes. Indicates the first The current load of each adjacent node.

[0059] The second step is based on the allocation to the first... Load of adjacent nodes , for the first The load is distributed among adjacent nodes.

[0060] For example, if the load of the faulty node is 6, and the load of the first adjacent node of the faulty node is calculated to be 3 according to the above steps, then the first adjacent node of the faulty node is allocated a load with a capacity of 3.

[0061] It should be noted that the above steps of allocating the load of the faulty node to its neighboring nodes based on the allocation parameters of the neighboring nodes are based on the condition that the sum of the capacity margins of all neighboring nodes of the faulty node in the target complex network is less than or equal to the load of the faulty node. Therefore, after the load is allocated, the load of some neighboring nodes will inevitably exceed the total load capacity. However, by using the objective function of the above load allocation optimization problem to allocate the load to the neighboring nodes of the faulty node, the number of neighboring nodes that exceed the total load capacity can be reduced to the expected number. Then, the neighboring nodes that exceed the total load capacity are regarded as faulty nodes, and the load of the faulty node is allocated.

[0062] For example, after the load of a faulty node in the target complex network is distributed to its neighboring nodes, the total load of the first neighboring node of the faulty node is 8, and the total load capacity of the first neighboring node is 6. Since the total load exceeds the total load capacity, the first neighboring node is designated as the faulty node, and the process returns to step 2 above to distribute the load of the faulty node. After the load of the neighboring nodes of the faulty node is distributed, the situation of the load exceeding the total load capacity no longer occurs, and the target complex network operates normally.

[0063] It is worth mentioning that by allocating the load to adjacent nodes according to the allocation parameters, it is possible to assign an appropriate load to adjacent nodes, reducing the possibility of adjacent nodes failing due to excessive load. By treating adjacent nodes with a load exceeding the total load capacity as faulty nodes and redistributing the load, it is possible to effectively handle adjacent nodes whose total load exceeds the total load capacity, ensuring the normal operation of the target complex network as a whole.

[0064] The specific steps of step 2 described above will be illustrated below with reference to specific embodiments.

[0065] In some embodiments of this application, the specific implementation process of step 2 above includes the following steps: Step 2.1: Based on the load of the faulty node and the importance weights of the adjacent nodes, construct the objective function for the load allocation optimization problem of the adjacent nodes.

[0066] The objective function for the above load distribution optimization problem is:

[0067] in, This represents a faulty node in the topology. The set of adjacent nodes of the corresponding node. For step function, when Greater than hour, ,when Less than hour, After L1 norm regularization, it can be expressed as , Indicates the first The total load capacity of the adjacent nodes. Indicates the first The probability of failure of each adjacent node. , Indicates the first The remaining capacity after the load is distributed to each adjacent node. Indicates assignment to the first The load of each adjacent node Indicates the first The current load of each adjacent node Indicates the first The total load capacity of the adjacent nodes. , Indicates the first The importance weights of each adjacent node, when hour, , ,when hour, .

[0068] Step 2.2: Construct an optimization model based on the objective function and constraints of the load allocation optimization problem, and obtain the Lagrange augmented function of the optimization model.

[0069] The above optimization model is:

[0070]

[0071] in, , , Indicates the faulty node The remaining capacity vector after all adjacent network nodes have been loaded. Indicates the faulty node The current load after all adjacent network nodes have been assigned load, , This represents a faulty node in the topology. The set of adjacent nodes of the corresponding node. , This represents the total number of network nodes in the target complex network. Indicates an indicator function, when hour, ,when hour, , Indicates the faulty node The total load capacity matrix of all adjacent nodes. This represents a parameter matrix where the elements are either 1 or 0. This represents a parameter matrix where the elements are 0 or -1. Representing vectors Importance weight matrix:

[0072]

[0073]

[0074]

[0075] in, This represents the total load capacity of the first adjacent node. This represents the total load capacity of the second adjacent node. Indicates the first The total load capacity of the adjacent nodes. Represents a set The total number of elements in the array. Indicates the faulty node capacity, , This represents the weighted parameter of the 0th network node. This represents the weighted parameters of the first network node. Indicates the first Weighted parameters of each network node, This represents the importance weight of the 0th network node. This represents the importance weight of the first network node. Indicates the first The importance weight of each network node. It represents the 1-norm.

[0076] The Lagrange augmented function of the above optimization model is:

[0077] in, This represents the value of the Lagrange augmented function. Represents the dual variable. This represents the matrix transpose operation. The coefficient representing the penalty term. This represents the square of the vector's magnitude.

