A hierarchical collaborative optimization method for coupled network structure design

Abstract

The application relates to a layered collaborative optimization method for coupling network structure design and belongs to the technical field of network structures, and solves the problems that the propagation influence of dynamic load is not considered and optimization is not comprehensive during the design of an existing coupling network topology structure. The method comprises the following steps: a plurality of coupling networks are constructed as individuals, the topological structure of the coupling network is coded as a chromosome, and a plurality of initial populations are constructed through an initialization operator; a plurality of initial populations are iteratively genetically optimized based on a fitness function, and the individual with the maximum fitness value is taken after a termination condition is met; each generation genetic optimization comprises the following steps: the individuals in the initial population are sequentially subjected to a crossover operator and a local search operator to generate new individuals, and a local search population is obtained; an initial population of the next generation is selected from the local search population through a selection operator; and a coupling network resilience measurement index is constructed based on a dynamic load coupling network cascading failure model, and the fitness function is the coupling network resilience measurement index. The method improves the optimization efficiency and effect of the coupling network.

Description

Technical Field

[0001] This invention relates to the field of network structure optimization technology, and in particular to a hierarchical collaborative optimization method for coupled network structure design. Background Technology

[0002] In recent years, with the in-depth development of complex network theory, researchers have gradually realized that many real-world infrastructures can be represented by network structures, such as transportation networks, communication networks, power networks, and computer networks. As one of the key research areas in complex networks, network robustness has attracted widespread academic attention. Network robustness generally refers to the ability of a network to maintain functional integrity when subjected to attacks or failures. Driven by the rapid advancement of modern technology, the relationships between various industries are becoming increasingly close, and the interdependence between these networked systems is deepening, exhibiting coupling characteristics. Such networks are called coupled networks. However, research shows that coupled networks are more vulnerable to deliberate attacks than single-layer networks. The failure of a node or edge in a network not only affects the network itself but also spreads to other networks through coupling relationships, triggering cascading failures and ultimately leading to the collapse of the entire system. For example, the coupling between power networks and communication networks means that a local power failure can cause the failure of nodes in the communication network, thereby affecting more power nodes and causing serious losses. Therefore, studying the robustness of coupled networks and enhancing their resilience against cascading failures has become a critical problem that urgently needs to be solved.

[0003] A key strategy for improving network robustness is network structure optimization. Adjusting the topology of coupled networks can fundamentally enhance network resilience. The resilience of coupled networks is influenced not only by the intra-layer topology of sub-networks but also by the inter-layer coupling connections. However, because the intra-layer and inter-layer structures have different network characteristics, existing research is usually limited to adjusting a single part of either the intra-layer or inter-layer structure. For example, using optimization strategies on single-layer networks to optimize the intra-layer topology of coupled networks, optimizing each layer into a more resilient "onion-like structure"—where highly clustered nodes form a core region, and the remaining nodes surround the core in descending order of degree—is effective for optimizing attacked networks but has limited effect on networks already affected. Alternatively, memetic algorithms can be used to optimize the coupling connections.

[0004] Despite progress in the optimization design of coupled network structures, shortcomings remain. First, existing research focuses solely on structural topology factors, neglecting the propagation of dynamic loads on the network, making it difficult to apply to real-world models involving traffic, such as communication and transportation networks. Second, due to the different network characteristics of the inter-layer and intra-layer structures, current research treats intra-layer edge optimization and inter-layer coupling edge optimization as two separate optimization problems, failing to coordinate the optimization of the intra-layer and inter-layer structures of coupled networks and neglecting the interaction between the network's internal structure and coupling relationships. Finally, co-optimizing coupled network structures involves large decision variables and numerous, complex constraints, making it a complex discrete variable combinatorial optimization problem. Traditional optimization algorithms often only yield locally optimal solutions, resulting in poor optimization performance for coupled network topologies. Summary of the Invention

[0005] Based on the above analysis, the embodiments of the present invention aim to provide a hierarchical collaborative optimization method for coupled network structure design, in order to solve the problems of not considering the propagation effect of dynamic load and incomplete optimization in existing coupled network topology design.

[0006] This invention provides a hierarchical collaborative optimization method for coupled network structure design, comprising the following steps:

[0007] Multiple coupled networks are constructed as individuals, and the topology of the coupled networks is encoded as chromosomes. Multiple initial populations are constructed through initialization operators.

