Heterogeneous cascade target system key node strike sorting method and system oriented to fuzzy condition

Abstract

The invention discloses a heterogeneous cascade target system key node strike sorting method and system oriented to fuzzy conditions. The method specifically comprises the steps that firstly, a heterogeneous cascade target system key node strike sorting model is constructed; then key node strike sorting based on fuzzy conditions is carried out; carrying out key node strike sorting of the heterogeneous cascade target system based on an optimization algorithm; and finally, striking key nodes in the heterogeneous cascade target system based on the determined network. According to the method, the strike sequence of the key nodes in the large-scale target system can be efficiently and accurately determined, the uncertainty problem can be converted into the node strike sorting problem of the known environment, the problem of breaking of the uncertain target system is effectively solved, and a basis is provided for networked analysis of a military information system.

Description

Technical Field

[0001] The present invention relates to the technical field of joint combat mission planning, and in particular to a method and system for sorting key nodes of a heterogeneous cascade target system under fuzzy conditions. Background Art

[0002] With the continuous deepening and expansion of intelligent technology, the face of joint combat command is undergoing profound changes. The combat command mode is gradually changing from informatization with links as the way to open up to intelligentization with the goal of assisting decision-making. The target system evaluation method based on system integration, association recommendation, and breaking links and networks will become the mainstream of joint strike target optimization and recommendation in the future. For commanders, being able to find key targets and implement strikes in the shortest time will have an important impact on the accuracy and timeliness of commanders' decisions, and thus affect the implementation of the entire combat plan.

[0003] Invention patent CN108416441A discloses a method for allocating firepower for ship-to-shore strikes based on a genetic algorithm. A weapon on a ship is used as a firepower unit, and the number of firepower allocations of the firepower unit to the target on the shore is used as a coding bit. Each firepower unit is encoded using a random distribution generation method to obtain an initial population; the population fitness of the initial population is calculated using a fitness function, and the initial population is selected based on the population fitness combined with roulette to obtain a selected population, and chromosome crossover and mutation are performed on the selected population to obtain a new population; the initial population is updated with the new population and the previous step is repeated. After repeated multiple times, a ship-to-shore strike firepower allocation plan is obtained. This technology fails to consider the system value association factors between targets, and cannot realize 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 a joint firepower strike target system, it realizes the automatic linking of target association relationships; establishes an emergent evaluation index model in a complex hypernetwork system, and realizes the emergent value measurement of the strike target hypernetwork; realizes the association recommendation and optimal recommendation of commanders' preferred strike targets, and improves the level of intelligent decision-making support. However, it is unable to perform strike sorting of key nodes under fuzzy conditions and cannot solve the problem of breaking through uncertain target systems.

[0005] Therefore, it is urgent to study a strike ranking method that can cope with the situation where some relationships are missing or uncertain in a large-scale cascade target system, so as to effectively solve the problem of defeating an uncertain target system. Summary of the invention

[0006] The object of the present invention is to provide a key node strike ranking method and system that can effectively perform strike ranking on key nodes, can handle the situation of partial missing or uncertain relationships in a large-scale cascading target system, and can effectively solve the problem of breaking through an uncertain target system.

[0007] The technical solution for achieving the object of the present invention is: a key node strike ranking method for a heterogeneous cascading target system under fuzzy conditions, including the following steps:

[0008] Step 1, construct a key node strike ranking model for the heterogeneous cascading target system;

[0009] Step 2, perform key node strike ranking based on fuzzy conditions;

[0010] Step 3, perform key node strike ranking for the heterogeneous cascading target system based on an optimization algorithm;

[0011] Step 4, strike the key nodes in the heterogeneous cascading target system based on the network determined above.

[0012] A key node strike ranking system for a heterogeneous cascading target system under fuzzy conditions, which is used to implement the key node strike method for a heterogeneous cascading target system under fuzzy conditions. The system includes first to fourth units, and the functions of each unit are as follows:

[0013] The first unit constructs a key node strike ranking model for the heterogeneous cascading target system;

[0014] The second unit performs key node strike ranking based on fuzzy conditions;

[0015] The third unit performs key node strike ranking for the heterogeneous cascading target system based on an optimization algorithm;

[0016] The fourth unit strikes the key nodes in the heterogeneous cascading target system based on the network determined above.

[0017] Compared with the prior art, the significant advantages of the present invention are as follows: (1) By abstracting the enemy target types into the corresponding attribute nodes in the network system and the relationships between targets into the edges of the corresponding attributes in the network system, the overall enemy target system is networked. The system network topology based on the network node and edge model can not only show the network structure properties of the entire 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-objective algorithm is improved to be more suitable for practical problems, including adjusting the initialization strategy to sort and initialize according to the basic value range of target nodes, adaptively adjusting the reference vector, etc. The key node strike sorting result after improvement is better than that of the traditional multi-objective optimization algorithm, and it can efficiently and accurately determine the key node strike order in a large-scale target system; (3) Combining machine learning methods such as Bayesian theory and neural networks for the classification of heterogeneous nodes, thereby transforming the uncertainty problem into a node strike sorting problem in a known environment, and effectively solving the problem of breaking through an uncertain target system. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 is a flowchart of the method for sorting key node strikes in a heterogeneous cascaded target system under fuzzy conditions according to the present invention.

[0019] Figure 2 is a schematic structural diagram of the node and edge model of the heterogeneous cascaded target network system according to the present invention.

[0020] Figure 3 is a schematic structural diagram of the node classification and link prediction framework of the heterogeneous cascaded target system according to the present invention.

[0021] Figure 4 is a schematic flowchart of the dual-strategy hybrid crossover operation according to the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0022] The present invention provides a method for sorting key node strikes in a heterogeneous cascaded target system under fuzzy conditions, including the following steps:

[0023] Step 1, construct a key node strike sorting model for the heterogeneous cascaded target system;

[0024] Step 2, perform key node strike sorting based on fuzzy conditions;

[0025] Step 3, perform key node strike sorting for the heterogeneous cascaded target system based on an optimization algorithm;

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

[0027] As a specific example, the key node strike ranking model for constructing a heterogeneous cascading target system in step 1 is as follows:

[0028] Step 1.1: According to the descriptions of network nodes and edges in the heterogeneous cascading target system, construct a node and edge model for the heterogeneous cascading target network system:

[0029] Suppose the target network contains n combat units. According to different functions, the nodes are divided into five types: firepower node F, intelligence node I, command node Z, communication node C, and support node G. Multifunctional composite equipment can be abstracted into multiple different types of nodes according to the functions it possesses; the edges in the target network are abstractions of the complex cooperation and information sharing relationships between nodes. The various relationships between different nodes are abstracted and simplified into edges between multiple different nodes. The connections between nodes of different functional types represent different meanings, including intelligence relationship q ij , communication relationship t ij , command relationship z ij , firepower protection relationship h ij , support relationship b ij ; The mutual relationships between nodes V are abstracted into edges to obtain the edge set E, and the resulting network model Net = {N, E};