[0078] It should be noted that, This represents the total number of network nodes. This represents the total number of neighboring nodes of a faulty node. In the same complex network, these neighboring nodes are also network nodes within the complex network. However, due to different sets they belong to, a node may have two different indices; that is, the first neighboring node of a faulty node may be the third network node. In reality, both indices represent the same node. However, in practical applications, indices are not used to represent nodes. Instead, nodes are selected for calculation according to the actual situation in the above formula. A unified description is used for node representation, such as: network node. a These are the adjacent nodes of the faulty node.

[0079] Step 2.3: Design an iterative algorithm based on the Lagrange augmented function to obtain the allocation parameters of adjacent nodes.

[0080] The first step is to iterate the parameters in the Lagrange augmented function using an iterative formula, incrementing the iteration count by 1. The iterative formula is as follows:

[0081]

[0082]

[0083] in, Indicates the first Faulty node during the next iteration The remaining capacity matrix after all adjacent nodes have been assigned load. Indicates the first During the next iteration The value, Indicates the first During the next iteration The value, Represents the importance weight matrix, The coefficient representing the penalty term. Represents the identity matrix. This represents a parameter matrix where the elements are either 1 or 0. This represents a parameter matrix where the elements are 0 or -1. , This represents a mapping function.

[0084] The second step is to use the formula:

[0085] Calculate the remaining capacity difference ; Determine the difference in remaining capacity Is it less than or equal to the preset difference in remaining capacity?

[0086] If the remaining capacity difference If the remaining capacity difference is less than or equal to the preset difference, the weighted parameters are updated using the weighted parameter update formula, and the update count is incremented by 1. The weighted parameter update formula is:

[0087] in, Indicates the first During the nth iteration The remaining capacity after the load is distributed to each adjacent node. Indicates the first The first update The values ​​of the weighted parameters of the neighboring nodes, Represents a constant. , This represents a faulty node in the topology. The set of adjacent nodes of the corresponding node. , This represents the total number of network nodes in the target complex network.

[0088] judge Is it less than ;in, Indicates the first The first update The value of the weighted parameter of each of the adjacent nodes.

[0089] like Less than Then As the first The allocation parameters for each adjacent node.

[0090] like Greater than or equal to This returns the steps of iterating over the parameters in the Lagrange augmented function using an iterative formula.

[0091] If the remaining capacity difference If the difference exceeds the preset remaining capacity, return to the steps of iterating the parameters in the Lagrange augmented function using the iterative formula.

[0092] It should be noted that the above mapping function satisfy ,in and They are all one-dimensional vectors.

[0093] For example, if the remaining capacity difference is greater than the preset remaining capacity difference in the 10th iteration, then return to the step of iterating the parameters in the Lagrange augmented function using the iterative formula and incrementing the iteration count by 1, and perform the 11th iteration. If the remaining capacity difference is less than or equal to the preset remaining capacity difference in the 10th iteration, then based on the 10th iteration... The remaining capacity after the load is allocated to each adjacent node is used to update the weighting parameters, and it is determined whether the difference between the updated weighting parameters and the original weighting parameters is less than 1. If so, then the 10th iteration will be the... The remaining capacity after the load is allocated to the nth adjacent node is used as the th If the parameters of the adjacent nodes are not assigned, return to the step of iterating the parameters in the Lagrange augmented function using the iterative formula and incrementing the iteration count by 1, and perform the 11th iteration.

[0094] It is worth mentioning that by obtaining the allocation parameters of neighboring nodes based on the load of the faulty node and the importance weights of neighboring nodes, and by performing load allocation based on the allocation parameters, the rationality of load allocation to neighboring nodes can be improved, the possibility of neighboring nodes failing due to excessive load allocation can be reduced, the scale of network node failure caused by network node failure in complex networks can be reduced, and the robustness of complex networks can be effectively improved.

[0095] The following example illustrates the load distribution method for the aforementioned complex network.

[0096] like Figure 3As shown, after starting, the set of nodes (i.e., network nodes) and edges in the complex network (i.e., the target complex network mentioned above) is obtained, and the topology of the complex network is constructed. Then, based on the initial load and capacity of the nodes in the complex network, a load network model under cascading failures is constructed (i.e., the topology mentioned above, where the initial load and capacity of the network nodes are the attributes of the corresponding nodes in the topology). Next, it is determined whether the sum of the margins of the neighboring nodes (i.e., adjacent nodes mentioned above) of the faulty node is sufficient. If so, the load is allocated according to the margin ratio, and a load redistribution method is obtained (i.e., the load of the faulty node is allocated to the adjacent nodes). Otherwise, a robustness enhancement model of the complex network under cascading failures based on node load redistribution optimization is established (i.e., the objective function of the load allocation optimization problem mentioned above). Then, the model is solved based on the weighted L1 algorithm and the alternating direction multiplier method to obtain the load redistribution method, and the process ends.

