Method and system for sorting key nodes of heterogeneous cascading target system under fuzzy conditions

Abstract

The application discloses a kind of fuzzy condition-oriented heterogeneous cascading target system key node attack sequencing method and system, specifically is: first, build heterogeneous cascading target system key node attack sequencing model;Then carry out key node attack sequencing based on fuzzy condition;Then carry out heterogeneous cascading target system key node attack sequencing based on optimization algorithm;Finally, based on the network determined above, the key node in heterogeneous cascading target system is attacked.The application can efficiently and accurately determine the key node attack sequence in large-scale target system, and can convert the uncertainty problem into the node attack sequencing problem of known environment, effectively solve the problem of breaking uncertain target system, provide the basis for network analysis of military information system.

Description

Technical Field

[0001] This invention relates to the field of joint operations mission planning technology, and in particular to a method and system for prioritizing the strikes of key nodes in a heterogeneous cascaded target system under fuzzy conditions. Background Technology

[0002] With the continuous deepening and expansion of intelligent technologies, the landscape of joint operations command is undergoing profound changes. Command methods are gradually shifting from information-based approaches focused on establishing communication links to intelligent approaches aimed at supporting decision-making. Target system evaluation methods, primarily based on system integration, correlation recommendation, and network disruption, are becoming the mainstream for target selection and recommendation in future joint strikes. For commanders, the ability to locate and strike key targets in the shortest possible time will significantly impact the accuracy and timeliness of their decisions, thereby affecting the implementation of the entire operational plan.

[0003] Invention patent CN108416441A discloses a method for allocating ship-to-shore strike firepower based on a genetic algorithm. This method uses a weapon type on a ship as a firepower unit, assigning the number of targets to be attacked from the shore as a coding bit. Each firepower unit is encoded using a random distribution generation method to obtain an initial population. The fitness of the initial population is calculated using a fitness function. Based on the fitness, a selection process is performed on the initial population using a combination of roulette wheel selection, resulting in a selected population. Chromosome crossover and mutation are then performed on the selected population to obtain a new population. This process is repeated multiple times to update the initial population and obtain the ship-to-shore strike firepower allocation scheme. However, this technology fails to consider the system value correlation factors between targets, thus failing to achieve target system value analysis and system-based target firepower allocation.

[0004] Invention patent CN 113887888 A discloses a method and system for adaptive scoring and association recommendation of joint strike targets. By introducing knowledge graph reasoning technology into the construction of the joint fire strike target system, it realizes the automatic linking of target association relationships; it establishes an emergent evaluation index model in a complex hypernetwork system, realizing the emergent value measurement of the strike target hypernetwork; it realizes the association recommendation and optimal recommendation of commanders to select strike targets, improving the level of intelligent auxiliary decision-making. However, it cannot perform key node strike ranking under fuzzy conditions and cannot solve the problem of breaking through uncertain target systems.

[0005] Therefore, there is an urgent need to study a strike sequencing method that can cope with the situation where some relationships are missing or uncertain in a large-scale cascaded target system, so as to effectively solve the problem of breaking through uncertain target systems. Summary of the Invention

[0006] The purpose of this invention is to provide a method and system for attacking and ranking key nodes, which can effectively sort out key nodes, cope with situations where some relationships are missing or uncertain in a large-scale cascaded target system, and effectively solve the problem of breaking through uncertain target systems.

[0007] The technical solution to achieve the purpose of this invention is: a method for ranking the key nodes of a heterogeneous cascaded target system under fuzzy conditions, comprising the following steps:

[0008] Step 1: Construct a strike ranking model for key nodes in a heterogeneous cascaded target system;

[0009] Step 2: Perform key node attack ranking based on fuzzy conditions;

[0010] Step 3: Perform attack ranking of key nodes in the heterogeneous cascaded target system based on optimization algorithms;

[0011] Step 4: Target key nodes in the heterogeneous cascaded target system based on the network determined above.

[0012] A critical node attack sequencing system for heterogeneous cascaded target systems under fuzzy conditions is disclosed. This system is used to implement the aforementioned critical node attack method for heterogeneous cascaded target systems under fuzzy conditions. The system comprises first to fourth units, each with the following functions:

[0013] A single unit is used to construct a key node attack ranking model for a heterogeneous cascaded target system;

[0014] The second unit involves ranking key nodes based on fuzzy conditions.

[0015] The third unit involves ranking the key nodes of a heterogeneous cascaded target system based on optimization algorithms.

[0016] The fourth unit involves striking key nodes in the heterogeneous cascaded target system based on the network determined above.

[0017] Compared with the prior art, the present invention has the following significant advantages: (1) By abstracting the enemy target type into the corresponding attribute node in the network system and the relationship between targets into the corresponding attribute edge in the network system, the network of the enemy's overall target system is realized. The system network topology based on the network node and edge model can not only show the overall network structure properties of the combat system, but also selectively study the local network structure characteristics of the system, providing a basis for the network analysis of military information systems; (2) The multi-target algorithm has been improved to be more suitable for actual problems, including adjusting the initialization strategy to sort the initialization according to the basic value range of the target node and adaptively adjusting the reference vector, etc. The improved key node strike ranking result is better than the traditional multi-target optimization algorithm, which can efficiently and accurately determine the key node strike order in a large-scale target system; (3) Combining Bayesian theory, neural network and other machine learning methods to classify heterogeneous nodes, thereby transforming the uncertainty problem into a node strike ranking problem of a known environment, effectively solving the problem of breaking the uncertain target system. Attached Figure Description

[0018] Figure 1 This is a flowchart of the method for attacking and ranking key nodes of a heterogeneous cascaded target system under fuzzy conditions, as proposed in this invention.

[0019] Figure 2 This is a schematic diagram of the structure of the nodes and edges of the heterogeneous cascaded target network system in this invention.

[0020] Figure 3 This is a schematic diagram of the node classification and link prediction framework for the heterogeneous cascaded target system in this invention.

[0021] Figure 4 This is a flowchart illustrating the dual-strategy hybrid cross-operation process in this invention. Detailed Implementation

[0022] This invention provides a method for ranking the critical nodes of a heterogeneous cascaded target system under fuzzy conditions, comprising the following steps:

[0023] Step 1: Construct a strike ranking model for key nodes in a heterogeneous cascaded target system;

[0024] Step 2: Perform key node attack ranking based on fuzzy conditions;

[0025] Step 3: Perform attack ranking of key nodes in the heterogeneous cascaded target system based on optimization algorithms;

[0026] Step 4: Target key nodes in the heterogeneous cascaded target system based on the network determined above.

[0027] As a specific example, the construction of the key node attack ranking model for the heterogeneous cascaded target system described in step 1 is as follows:

[0028] Step 1.1: Based on the description of network nodes and edges in the heterogeneous cascaded target system, construct the node and edge model of the heterogeneous cascaded target network system:

[0029] The target network is defined as containing n combat units. Based on their functions, the nodes are categorized into five types: fire support nodes (F), intelligence nodes (I), command and control nodes (Z), communication nodes (C), and support nodes (G). Multifunctional, composite equipment can be abstracted into multiple different types of nodes according to their functions. The edges in the target network are abstractions of the complex collaborative and information-sharing relationships between nodes. The various relationships between different nodes are simplified into multiple different types of edges between nodes. Connections between nodes of different functional types represent different meanings, including intelligence relationships (q). ij Communication relationship t ij , accusation relationship z ij Firepower protection relationship h ij , Protection relationship b ij Abstracting the relationships between nodes V into edges yields an edge set E, resulting in the network model Net = {N, E}.

[0030] Step 1.2: Construct the objective functions in the key node strike ranking model of the heterogeneous cascaded target system, including the objective function of maximizing the reduction of enemy strike benefits and the objective function of minimizing our strike costs:

[0031] Step 1.2.1: Maximize the objective function of reducing the effectiveness of enemy attacks.