[0030] Step 1.2: Construct the objective functions in the key node strike ranking model for the heterogeneous cascading target system, including the objective function of maximizing the reduction of the enemy's strike effectiveness and the objective function of minimizing the strike cost of our side:

[0031] Step 1.2.1: Objective function of maximizing the reduction of the enemy's strike effectiveness

[0032] The calculation formula for strike effectiveness is as follows:

[0033]

[0034] Among them, Eff i = ωF base + F sys , representing the remaining system combat capabilities after hitting the first i targets. It is composed of the basic capabilities F base of the nodes and the system combat capabilities F sys , where the weight ω = 0.05; x ij represents 1 when the i-th target is struck at the j-th time sequence and 0 otherwise; N represents the set of all nodes in the initial combat network;

[0035] The basic capabilities of the nodes are:

[0036]

[0037] Among them, Represents the set of remaining nodes in the combat network, that is, the set of nodes not yet attacked currently, f s Represents the basic ability of the remaining node s;

[0038] The combat system ability is:

[0039]

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

[0041] Among them, Represents the element in the command relationship Z, Represents the element in the intelligence relationship matrix Q, Represents the element in the communication relationship matrix T, Represents the element in the fire protection relationship matrix H, Represents the element in the support relationship matrix B; Represents the updated element in the command relationship Z;

[0042] Step 1.2.2, the objective function of minimizing the cost of our side's strikes

[0043] It is assumed that the target network contains n combat units, including the following specific combat unit types: firepower units, intelligence units, command units, communication units, and support units. All corresponding nodes are denoted as set N, ||N|| = n. Among them, the firepower units are abstracted as firepower nodes F, the intelligence units are abstracted as sensing nodes I, the command units are abstracted as command nodes D, the communication units are abstracted as communication nodes T, and the support units are abstracted as support nodes G. Then the function for minimizing the strike cost of our side is:

[0044]

[0045] Among them, the total strike cost of our side consists of ammunition consumption and loss of military force resources. C 1i Is the ammunition consumption for striking the i-th target node, C 2i Is the loss of military force resources, w c1 Is the weight of ammunition consumption in the strike cost, w c2 Is the weight of the loss of military force resources in the strike cost;

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

[0047]

[0048] Among them, C 0i Is the basic ammunition consumption of the i-th target node, qki It is 0 / 1 value indicating that the k-th target node in the intelligence relationship matrix Q provides intelligence to the i-th target node; h ki It is 0 / 1 value indicating that the k-th target node in the firepower relationship matrix H provides fire protection to the i-th target node; b ki It is 0 / 1 value indicating that the k-th target node in the support relationship matrix G provides support to the i-th target node; The sum of the three represents that the k-th target node provides intelligence or fire protection or support to the i-th target node. When the value is 1, it will increase the ammunition consumption of our side to strike the i-th target node; At this time, the added term is multiplied by the basic ability f k of the k-th target node and then add 1 for processing, indicating the multiple of the increase in the ammunition consumption for striking the i-th target node on the basis of 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 is the hit rate for striking the i-th target node;

[0049] The loss of force resources C for striking the i-th target node 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 is the weight of aircraft consumption in the loss of force resources, W c4 is the weight of fuel consumption in the loss of force resources; P 2i is the probability of aircraft damage when striking the i-th target node, multiplied by the number of aircraft sorties NF i for striking the i-th target node, indicating aircraft consumption; D i is the required aircraft range for striking the i-th target node;

[0053] Step 1.3. Construct the constraint conditions in the key node strike sorting model of the heterogeneous cascade 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 jrepresents the lower limit of damage to the j-th target node, U j represents the upper limit of damage to the j-th target node;

[0057] Step 1.3.2, force constraints: Force constraints include allocating at least one firepower unit to each target, each firepower unit only focuses on one target at a time, and there are upper limits on the ammunition, the number of personnel involved in the combat, and the funds that can be consumed by the combat mission;

[0058] Step 1.3.3, time and space constraints: The duration of different waves of attacks is limited, and the upper limit of the duration of the jth wave of the i-th round is T ijh , the lower limit of time is T ijl , then:

[0059] T ijl ≤T ij ≤T ijh

[0060] Assume that there are M types of weapon platforms facing N types of targets to be attacked, and the single attack of the i-th weapon on the j-th target needs to be completed within the specified time window, then:

[0061] t ijl ≤t ij ≤t ijh

[0062] As a specific example, the key node attack sorting based on fuzzy conditions described in step 2 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 of the framework is as follows:

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

[0065] (2) Node characteristics: Node characteristics include node coordinate information, basic ammunition consumption of node strikes, node search capability, command and control capability, transmission capability, anti-missile capability, support capability, strike risk, counterattack probability, counterattack cost, aircraft sorties, aircraft range, penetration rate, hit rate, damage probability, target intention, combat capability, anti-destruction capability. When training data, these characteristics need to be processed through normalization or embedding mapping technology to ensure the adaptability of the model to heterogeneous data.

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

[0067] The framework structure is divided into 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 follows:

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

[0069]

[0070] where is the neighbor of node v i , A ij is an element of the adjacency matrix, that is, the edge weight; W (l) is the weight matrix of the l-th layer, and σ is the activation function;

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

[0072] (3) Multi-layer information propagation: Through multi-layer graph convolution and graph attention network, the 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 the GCN layer and the GAT layer, so that the representation of the node gradually integrates the information of the neighbors and enhances the expressive ability of the model;

[0073] (4) Classification layer: After multi-layer information propagation, the embedding representation of each node is finally obtained These embedding representations will be input into a fully connected layer or a Softmax layer for predicting the category of the node; Softmax classification is as follows:

[0074]

[0075] where c represents the category, and W c is the weight vector of category c;

[0076] (5) Loss function:

[0077] For the node classification task of a large-scale heterogeneous cascade target system, the cross-entropy loss function is adopted, as shown in the following formula:

[0078]

[0079] where is the prediction of the model for node vi Predicted class probability, y i is the true label of the node;

[0080] (6) Evaluation metrics: The performance of the large-scale cascaded target system node classification model is evaluated using metrics such as Accuracy, F1-score, Precision, and Recall;

[0081] Step 2.2: Based on the graph convolutional network and graph attention network models, construct a GCN-GAT link prediction model for heterogeneous networks. The input data of 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, firepower, support, and communication types;

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

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

[0085] The framework structure is divided into node pair embedding calculation, similarity calculation, link prediction layer, loss function, and evaluation metrics, as follows:

[0086] (1) Node pair embedding calculation: Extract the embedding representation h i 、h j of each node through graph convolution and graph attention, and then use these embedding representations to calculate the similarity between node pairs (v i , v j ). Calculate the embedding of each node through graph convolution and graph attention mechanism, and then perform concatenation or addition operation on the representations of node pairs to obtain the joint representation of node pairs as follows:

[0087]

[0088] Among them, can be concatenation, addition, or other forms of combination. In addition to concatenation or addition, the Hadamard product or element difference of node pairs can also be calculated to more finely characterize the relationship features between nodes and capture complex interaction patterns;

[0089] (2) Similarity calculation: Use the inner product or Euclidean distance method to calculate the similarity of node pairs (v i , v j) The similarity between them is used to predict the existence probability of the edge, and the formula is as follows:

[0090]

[0091] (3) Link prediction layer: For each pair of nodes (v i , v j ) whose connection is unknown, a Sigmoid function is used to output the probability of the existence of an edge between the node pair:

[0092]

[0093] Among them, is the Sigmoid function;

[0094] (4) Loss function: Binary cross-entropy loss is used as the loss function for link prediction in the large-scale heterogeneous cascade target system:

[0095]

[0096] Among them, yij is the flag indicating whether the edge (v i , v j ) exists, is the 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: Combine the graph convolutional network GCN and the graph attention network GAT to construct a node classification and link prediction framework for the heterogeneous cascade target system, and perform node classification and link prediction, specifically as follows:

[0099] (1) Use the input including the graph structure, node features, and edge features, combined with the information of the node or link to be predicted.