[0097] Figure 4 The robustness curve in scale-free networks is shown. Figure 5 The robustness curve in small-world networks. Figure 6 The robustness curve in the random network is shown, and in Figure 4 , Figure 5 and Figure 6 The middle and vertical axes both represent robustness indicators. This indicates the size of the largest connected subgraph in the target complex network after the cascading failures stop, with the horizontal axis representing... , The curve represents the ratio of initial remaining capacity to initial load. The curve with a triangle represents the robustness curve of the load distribution method (AFS) for complex networks provided in this application, and the curve with a cross represents the distribution strategy according to degree ratio (PDS). The robustness curve at that time, the curve with the vertical line represents the strategy of proportional distribution according to degree (PDS) and The robustness curve at that time, the circled curve represents the allocation strategy according to the margin ratio (PFS) and Robustness curves at different times, with the boxed curves representing the allocation strategy according to the margin ratio (PFS) and... Robustness curve at time, The allocation parameter indicates how much load should be allocated to each node.

[0098] Therefore, it can be seen that the load distribution method for complex networks provided in this application can reduce the scale of network node failures caused by network node failures in complex networks, and effectively improve the robustness of complex networks.

[0099] The following is an exemplary description of the load distribution device for complex networks provided in this application.

[0100] like Figure 7As shown, this application embodiment provides a load distribution device for complex networks. The load distribution device 700 for complex networks includes: Module 701 is used to perform step 1: obtain multiple network nodes in the target complex network and construct the topology of the target complex network; the multiple nodes in the topology correspond one-to-one with the multiple network nodes, and the edge between each two nodes represents the adjacency relationship between the corresponding two network nodes; The acquisition module 702 is used to execute step 2: If the sum of the capacity margins of all neighboring nodes of the faulty node in the target complex network is less than or equal to the load of the faulty node, then for each neighboring node of the faulty node, the allocation parameters of the neighboring nodes are obtained based on the load of the faulty node and the importance weight of the neighboring nodes. The allocation module 703 is used to perform step 3: for each adjacent node of the faulty node, the load of the faulty node is allocated to the adjacent nodes according to the allocation parameters of the adjacent nodes. When the load of the adjacent node after being allocated is greater than the total load capacity of the adjacent nodes, the adjacent node is regarded as the faulty node in step 2 and the acquisition module 702 is triggered to execute step 2.

[0101] It should be noted that the information interaction and execution process between the above-mentioned devices / units are based on the same concept as the method embodiments of this application. For details on their specific functions and technical effects, please refer to the method embodiments section, and they will not be repeated here.

[0102] Those skilled in the art will clearly understand that, for the sake of convenience and brevity, the above-described division of functional units and modules is merely an example. In practical applications, the above functions can be assigned to different functional units and modules as needed, that is, the internal structure of the device can be divided into different functional units or modules to complete all or part of the functions described above. The functional units and modules in the embodiments can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit. Furthermore, the specific names of the functional units and modules are only for easy differentiation and are not intended to limit the scope of protection of this application. The specific working process of the units and modules in the above system can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0103] like Figure 8 As shown, an embodiment of this application provides a terminal device, wherein the terminal device D10 of this embodiment includes: at least one processor D100 ( Figure 8The diagram shows only one processor, a memory D101, and a computer program D102 stored in the memory D101 and executable on the at least one processor D100, wherein the processor D100 executes the computer program D102 to implement the steps in any of the above method embodiments.

[0104] Specifically, when the processor D100 executes the computer program D102, it acquires multiple network nodes in the target complex network and constructs the topology of the target complex network. If the sum of the capacity margins of all adjacent nodes of the faulty node in the target complex network is less than or equal to the load of the faulty node, then for each adjacent node of the faulty node, based on the load of the faulty node and the importance weight of the adjacent nodes, it acquires the allocation parameters of the adjacent nodes. Finally, for each adjacent node of the faulty node, according to the corresponding allocation parameters, it allocates the load of the faulty node to the adjacent nodes. When the load of an adjacent node after being allocated is greater than the total load capacity of the adjacent nodes, the adjacent node is designated as the faulty node, and its load is allocated accordingly. Acquiring the allocation parameters of adjacent nodes based on the load of the faulty node and the importance weight of the adjacent nodes, and then allocating the load based on these parameters, can improve the rationality of load allocation to adjacent nodes, reduce the possibility of adjacent nodes failing due to excessive load allocation, reduce the scale of network node failures in the complex network, and effectively improve the robustness of the complex network.