[0032] The formula for calculating the effectiveness of the attack is as follows:

[0033]

[0034] Among them, Eff i =ωF base +F sys This represents the remaining system combat capability after the first i targets have been eliminated; it consists of the basic capabilities F of each node. base and system combat capability F sys Composition, where weight ω = 0.05; x ij The value is 1 when the j-th time sequence attacks the i-th target, and 0 otherwise; N represents the set of all nodes in the initial combat network;

[0035] The basic capabilities of a node are:

[0036]

[0037] in, f represents the set of remaining nodes in the combat network, i.e., the set of nodes that have not yet been attacked. s This represents the basic capabilities of the remaining node s;

[0038] The system combat capability is:

[0039]

[0040] w z +w q +w b +w h =1

[0041] in, Represents the elements in the accusation relationship Z. This represents an element in the intelligence relationship matrix Q. This represents the elements in the communication relationship matrix T. This represents the elements in the fire protection relationship matrix H. This represents the elements in the security relation matrix B; This represents the updated element in the accusation relationship Z;

[0042] Step 1.2.2: Minimize the objective function of our attack cost.

[0043] Given a target network comprising n combat units, including the following specific combat unit types: firepower units, intelligence units, command and control units, communication units, and support units, with all corresponding nodes denoted as set N, ||N|| = n, where a firepower unit is abstracted as a firepower node F, an intelligence unit as a sensor node I, a command and control unit as a command and control node D, a communication unit as a communication node T, and a support unit as a support node G, then our minimization attack cost function is:

[0044]

[0045] The total cost of our attack consists of ammunition consumption and troop resource losses, C 1i To reduce ammunition consumption for attacking the i-th target node, C 2i For the loss of troop resources, w c1 w represents the weight of ammunition consumption in the cost of an attack. c2 The weight of troop resource losses in the cost of an attack;

[0046] Ammunition consumption C for attacking the i-th target node 1i The calculation formula is:

[0047]

[0048] Among them, C 0i Let qk be the basic ammunition consumption for the i-th target node.i For the k-th target node in the intelligence relationship matrix Q, the intelligence provided to the i-th target node is represented by a 0 / 1 value; h ki For the k-th target node in the firepower relationship matrix H, firepower protection is provided to the i-th target node, and the value is 0 / 1; b ki To ensure that the k-th target node in the relationship matrix G provides protection to the i-th target node, the value is 0 / 1; the sum of the three represents the intelligence, fire protection, or support provided by the k-th target node to the i-th target node, and only when its value is 1 will it increase the ammunition consumption for our side to attack the i-th target node; at this time, the sum of the terms and the basic capability f of the k-th target node are considered. k Multiplying and then adding 1 indicates the multiplier by which the ammunition consumption for attacking the i-th target node increases from the original basic ammunition consumption of the i-th target node when the k-th target node provides a relationship to the i-th target node; P 1i To determine the hit rate against the i-th target node;

[0049] The loss of troops and resources in attacking the i-th target node is C. 2i The calculation formula is:

[0050] C 2i =w c3 *P 2i *NF i +w c4 *W r3 *D i

[0051] s.tW c3 +W c4 =1

[0052] In the formula, w c3 Assuming the weight of aircraft consumption in troop resource losses, W c4 P represents the weight of fuel consumption in troop resource losses. 2i The probability of aircraft damage when attacking the i-th target node is multiplied by the number of aircraft sorties NF used to attack the i-th target node. i Indicates aircraft consumption; D i The required flight range for striking the i-th target node;

[0053] Step 1.3: Constructing the constraints in the key node attack ranking model of the heterogeneous cascaded target system:

[0054] Step 1.3.1, Damage Degree Constraint: The damage degree constraint is expressed as:

[0055] L j ≤F0-F j ≤U j

[0056] Where L jU represents the lower limit of damage to the j-th target node. j This represents the maximum damage limit for the j-th target node;

[0057] Step 1.3.2, Force Constraints: Force constraints include allocating at least one fire unit to each target, concentrating each fire unit on only one target at a time, and setting upper limits on the amount of ammunition that can be consumed, the number of personnel involved in the operation, and the amount of funds that can be consumed in the operation.

[0058] Step 1.3.3, Spatiotemporal Constraints: The duration of attacks in different waves is finite. The upper limit of the duration of the j-th wave attack in the i-th round is T. ijh The lower time limit is T. ijl Then we have:

[0059] T ijl ≤T ij ≤T ijh

[0060] Assuming there are M types of weapon platforms facing N types of targets, and the i-th weapon needs to complete a single strike against the j-th target within a specified time window, then:

[0061] t ijl ≤t ij ≤t ijh

[0062] As a specific example, step 2, which involves ranking key nodes based on fuzzy conditions, is as follows:

[0063] Step 2.1: Based on the graph neural network model, design a heterogeneous network node classification framework that integrates GCN and GAT. The input data for the framework is as follows:

[0064] (1) Graph structure: It consists of a set of nodes and a set of edges. The nodes include intelligence, command and control, firepower, support and communication types.

[0065] (2) Node features: Node features include node coordinate information, basic ammunition consumption for node strikes, node search capabilities, command and control capabilities, transmission capabilities, anti-missile capabilities, support capabilities, strike risks, counterattack probability, counterattack costs, number of aircraft sorties, aircraft range, penetration rate, hit rate, damage probability, target intent, combat capabilities, and anti-destruction capabilities. These features need to be processed through normalization or embedding mapping techniques when training data to ensure the model's adaptability to heterogeneous data.

[0066] (3) Node labels and edge features: Node labels identify the category, and edge features reflect the relationship between nodes. The input format is unified through standardization or dimensionality reduction.

[0067] The framework structure consists of a Graph Convolutional Network (GCN) layer, a Graph Attention Network (GAT) layer, a multi-layer information propagation layer, a classification layer, a loss function, and evaluation metrics, as detailed below:

[0068] (1) The GCN layer performs convolution operations using the adjacency matrix and node features, which can capture information about neighboring nodes in the graph; in heterogeneous graphs, different types of convolution operations can be used to process different types of nodes and edges; in each GCN layer, for each node v i The data is aggregated using the information of its neighboring nodes in a weighted manner, as shown in the following formula:

[0069]

[0070] in, It is node v i A's neighbor ij These are the elements of the adjacency matrix, i.e., the edge weights; W (l) σ is the weight matrix of the l-th layer, and σ is the activation function;

[0071] (2) The GAT layer uses a self-attention mechanism to calculate attention weights from the features of neighboring nodes and the features of the target node, dynamically allocates neighbor weights, and learns node relationship characteristics from different perspectives through multi-head attention.

[0072] (3) Multi-layer information propagation: Through multi-layer graph convolution and graph attention network, information from different types of neighbors is aggregated into the representation of the target node layer by layer. The information propagation of each layer is iteratively updated through GCN layer and GAT layer, so that the representation of the node gradually integrates the information of the neighbors and enhances the expressive power of the model.

[0073] (4) Classification layer: After multiple layers of information propagation, the final embedded representation of each node is obtained. These embeddings will be fed into a fully connected layer or a Softmax layer to predict the node's class; the Softmax classification is as follows:

[0074]

[0075] Where c represents the category, W c It is the weight vector of category c;

[0076] (5) Loss function:

[0077] For the task of classifying nodes in a large-scale heterogeneous cascaded target system, the cross-entropy loss function is used, as shown in the following equation:

[0078]

[0079] in, It is a model for node vi Predicted class probability, y i It is the actual label of the node;

[0080] (6) Evaluation metrics: The performance of the large-scale cascaded target system node classification model is evaluated using the metrics of accuracy, F1 score, precision and recall.

[0081] Step 2.2: Based on graph convolutional networks and graph attention networks, construct a GCN-GAT link prediction model for heterogeneous networks. The input data for the model is as follows:

[0082] (1) Graph structure: It consists of a set of nodes and a set of edges. The nodes include intelligence, command and control, firepower, support and communication types.

[0083] (2) Node characteristics: Node characteristics include node coordinate information, basic ammunition consumption for node strikes, node search capabilities, command and control capabilities, transmission capabilities, anti-missile capabilities, support capabilities, strike risks, counterattack probability, counterattack costs, number of aircraft sorties, aircraft range, penetration rate, hit rate, damage probability, target intent, combat capabilities, and anti-destruction capabilities.