[0100] (2) In the graph neural network layer, the graph convolutional network GCN generates initial node embeddings by integrating neighbor node information, thereby capturing the local relationships between nodes; the graph attention network GAT optimizes the information transmission process by dynamically adjusting the weights of neighbor nodes, making the information of important neighbor nodes have a greater impact on the target node.

[0101] (3) In the node classification task, the model uses node embeddings and a 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 existence of the link is calculated through the Sigmoid function.

[0102] As a specific example, the key node strike ranking of the heterogeneous cascade target system based on the optimization algorithm in step 3 is as follows:

[0103] Step 3.1: Construct an improved NSGA-II multi-objective optimization algorithm based on double-strategy hybrid evolution, use tournament selection based on Pareto dominance and crowding degree and double-strategy hybrid crossover, based on the global search operator and the local search operator, introduce a hybrid evolution strategy based on global search and local search, and randomly select a global search operator and a local search operator for each individual to generate the next generation, specifically as follows:

[0104] Step 3.1.1: During the algorithm iteration process, set the Pareto optimal front obtained in each iteration as the elite library, and perform crossover operations between the individuals in the elite library and some individuals in the new population to guide the optimization process of the population. On this basis, design a double-strategy hybrid crossover operation, specifically as follows: Strategy 1, that is, ordinary crossover, is to randomly select 2 individuals in the new population for crossover operation; Strategy 2, that is, elite crossover, is to randomly select 2 individuals in the elite library and the new population respectively for crossover operation;

[0105] The global search operator is used to conduct extensive exploration in the entire decision space, promote the maintenance of population diversity by introducing a large range of random perturbations, enable the algorithm to jump out of the local optimal trap, and discover potential promising regions; in the global search stage, 3 effective crossover operators are used, including the order crossover operator, the multi-point crossover operator, and the partially mapped crossover operator;

[0106] In the crossover operator algorithm, some new individuals are obtained by randomly selecting different crossover methods. The multi-point crossover randomly selects multiple crossover points; the order crossover randomly selects two crossover points, determines the segments to be inherited, directly copies the segments to the same positions of the offspring, and fills the remaining positions according to the relative order of the elements in the other parent from the second crossover point; the partially mapped crossover operator (PMX), PMX obtains a feasible solution through the gene mapping relationship between two parents and is especially suitable for dealing with permutation problems.

[0107] The crossover operator can be generated by multiple parent individuals according to a certain custom algorithm rule. The obtained offspring individuals may have better characteristics because they inherit the excellent genes in the parent individuals. For the individuals x1 and x2 in the weapon equipment allocation population, the offspring individual x3 can be generated through the global search operator;

[0108] Step 3.1.3: The local search operator improves the quality of the solution by making small and targeted adjustments to the existing solution; in the local search stage, the flip operator and the swap operator are implemented on the individuals in the non-dominated solution set. The flip operator randomly selects a sequence of the solution vector for inversion, and the sliding mutation operator randomly selects a gene to generate a sliding value within a small range, adds the sliding value to the gene to complete the mutation, and performs constraint processing on the gene values that exceed the range; the basic principle of the perturbation mutation is to add random perturbations within a certain range to the gene values of the individual;

[0109] For an individual x in the population of weapon equipment allocation plans, the offspring individual x1 can be generated through the local search operator. The new individuals generated by the local search operator are all feasible solutions;

[0110] Step 3.2: Combine the deep Q-network with the improved NSGA-II algorithm, evaluate the quality of the current population using a dual index, and design the action space and reward space of the DQN accordingly. Use the DQN to optimize the hyperparameters of the improved NSGA-II algorithm, and use the experience replay and dual-network training of the DQN to optimize the selection, crossover, and mutation operators of the NSGA-II algorithm. By designing diversity metrics and population uniformity indicators, evaluate the state space under different populations, specifically as follows:

[0111] Step 3.2.1: Design diversity metrics and population uniformity indicators, specifically as follows:

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

[0113] Δ t ={S i , D[v]}

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

[0115]

[0116] where A is the number of individuals in the Pareto front; obj_n is the number of objective functions; d v is the solution spacing value of the v-th individual, that is, calculate the solution spacing value of each individual with other individuals, and select the minimum value from them; f l(x v ) and f l (x u ) are the first objective function values of the v-th individual and the u-th individual, respectively; is the average value of all d v ;

[0117] Diversity index, population diversity measurement: Compare the two objective functions of the individuals in the decoded population to determine whether they correspond to the same point in the feasible scheduling solution space and calculate 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 the global search operator and the local search operator, six different action selection strategies are adopted. The specific actions of the agent at each decision moment are represented in the form of a mathematical formula as:

[0121]

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

[0123] Step 3.2.3, The reward space attention operator of DQN generates the probability distribution of fitness improvement within a specific time window. When the operator can achieve fitness improvement, it is given a unit reward value of 1; otherwise, it is given a reward value of 0. For the minimization optimization problem, the calculation formula for the immediate reward r of the operator is:

[0124]

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

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

[0127]

[0128] In the formula, where |op i | represents the number of op R in the sliding window W i , represents the tuple in the sliding window.

[0129] The following is combined withFigures 1 to 4 and specific embodiments to further elaborate on the present invention.

[0130] Embodiment

[0131] As Figure 1 shown, a method for strike ranking of key nodes in a heterogeneous cascaded target system under fuzzy conditions according to the present invention is characterized by including the following steps:

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

[0133] Constructing a networked target system model can not only reduce the loss of decision-making quality caused by communication delays or even disconnections between decision-making nodes, but also has the ability to integrate combat nodes to form an integrated combat situation. The system network topology based on the network node and edge model can not only display 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 networked analysis of military information systems.