[0105] The processor D100 can be a central processing unit (CPU), or it can be other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor or any conventional processor.

[0106] In some embodiments, the memory D101 may be an internal storage unit of the terminal device D10, such as a hard disk or memory of the terminal device D10. In other embodiments, the memory D101 may be an external storage device of the terminal device D10, such as a plug-in hard disk, smart media card (SMC), secure digital card (SD), flash card, etc., equipped on the terminal device D10. Furthermore, the memory D101 may include both internal and external storage units of the terminal device D10. The memory D101 is used to store the operating system, applications, bootloader, data, and other programs, such as the program code of the computer program. The memory D101 can also be used to temporarily store data that has been output or will be output.

[0107] This application also provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps described in the various method embodiments above.

[0108] This application provides a computer program product that, when run on a terminal device, enables the terminal device to implement the steps described in the various method embodiments above.

[0109] If the integrated unit is implemented as 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, all or part of the processes in the methods of the above embodiments of this application can be implemented by a computer program instructing related hardware. The computer program can be stored in a computer-readable storage medium, and when executed by a processor, it can implement the steps of the various method embodiments described above. The computer program includes computer program code, which can be in the form of source code, object code, executable files, or certain intermediate forms. The computer-readable medium can include at least: any entity or device capable of carrying computer program code to a load distribution method apparatus / terminal device in a complex network, a recording medium, a computer memory, a read-only memory (ROM), a random access memory (RAM), an electrical carrier signal, a telecommunication signal, and a software distribution medium. Examples include USB flash drives, portable hard drives, magnetic disks, or optical disks. In some jurisdictions, according to legislation and patent practice, computer-readable media cannot be electrical carrier signals or telecommunication signals.

[0110] In the above embodiments, the descriptions of each embodiment have different focuses. For parts that are not described in detail or recorded in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0111] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0112] The above description is the preferred embodiment of this application. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of this invention, and these improvements and modifications should also be considered within the scope of protection of this invention.

Claims

1. A load distribution method for complex networks, characterized in that, include: Step 1: Obtain multiple network nodes in the target complex network and construct the topology of the target complex network; the multiple nodes of the topology correspond one-to-one with the multiple network nodes, and the edge between each two nodes represents the adjacency relationship between the corresponding two network nodes; Step 2: If the sum of the capacity margins of all neighboring nodes of the faulty node in the target complex network is less than or equal to the load of the faulty node, then for each neighboring node of the faulty node, the allocation parameters of the neighboring nodes are obtained based on the load of the faulty node and the importance weight of the neighboring nodes. Step 3: For each neighboring node of the faulty node, the load of the faulty node is allocated to the neighboring node according to the allocation parameters corresponding to the neighboring node. When the load of the neighboring node after being allocated the load is greater than the total load capacity of the neighboring node, the neighboring node is returned as the faulty node in step 2 and step 2 is executed again. The step of obtaining the allocation parameters of the adjacent nodes based on the load of the faulty node and the importance weight of the adjacent nodes includes: Based on the load of the faulty node and the importance weights of the adjacent nodes, an objective function is constructed for the load allocation optimization problem of the adjacent nodes. An optimization model is constructed based on the objective function and constraints of the load allocation optimization problem, and the Lagrange augmented function of the optimization model is obtained. Based on the Lagrange augmented function, an iterative algorithm is designed to obtain the allocation parameters of the adjacent nodes; The objective function of the load allocation optimization problem is: in, The faulty node in the topology is represented by The set of adjacent nodes of the corresponding node. For step function, when Greater than hour, ,when Less than hour, After L1 norm regularization, it can be expressed as , Indicates the first The total load capacity of the adjacent nodes. Indicates the first The probability of failure of each adjacent node. , Indicates the first The remaining capacity after the load is distributed to each adjacent node. Indicates the assignment to the first The load of each adjacent node Indicates the first The current load of each adjacent node Indicates the first The total load capacity of the adjacent nodes. , Indicates the first The importance weights of each adjacent node, when hour, , ,when hour, .

2. The load distribution method according to claim 1, characterized in that, Also includes: If the sum of the capacity margins of all neighboring nodes of the faulty node in the target complex network is greater than the load of the faulty node, then the load of the faulty node is proportionally distributed to all neighboring nodes of the faulty node.