[0008] Iterative genetic optimization is performed on multiple initial populations based on the fitness function until the termination condition is met, at which point the individual with the highest fitness value is selected as the optimal coupled network structure. Each generation of genetic optimization for each initial population includes: generating new individuals from the individuals in the initial population by sequentially passing them through crossover and local search operators to obtain a local search population; and selecting the next generation of initial population from the local search population by a selection operator. The fitness function is a coupled network resilience measure constructed based on a coupled network cascade failure model under dynamic load.

[0009] Based on the further improvement of the above method, the fitness function is expressed by the following formula:

[0010]

[0011] Where R represents the fitness function, and N represents the number of nodes in the upper layer of the coupled network. A Or the number of nodes N in the lower layer network BT represents the total number of attack rounds when all nodes in the coupled network fail; s(q) represents the number of nodes in the maximum connected subgraph of the upper network of the coupled network after removing a node with the highest degree from the upper network of the coupled network in the q-th attack round. The number of nodes in the maximum connected subgraph of the lower layer network The proportion of the total number of nodes in the coupled network.

[0012] Based on further improvements to the above methods, the initialization operator, crossover operator, and local search operator all include optimization of the intra-layer topology and inter-layer coupling structure of individuals; the selection operator includes roulette wheel selection and random selection strategies.

[0013] Based on the further improvement of the above method, multiple initial populations are constructed by initialization operators. This is achieved by randomly reconnecting the degree-preserving edges of the intra-layer topology of each coupled network while keeping the degree of each node in the coupled network unchanged, and generating random coupling edges for the inter-layer coupled structure, according to the preset initial population and the number of its individuals.

[0014] Based on further improvements to the above method, individuals in the initial population are sequentially processed using crossover and local search operators to generate new individuals, resulting in a local search population, including:

[0015] Traverse the initial population, and each time select two individuals as two parents to be crossed based on the crossover probability. Perform neighborhood crossover on the intra-layer topology of the two parents to be crossed, and perform coupling edge crossover on the inter-layer coupling structure to generate two offspring. The individuals not selected in the initial population and the generated offspring form the crossover population.

[0016] Traverse the crossover population, and each time select an individual as the individual to be mutated based on the local search probability. Perform node-edge mutation on the intra-layer topology of the individual to be mutated, and perform coupling-edge mutation on the inter-layer coupling structure to generate mutated individuals. The individuals not selected in the crossover population and the generated mutated individuals form the local search population.

[0017] A further improvement to the above method involves performing random degree-preserving edge reconnection on the intra-layer topology of each coupled network. This involves performing multiple random degree-preserving reconnections on both the upper and lower layers of each coupled network according to a preset number of times. Each random degree-preserving reconnection involves randomly selecting connected nodes i and j in the current network, and then randomly selecting two other nodes m and k. If nodes m and k are connected, and there is no connecting edge e in the current network, then the reconnection is performed. im and e jk Then delete the original edge e. ij and e mk And establish new connection e im and e jk .

[0018] Based on further improvements to the above method, neighborhood crossing is performed on the intra-layer topology of the two parent generations to be crossed, including:

[0019] The chromosomes of the two parents to be crossed are passed on to their respective offspring;

[0020] Select the same nodes from the chromosomes of the two offspring in turn as the nodes to be crossed. Based on the neighbor set of each node to be crossed in its respective chromosome, obtain two completely different neighbor subsets. Randomly select a node from each of the two neighbor subsets that is connected to the node to be crossed in the other chromosome. Perform edge deletion and migration on the chromosomes of the two offspring and perform degree preservation operation on the edge nodes.

[0021] Based on the above method, further improvements are made to the interlayer coupling structure, including:

[0022] Based on the coupling edges of a node corresponding to a coupling edge in the chromosome of one of the parent generations to be crossed, and the coupling edges of the chromosomes of the offspring generated by the other parent generation to be crossed are added or deleted.

[0023] Based on further improvements to the above method, node-edge mutations are performed on the intra-layer topology of the individual to be mutated, including:

[0024] Based on the chromosome of the individual to be mutated and the local search operator adjustment factor, when the degree difference between the two nodes of any two edges in the upper network of the individual to be mutated is reduced to below a certain proportion, the two nodes are reconnected to generate the mutated individual.

[0025] Further improvements to the above method involve abrupt changes in the coupling edges of the interlayer coupling structure, including:

[0026] Based on the chromosome of the mutant individual, identify the common neighbor nodes of the coupled nodes in the mutant individual, traverse the set of coupled edges corresponding to the common neighbor nodes, and reconnect the coupled edges of the common neighbor nodes according to the same-match coupling connection mode.