[0134] Step 1.1. The nodes in the strike target network are abstracted from constituent elements such as equipment, personnel, positions, etc. How to accurately abstract the key functions of the strike targets among them is the primary task of establishing the network model. According to the description of network nodes and edges in the heterogeneous cascaded target system, construct a node and edge model for the heterogeneous cascaded target network system, as Figure 2 shown, specifically as follows:

[0135] Suppose the target network contains n combat units. According to different functions, the nodes are divided into five types of nodes: firepower node F, intelligence node I, command node Z, communication node C, and support node G. Multifunctional composite equipment can be abstracted into multiple different types of nodes according to the functions it possesses; the edges in the target network are abstractions of the complex cooperation and information sharing relationships between nodes. Abstract and simplify the various relationships between different nodes into edges between multiple different nodes. The connections between different functional types of nodes represent different meanings, including intelligence relationship q ij , communication relationship t ij , command relationship z ij , firepower protection relationship h ij , support relationship b ij ; Abstract the mutual relationships between nodes V into edges to obtain the edge set E, and the obtained network model Net = {N, E};

[0136] Step 1.2: Set the target network to include n combat units. According to different functions, nodes can be classified into types such as firepower nodes F, intelligence nodes I, command and control nodes Z, communication nodes C, support nodes G, etc. Multifunctional composite equipment can be abstracted into multiple different types of nodes according to the functions it possesses. The edges in the target network are abstractions of the complex coordination and information sharing relationships between nodes. The abstraction of edges is to abstract and simplify the various relationships between different nodes into edges between multiple different types of nodes. The connections between nodes of different functional types represent different meanings, such as intelligence relationship q ij , communication relationship t ij , command and control relationship z ij , firepower protection relationship h ij , support relationship b ij . Abstract the mutual relationships between nodes V into edges to obtain the edge set E, and the resulting network model Net = {N, E};

[0137] Step 1.2.1: Enemy strike benefit reduction maximization objective function

[0138] The calculation formula for the strike benefit is as follows:

[0139]

[0140] Among them, Eff i = ωP base + F sys , representing the remaining system combat capability after knocking out the first i targets. It is composed of the basic capability F base of the node and the system combat capability F sys . Among them, the weight ω = 0.05; x ij represents that its 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;

[0141] The basic capability of the node is:

[0142]

[0143] Among them, represents the set of remaining nodes in the combat network, that is, the set of currently unstruck nodes, and f s represents the basic capability of the remaining node s;

[0144] The system combat capability is:

[0145]

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

[0147] Among them, represents an element in the accusation relationship Z, represents an element in the intelligence relationship matrix Q, represents an element in the communication relationship matrix T, represents an element in the fire protection relationship matrix H, represents an element in the support relationship matrix B; represents the updated element in the accusation relationship Z;

[0148] Step 1.2.2, the objective function of minimizing our side's strike cost

[0149] It is assumed that the target network contains n combat units, including the following specific combat unit types: firepower units, intelligence units, command units, communication units, and support units. All corresponding nodes are denoted as set N, ||N|| = n. Among them, the firepower unit is abstracted as the firepower node F, the intelligence unit is abstracted as the sensing node I, the command unit is abstracted as the command node D, the communication unit is abstracted as the communication node T, and the support unit is abstracted as the support node G. Then the function for minimizing our side's strike cost is:

[0150]

[0151] Among them, our side's total strike cost consists of ammunition consumption and loss of military strength resources. C 1i is the ammunition consumption for striking the i-th target node, C 2i is the loss of military strength resources, w c1 is the weight of ammunition consumption in the strike cost, w c2 is the weight of the loss of military strength resources in the strike cost;

[0152] The ammunition consumption C for striking the i-th target node 1i is calculated by the formula:

[0153]

[0154] Among them, C 0i is the basic ammunition consumption of the i-th target node, q ki is the intelligence provided by the k-th target node to the i-th target node in the intelligence relationship matrix Q, which is a 0 / 1 value; h ki is the fire protection provided by the k-th target node to the i-th target node in the firepower relationship matrix H, which is a 0 / 1 value; b ki is the support provided by the k-th target node to the i-th target node in the support relationship matrix G, which is a 0 / 1 value; The sum of the three represents that the k-th target node provides intelligence or fire protection or support to the i-th target node. When its value is 1, it will increase the ammunition consumption for our side to strike the i-th target node; At this time, the added term and the basic ability f of the k-th target node kMultiplying and adding 1 means that when the kth target node provides a relationship to the ith target node, the ammunition consumption of attacking the ith target node is increased by a multiple based on the basic ammunition consumption of the original ith target node; P 1i is the hit rate of attacking the i-th target node;

[0155] The loss of manpower resources when 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 is the weight of aircraft consumption in the loss of military resources, W c4 is the weight of fuel consumption in the loss of military resources; P 2i is the probability of aircraft damage when attacking the i-th target node, multiplied by the number of aircraft dispatched to attack the i-th target node NF i Indicates aircraft consumption; D i The aircraft range required to strike the i-th target node;

[0159] Step 1.3: Construct constraints in the key node attack ranking model of the heterogeneous cascade 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 represents the lower limit of damage to the j-th target node, U j represents the upper limit of damage to the j-th target node;

[0163] Step 1.3.2, force constraints: Force constraints include allocating at least one firepower unit to each target, each firepower unit only focuses on one target at a time, and there are upper limits on the ammunition, the number of personnel involved in the combat, and the funds that can be consumed by the combat mission;

[0164] Step 1.3.3, Spatiotemporal Constraint: The strike duration for different waves is limited. The upper limit of the strike duration for the j-th wave in the i-th round is T ijh , and the lower limit of the time is T ijl , then we have:

[0165] T ijl ≤ T ij ≤ T ijh

[0166] Suppose there are M types of weapon platforms facing N types of targets to be struck. The single strike of the i-th weapon on the j-th type of target needs to be completed within a specified time window. Then we have:

[0167] t ijl ≤ t ij ≤ t ijh

[0168] Step 2: Conduct the strike ranking of key nodes based on fuzzy conditions, specifically as follows:

[0169] In modern warfare, the combat situation changes rapidly, and the attributes, positions, etc. of key nodes may also change at any time. This dynamic change makes there are many fuzzy factors in the determination of key nodes and the grasp of the strike timing. In the case of inaccurate intelligence, unclear target characteristics, etc., in order to improve combat effectiveness, enhance the stability of the combat system, and improve the scientific nature of decision-making, it is of great significance to rank the strikes on key nodes;

[0170] Step 2.1, Node classification is of great significance in complex network analysis. Especially in a heterogeneous cascading target system, the node classification results can directly affect the formulation of combat plans and resource allocation. According to the graph neural network model, design a heterogeneous network node classification framework that integrates GCN and GAT. The input data of the framework is as follows:

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

[0172] (2) Node features: Node features cover node coordinate information, the basic ammunition consumption for node strikes, the search ability, command ability, transmission ability, anti-missile ability, support ability, strike risk, counterattack probability, counterattack cost, the number of aircraft sorties, aircraft range, penetration rate, hit rate, damage probability, target intention, combat ability, anti-damage ability, combat ability, anti-damage ability. When training data, these features need to be processed through normalization or embedding mapping techniques to ensure the adaptability of the model to heterogeneous data;

[0173] (3) Node labels and edge features: Node labels identify categories, and edge features reflect the relationships between nodes, such as command, communication, support, etc. The input format is unified through standardization or dimensionality reduction processing;