[0084] (3) Edge features: Edge features reflect the relationships between nodes;

[0085] The framework structure consists of node pair embedding computation, similarity calculation, link prediction layer, loss function, and evaluation metrics, as detailed below:

[0086] (1) Node pair embedding computation: Extract the embedding representation h of each node through graph convolution and graph attention. i h j Then, these embedding representations are used to compute node pairs (v i v j The similarity between nodes is calculated by using graph convolution and graph attention mechanisms to compute the embedding of each node. Then, the representations of the node pairs are concatenated or added to obtain the joint representation of the node pairs as follows:

[0087]

[0088] in, It can be splicing, addition, or other forms of combination. In addition to splicing or addition, it can also calculate the Hadamard product or element difference of node pairs, thereby more finely characterizing the relationship features between nodes and capturing complex interaction patterns.

[0089] (2) Similarity calculation: The inner product or Euclidean distance method is used to calculate the similarity between node pairs (v). i v jThe similarity between the edges is used to predict the probability of the edge's existence, as shown in the following formula:

[0090]

[0091] (3) Link prediction layer: For each pair of nodes (v) whose existence is unknown, i v j The probability of an edge existing between pairs of nodes is output using a sigmoid function.

[0092]

[0093] in, It is the Sigmoid function;

[0094] (4) Loss function: The binary cross-entropy loss is used as the loss function for link prediction in large-scale heterogeneous cascaded target systems.

[0095]

[0096] Where yij is the edge (v i v j A sign indicating whether something exists. It is a predicted probability;

[0097] (5) Evaluation metrics: The performance of the trained large-scale heterogeneous cascade target system link prediction model is evaluated by calculating the AUC score and analyzing the ROC curve.

[0098] Step 2.3: Combining Graph Convolutional Network (GCN) and Graph Attention Network (GAT), construct a node classification and link prediction framework for heterogeneous cascaded target systems, and perform node classification and link prediction as follows:

[0099] (1) The graph structure, node features and edge features are combined with the node or link information to be predicted as input;

[0100] (2) In the graph neural network layer, the graph convolutional network GCN generates the initial node embedding by integrating the information of neighboring nodes, thereby capturing the local relationship between nodes; the graph attention network GAT optimizes the information transmission process by dynamically adjusting the weights of neighboring nodes, so that the information of important neighboring nodes has a greater impact on the target node.

[0101] (3) In the node classification task, the model uses node embedding and Softmax classifier to predict the category of each node; in the link prediction task, the embedding features of the nodes at both ends of the edge are extracted and the probability of the link exists is calculated by the Sigmoid function.

[0102] As a specific example, step 3, which involves ranking the key nodes of a heterogeneous cascaded target system based on an optimization algorithm, is as follows:

[0103] Step 3.1: Construct an improved NSGA-II multi-objective optimization algorithm based on dual-strategy hybrid evolution. This algorithm uses tournament selection based on Pareto dominance and crowding, along with dual-strategy hybrid crossover. It introduces a hybrid evolutionary strategy based on global and local search operators, randomly selecting one global search operator and one local search operator for each individual to generate the next generation, as detailed below:

[0104] Step 3.1.1: During the algorithm iteration process, the Pareto optimal front obtained in each iteration is set as the elite pool. The optimization process of the population is guided by crossover operations between individuals in the elite pool and individual individuals in the new population. Based on this, a dual-strategy hybrid crossover operation is designed as follows: Strategy 1, i.e., ordinary crossover, randomly selects 2 individuals in the new population for crossover operation; Strategy 2, i.e., elite crossover, randomly selects 2 individuals in the elite pool and 2 individuals in the new population for crossover operation respectively.

[0105] Step 3.1.2: The global search operator is used to conduct extensive exploration throughout the decision space. By introducing a large-scale random perturbation, it promotes the maintenance of population diversity, enabling the algorithm to escape the local optimum trap and discover potential promising regions. In the global search phase, three effective crossover operators are used, including the sequential crossover operator, the multi-point crossover operator, and the partial mapping crossover operator.

[0106] In crossover algorithms, different crossover methods are randomly selected to obtain new individuals. Multi-point crossover randomly selects multiple crossover points; sequential crossover randomly selects two crossover points, determines the segment to be inherited, directly copies the segment to the same position in the offspring, and starts from the second crossover point to fill the remaining positions according to the relative order of elements in the other parent; Partially Mapped Crossover (PMX) obtains feasible solutions through the gene mapping relationship between two parents, and is particularly suitable for handling permutation problems.

[0107] The crossover operator can generate offspring individuals from multiple parent individuals according to a certain custom algorithm rule. The offspring individuals may have better characteristics due to inheriting superior genes from the parent individuals. For individuals x1 and x2 in the weapon and equipment allocation population, offspring individual x3 can be generated through the global search operator.

[0108] Step 3.1.3: Local search operators improve the quality of solutions by making small, targeted adjustments to existing solutions. During the local search phase, flip and exchange operators are applied to individuals in the non-dominated solution set. The flip operator randomly selects a sequence of solution vectors and reverses it, while the sliding mutation operator randomly selects genes, generates a sliding value within a small range, adds the sliding value to the gene to complete the mutation, and constrains gene values ​​that exceed the range. The basic principle of perturbation mutation is to add random perturbations within a certain range to the gene values ​​of individuals.

[0109] For an individual x in the weapon and equipment allocation scheme population, a child individual x1 can be generated using a local search operator. All new individuals generated by the local search operator represent feasible solutions.

[0110] Step 3.2: Combine the Deep Q-Network with the improved NSGA-II algorithm, use dual metrics to evaluate the current population quality, and design the action space and reward space of DQN accordingly. Use DQN to optimize the hyperparameters of the improved NSGA-II algorithm. Use DQN's experience replay and dual-network training to optimize the selection, crossover, and mutation operators of the NSGA-II algorithm. By designing diversity measures and population evenness metrics, evaluate the state space under different populations, as detailed below:

[0111] Step 3.2.1: Design diversity measures and population evenness indices, as follows:

[0112] Diversity metric: This metric compares three optimization metrics of individuals in the decoded population to determine whether they correspond to the same point in the feasible scheduling solution space and calculates the individual difference value. The larger the metric, the better the population diversity; the diversity metric Δ of the population in the t-th iteration. t The definition is as follows:

[0113] Δ t ={S i ,D[v]}

[0114] Population evenness index: This index is used to evaluate the evenness of the distribution of solutions at the current Pareto front. The smaller the index, the more evenly the solutions are distributed. If the index is 0, it means that the obtained non-dominated solutions are evenly distributed in the target space; the evenness index S of the population in the t-th iteration. i The definition is as follows:

[0115]

[0116] In the formula, A is the number of individuals in the Pareto front; obj_n is the number of objective functions; d v f is the solution gap value for the v-th individual, which is calculated by taking the solution gap value between each individual and other individuals, and then selecting the smallest value; l(x v ) and f l (x u ) are the first objective function values ​​for the v-th individual and the u-th individual, respectively; For all d v The average value;

[0117] Diversity index, population diversity measure: This involves comparing the two objective functions of individuals in the decoded population to determine if they correspond to the same point in the feasible scheduling solution space and calculating the individual difference value. The mathematical expression is as follows:

[0118] D[v](v=1,2,...popsize)

[0119] Where popsize is the population size;

[0120] Step 3.2.2: Based on any combination of global and local search operators, six different action selection strategies are adopted. The specific actions of the agent at each decision moment are expressed in mathematical form as follows:

[0121]

[0122] In the formula, n G nL represents the number of global search operators, and nL represents the number of local search operators;

[0123] Step 3.2.3: The reward space of DQN focuses on the probability distribution of fitness improvement achieved by the operator within a specific time window. When the operator achieves fitness improvement, it is assigned a unit reward value of 1; otherwise, it is assigned a reward value of 0. For the minimization optimization problem, the formula for calculating the immediate reward r of the operator is:

[0124]

[0125] In the formula, f 0 and f p Represents the fitness values ​​of the offspring and parent generations;

[0126] After adding a reward window, the actual reward value can be calculated based on the currently received instant reward and the historical rewards of this operator in the sliding window. The calculation formula is as follows:

[0127]

[0128] In the formula, |op i | indicates that in the sliding window W R Chinese op i Quantity, This represents a tuple in the sliding window.