[0027] Compared with the prior art, the present invention can achieve at least one of the following beneficial effects:

[0028] 1. The dynamic load propagation effect on coupled networks is considered, and a coupled network resilience metric is used to evaluate the resilience of coupled networks under cascading failures. This effectively improves the robustness of coupled networks when subjected to attacks or disturbances, and is suitable for structural optimization of coupled networks containing loads.

[0029] 2. It not only optimizes the internal edge structure of the network, but also optimizes the coupling edge structure between networks, treating the coupled network as a whole for design. It fully considers the interaction between the internal structure and the coupling relationship of the network, overcomes the limitation of the existing separate processing of the optimization of the internal edge structure and the optimization of the coupling edge structure between networks, and realizes the coordinated optimization of the intra-layer topology and the inter-layer coupling relationship, thereby improving the optimization effect of the overall coupled network.

[0030] 3. Combining prior knowledge of the topological characteristics of the coupled network, a variety of differentiated operators were designed during the genetic optimization process. While keeping the degree distribution of the coupled network unchanged, the diversity of the population was increased, the global search efficiency was improved, and the resilience of the network to attacks was enhanced.

[0031] In this invention, the above-described technical solutions can be combined with each other to achieve more preferred combinations. Other features and advantages of this invention will be set forth in the following description, and some advantages may become apparent from the description or be learned by practicing the invention. The objects and other advantages of this invention can be realized and obtained from what is particularly pointed out in the description and drawings. Attached Figure Description

[0032] The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. Throughout the drawings, the same reference numerals denote the same parts.

[0033] Figure 1 This is a flowchart of a hierarchical collaborative optimization method for coupled network structure design in an embodiment of the present invention;

[0034] Figure 2 This describes the iterative genetic optimization process of the initial population in this embodiment of the invention. Detailed Implementation

[0035] Preferred embodiments of the present invention will now be described in detail with reference to the accompanying drawings, which form part of this application and are used together with the embodiments of the present invention to illustrate the principles of the present invention, but are not intended to limit the scope of the present invention.

[0036] A specific embodiment of the present invention discloses a hierarchical collaborative optimization method for coupled network structure design, such as... Figure 1 As shown, it includes the following steps:

[0037] S1. Construct multiple coupled networks as individuals, encode the topology of the coupled networks as chromosomes, and construct multiple initial populations through initialization operators.

[0038] It should be noted that the coupled network includes the upper-layer network G. A and lower layer network G B And GA and G B The number of nodes is the same in the upper layer network. Nodes in the upper layer network establish a one-to-one correspondence with nodes in the lower layer network through coupling edges, thus forming a set E of coupling edges. AB Therefore, the coupled network model can be represented as G AB ={G A G B E AB}

[0039] Specifically, the upper-layer network G A and lower layer network G B Both are unweighted, undirected networks, each consisting of a set of nodes V and a set of edges E, denoted as G respectively. A ={V A E A} and G B ={V B E B}, where V A and V B G A and G B All nodes in E A and E B G A and G B All edges connecting nodes in the middle layer; upper network G A The set of nodes is represented as V A ={1,2,3,...,N A}, N A This represents the number of nodes in the upper-layer network; the lower-layer network G... B The set of nodes is represented as V B ={1,2,3,...,N B}, N B This represents the number of nodes in the lower-level network. The number of nodes in any layer of the network is N = N0. A =N B .

[0040] In practical applications, the power network in a power-communication coupled network provides energy support for the communication network, while the communication network is responsible for information transmission from the power network. The communication network is typically built in conjunction with the power network, and their topologies highly overlap. The upper-layer power network connects to the lower-layer communication network through a one-to-one random coupling pattern, thus constructing a power-communication coupled network to simulate the topological characteristics of a real power dispatching and communication control system. In this network, nodes represent various power plants and substations, and edges represent transmission lines between stations; in the communication network, nodes represent various communication stations, switches, or routers, and edges represent information transmission paths.

[0041] It should be noted that constructing multiple coupled networks is based on the same number of nodes and each node having the same degree (i.e., the number of edges connected to the node). Coupled network models are used to construct upper and lower layer networks of the same model type, and coupling edges between the upper and lower layer networks are established through a one-to-one random coupling connection pattern. The coupled network models include: the Barabási-Albert (BA) scale-free network model, the Watts-Strogatz (WS) small-world network, and others. -Rényi(ER) random network.