3. The load distribution method according to claim 2, characterized in that, The step of distributing the load of the faulty node proportionally to all its neighboring nodes includes: Through the formula: Calculate the first The load distributed to each adjacent node ; in, Indicates the faulty node The current load, Indicates the first The current load of each adjacent node. Indicates the first The total load capacity of the adjacent nodes. , Indicates the first Initial load of adjacent nodes, This represents the capacity threshold parameter. The faulty node in the topology is represented by The set of adjacent nodes of the corresponding node. , This represents the total number of network nodes in the target complex network; The first The load distributed to each adjacent node Assigned to the first 1 neighboring node.

4. The load distribution method according to claim 1, characterized in that, The optimization model is as follows: in, , , Indicates the faulty node The remaining capacity vector after all adjacent network nodes have been loaded. Indicates the faulty node The current load after all adjacent network nodes have been assigned load, , The faulty node in the topology is represented by The set of adjacent nodes of the corresponding node. , This represents the total number of network nodes in the target complex network. Indicates an indicator function, when hour, ,when hour, , Indicates the fault node The total load capacity matrix of all adjacent nodes. This represents a parameter matrix where the elements are either 1 or 0. This represents a parameter matrix where the elements are 0 or -1. Represents a vector. The importance weight matrix is ​​represented as follows: in, This represents the total load capacity of the first adjacent node. This represents the total load capacity of the second adjacent node. Indicates the first The total load capacity of the adjacent nodes. Represents a set The total number of elements in Indicates the faulty node capacity, , This represents the weighted parameters of the 0th network node. This represents the weighted parameter of the first network node. Indicates the first Weighted parameters of each network node, This represents the importance weight of the 0th network node. This represents the importance weight of the first network node. Indicates the first The importance weight of each network node. Represents the 1-norm; The Lagrange augmented function of the optimization model is: in, This represents the value of the Lagrange augmented function. Represents the dual variable. This represents the matrix transpose operation. The coefficient representing the penalty term. This represents the square of the vector's magnitude.

5. The load distribution method according to claim 1, characterized in that, The step of designing an iterative algorithm based on the Lagrange augmented function to obtain the allocation parameters of the adjacent nodes includes: The parameters in the Lagrange augmented function are iterated using an iterative formula, with the iteration count incremented by 1. The iterative formula is as follows: in, Indicates the first Faulty node during the next iteration The remaining capacity matrix after all adjacent nodes have been assigned load. Indicates the first During the next iteration The value, Indicates the first During the next iteration The value, Represents the importance weight matrix, The coefficient representing the penalty term. Represents the identity matrix. This represents a parameter matrix where the elements are either 1 or 0. This represents a parameter matrix where the elements are 0 or -1. , Represents a mapping function; Through the formula: Calculate the remaining capacity difference ; Determine the remaining capacity difference Is it less than or equal to the preset difference in remaining capacity? If the remaining capacity difference If the remaining capacity difference is less than or equal to the preset difference, the weighted parameters are updated using the weighted parameter update formula, and the update count is incremented by 1. The weighted parameter update formula is as follows: in, Indicates the first The first iteration The remaining capacity after the load is distributed to each adjacent node. Indicates the first The first update mentioned The values ​​of the weighted parameters of the neighboring nodes, Represents a constant. , The faulty node in the topology is represented by The set of adjacent nodes of the corresponding node. , This represents the total number of network nodes in the target complex network; judge Is it less than ;in, Indicates the first The first update mentioned The values ​​of the weighted parameters of the adjacent nodes; like Less than Then As the first The allocation parameters for each adjacent node; like Greater than or equal to Return to the step of iterating over the parameters in the Lagrange augmented function using the iterative formula; If the remaining capacity difference If the difference is greater than the preset value of the remaining capacity, return to the step of iterating the parameters in the Lagrange augmented function using the iterative formula.

6. The load distribution method according to claim 5, characterized in that, The step of allocating the load of the faulty node to the adjacent nodes according to the allocation parameters corresponding to the adjacent nodes includes: Through the formula: Calculate the allocation to the first Load of adjacent nodes ; in, Indicates the first The allocation parameters for each adjacent node. Indicates the first The total load capacity of the adjacent nodes. Indicates the first The current load of each adjacent node; According to the allocation to the Load of adjacent nodes , for the first The load is distributed among adjacent nodes.

7. A terminal device, comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the computer program, it implements the load distribution method for complex networks as described in any one of claims 1 to 6.

8. A computer-readable storage medium storing a computer program, characterized in that, When a computer program is executed by a processor, it implements the load distribution method for complex networks as described in any one of claims 1 to 6.

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