[0174] The framework structure is divided into 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, which are specifically as follows:

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

[0176]

[0177] where, is the neighbor of node v i , A ij is the element of the adjacency matrix, that is, the edge weight; W (l) is the weight matrix of the l-th layer, and σ is the activation function;

[0178] (2) The GAT layer utilizes the self-attention mechanism to calculate the attention weights from the features of neighboring nodes and the target node, dynamically allocate neighbor weights, and learn the characteristics of node relationships from different perspectives through multi-head attention;

[0179] (3) Multi-layer information propagation: Through multi-layer graph convolution and graph attention network, the 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 the GCN layer and the GAT layer, so that the representation of the node gradually integrates the information of the neighbors and enhances the expressive ability of the model;

[0180] (4) Classification layer: After multi-layer information propagation, the embedding representation of each node is finally obtained These embedding representations will be input into a fully connected layer or a Softmax layer for predicting the category of the node; Softmax classification is as follows:

[0181]

[0182] where, c represents the category, and W c is the weight vector of category c;

[0183] (5) Loss function:

[0184] For the node classification task of large-scale heterogeneous cascade target systems, the cross-entropy loss function is adopted, as shown in the following formula:

[0185]

[0186] where, is the class probability predicted by the model for node v i and y i is the true label of the node;

[0187] (6) Evaluation metrics: The accuracy, F1-score, precision, and recall metrics are used to evaluate the performance of the large-scale cascaded target system node classification model;

[0188] Step 2.2: Based on the graph convolutional network and graph attention network models, construct a GCN-GAT link prediction model for heterogeneous networks. Link prediction is an important task in complex network analysis, aiming to infer potential connection relationships in the 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 input data of the model is as follows:

[0190] (1) Graph structure: It consists of a node set and an edge set. Nodes include intelligence, accusation, firepower, support, and communication types;

[0191] (2) Node features: Node features cover node coordinate information, basic ammunition consumption for node strikes, node search capabilities, accusation capabilities, transmission capabilities, anti-missile capabilities, support capabilities, strike risks, counterattack probabilities, counterattack costs, number of aircraft sorties, aircraft ranges, penetration rates, hit rates, damage probabilities, target intentions, combat capabilities, and anti-damage capabilities;

[0192] (3) Edge features: Edge features reflect the relationships between nodes, such as accusation, communication, support, etc.;

[0193] The framework structure is divided into node pair embedding calculation, similarity calculation, link prediction layer, loss function, and evaluation metrics, as follows:

[0194] (1) Node pair embedding calculation: Extract the embedding representation h i 、h j of each node through graph convolution and graph attention, and then use these embedding representations to calculate the similarity between node pairs (v i , v j ). Calculate the embedding of each node through graph convolution and graph attention mechanisms, and then perform concatenation or addition operations on the representations of node pairs to obtain the joint representation of node pairs as follows:

[0195]

[0196] where It can be a combination in the form of splicing, addition, or other forms. In addition to splicing or addition, the Hadamard product or element difference of node pairs can also be calculated to more finely characterize the relationship features between nodes and capture complex interaction patterns;

[0197] (2) Similarity calculation: The cosine similarity or Euclidean distance method is used to calculate the similarity between node pairs (v i , v j ) to predict the existence probability of edges. The formula is as follows:

[0198]

[0199] (3) Link prediction layer: For each pair of nodes (v i , v j ) whose connection is unknown, a Sigmoid function is used to output the probability of the existence of an edge between the node pairs:

[0200]

[0201] where, is the Sigmoid function;

[0202] (4) Loss function: Binary cross-entropy loss is used as the loss function for link prediction in the large-scale heterogeneous cascade target system:

[0203]

[0204] where, y ij is the flag indicating whether the edge (v i , v j ) exists, is the 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. Combine the graph convolutional network GCN and the graph attention network GAT to construct a node classification and link prediction framework for the heterogeneous cascade target system, as shown in Figure 3 for node classification and link prediction, specifically as follows:

[0207] (1) Take as input the graph structure, node features, and edge features, combined with the information of the nodes or links to be predicted;

[0208] (2) In the graph neural network layer, the graph convolutional network (GCN) generates initial node embeddings by integrating neighbor node information, thereby capturing the local relationships between nodes; the graph attention network (GAT) optimizes the information transmission process by dynamically adjusting the weights of neighbor nodes, making the information of important neighbor nodes have a greater impact on the target node;

[0209] (3) In the node classification task, the model uses node embeddings and a Softmax classifier to predict the class 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 existence of the link is calculated through a Sigmoid function;

[0210] In terms of node classification, the framework takes into account both local feature integration and global relationship modeling, and can accurately distinguish nodes of different categories. In link prediction, the mechanism combining graph convolution and graph attention assigns different weights to edges with different relationships, effectively filling the structural gaps in the target network. These technologies not only enhance the information processing ability under fuzzy conditions, but also provide important decision-making support for combat planning and resource allocation.

[0211] Step 3: Perform the key node strike ranking of the heterogeneous cascading target system based on the optimization algorithm, specifically as follows:

[0212] Step 3.1: Construct an improved NSGA-II multi-objective optimization algorithm based on dual-strategy hybrid evolution, use tournament selection based on Pareto domination and crowding degree and dual-strategy hybrid crossover, based on the global search operator and local search operator, introduce a hybrid evolution strategy based on global search and local search, and randomly select a global search operator and a local search operator for each individual to generate the next generation, specifically as follows:

[0213] Step 3.1.1: During the algorithm iteration process, set the Pareto optimal front obtained in each iteration as the elite library, and perform crossover operations between the individuals in the elite library and individual individuals in the new population to guide the optimization process of the population. On this basis, design a dual-strategy hybrid crossover operation, as Figure 4 shown below. Specifically: Strategy 1, that is, ordinary crossover, is to randomly select 2 individuals in the new population for crossover operation; Strategy 2, that is, elite crossover, is to randomly select 2 individuals in the elite library and the new population respectively for crossover operation. The pseudocode is as follows:

[0214]

[0215] Step 3.1.2: The global search operator is used to conduct extensive exploration in the entire decision space. By introducing a relatively large random perturbation, it promotes the maintenance of population diversity, enabling the algorithm to jump out of the local optimal trap and discover potential promising regions. In the global search phase, 3 effective crossover operators are used, including the order crossover operator, the multi-point crossover operator, and the partially mapped crossover operator.

[0216] In the crossover operator algorithm, different crossover methods are randomly selected to obtain some new individuals. For multi-point crossover, multiple crossover points are randomly selected; for order crossover, two crossover points are randomly selected to determine the segments to be inherited, and these segments are directly copied to the same positions in the offspring. Starting from the second crossover point, the remaining positions are filled according to the relative order of the elements in the other parent. The partially mapped crossover operator (PMX) obtains a feasible solution through the gene mapping relationship between two parents and is particularly suitable for dealing with permutation problems.