[0042] Furthermore, the topology encoding of the coupled network includes an upper-layer adjacency matrix A, a lower-layer adjacency matrix B, and a coupling edge adjacency matrix C. Adjacency matrices A and B are both binary symmetric matrices, with elements consisting only of 0s and 1s. Since self-joins are not allowed in the network, all elements on the main diagonal of the adjacency matrix are 0s. Due to symmetry, adjacency matrices A or B are encoded using their upper triangular matrices, with an encoding length of N(N-1) / 2. Additionally, each element in adjacency matrix C represents whether an upper-layer node forms a coupling edge with a lower-layer node, and its encoding length is N. 2 Therefore, the total length of the topology encoding for each coupled network is 2N. 2 -N.

[0043] Furthermore, in order to ensure the diversity of the initial population while maintaining the network degree distribution, this embodiment constructs multiple initial populations by optimizing the intra-layer topology and inter-layer coupling structure of the coupled network through initialization operators.

[0044] Specifically, based on a pre-set initial population and the number of its individuals, while keeping the degree of each node in the coupled network unchanged, random degree-preserving edge reconnection is performed on the intra-layer topology of each coupled network, and random coupling edges are generated on the inter-layer coupled structure.

[0045] The process of performing random degree-preserving edge reconnection within the intra-layer topology of each coupled network involves performing multiple random degree-preserving reconnections on both the upper and lower layers of each coupled network according to a preset number of times. Each random degree-preserving reconnection involves randomly selecting connected nodes i and j in the current network, and then randomly selecting two other nodes m and k. If nodes m and k are connected, and there is no connecting edge e in the current network, then the process continues. im and e jk Then delete the original edge e. ij and e mk And establish new connection e im and e jk .

[0046] Generating random coupling edges for inter-layer coupling structures involves generating them from the upper-layer network G.A and lower layer network G B Randomly select a pair of nodes that have not yet formed a coupled edge, establish a coupled edge between the two nodes, and repeat the process until the total number of coupled edges reaches the preset number of times.

[0047] Ultimately, multiple initial populations were constructed with the same number of individuals, each representing a complete coupled network, with the topology of the coupled network encoded as the chromosome of the individual.

[0048] S2. Based on the fitness function, iterative genetic optimization is performed on multiple initial populations until the termination condition is met, and the individual with the largest fitness value is selected as the optimal coupled network structure. The genetic optimization of each generation of each initial population includes: generating new individuals from the individuals in the initial population by sequentially passing them through the crossover operator and the local search operator to obtain the local search population; selecting the next generation of the initial population from the local search population by the selection operator; the fitness function is a coupled network resilience measure constructed based on the coupled network cascade failure model of dynamic load.

[0049] It should be noted that in the coupled network of this embodiment, each node has an initial load. For example, in a power network, the load of each node is the amount of electricity transmitted; in a communication network, the load of each node is the amount of data transmitted. When a node in the upper-layer network fails due to an attack, its load is distributed to adjacent normal nodes according to certain rules. If the load borne by each node does not exceed its node capacity, it is in a normal working state; if it exceeds its node capacity, it is in a failed state, thus forming a cascading failure model of a coupled network with dynamic load.

[0050] Specifically, the initial load of each node is proportional to the node's degree, as shown in the following formula:

[0051] L i =k i α ,

[0052] Among them, L i Let α represent the initial load of node i, α be a non-negative constant, represent the initial load adjustment coefficient, and k be the load. i Let be the degree of node i.

[0053] Node capacity refers to the maximum load processing capability of a node, as shown in the formula below:

[0054] C i =(1+β)L i ,

[0055] Among them, C iβ represents the node capacity of node i, and β is a non-negative constant representing the node capacity redundancy coefficient, used to quantify the node's ability to handle additional load.

[0056] Node load is distributed to adjacent normal nodes using the following formula:

[0057]

[0058] Where, ΔL ij This represents the load redistributed from the failed node i to the adjacent healthy node j, Γ i Let j ∈ Γ be the set of normal nodes adjacent to node i in the same layer. i .

[0059] Furthermore, if a normal node j increases its allocated load beyond its initial load, and this exceeds its maximum capacity C... j If node j fails, it will trigger a new round of load redistribution, which in turn will cause more nodes to fail in a cascading manner.

[0060] Considering that in real-world applications, most failures typically begin with the failure of a few nodes within a single network layer, rather than multiple network layers simultaneously suffering a large-scale attack, this embodiment couples the upper-layer network G within the network. A This indicates the attacked layer, the lower network G. B This indicates the affected layer. The cascading failure process following an attack on an upper-layer network includes:

[0061] ① Initial attack: In the upper layer network G A The node with the highest degree is selected as the initial attack node, and that node and its connected edges are removed from the network.

[0062] ② Load redistribution and overload node removal: Recalculate the load of each neighboring node in the network where the node is located. For nodes that exceed the node's capacity, mark them as failed nodes and delete these nodes and their connected edges.