[0129] The following is combined with Figures 1-4 The present invention will be further described in detail with reference to specific embodiments.

[0130] Example

[0131] like Figure 1 As shown, the present invention provides a method for ranking key nodes in a heterogeneous cascaded target system under fuzzy conditions, characterized by comprising the following steps:

[0132] Step 1: Construct a strike ranking model for key nodes in a heterogeneous cascaded target system, as detailed below:

[0133] Constructing a networked target system model not only reduces the loss of decision-making quality caused by communication delays or even communication failures between decision-making nodes, but also has the ability to integrate combat nodes and form an integrated combat posture. The system network topology based on network node and edge models can not only reveal the overall network structure of the combat system, but also selectively study the local network structure characteristics of the system, providing a foundation for the networked analysis of military information systems.

[0134] Step 1.1: The nodes in the target network are abstracted from constituent elements such as equipment, personnel, and positions. Accurately abstracting the key functions of the target is the primary task in building the network model. Based on the description of network nodes and edges in the heterogeneous cascaded target system, a node and edge model of the heterogeneous cascaded target network system is constructed, such as... Figure 2 As shown, the details are as follows:

[0135] The target network is defined as containing n combat units. Based on their functions, the nodes are categorized into five types: fire support nodes (F), intelligence nodes (I), command and control nodes (Z), communication nodes (C), and support nodes (G). Multifunctional, composite equipment can be abstracted into multiple different types of nodes according to their functions. The edges in the target network are abstractions of the complex collaborative and information-sharing relationships between nodes. The various relationships between different nodes are simplified into multiple different types of edges between nodes. Connections between nodes of different functional types represent different meanings, including intelligence relationships (q). ij Communication relationship t ij , accusation relationship z ij Firepower protection relationship h ij , Protection relationship b ij Abstracting the relationships between nodes V into edges yields an edge set E, resulting in the network model Net = {N, E}.

[0136] Step 1.2: Define the target network as containing n combat units. Based on their functions, nodes can be categorized into types such as fire support nodes (F), intelligence nodes (I), command and control nodes (Z), communication nodes (C), and support nodes (G). Multifunctional, composite equipment can be abstracted into multiple different types of nodes according to their functions. Edges in the target network are abstractions of the complex collaboration and information sharing relationships between nodes. This edge abstraction simplifies the various relationships between different nodes into multiple different types of edges between nodes. Connections between nodes of different functional types represent different meanings, such as intelligence relationships (q). ij Communication relationship t ij , accusation relationship z ij Firepower protection relationship h ij , Protection relationship b ij Abstracting the relationships between nodes V into edges yields an edge set E, resulting in the network model Net = {N, E}.

[0137] Step 1.2.1: Maximize the objective function of reducing the effectiveness of enemy attacks.

[0138] The formula for calculating the effectiveness of the attack is as follows:

[0139]

[0140] Among them, Eff i =ωP base +F sys This represents the system's combat capability remaining after the first i targets have been eliminated; it consists of the basic capabilities F of each node. base and system combat capability F sys Composition, where weight ω = 0.05; x ij The value is 1 when the j-th time sequence attacks the i-th target, and 0 otherwise; N represents the set of all nodes in the initial combat network;

[0141] The basic capabilities of a node are:

[0142]

[0143] in, f represents the set of remaining nodes in the combat network, i.e., the set of nodes that have not yet been attacked. s This represents the basic capabilities of the remaining node s;

[0144] The system combat capability is:

[0145]

[0146] w z +w q +W b +W h =1

[0147] in, Represents the elements in the accusation relationship Z. This represents an element in the intelligence relationship matrix Q. This represents the elements in the communication relationship matrix T. This represents the elements in the fire protection relationship matrix H. This represents the elements in the security relation matrix B; This represents the updated element in the accusation relationship Z;

[0148] Step 1.2.2: Minimize the objective function of our attack cost.

[0149] Given a target network comprising n combat units, including the following specific combat unit types: firepower units, intelligence units, command and control units, communication units, and support units, with all corresponding nodes denoted as set N, ||N|| = n, where a firepower unit is abstracted as a firepower node F, an intelligence unit as a sensor node I, a command and control unit as a command and control node D, a communication unit as a communication node T, and a support unit as a support node G, then our minimization attack cost function is:

[0150]

[0151] The total cost of our attack consists of ammunition consumption and troop resource losses, C 1i To reduce ammunition consumption for attacking the i-th target node, C 2i For the loss of troop resources, w c1 w represents the weight of ammunition consumption in the cost of an attack. c2 The weight of troop resource losses in the cost of an attack;

[0152] Ammunition consumption C for attacking the i-th target node 1i The calculation formula is:

[0153]

[0154] Among them, C 0i Let q be the basic ammunition consumption for the i-th target node. ki For the k-th target node in the intelligence relationship matrix Q, the intelligence provided to the i-th target node is represented by a 0 / 1 value; h ki For the k-th target node in the firepower relationship matrix H, firepower protection is provided to the i-th target node, and the value is 0 / 1; b ki To ensure that the k-th target node in the relationship matrix G provides protection to the i-th target node, the value is 0 / 1; the sum of the three represents the intelligence, fire protection, or support provided by the k-th target node to the i-th target node, and only when its value is 1 will it increase the ammunition consumption for our side to attack the i-th target node; at this time, the sum of the terms and the basic capability f of the k-th target node are considered. kMultiplying and then adding 1 indicates the multiplier by which the ammunition consumption for attacking the i-th target node increases from the original basic ammunition consumption of the i-th target node when the k-th target node provides a relationship to the i-th target node; P 1i To determine the hit rate against the i-th target node;

[0155] The loss of troops and resources in attacking the i-th target node is C. 2i The calculation formula is:

[0156] C 2i =w c3 *P 2i *NF i +w c4 *W r3 *D i

[0157] s.tW c3 +W c4 =1

[0158] In the formula, w c3 Assuming the weight of aircraft consumption in troop resource losses, W c4 P represents the weight of fuel consumption in troop resource losses. 2i The probability of aircraft damage when attacking the i-th target node is multiplied by the number of aircraft sorties NF used to attack the i-th target node. i Indicates aircraft consumption; D i The required flight range for striking the i-th target node;

[0159] Step 1.3: Constructing the constraints in the key node attack ranking model of the heterogeneous cascaded target system:

[0160] Step 1.3.1, Damage Degree Constraint: The damage degree constraint is expressed as:

[0161] L j ≤F0-F j ≤U j

[0162] Where L j U represents the lower limit of damage to the j-th target node. j This represents the maximum damage limit for the j-th target node;

[0163] Step 1.3.2, Force Constraints: Force constraints include allocating at least one fire unit to each target, concentrating each fire unit on only one target at a time, and setting upper limits on the amount of ammunition that can be consumed, the number of personnel involved in the operation, and the amount of funds that can be consumed in the operation.

[0164] Step 1.3.3, Spatiotemporal Constraints: The duration of attacks in different waves is finite. The upper limit of the duration of the j-th wave attack in the i-th round is T. ijh The lower time limit is T. ijl Then we have:

[0165] T ijl ≤T ij ≤T ijh

[0166] Assuming there are M types of weapon platforms facing N types of targets, and the i-th weapon needs to complete a single strike against the j-th target within a specified time window, then:

[0167] t ijl ≤t ij ≤t ijh

[0168] Step 2: Perform key node attack ranking based on fuzzy conditions, as follows:

[0169] In modern warfare, the operational situation changes rapidly, and the attributes and locations of key nodes can change at any time. This dynamic change introduces many ambiguities into the identification of key nodes and the timing of strikes. When intelligence is not precise enough or target characteristics are unclear, prioritizing strikes on key nodes plays a crucial role in improving operational effectiveness, enhancing the stability of the operational system, and improving the scientific nature of decision-making.

[0170] Step 2.1: Node classification is of great significance in complex network analysis, especially in heterogeneous cascaded target systems, where the results can directly affect the formulation of operational plans and resource allocation. Based on the graph neural network model, a heterogeneous network node classification framework integrating GCN and GAT is designed. The input data for the framework is as follows:

[0171] (1) Graph structure: It consists of a set of nodes and a set of edges. The nodes include intelligence, command and control, firepower, support and communication types.