[0217] The crossover operator can generate offspring individuals from multiple parent individuals according to a certain custom algorithm rule. The obtained offspring individuals may have better characteristics due to inheriting excellent genes from the parent individuals. For individuals x1 and x2 in the weapon equipment allocation population, the offspring individual x3 can be generated through the global search operator. The pseudocode is as follows:

[0218]

[0219]

[0220] Step 3.1.3: The local search operator focuses on fine-grained exploitation in the neighborhood of the known solutions. By making small-scale and targeted adjustments to the existing solutions, it improves the quality of the solutions. In the local search phase, the flip operator and the swap operator are implemented on the individuals in the non-dominated solution set. The flip operator randomly selects a sequence of the solution vector for inversion, and the sliding mutation operator randomly selects a gene to generate a sliding value within a small range. The sliding value is added to the gene to complete the mutation, and the gene values outside the range are constrained. The basic principle of perturbation mutation is to add a random perturbation within a certain range to the gene values of the individuals. This multi-level hybrid search strategy not only ensures the wide-area exploration ability of the algorithm in the solution space but also effectively balances the exploration and exploitation of the algorithm, improving the solution performance of NSGA-II in complex multi-objective optimization problems.

[0221] For an individual x in the weapon equipment allocation plan population, the offspring individual x1 can be generated through the 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, evaluate the quality of the current population using dual metrics, and accordingly design the action space and reward space of the DQN. Optimize the hyperparameters of the improved NSGA-II algorithm using the DQN, and use the experience replay and dual-network training of the DQN to optimize the selection, crossover, and mutation operators of the NSGA-II algorithm. Evaluate the state space under different populations by designing diversity metrics and population uniformity metrics, as follows:

[0224] Step 3.2.1: Design diversity metrics and population uniformity metrics, as follows:

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

[0226] Δ t ={S i , D[v]}

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

[0228]

[0229] where A is the number of individuals in the Pareto front; obj_n is the number of objective functions; d v is the solution spacing value of the v-th individual, that is, calculate the solution spacing value of each individual from other individuals and select the minimum value; f l (x v ) and f l (x u ) are the first objective function values of the v-th individual and the u-th individual, respectively; is the average value of all d v ; The pseudocode is as follows:

[0230]

[0231]

[0232] Diversity index, population diversity measurement: Compare the two objective functions of the individuals in the decoded population, determine whether they correspond to the same point in the feasible scheduling solution space, and calculate 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 the global search operator and the local search operator, six different action selection strategies are adopted. The specific action of the agent at each decision moment is represented in the form of a mathematical formula as follows:

[0236]

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

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

[0239]

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

[0241]

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

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

[0244]

[0245] In the formula, where |op i | represents the number of op R in the sliding window W i ; represents the tuple in the sliding window;

[0246] The pseudo-code for the reward window is as follows:

[0247]

[0248] The pseudo-code of the overall RL-INSGA-II algorithm process is as follows:

[0249]

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

[0251] The above is only the preferred embodiment of the present invention. It should be noted that for those of ordinary skill in the art, without departing from the principle of the present invention, several improvements and refinements can be made, and these improvements and refinements should also be regarded as the protection scope of the present invention.

Claims

1. A method for striking and ranking key nodes of a heterogeneous cascaded target system under fuzzy conditions, characterized in that The following steps are involved: Step 1: Construct a key node strike ranking model for the heterogeneous cascade target system; Step 2: sort the key nodes based on fuzzy conditions; Step 3: sorting the key nodes of the heterogeneous cascade target system based on the optimization algorithm; Step 4: Strike the key nodes in the heterogeneous cascade target system based on the network determined above.

2. The key node strike ranking method for heterogeneous cascaded target systems under fuzzy conditions according to claim 1, characterized in that The construction of the key node attack ranking model of the heterogeneous cascade target system described in step 1 is as follows: Step 1.1: Based on the description of network nodes and edges in the heterogeneous cascade target system, construct a node and edge model of the heterogeneous cascade target network system: It is assumed that the target network includes n combat units. According to different functions, the nodes are divided into five types: firepower nodes F, intelligence nodes I, command nodes Z, communication nodes C, and support nodes G. Multifunctional composite equipment is abstracted into multiple different types of nodes according to the functions it possesses; the edges in the target network are abstractions of the complex cooperation and information sharing relationships between nodes. The various relationships between different nodes are abstracted and simplified into edges between multiple different nodes. The connections between nodes of different functional types represent different meanings, including intelligence relationship q ij , communication relationship t ij , command relationship z ij , firepower protection relationship h ij , support relationship b ij ; The mutual relationships between nodes V are abstracted into edges to obtain the edge set E, and the resulting network model Net = {N, E}; Step 1.2, construct the objective function in the attack sorting model of the key nodes of the heterogeneous cascade target system, including the objective function of maximizing the enemy's attack benefit reduction and the objective function of minimizing our attack cost; Step 1.3: Construct the constraints in the key node strike ranking model of the heterogeneous cascade target system.

3. The method for ranking key node strikes in a heterogeneous cascading target system under fuzzy conditions according to claim 2, wherein The objective functions in the key node strike ranking model of the heterogeneous cascade target system constructed in step 1.2 include the objective function of maximizing the enemy's strike benefit reduction and the objective function of minimizing our strike cost, as follows: Step 1.2.1, the enemy's attack effectiveness reduction maximization objective function; The calculation formula of strike benefit is as follows: Among them, Eff i = ωF base + F sys , representing the remaining system combat capabilities after the first i targets are eliminated, is composed of the basic capabilities F base of the nodes and the system combat capabilities F sys , where the weight ω = 0.05; x ij represents 1 when the i-th target is struck at the j-th time sequence and 0 otherwise; N represents the set of all nodes in the initial combat network; The basic capabilities of the node are: Among them, represents the remaining node set of the combat network, that is, the set of nodes not yet attacked currently, and f s represents the basic capabilities of the remaining node s; The system's combat capabilities are: w z +w q +w b +w h = 1 Among them, represents an element in the accusation relationship Z, represents an element in the intelligence relationship matrix Q, represents an element in the communication relationship matrix T, represents an element in the fire protection relationship matrix H, represents an element in the support relationship matrix B; represents an element after update in the accusation relationship Z; Step 1.2.2, our attack cost minimizes the objective function; Assume that the target network contains n combat units, including the following specific combat unit types: firepower unit, intelligence unit, command unit, communication unit and support unit. All corresponding nodes are recorded as set N, ‖N‖=n, where the firepower unit is abstracted as firepower node F, the intelligence unit is abstracted as sensor node I, the command unit is abstracted as command node D, the communication unit is abstracted as communication node T, and the support unit is abstracted as support node G. Then our minimized attack cost function is: Among them, our total strike cost consists of ammunition consumption and loss of military force resources, where C 1i is the ammunition consumption for striking the i-th target node, and C 2i is the loss of military force resources, w c1 is the weight of ammunition consumption in the strike cost, and w c2 is the weight of the loss of military force resources in the strike cost; The ammunition consumption C for striking the i-th target node 1i The calculation formula is as follows: Among them, C 0i is the basic ammunition consumption of the i-th target node, q ki is the intelligence provided by the k-th target node to the i-th target node in the intelligence relationship matrix Q, which is a 0 / 1 value; h ki is the fire protection provided by the k-th target node to the i-th target node in the firepower relationship matrix H, which is a 0 / 1 value; b ki is the support provided by the k-th target node to the i-th target node in the support relationship matrix G, which is a 0 / 1 value; the sum of the three represents the intelligence or fire protection or support provided by the k-th target node to the i-th target node. When its value is 1, it will increase the ammunition consumption of our side to strike the i-th target node; at this time, the added term is multiplied by the basic ability f k of the k-th target node and then added with 1, which means the multiple of the increase in the ammunition consumption for striking the i-th target node on the basis of 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 is the hit rate for striking the i-th target node. The combat power resource loss C for attacking the i-th target node 2i is calculated by the following formula: C 2i = w c3 * P 2i * NF i + w c4 * w r3 * D i s.tw c3 +w c4 = 1 where, w c3 is the weight of the aircraft consumption in the loss of combat power resources, and w c4 is the weight of the fuel consumption in the loss of combat power resources; P 2i is the aircraft damage probability when hitting the i-th target node, multiplied by the number of aircraft missions NF i representing the aircraft consumption; D i is the aircraft range required when hitting the i-th target node.