[0063] ③ Maximum connected subgraph selection: Identifying the upper-layer network G A LCC (Largest Connected Subgraph) A It will not belong to LCC A Nodes that fail are considered invalid nodes, and these nodes and their connected edges are deleted.

[0064] ④ The failure propagates to another network layer through coupling: Through coupling, the cascading failure affects another network layer, the upper network G. A The status of the failed node is synchronized to the lower-level network G. B Delete the lower-level network G B The corresponding coupled nodes and their connected edges.

[0065] ⑤ Load redistribution and overload node removal (lower network G) B ): Recalculate the lower-level network G B The node load is assessed, and nodes exceeding their capacity are marked as failed nodes and their connected edges are deleted.

[0066] ⑥ Maximum connected subgraph selection (lower network G) B ): Identify the lower-layer network G B LCC (Largest Connected Subgraph) B It will not belong to LCC B Nodes that fail are considered invalid nodes, and these nodes and their connected edges are deleted.

[0067] ⑦ Feedback to the attacked network through coupling: Through coupling, the lower-layer network G... B The state of the failed node is synchronized back to the upper-layer network G. A Delete the upper-layer network G A The corresponding coupled nodes and their connected edges.

[0068] ⑧ Repeat the above process until steady state: in the upper network G A and lower layer network G B Repeat the above steps until the coupled network reaches a steady state, that is, when no new failed nodes appear in the coupled network, the cascading failure process of an attack terminates.

[0069] This embodiment uses a coupled network resilience metric to evaluate the resilience of coupled networks under cascading failure, and uses the coupled network resilience metric as a fitness function, as shown in the following formula:

[0070]

[0071] Where R represents the fitness function, T represents the total number of attack rounds when all nodes in the coupled network fail, and s(q) represents the number of nodes in the maximum connected subgraph of the upper network of the coupled network after removing a node with the highest degree from the upper network of the coupled network in the q-th attack round. The number of nodes in the maximum connected subgraph of the lower layer network The proportion of nodes in the coupled network; 1 / N represents the normalization factor, used to ensure comparability between networks of different sizes. The value of R ranges from [0, 0.5], and a higher R value indicates that the coupled network has stronger resilience after being attacked.

[0072] It should be noted that, as Figure 2As shown, when performing iterative genetic optimization on multiple initial populations, a maximum number of iterations is typically set. The iteration terminates when the maximum number of iterations is reached, satisfying the termination condition. Each generation of genetic optimization includes: S21, performing crossover using the crossover operator; S22, performing mutation using the local search operator; and S23, selecting individuals using the selection operator. Both the crossover and local search operators optimize the intra-layer topology and inter-layer coupling structure of individuals. The selection operator includes roulette wheel selection and random selection strategies. The implementation process of each step is described below.

[0073] S21. Use the crossover operator to perform individual crossover.

[0074] It should be noted that during the crossover process, the intra-layer topology adopts a neighborhood crossover mechanism based on intra-layer structure migration; the inter-layer coupling structure adopts an inter-layer crossover mechanism based on coupling connection constraints to generate new offspring. While maintaining the original network degree distribution, this effectively compresses the feasible solution space and improves the global search efficiency of the algorithm.

[0075] During implementation, the initial population is traversed, and two individuals are selected as two parents to be crossed each time according to the crossover probability. Neighborhood crossover is performed on the intra-layer topology of the two parents to be crossed, and coupling edge crossover is performed on the inter-layer coupling structure to generate two offspring. The individuals not selected in the initial population and the generated offspring form the crossover population.

[0076] It should be noted that two individuals are selected from the initial population, and a random number in the range (0,1) is generated. If the random number is less than the crossover probability, the two individuals are used as two parents to be crossovered. Otherwise, the two individuals are not selected and no crossover operation is performed.

[0077] This includes performing neighborhood crosses on the intra-layer topology of two parent generations to be crossed, including:

[0078] The chromosomes of the two parents to be crossed are passed on to their respective offspring;

[0079] Select the same nodes from the chromosomes of the two offspring as their respective nodes to be crossed. Based on the neighbor set of each node to be crossed in its respective chromosome, obtain two completely different neighbor subsets. Randomly select a node from each of the two neighbor subsets that is connected to the node to be crossed in the other chromosome. Perform edge deletion and migration on the chromosomes of the two offspring and perform degree preservation operation on the edge nodes.