[0172] (2) Node features: Node features include node coordinate information, basic ammunition consumption for node strikes, node search capabilities, command and control capabilities, transmission capabilities, anti-missile capabilities, support capabilities, strike risks, counterattack probability, counterattack costs, number of aircraft sorties, aircraft range, penetration rate, hit rate, damage probability, target intent, combat capabilities, and anti-destruction capabilities. These features need to be processed through normalization or embedding mapping techniques when training data to ensure the model's adaptability to heterogeneous data.

[0173] (3) Node labels and edge features: Node labels identify the category, and edge features reflect the relationship between nodes, such as command and control, communication, and security. The input format is unified through standardization or dimensionality reduction.

[0174] The framework structure consists of a Graph Convolutional Network (GCN) layer, a Graph Attention Network (GAT) layer, a multi-layer information propagation layer, a classification layer, a loss function, and evaluation metrics, as detailed below:

[0175] (1) The GCN layer performs convolution operations using the adjacency matrix and node features, which can capture information about neighboring nodes in the graph; in heterogeneous graphs, different types of convolution operations can be used to process different types of nodes and edges; in each GCN layer, for each node v i The data is aggregated using the information of its neighboring nodes in a weighted manner, as shown in the following formula:

[0176]

[0177] in, It is node v i A's neighbor ij These are the elements of the adjacency matrix, i.e., the edge weights; W (l) σ is the weight matrix of the l-th layer, and σ is the activation function;

[0178] (2) The GAT layer uses a self-attention mechanism to calculate attention weights from the features of neighboring nodes and the features of the target node, dynamically allocates neighbor weights, and learns node relationship characteristics from different perspectives through multi-head attention.

[0179] (3) Multi-layer information propagation: Through multi-layer graph convolution and graph attention network, information from different types of neighbors is aggregated into the representation of the target node layer by layer. The information propagation of each layer is iteratively updated through GCN layer and GAT layer, so that the representation of the node gradually integrates the information of the neighbors and enhances the expressive power of the model.

[0180] (4) Classification layer: After multiple layers of information propagation, the final embedded representation of each node is obtained. These embeddings will be fed into a fully connected layer or a Softmax layer to predict the node's class; the Softmax classification is as follows:

[0181]

[0182] Where c represents the category, W c It is the weight vector of category c;

[0183] (5) Loss function:

[0184] For the task of classifying nodes in a large-scale heterogeneous cascaded target system, the cross-entropy loss function is used, as shown in the following equation:

[0185]

[0186] in, It is a model for node v i Predicted class probability, y i It is the actual label of the node;

[0187] (6) Evaluation metrics: The performance of the large-scale cascaded target system node classification model is evaluated using the metrics of accuracy, F1 score, precision and recall.

[0188] Step 2.2: Based on graph convolutional networks and graph attention networks, construct a GCN-GAT link prediction model for heterogeneous networks. Link prediction is an important task in complex network analysis, aiming to infer potential connections in a graph. Especially under fuzzy conditions, link prediction can effectively fill in incomplete information and provide an accurate structural basis for ranking key nodes.

[0189] The model's input data is as follows:

[0190] (1) Graph structure: It consists of a set of nodes and a set of edges. The nodes include intelligence, command and control, firepower, support and communication types.

[0191] (2) Node characteristics: Node characteristics include node coordinate information, basic ammunition consumption for node strikes, node search capabilities, command and control capabilities, transmission capabilities, anti-missile capabilities, support capabilities, strike risks, counterattack probability, counterattack costs, number of aircraft sorties, aircraft range, penetration rate, hit rate, damage probability, target intent, combat capabilities, and anti-destruction capabilities.

[0192] (3) Edge features: Edge features reflect the relationships between nodes, such as command and control, communication, and security;

[0193] The framework structure consists of node pair embedding computation, similarity calculation, link prediction layer, loss function, and evaluation metrics, as detailed below:

[0194] (1) Node pair embedding computation: Extract the embedding representation h of each node through graph convolution and graph attention. i h j Then, these embedding representations are used to compute node pairs (v i v j The similarity between nodes is calculated by using graph convolution and graph attention mechanisms to compute the embedding of each node. Then, the representations of the node pairs are concatenated or added to obtain the joint representation of the node pairs as follows:

[0195]

[0196] in, It can be splicing, addition, or other forms of combination. In addition to splicing or addition, it can also calculate the Hadamard product or element difference of node pairs, thereby more finely characterizing the relationship features between nodes and capturing complex interaction patterns.

[0197] (2) Similarity calculation: The inner product or Euclidean distance method is used to calculate the similarity between node pairs (v). i v j The similarity between the edges is used to predict the probability of the edge's existence, as shown in the following formula:

[0198]

[0199] (3) Link prediction layer: For each pair of nodes (v) whose existence is unknown, i v j The probability of an edge existing between pairs of nodes is output using a sigmoid function.

[0200]

[0201] in, It is the Sigmoid function;

[0202] (4) Loss function: The binary cross-entropy loss is used as the loss function for link prediction in large-scale heterogeneous cascaded target systems.

[0203]

[0204] Among them, y ij It is an edge (v) i v j A sign indicating whether something exists. It is a predicted probability;

[0205] (5) Evaluation metrics: The performance of the trained large-scale heterogeneous cascade target system link prediction model is evaluated by calculating the AUC score and analyzing the ROC curve.

[0206] Step 2.3: Combining Graph Convolutional Network (GCN) and Graph Attention Network (GAT), construct a node classification and link prediction framework for heterogeneous cascaded target systems, such as... Figure 3 As shown, node classification and link prediction are performed as follows:

[0207] (1) The graph structure, node features and edge features are combined with the node or link information to be predicted as input;

[0208] (2) In the graph neural network layer, the graph convolutional network GCN generates the initial node embedding by integrating the information of neighboring nodes, thereby capturing the local relationship between nodes; the graph attention network GAT optimizes the information transmission process by dynamically adjusting the weights of neighboring nodes, so that the information of important neighboring nodes has a greater impact on the target node.

[0209] (3) In the node classification task, the model uses node embedding and Softmax classifier to predict the category of each node; in the link prediction task, the embedding features of the nodes at both ends of the edge are extracted and the probability of the link exists is calculated by the Sigmoid function.

[0210] In node classification, the framework balances local feature integration with global relationship modeling, enabling accurate differentiation of nodes across different categories. In link prediction, the combination of graph convolution and graph attention assigns differentiated weights to edges with different relationships, effectively filling structural gaps in the target network. These techniques not only enhance information processing capabilities under fuzzy conditions but also provide crucial decision support for operational planning and resource allocation.

[0211] Step 3: Perform attack ranking of key nodes in the heterogeneous cascaded target system based on optimization algorithms, as follows:

[0212] Step 3.1: Construct an improved NSGA-II multi-objective optimization algorithm based on dual-strategy hybrid evolution. This algorithm uses tournament selection based on Pareto dominance and crowding, along with dual-strategy hybrid crossover. It introduces a hybrid evolutionary strategy based on global and local search operators, randomly selecting one global search operator and one local search operator for each individual to generate the next generation, as detailed below:

[0213] Step 3.1.1: During the algorithm iteration process, the Pareto optimal front obtained in each iteration is set as the elite pool. Crossover operations are performed between individuals in the elite pool and individual individuals in the new population to guide the optimization process of the population. Based on this, a dual-strategy hybrid crossover operation is designed, such as... Figure 4 As shown, the specifics are as follows: Strategy 1, i.e., ordinary crossover, randomly selects 2 individuals from the new population for crossover; Strategy 2, i.e., elite crossover, randomly selects 2 individuals from both the elite pool and the new population for crossover; the pseudocode is as follows:

[0214]

[0215] Step 3.1.2: The global search operator is used to conduct extensive exploration throughout the decision space. By introducing a large-scale random perturbation, it promotes the maintenance of population diversity, enabling the algorithm to escape the local optimum trap and discover potential promising regions. In the global search phase, three effective crossover operators are used, including the sequential crossover operator, the multi-point crossover operator, and the partial mapping crossover operator.