4. The method for striking and ranking key nodes of a heterogeneous cascade target system under fuzzy conditions according to claim 3, characterized in that The constraints in the key node attack ranking model of the heterogeneous cascade target system described in step 1.3 are as follows: Step 1.3.1, Damage degree constraint: The damage degree constraint is expressed as: L j ≤F0 - F j ≤U j where L j represents the lower limit of damage to the j-th target node, and U j represents the upper limit of damage to the j-th target node; Step 1.3.2, force constraints: Force constraints include allocating at least one firepower unit to each target, each firepower unit only focuses on one target at a time, and there are upper limits on the ammunition, the number of personnel involved in the combat, and the funds that can be consumed by the combat mission; Step 1.3.3, Spatiotemporal Constraint: The strike duration of different waves is limited. The upper limit of the strike duration of the j-th wave in the i-th round is T ijh , and the lower limit of the time is T ijl , then we have: T ijl ≤T ij ≤T ijh Assume that there are M types of weapon platforms facing N types of targets to be attacked, and the single attack of the i-th weapon on the j-th target needs to be completed within the specified time window, then: t ijl ≤t ij ≤t ijh 。 5. The key node strike ranking method for heterogeneous cascaded target systems under fuzzy conditions according to claim 4, characterized in that, The key node attack sorting based on fuzzy conditions described in step 2 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 the graph convolutional network and graph attention network model, a GCN-GAT link prediction model for heterogeneous networks is constructed; Step 2.3: Combine the graph convolutional network GCN and the graph attention network GAT to build a node classification and link prediction framework for heterogeneous cascade target systems to perform node classification and link prediction.

6. The method for striking and ranking key nodes of a heterogeneous cascade target system under fuzzy conditions according to claim 5, characterized in that Step 2.1 Design a heterogeneous network node classification framework that combines GCN and GAT based on the graph neural network model. The input data of the framework is as follows: (1) Graph structure: It consists of a node set and an edge set. The nodes include intelligence, command, firepower, support, and communication types; (2) Node features: Node features cover node coordinate information, basic ammunition consumption for node strikes, node search capabilities, command capabilities, transmission capabilities, anti-missile capabilities, support capabilities, strike risks, counterattack probabilities, counterattack costs, number of aircraft sorties, aircraft range, penetration rate, hit rate, damage probability, target intent, combat capabilities, and anti-destruction capabilities. When training the data, these features need to be processed through normalization or embedding mapping techniques to ensure the adaptability of the model to heterogeneous data; (3) Node labels and edge features: Node labels identify categories, and edge features reflect the relationships between nodes. The input format is unified through standardization or dimensionality reduction processing; The framework structure is divided into 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, which are specifically as follows: (1) The GCN layer performs convolution operations through the adjacency matrix and node features, and can capture the information of neighbor nodes in the graph; in a heterogeneous graph, different types of convolution operations are used to process different types of nodes and edges; in each layer of GCN, for each node v i , weighted aggregation is performed through the information of neighbor nodes, as shown in the following formula: Among them, is the neighbor of node v i , A ij is an element of the adjacency matrix, that is, the edge weight; W (l) is the weight matrix of the l-th layer, and σ is the activation function; (2) The GAT layer uses the self-attention mechanism to calculate the attention weights from the features of neighbor nodes and the features of the target node, dynamically allocate neighbor weights, and learn the node relationship characteristics from different perspectives through multi-head attention; (3) Multi-layer information propagation: Through multi-layer graph convolution and graph attention networks, the 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 the GCN layer and the GAT layer, so that the representation of the node gradually integrates the information of the neighbors and enhances the expressive ability of the model; (4) Classification layer: After multiple layers of information propagation, the embedding representation of each node is finally obtained. These embedding representations will be input into a fully connected layer or a Softmax layer for predicting the category of the node; the Softmax classification is as follows: where c represents the category, and W c is the weight vector of category c; (5) Loss function: For the node classification task of a large-scale heterogeneous cascading target system, the cross-entropy loss function is adopted, as shown in the following formula: Among them, is the class probability predicted by the model for node v i , and y i is the true label of the node; (6) Evaluation metrics: The accuracy, F1-score, precision, and recall metrics are used to evaluate the performance of the node classification model for the large-scale cascading target system.

7. The key node strike ranking method for heterogeneous cascaded target systems under fuzzy conditions according to claim 6, characterized in that Step 2.2 Build a GCN-GAT link prediction model for heterogeneous networks based on the graph convolutional network and graph attention network models. The input data of the model is as follows: (1) Graph structure: It consists of a node set and an edge set. The nodes include intelligence, command, firepower, support, and communication types; (2) Node features: Node features cover node coordinate information, basic ammunition consumption for node strikes, node search capabilities, command capabilities, transmission capabilities, anti-missile capabilities, support capabilities, strike risks, counterattack probabilities, counterattack costs, number of aircraft sorties, aircraft range, penetration rate, hit rate, damage probability, target intent, combat capabilities, and anti-destruction capabilities; (3) Edge features: Edge features reflect the relationships between nodes; The framework structure is divided into node pair embedding calculation, similarity calculation, link prediction layer, loss function, and evaluation metrics, which are specifically as follows: (1) Node pair embedding calculation: Extract the embedding representation h of each node through graph convolution and graph attention i , h j . Then use these embedding representations to calculate the similarity between node pairs (v i , v j ). Calculate the embedding of each node through graph convolution and graph attention mechanisms. Then, splice or add the representations of node pairs to obtain the joint representation of node pairs as follows: h ij = h i ⊕ h j Among them, ⊕ is concatenation or addition; (2) Similarity calculation: The inner product or Euclidean distance method is used to calculate the similarity between node pairs (v i , v j ), and the existence probability of edges is predicted based on this. The formula is as follows: (3) Link prediction layer: For each pair of nodes (v i , v j ) for which it is unknown whether there is an edge, the probability of an edge existing between the node pairs is output through a Sigmoid function: Among them, is the Sigmoid function; (4) Loss function: The binary cross-entropy loss is used as the loss function for link prediction of the large-scale heterogeneous cascading target system: Among them, y ij is the flag indicating whether the edge (v i , v j ) exists, and it is the prediction 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.