[0080] Specifically, the chromosomes P of the two parents to be crossed are... r1 and P r2 The inheritance is passed on to their respective offspring, resulting in two offspring with chromosome C. r1 and C r2From the chromosomes of the two offspring, select the same node i sequentially as the crossover node for each, and identify the position of node i in C. r1 and C r2 The set of neighbor nodes in and Then, by removing the common neighbor portions from these two sets, we obtain two neighbor subsets with completely different nodes. and In C r1 and C r2 From the middle, respectively Randomly select a node j from the list, and from... Randomly select a node m from C, and then from C r1 Remove the connecting edge e in the middle ij From C r2 Remove the connecting edge e in the middle im To C r1 Add edge e to the middle im To C r2 Add edge e to the middle ij Furthermore, to ensure that the degree of deleted and added edge nodes remains unchanged, a degree-preserving operation is performed: in C... r1 Randomly select an edge e connected to node m. km Delete the edge e km And add a new connection e jk In C r2 Perform a similar operation, randomly selecting an edge e connected to node j. jl Delete the edge e jl And add a new connection e lm .

[0081] Furthermore, the interlayer coupling structure is coupled with cross-linking, including:

[0082] Based on the coupling edges of a node corresponding to a coupling edge in the chromosome of one of the parent generations to be crossed, and the coupling edges of the chromosomes of the offspring generated by the other parent generation to be crossed are added or deleted.

[0083] Specifically, for the chromosome P of the two parents to be crossed... r1 and P r2 If based on the parent chromosome P r1 The coupling edge A1B1 in the middle pairs with the offspring chromosome C. r2 If the coupled edges in the network are swapped, there are four different swap scenarios:

[0084] If the father's chromosome P r2 If nodes A1 and B1 in the sequence have no coupling edges, then in the offspring chromosome C... r2Add a coupling edge A1B1 from C, and from C r2 Randomly delete one existing coupled edge A3B2;

[0085] If the father's chromosome P r2 If nodes A1 and B1 have only one coupled edge, let's say A2B1, then the offspring chromosome C... r2 Add a coupling edge A1B1 and delete the coupling edge A2B1.

[0086] If the father's chromosome P r2 Both nodes A1 and B1 have existing coupled edges. Assuming these coupled edges are A1B2 and A2B1 respectively, then in the offspring chromosome C... r2 Add new coupling edges A1B1 and A2B2, and delete coupling edges A1B2 and A2B1;

[0087] If the father's chromosome P r2 If there is a coupled edge A1B1 in the middle, then no exchange will be performed.

[0088] Similarly, based on the paternal chromosome P r2 The coupling edges in the offspring chromosome C r1 The coupling edges in the middle are swapped.

[0089] S22. Use local search operators to perform individual mutations.

[0090] It should be noted that in highly resilient coupled networks, nodes with high degree values ​​cluster to form a core region, while other nodes surround the core in descending order of degree value, exhibiting a topological feature similar to an "onion structure." Such networks tend to prioritize connections between nodes with similar degree values, while connections between nodes with significantly different degree values ​​are relatively few. This topological characteristic helps enhance the network's resilience against attacks. Based on this, in this embodiment, during the local search process, the intra-layer topology structure employs a local search mechanism guided by an onion structure, promoting connections between nodes with similar degrees while maintaining the network's degree distribution. The inter-layer coupling structure employs a local search mechanism based on reconnecting common neighbor nodes to reduce the load difference between two nodes on a connection edge, further accelerating algorithm convergence.

[0091] During implementation, the crossover population is traversed, and each time an individual is selected as the individual to be mutated based on the local search probability. The intra-layer topology of the individual to be mutated is mutated by node-edge connection, and the inter-layer coupling structure is mutated by coupling-edge connection to generate the mutated individual. The individuals not selected in the crossover population and the generated mutated individuals form the local search population.

[0092] It should be noted that when an individual is selected from the crossover population, a random number in the range (0,1) is generated. If the random number is less than the local search probability, the individual is selected as the individual to be mutated and the mutation operation is performed. Otherwise, the individual is not selected and the mutation operation is not performed.

[0093] The process of performing node-edge mutations on the intra-layer topology of the individual to be mutated includes:

[0094] Based on the chromosome of the individual to be mutated and the local search operator adjustment factor, when the degree difference between the two nodes of any two edges in the upper network of the individual to be mutated is reduced to below a certain proportion, the two nodes are reconnected to generate the mutated individual.

[0095] Specifically, the upper-layer network G A any two edges e ij and e km Delete the existing edge e when the degree values ​​of the two endpoints meet the following conditions. ij and e km And add a new connection e ik and e jm :

[0096] μ(|k i -k j |-|k k -k m |≥|k i -k k |-|k j -k m |,

[0097] Where μ represents the local search operator adjustment factor, μ∈[0,1], k i k j k k and k m These represent the degree values ​​of the corresponding nodes.