[0216] In crossover algorithms, different crossover methods are randomly selected to obtain new individuals. Multi-point crossover randomly selects multiple crossover points; sequential crossover randomly selects two crossover points, determines the segment to be inherited, directly copies the segment to the same position in the offspring, and starts from the second crossover point to fill the remaining positions according to the relative order of elements in the other parent; Partially Mapped Crossover (PMX) obtains feasible solutions through the gene mapping relationship between two parents, and is particularly suitable for handling permutation problems.

[0217] The crossover operator can generate offspring individuals from multiple parent individuals according to a custom algorithm. The resulting offspring individuals may possess superior traits due to inheriting excellent genes from their parents. For individuals x1 and x2 in the weapon and equipment allocation population, offspring individual x3 can be generated using a global search operator. The pseudocode is as follows:

[0218]

[0219]

[0220] Step 3.1.3: The local search operator focuses on refined development within the neighborhood of known solutions, improving solution quality through small, targeted adjustments to existing solutions. During the local search phase, flip and exchange operators are applied to individuals in the non-dominated solution set. The flip operator randomly selects a sequence of solution vectors and reverses it, while the sliding mutation operator randomly selects genes, generates a sliding value within a small range, adds the sliding value to the gene to complete the mutation, and constrains gene values ​​outside the range. The basic principle of perturbation mutation is to add random perturbations within a certain range to the gene values ​​of individuals. This multi-level hybrid search strategy ensures the algorithm's wide-area exploration capability in the solution space while effectively balancing exploration and development, thus improving the solution performance of NSGA-II on complex multi-objective optimization problems.

[0221] For an individual x in the weapon and equipment allocation scheme population, a offspring individual x1 can be generated using a local search operator. The new individuals generated by the local search operator are all feasible solutions; the pseudocode is as follows:

[0222]

[0223] Step 3.2: Combine the Deep Q-Network with the improved NSGA-II algorithm, use dual metrics to evaluate the current population quality, and design the action space and reward space of DQN accordingly. Use DQN to optimize the hyperparameters of the improved NSGA-II algorithm. Use DQN's experience replay and dual-network training to optimize the selection, crossover, and mutation operators of the NSGA-II algorithm. By designing diversity measures and population evenness metrics, evaluate the state space under different populations, as detailed below:

[0224] Step 3.2.1: Design diversity measures and population evenness indices, as follows:

[0225] Diversity metric: This metric compares three optimization metrics of individuals in the decoded population to determine whether they correspond to the same point in the feasible scheduling solution space and calculates the individual difference value. The larger the metric, the better the population diversity; the diversity metric Δ of the population in the t-th iteration. t The definition is as follows:

[0226] Δ t ={S i ,D[v]}

[0227] Population evenness index: This index is used to evaluate the evenness of the distribution of solutions at the current Pareto front. The smaller the index, the more evenly the solutions are distributed. If the index is 0, it means that the obtained non-dominated solutions are evenly distributed in the target space; the evenness index S of the population in the t-th iteration. i The definition is as follows:

[0228]

[0229] In the formula, A is the number of individuals in the Pareto front; obj_n is the number of objective functions; d v f is the solution gap value for the v-th individual, which is calculated by taking the solution gap value between each individual and other individuals, and then selecting the smallest value; l (x v ) and f l (x u ) are the first objective function values ​​for the v-th individual and the u-th individual, respectively; For all d v The average value; pseudocode is as follows:

[0230]

[0231]

[0232] Diversity index, population diversity measure: Compares the two objective functions of individuals in the decoded population to determine if they correspond to the same point in the feasible scheduling solution space and calculates the individual difference value. The mathematical expression is as follows:

[0233] D[v](v=1,2,...popsize)

[0234] Where popsize is the population size.

[0235] Step 3.2.2: Based on any combination of global and local search operators, six different action selection strategies are adopted. The specific actions of the agent at each decision moment are expressed in mathematical form as follows:

[0236]

[0237] In the formula, n G nL represents the number of global search operators, and nL represents the number of local search operators;

[0238] The pseudocode for global-local operator selection in the action space is as follows:

[0239]

[0240] Step 3.2.3: The reward space of DQN focuses on the probability distribution of fitness improvement achieved by the operator within a specific time window. When the operator achieves fitness improvement, it is assigned a unit reward value of 1; otherwise, it is assigned a reward value of 0. For the minimization optimization problem, the formula for calculating the immediate reward r of the operator is:

[0241]

[0242] In the formula, f 0 and f p Represents the fitness values ​​of the offspring and parent generations;

[0243] After adding a reward window, the actual reward value can be calculated based on the currently received instant reward and the historical rewards of this operator in the sliding window. The calculation formula is as follows:

[0244]

[0245] In the formula, |op i | indicates that in the sliding window W R Chinese op i Quantity, Represents a tuple in a sliding window;

[0246] The pseudocode for the reward window is as follows:

[0247]

[0248] The overall pseudocode for the RL-INSGA-II algorithm is as follows:

[0249]

[0250] Step 4: Target key nodes in the heterogeneous cascaded target system based on the network determined above.

[0251] The above are merely preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for ranking the attack on key nodes of a heterogeneous cascaded target system under fuzzy conditions, characterized in that, Includes the following steps: Step 1: Construct a strike ranking model for key nodes in a heterogeneous cascaded target system, as detailed below: Step 1.1: Based on the description of network nodes and edges in the heterogeneous cascaded target system, construct the node and edge model of the heterogeneous cascaded target network system: Set the target network to include Each combat unit, according to its different functions, divides the nodes into fire nodes. Intelligence nodes , accusation node Communication nodes , guarantee nodes Five types of nodes: Multifunctional composite equipment is abstracted into multiple different types of nodes according to its functions; the edges in the target network are abstractions of the complex collaborative and information-sharing relationships between nodes. The various relationships between different nodes are simplified into edges between multiple different types of nodes. Connections between nodes of different functional types represent different meanings, including intelligence relationships. Communication Relationship accusation relationship Firepower protection relationship , guarantee relationship ; will node The relationships between them are abstracted into edges to obtain edge sets. The obtained network model ; Step 1.2: Construct the objective functions in the key node strike ranking model of the heterogeneous cascaded target system, including the objective function of maximizing the reduction of enemy strike benefits and the objective function of minimizing our strike costs; Step 1.3: Construct the constraints in the key node attack ranking model of the heterogeneous cascaded target system; Step 2: Perform key node attack ranking based on fuzzy conditions; Step 3: Perform attack ranking of key nodes in the heterogeneous cascaded target system based on optimization algorithms; Step 4: Target key nodes in the heterogeneous cascaded target system based on the network determined above.