8. The method for striking and ranking key nodes of a heterogeneous cascade target system under fuzzy conditions according to claim 7, characterized in that, As described in Step 2.3, combine the graph convolutional network GCN and the graph attention network GAT to construct a node classification and link prediction framework for the heterogeneous cascade target system, and perform node classification and link prediction as follows: (1) Use the input including the graph structure, node features, and edge features, combined with the information of the node or link to be predicted. (2) In the graph neural network layer, the graph convolutional network GCN generates initial node embeddings by integrating neighbor node information, thereby capturing the local relationships between nodes; the graph attention network GAT optimizes the information transmission process by dynamically adjusting the weights of neighbor nodes, making the information of important neighbor nodes have a greater impact on the target node. (3) In the node classification task, the model uses node embeddings and the 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 existence of the link is calculated through the Sigmoid function.

9. The method for striking and sorting key nodes of a heterogeneous cascade target system under fuzzy conditions according to claim 8, characterized in that Perform the key node strike ranking of the heterogeneous cascade target system based on the optimization algorithm as described in Step 3, as follows: Step 3.1: Construct an improved NSGA-II multi-objective optimization algorithm based on dual-strategy hybrid evolution, use tournament selection based on Pareto dominance and crowding degree and dual-strategy hybrid crossover, based on the global search operator and the local search operator, introduce a hybrid evolution strategy based on global search and local search, and randomly select a global search operator and a local search operator for each individual to generate the next generation, as follows: Step 3.1.1: During the algorithm iteration process, set the Pareto optimal front obtained in each iteration as the elite library, and perform crossover operations between the individuals in the elite library and some individuals in the new population to guide the optimization process of the population. On this basis, design a dual-strategy hybrid crossover operation, as follows: Strategy 1, that is, ordinary crossover, randomly selects 2 individuals in the new population for crossover operation; Strategy 2, that is, elite crossover, randomly selects 2 individuals in the elite library and the new population respectively for crossover operation. Step 3.1.2: The global search operator is used to conduct extensive exploration in the entire decision space, and promotes the maintenance of population diversity by introducing a large-scale random perturbation, enabling the algorithm to jump out of the local optimal trap and discover potential promising regions. In the global search stage, use 3 effective crossover operators, including the order crossover operator, the multi-point crossover operator, and the partially mapped crossover operator. In the crossover operator algorithm, new individuals are obtained by randomly selecting different crossover methods respectively; multi-point crossover randomly selects multiple crossover points; order crossover randomly selects two crossover points, determines the segments to be inherited, directly copies the segments to the same positions in the offspring, and fills the remaining positions in the relative order of the elements in the other parent from the second crossover point; the partially mapped crossover operator obtains a feasible solution through the gene mapping relationship between two parents. The crossover operator is generated by using multiple parent individuals according to a custom algorithm rule. The resulting offspring individuals may have better characteristics because they inherit the excellent genes in the parent individuals. For individuals x1 and x2 in the weapon equipment allocation population, an offspring individual x3 is generated through the global search operator; Step 3.1.3: The local search operator improves the quality of the solution by making small and targeted adjustments to the existing solution. In the local search stage, the flip operator and the swap operator are implemented on the individuals in the non-dominated solution set. The flip operator randomly selects a sequence of the solution vector and reverses it. The sliding mutation operator randomly selects a gene and generates a sliding value within a small range, adds the sliding value to the gene to complete the mutation, and performs constraint processing on the gene values that exceed the range. The basic principle of the perturbation mutation is to add a random perturbation within a certain range to the gene values of the individual; For an individual x in the weapon equipment allocation plan population, an offspring individual x1 is generated through the 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, evaluate the quality of the current population using dual indicators, and design the action space and reward space of the DQN accordingly. Use the DQN to optimize the hyperparameters of the improved NSGA-II algorithm, and use the experience replay and dual network training of the DQN to optimize the selection, crossover, and mutation operators of the NSGA-II algorithm. By designing diversity metrics and population uniformity indicators, evaluate the state space under different populations, as follows: Step 3.2.1: Design diversity metrics and population uniformity indicators, as follows: Diversity metric: This metric is used to compare the three optimization metrics of individuals in the decoded population, determine whether they correspond to the same point in the feasible scheduling solution space, and calculate the individual difference value. The larger this metric is, the better the population diversity; the diversity metric Δ of the population in the t-th iteration t is defined as follows: Δ t ={S i , D[v]} Population uniformity index: This index is used to evaluate the uniformity of the distribution of the current Pareto front solutions. 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 equidistantly distributed in the objective space; the uniformity index \(S\) of the population in the \(t\)th iteration i is defined as follows: Where A is the number of individuals in the Pareto front; obj_n is the number of objective functions; d v is the solution distance value of the v-th individual, that is, calculate the solution distance values of each individual to other individuals and select the minimum value from them; f l (x v ) and f l (x u ) are the l-th objective function values of the v-th individual and the u-th individual respectively; is the average value of all d v ; Diversity index, population diversity metric: Compare the two objective functions of the individuals in the decoded population, determine whether they correspond to the same point in the feasible scheduling solution space, and calculate the individual difference value. The mathematical expression is as follows D[v](v = 1, 2, … popsize) where popsize is the population size; Step 3.2.2: Based on any combination of the global search operator and the local search operator, adopt 6 different action selection strategies. The specific actions of the agent at each decision moment are represented in the form of mathematical formulas: where n G represents the number of global search operators, and n L represents the number of local search operators; Step 3.2.3: The reward space of the DQN focuses on the probability distribution of the fitness improvement generated by the operator within a characteristic time window. When the operator can achieve fitness improvement, a unit reward value of 1 is given; otherwise, a reward value of 0 is given. For the minimization optimization problem, the calculation formula for the immediate reward r of the operator is: where f 0 and f p represent the fitness values of the offspring and the parent, respectively; After adding the reward window, the actual reward value is calculated based on the currently received immediate reward and the historical rewards of the operator in the sliding window. The calculation formula is: where |op i | represents the number of op R in the sliding window W i , and represents the tuple in the sliding window.

10. A key node strike ranking system for heterogeneous cascaded target systems under fuzzy conditions, characterized in that, This system is used to implement the key node strike method for heterogeneous cascaded target systems under fuzzy conditions described in any one of claims 1 to 9. The system includes the first to fourth units, and the functions of each unit are as follows: The single unit constructs a key node strike ranking model for heterogeneous cascaded target systems; The second unit performs key node strike ranking based on fuzzy conditions; The third unit performs key node strike ranking for heterogeneous cascaded target systems based on optimization algorithms; Unit 4, based on the network determined above, strikes the key nodes in the heterogeneous cascading target system.

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