[0098] Furthermore, abrupt changes are made to the coupling edges of the interlayer coupling structure, including:

[0099] Based on the chromosome of the mutant individual, identify the common neighbor nodes of the coupled nodes in the mutant individual, traverse the set of coupled edges corresponding to the common neighbor nodes, and reconnect the coupled edges of the common neighbor nodes according to the same-match coupling connection mode.

[0100] It should be noted that, according to the dynamic load coupled network cascading failure model, when a node i is attacked, the fault propagates to its neighboring nodes and further spreads to another network layer through coupling edges, causing a large-scale cascading failure. Based on this, if two nodes are neighbors in one network layer, and their corresponding coupled nodes are also neighbors in another network layer, they are called "common neighbor nodes." The coupling connection method of common neighbor nodes often has a more significant impact on the fault propagation after node i is attacked. Therefore, prioritizing the optimization of the coupling edges of common neighbor nodes can reduce the risk of fault propagation across layers.

[0101] The co-location coupling connection mode prioritizes connecting nodes with similar initial loads between coupled network layers. According to this mode, the difference in initial load between common neighbor nodes is calculated, and the edges connecting common neighbor nodes are reconnected.

[0102] S23. Use selection operators to screen individuals.

[0103] For each individual in the local search population obtained in step S22, the first round of attack is carried out starting from the node with the largest degree value in the upper layer network. After the cascading failure process ends, the node with the largest degree value is selected from the remaining nodes for the second round of attack, until all nodes in the individual fail. The fitness value of each individual is calculated according to the formula of the fitness function.

[0104] Furthermore, based on the number of individuals in each population, a roulette wheel selection strategy is used to select half of the individuals from the local search population, and a random selection strategy is used to select the other half of the individuals from the local search population, together forming the initial population for the next generation of genetic optimization.

[0105] Finally, after completing the iterative genetic optimization, the individual with the highest fitness value is selected as the optimal coupled network structure, thereby achieving synergistic optimization of intra-layer topology and inter-layer coupling relationship.

[0106] To verify the effectiveness of the method in real-world applications, experiments were conducted on a power communication coupled network using both the method of this embodiment and the classic hill-climbing method. In the experiments, the power network was set as the attacked layer network G. A The data comes from the IEEE 300 power grid bus test dataset; the communication network is the affected layer network G. B The data comes from the network communication dataset provided by the Stanford Network Analysis Platform. Experimental results show that the robustness (fitness value) of the coupled network obtained using this embodiment is improved by approximately 23.5% compared to the classic hill-climbing method, and the optimization method of this embodiment is stable and effective.

[0107] Compared with existing technologies, this embodiment provides a hierarchical collaborative optimization method for coupled network structure design that considers the impact of dynamic load propagation on the coupled network. It employs a coupled network resilience metric to evaluate the resilience of the coupled network under cascading failures, effectively improving the robustness of the coupled network under attacks or disturbances. This method is suitable for optimizing the structure of coupled networks containing loads. It optimizes not only the internal edge structure of the network but also the coupling edge structure between networks, treating the coupled network as a whole for design. It fully considers the interaction between the internal structure and coupling relationships, overcoming the limitations of existing methods that separate the optimization of internal edge structures from the optimization of inter-network coupling edges. This achieves collaborative optimization of intra-layer topology and inter-layer coupling relationships, thereby improving the overall optimization effect of the coupled network. Combining prior knowledge of the coupled network's topological characteristics, it designs multiple differentiated operators during the genetic optimization process. While maintaining the degree distribution of the coupled network, it increases population diversity, improves global search efficiency, and enhances the network's resilience under attacks.

[0108] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware, and the program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0109] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A hierarchical collaborative optimization method for coupled network structure design, characterized in that, Includes the following steps: Multiple coupled networks are constructed as individuals, and the topology of the coupled networks is encoded as chromosomes. Multiple initial populations are constructed through initialization operators. Iterative genetic optimization is performed on the multiple initial populations based on the fitness function until the termination condition is met, at which point the individual with the largest fitness value is selected as the optimal coupled network structure. Each generation of genetic optimization for each initial population includes: generating new individuals from the individuals in the initial population by sequentially passing them through crossover and local search operators to obtain a local search population; and selecting the next generation of initial population from the local search population by a selection operator. The fitness function is a coupled network resilience measure constructed based on a coupled network cascade failure model under dynamic load.