2. The method for attacking and ranking key nodes of a heterogeneous cascaded target system under fuzzy conditions as described in claim 1, characterized in that, The objective functions in the key node strike ranking model of the heterogeneous cascaded target system described in step 1.2 include the objective function of maximizing the reduction of enemy strike benefits and the objective function of minimizing our strike costs, as detailed below: Step 1.2.1: Maximize the objective function of reducing the effectiveness of enemy attacks; The formula for calculating the effectiveness of the attack is as follows: ； in, This represents the remaining system combat capability after the first i targets have been eliminated, consisting of the basic capabilities of the nodes. and system combat capability Composition, where weights =0.05; The value is 1 when the j-th time sequence strikes the i-th target, and 0 for the rest; N represents the set of all nodes in the initial combat network; The basic capabilities of a node are: ； in, This represents the set of remaining nodes in the combat network, i.e., the set of nodes that have not yet been attacked. This represents the basic capabilities of the remaining node s; The system combat capability is: ； ； ； ； in, Represents the elements in the accusation relationship Z. This represents an element in the intelligence relationship matrix Q. This represents the elements in the communication relationship matrix T. This represents the elements in the fire protection relationship matrix H. This represents the elements in the security relation matrix B; This represents the updated element in the accusation relationship Z; Step 1.2.2: Minimize the objective function of our attack cost; Set the target network to include Each combat unit comprises the following specific combat unit types: fire unit, intelligence unit, command and control unit, communication unit, and support unit. All corresponding nodes are denoted as the set. , The fire unit is abstracted as a fire node. Intelligence units are abstracted as sensor nodes. The charge unit is abstracted as a charge node. The communication unit is abstracted as a communication node. The guarantee unit is abstracted as a guarantee node. Then our minimization attack cost function is: ； ； The total cost of our attack consists of ammunition consumption and troop resource losses. To combat the Ammunition consumption at the target node. For the loss of troop resources, The weight of ammunition consumption in the cost of an attack. The weight of troop resource losses in the cost of an attack; Strike the first Ammunition consumption at the target node The calculation formula is: ； in, For the first Basic ammunition consumption of the target node Intelligence Relationship Matrix The first in Target node pair The target node provides intelligence, represented by a 0 / 1 value. Firepower Relationship Matrix The Middle Target node pair The target node provides fire protection, with a value of 0 / 1. To ensure the relationship matrix The first in Target node pair The target node provides a guarantee, represented by a 0 / 1 value; the sum of the three values ​​indicates the first node. Target node pair The target node provides intelligence, fire protection, or support; only when its value is 1 will our attack on the target node increase. Ammunition consumption at the target node; at this point, the summation term is equal to the first term. Basic capabilities of the target node Multiply and then add 1 to represent the first product. Target node pair When the target node provides a relationship, strike the first The target node's ammunition consumption is in the original number The multiplier added to the target node's basic ammunition consumption; To combat the Hit rate of the target node; Strike the first Loss of troop resources at the target node The calculation formula is: ； ； In the formula, The weight of aircraft consumption in troop resource losses. The weight of fuel consumption in troop resource losses; To combat the The probability of aircraft destruction at the target node, multiplied by the number of hits. Number of aircraft sorties at target node Indicates aircraft consumption; To combat the The required flight distance to reach the target node.

3. The method for attacking and ranking key nodes of a heterogeneous cascaded target system under fuzzy conditions as described in claim 2, characterized in that, The constraints in step 1.3 for constructing the key node attack ranking model of the heterogeneous cascaded target system are as follows: Step 1.3.1, Damage Degree Constraint: The damage degree constraint is expressed as: ； in Indicates the first The lower limit of damage to a target node Indicates the first The maximum damage limit for each target node; Step 1.3.2, Force Constraints: Force constraints include allocating at least one fire unit to each target, concentrating each fire unit on only one target at a time, and setting upper limits on the amount of ammunition that can be consumed, the number of personnel involved in the operation, and the amount of funds that can be consumed in the operation. Step 1.3.3, Spatiotemporal Constraints: The duration of different waves of attacks is finite. Round number The maximum duration of wave strikes is The time limit is Then we have: ； Setting up a total Weapon-like platforms facing Type of target to be attacked, number The first single strike of this type of weapon If a target needs to be completed within a specified time window, then: 。 4. The method for attacking and ranking key nodes of a heterogeneous cascaded target system under fuzzy conditions as described in claim 3, characterized in that, Step 2, which involves ranking key nodes based on fuzzy conditions, is as follows: Step 2.1: Based on the graph neural network model, design a heterogeneous network node classification framework that integrates GCN and GAT; Step 2.2: Based on graph convolutional network and graph attention network models, construct a GCN-GAT link prediction model for heterogeneous networks; Step 2.3: Combine Graph Convolutional Network (GCN) and Graph Attention Network (GAT) to construct a node classification and link prediction framework for heterogeneous cascaded target systems, and perform node classification and link prediction.

5. The method for attacking and ranking key nodes of a heterogeneous cascaded target system under fuzzy conditions as described in claim 4, characterized in that, Step 2.1 describes the design of a heterogeneous network node classification framework that integrates GCN and GAT based on the graph neural network model. The input data for the framework is as follows: (1) Graph structure: It consists of a set of nodes and a set of edges. The nodes include intelligence, command and control, firepower, support and communication types; (2) Node features: Node features include node coordinate information, basic ammunition consumption for node strikes, node search capability, command and control capability, transmission capability, anti-missile capability, support capability, strike risk, counterattack probability, counterattack cost, number of aircraft sorties, aircraft range, penetration rate, hit rate, damage probability, target intent, combat capability, and anti-destruction capability. These features need to be processed through normalization or embedding mapping techniques when training data to ensure the model's adaptability to heterogeneous data. (3) Node labels and edge features: Node labels identify the category, and edge features reflect the relationship between nodes. The input format is unified through standardization or dimensionality reduction. The framework structure consists of a Graph Convolutional Network (GCN) layer, a Graph Attention Network (GAT) layer, a multi-layer information propagation layer, a classification layer, a loss function, and evaluation metrics, as detailed below: (1) The GCN layer performs convolution operations using the adjacency matrix and node features, which can capture information about neighboring nodes in the graph; in heterogeneous graphs, different types of convolution operations are used to process different types of nodes and edges; in each GCN layer, for each node The weighted aggregation is performed using information from neighboring nodes, as shown in the following formula: ； in, It is a node Neighbors These are the elements of the adjacency matrix, i.e., the edge weights; It is the weight matrix of the l-th layer. It is an activation function; (2) The GAT layer uses a self-attention mechanism to calculate attention weights based on the features of neighboring nodes and the features of the target node, dynamically allocates neighbor weights, and learns node relationship characteristics from different perspectives through multi-head attention. (3) Multi-layer information propagation: Through multi-layer graph convolution and graph attention network, information from different types of neighbors is aggregated into the representation of the target node layer by layer. The information propagation of each layer is iteratively updated through GCN layer and GAT layer, so that the representation of the node gradually integrates the information of the neighbors and enhances the expressive power of the model. (4) Classification layer: After multiple layers of information propagation, the embedding representation of each node is finally obtained. These embeddings will be fed into a fully connected layer or a Softmax layer to predict the node category; the Softmax classification is as follows: ； in, Indicates category, It is a category The weight vector; (5) Loss function: For the task of classifying nodes in a large-scale heterogeneous cascaded target system, the cross-entropy loss function is used, as shown in the following equation: ； in, It is a model for nodes Predicted class probabilities It is the actual label of the node; (6) Evaluation metrics: The performance of the large-scale cascaded target system node classification model is evaluated using the metrics of accuracy, F1 score, precision and recall.

6. The method for attacking and ranking key nodes of a heterogeneous cascaded target system under fuzzy conditions as described in claim 5, characterized in that, Step 2.2 describes the construction of a GCN-GAT link prediction model for heterogeneous networks based on graph convolutional networks and graph attention networks. The input data for the model is as follows: (1) Graph structure: It consists of a set of nodes and a set of edges. The nodes include intelligence, command and control, firepower, support and communication types; (2) Node characteristics: Node characteristics include node coordinate information, basic ammunition consumption for node strikes, node search capability, command and control capability, transmission capability, anti-missile capability, support capability, strike risk, counterattack probability, counterattack cost, number of aircraft sorties, aircraft range, penetration rate, hit rate, damage probability, target intent, combat capability, and anti-destruction capability. (3) Edge features: Edge features reflect the relationships between nodes; The framework structure consists of node pair embedding computation, similarity calculation, link prediction layer, loss function, and evaluation metrics, as detailed below: (1) Node pair embedding computation: Extract the embedding representation of each node through graph convolution and graph attention. Then, these embedding representations are used to compute node pairs. The similarity between nodes is calculated by using graph convolution and graph attention mechanisms to compute the embedding of each node. Then, the representations of the node pairs are concatenated or added to obtain the joint representation of the node pairs as follows: ； in, It's either splicing or addition; (2) Similarity calculation: The inner product or Euclidean distance method is used to calculate the similarity between node pairs. The similarity between the edges is used to predict the probability of an edge's existence, as shown in the following formula: ； ； (3) Link prediction layer: For each pair of nodes whose existence is unknown, The probability of an edge existing between pairs of nodes is output using a sigmoid function: ； in, It is the Sigmoid function; (4) Loss function: The binary cross-entropy loss is used as the loss function for link prediction in large-scale heterogeneous cascaded target systems: ； in, It is the edge A sign of existence. It is a predicted probability; (5) Evaluation metrics: The performance of the trained large-scale heterogeneous cascade target system link prediction model is evaluated by calculating the AUC score and analyzing the ROC curve.

7. The method for attack ranking of key nodes in a heterogeneous cascaded target system under fuzzy conditions as described in claim 6, characterized in that, Step 2.3 describes the construction of a node classification and link prediction framework for heterogeneous cascaded target systems by combining Graph Convolutional Network (GCN) and Graph Attention Network (GAT). The specific details are as follows: (1) The graph structure, node features and edge features are combined with the node or link information to be predicted as input; (2) In the graph neural network layer, the graph convolutional network GCN generates the initial node embedding by integrating the information of neighboring nodes, thereby capturing the local relationship between nodes; the graph attention network GAT optimizes the information transmission process by dynamically adjusting the weights of neighboring nodes, so that the information of important neighboring nodes has a greater impact on the target node. (3) In the node classification task, the model uses node embedding and Softmax classifier to predict the category of each node; in the link prediction task, the embedding features of the nodes at both ends of the edge are extracted and the probability of the link exists is calculated by the Sigmoid function.

8. The method for attack ranking of key nodes in a heterogeneous cascaded target system under fuzzy conditions as described in claim 7, characterized in that, Step 3, which involves ranking the key nodes of a heterogeneous cascaded target system based on an optimization algorithm, is as follows: Step 3.1: Construct an improved NSGA-II multi-objective optimization algorithm based on dual-strategy hybrid evolution. This algorithm uses tournament selection based on Pareto dominance and crowding, along with dual-strategy hybrid crossover. It introduces a hybrid evolutionary strategy based on global and local search operators, randomly selecting one global search operator and one local search operator for each individual to generate the next generation, as detailed below: Step 3.1.1: During the algorithm iteration process, the Pareto optimal front obtained in each iteration is set as the elite pool. The optimization process of the population is guided by crossover operations between individuals in the elite pool and individual individuals in the new population. Based on this, a dual-strategy hybrid crossover operation is designed as follows: Strategy 1, i.e., ordinary crossover, randomly selects 2 individuals in the new population for crossover operation; Strategy 2, i.e., elite crossover, randomly selects 2 individuals in the elite pool and 2 individuals in the new population for crossover operation respectively. Step 3.1.2: The global search operator is used to conduct extensive exploration throughout the decision space. By introducing a large-scale random perturbation, it promotes the maintenance of population diversity, enabling the algorithm to escape the local optimum trap and discover potential promising regions. During the global search phase, three effective crossover operators are used, including the sequential crossover operator, the multi-point crossover operator, and the partial mapping crossover operator. In the crossover operator algorithm, new individuals are obtained by randomly selecting different crossover methods; multi-point crossover randomly selects multiple crossover points; sequential crossover randomly selects two crossover points, determines the segment to be inherited, directly copies the segment to the same position in the offspring, and fills the remaining positions from the second crossover point according to the relative order of the elements in the other parent; the partial mapping crossover operator obtains a feasible solution through the gene mapping relationship between two parents. The crossover operator generates offspring individuals using multiple parent individuals according to a custom algorithm rule. The offspring individuals may have better characteristics due to inheriting superior genes from the parent individuals. For individuals x1 and x2 in the weapon and equipment allocation population, offspring individual x3 is generated through a global search operator. Step 3.1.3: Local search operators improve the quality of solutions by making small, targeted adjustments to existing solutions. During the local search phase, flip and exchange operators are applied to individuals in the non-dominated solution set. The flip operator randomly selects a sequence of solution vectors and reverses it, while the sliding mutation operator randomly selects genes, generates a sliding value within a small range, adds the sliding value to the gene to complete the mutation, and constrains gene values ​​that exceed the range. The basic principle of perturbation mutation is to add random perturbations within a certain range to the gene values ​​of individuals. For an individual x in the population of weapon and equipment allocation schemes, a child individual x1 is generated through a local search operator; the new individuals generated by the local search operator are all feasible solutions. Step 3.2: Combine the Deep Q-Network with the improved NSGA-II algorithm, use dual metrics to evaluate the current population quality, and design the action space and reward space of DQN accordingly. Use DQN to optimize the hyperparameters of the improved NSGA-II algorithm. Use DQN's experience replay and dual-network training to optimize the selection, crossover, and mutation operators of the NSGA-II algorithm. By designing diversity measures and population evenness metrics, evaluate the state space under different populations, as detailed below: Step 3.2.1: Design diversity measures and population evenness indices, as follows: Diversity metric: This metric compares three optimization metrics of individuals in the decoded population to determine whether they correspond to the same point in the feasible scheduling solution space and calculates the individual difference value. A higher metric indicates better population diversity. The diversity metric for the population in the t-th iteration is... The definition is as follows: ； Population evenness index: This index is used to evaluate the evenness of the distribution of solutions at the current Pareto front. The smaller the index, the more evenly the solutions are distributed. If the index is 0, it means that the obtained non-dominated solutions are evenly distributed in the target space; the evenness index of the population in the t-th iteration. The definition is as follows: ； ； In the formula, A is the number of individuals in the Pareto front; For the first The solution gap value for each individual is calculated, that is, the solution gap value between each individual and other individuals is calculated, and the smallest value is selected from them; and These are the l-th objective function values ​​for the v-th individual and the u-th individual, respectively; For all The average value; Diversity index, population diversity measure: Compares the two objective functions of individuals in the decoded population to determine if they correspond to the same point in the feasible scheduling solution space and calculates the individual difference value. The mathematical expression is as follows: ； in, Population size; Step 3.2.2: Based on any combination of global and local search operators, six different action selection strategies are adopted. The specific actions of the agent at each decision moment are expressed in mathematical form as follows: ； In the formula, This indicates the number of global search operators. Indicates the number of local search operators; Step 3.2.3: The reward space of DQN focuses on the probability distribution of fitness improvement achieved by the operator within a specific time window. When the operator achieves fitness improvement, a unit reward value of 1 is assigned; otherwise, a reward value of 0 is assigned. For minimization optimization problems, the operator's timely reward... The calculation formula is: ； In the formula, and Represents the fitness values ​​of the offspring and parent generations; After adding the reward window, the actual reward value is calculated based on the currently received instant reward and the operator's historical rewards in the sliding window. The calculation formula is as follows: ； In the formula, where Indicates a sliding window middle Quantity, This represents a tuple in the sliding window.

9. A system for ranking key nodes in a heterogeneous cascaded target system under fuzzy conditions, characterized in that, This system is used to implement the method for striking key nodes of a heterogeneous cascaded target system under fuzzy conditions as described in any one of claims 1 to 8. The system comprises first to fourth units, and the functions of each unit are as follows: A single unit is used to construct a key node attack ranking model for a heterogeneous cascaded target system, as detailed below: Step 1.1: Based on the description of network nodes and edges in the heterogeneous cascaded target system, construct the node and edge model of the heterogeneous cascaded target network system: Set the target network to include Each combat unit, according to its different functions, divides the nodes into fire nodes. Intelligence nodes , accusation node Communication nodes , guarantee nodes Five types of nodes: Multifunctional composite equipment is abstracted into multiple different types of nodes according to its functions; the edges in the target network are abstractions of the complex collaborative and information-sharing relationships between nodes. The various relationships between different nodes are simplified into edges between multiple different types of nodes. Connections between nodes of different functional types represent different meanings, including intelligence relationships. Communication Relationship accusation relationship Firepower protection relationship , guarantee relationship ; will node The relationships between them are abstracted into edges to obtain edge sets. The obtained network model ; Step 1.2: Construct the objective functions in the key node strike ranking model of the heterogeneous cascaded target system, including the objective function of maximizing the reduction of enemy strike benefits and the objective function of minimizing our strike costs; Step 1.3: Construct the constraints in the key node attack ranking model of the heterogeneous cascaded target system; The second unit involves ranking key nodes based on fuzzy conditions. The third unit involves ranking the key nodes of a heterogeneous cascaded target system based on optimization algorithms. The fourth unit involves striking key nodes in the heterogeneous cascaded target system based on the network determined above.

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