2. The hierarchical collaborative optimization method for coupled network structure design according to claim 1, characterized in that, The fitness function is expressed by the following formula: Where R represents the fitness function, and N represents the number of nodes in the upper layer of the coupled network. A Or the number of nodes N in the lower layer network B T represents the total number of attack rounds when all nodes in the coupled network fail; s(q) represents the number of nodes in the maximum connected subgraph of the upper network of the coupled network after removing a node with the highest degree from the upper network of the coupled network in the q-th attack round. The number of nodes in the maximum connected subgraph of the lower layer network The proportion of the total number of nodes in the coupled network.

3. The hierarchical collaborative optimization method for coupled network structure design according to claim 1, characterized in that, The initialization operator, the crossover operator, and the local search operator all include optimization of the intra-layer topology and inter-layer coupling structure of individuals; the selection operator includes roulette wheel selection and random selection strategies.

4. The hierarchical collaborative optimization method for coupled network structure design according to any one of claims 1-3, characterized in that, The construction of multiple initial populations by initialization operators is achieved by, based on a preset initial population and the number of its individuals, performing random degree-preserving edge reconnection on the intra-layer topology of each coupled network while keeping the degree of each node in the coupled network constant, and generating random coupling edges on the inter-layer coupled structure.

5. The hierarchical collaborative optimization method for coupled network structure design according to any one of claims 1-3, characterized in that, The process of generating new individuals from the initial population by sequentially applying crossover and local search operators to obtain a local search population includes: Traverse the initial population, and each time select two individuals as two parents to be crossed based on the crossover probability. Perform neighborhood crossover on the intra-layer topology of the two parents to be crossed, and perform coupling edge crossover on the inter-layer coupling structure to generate two offspring. The individuals not selected in the initial population and the generated offspring form the crossover population. Traverse the crossover population, and each time select an individual as the individual to be mutated based on the local search probability. Perform node-edge mutation on the intra-layer topology of the individual to be mutated, and perform coupling-edge mutation on the inter-layer coupling structure to generate mutated individuals. The individuals not selected in the crossover population and the generated mutated individuals form the local search population.

6. The hierarchical collaborative optimization method for coupled network structure design according to claim 4, characterized in that, The step of performing random degree-preserving edge reconnection on the intra-layer topology of each coupled network involves performing multiple random degree-preserving reconnections on both the upper and lower layers of each coupled network according to a preset number of times. Each random degree-preserving reconnection involves randomly selecting connected nodes i and j in the current network, and then randomly selecting two other nodes m and k. If nodes m and k are connected, and there is no connecting edge e in the current network, then the reconnection is performed. im and e jk Then delete the original edge e. ij and e mk And establish new connection e im and e jk .

7. The hierarchical collaborative optimization method for coupled network structure design according to claim 5, characterized in that, The process of performing neighborhood cross-multiplication on the intra-layer topology of two parent generations to be crossed includes: The chromosomes of the two parents to be crossed are passed on to their respective offspring; Select the same nodes from the chromosomes of the two offspring in turn as the nodes to be crossed. Based on the neighbor set of each node to be crossed in its respective chromosome, obtain two completely different neighbor subsets. Randomly select a node from each of the two neighbor subsets that is connected to the node to be crossed in the other chromosome. Perform edge deletion and migration on the chromosomes of the two offspring and perform degree preservation operation on the edge nodes.

8. The hierarchical collaborative optimization method for coupled network structure design according to claim 7, characterized in that, The coupling and connection of the interlayer coupling structure includes: Based on the coupling edges of a node corresponding to a coupling edge in one of the chromosomes of the parent generation to be crossed and the coupling edges in the chromosome of the other parent generation to be crossed, the coupling edges of the chromosomes of the offspring generated by the other parent generation to be crossed are added or deleted.

9. The hierarchical collaborative optimization method for coupled network structure design according to claim 5, characterized in that, The process of performing node-edge mutation on the intra-layer topology of the individual to be mutated includes: Based on the chromosome of the individual to be mutated and the local search operator adjustment factor, when the degree difference between the two nodes of any two edges in the upper network of the individual to be mutated is reduced to below a certain proportion, the two edges are reconnected to generate the mutated individual.

10. The hierarchical collaborative optimization method for coupled network structure design according to claim 9, characterized in that, The abrupt change in coupling edges of the interlayer coupling structure includes: Based on the chromosome of the mutant individual, identify the common neighbor nodes of the coupled nodes in the mutant individual, traverse the set of coupled edges corresponding to the common neighbor nodes, and reconnect the coupled edges of the common neighbor nodes according to the same-match coupling connection mode.

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