A Rapid Target Assignment Method for UAV Cooperative Attack Based on Case-Based Reasoning

Abstract

The present invention provides a rapid target allocation method for UAV cooperative attacks based on case-based reasoning, which relates to the technical field of cooperative combat decision-making for self-destructing UAV clusters. This method designs a rapid target allocation algorithm model with a switchable mechanism. The algorithm can implement the solution of the optimization algorithm model for cooperative combat tasks, switch the algorithm mechanism under different combat task requirements, improve the solving efficiency of the algorithm, ensure the optimality of the solution, and has excellent adaptability to the target allocation tasks of large-scale high-intensity strikes. To a certain extent, it can overcome the problems of long solution time of traditional allocation algorithms and the continuous decline of the solution quality with the increase in the number of weapons on both sides of the combat.

Description

Technical Field

[0001] The present invention relates to the technical field of self - detonating UAV swarm collaborative combat decision - making, and in particular to a method for rapid target allocation of UAV collaboration attacks based on case - based reasoning. Background Art

[0002] The collaborative attack strategy of multiple self - detonating UAVs is a new type of weapon combat style that has gradually developed under the complex and changeable military combat requirements. Essentially, it is a multi - dimensional variable non - linear combinatorial optimization problem with multiple complexities and time sensitivities. The combat of self - detonating UAV swarms can meet the requirements of future information - based combat due to its unique advantage of integrating reconnaissance and strike, and is a commonly used combat means at present. As a new type of intelligent weapon ammunition equipment, self - detonating UAVs combine advanced artificial intelligence control technology and UAV technology, and are mostly used in large - scale swarm combat. At the same time, the collaborative combat mode also makes up for the deficiency of the damage ability of a single self - detonating UAV, and can cause more powerful attacks on enemy targets. In the context of highly information - based military wars, the multi - missile collaborative strike strategy plays a key role in military combat tasks.

[0003] Swarm combat can perform more complex combat tasks compared to single - unit combat, such as single - target convergence attack, single - target sequential attack, and multi - target collaborative attack. It can improve the success rate of task completion, has stronger fault tolerance and robustness, and can still complete tasks in the case of single - unit damage or failure. At present, the combat of self - detonating UAV swarms also faces many challenges. In addition to the constraints of single - unit performance, it is also necessary to consider the collaborative constraints among self - detonating UAVs, such as spatial collaborative constraints and time collaborative constraints. At the same time, it also increases the difficulty of planning problems, greatly improving the algorithm complexity and computational time cost. Summary of the Invention

[0004] Aiming at the deficiencies of the prior art, the present invention provides a method for rapid target allocation of UAV collaboration attacks based on case - based reasoning. The present invention optimizes and improves the target allocation algorithm for self - detonating UAV collaborative combat, and designs a fast target allocation algorithm model with a switchable mechanism. This algorithm can realize the solution of the optimization algorithm model for collaborative combat tasks, switch the algorithm mechanism under different combat task requirements, improve the solution efficiency of the algorithm, ensure the optimality of the solution, and has excellent adaptability to the target allocation tasks of large - scale high - intensity strikes. To a certain extent, it can overcome the problems of long solution time of traditional allocation algorithms and the continuous decline of the solution quality with the increase in the number of weapons on both sides of the combat.

[0005] A method for rapid target allocation of UAV collaboration attacks based on case - based reasoning includes the following steps:

[0006] Step 1: Uniformly model the battlefield space environment according to the requirements of swarm combat strike tasks and the battlefield environment;

[0007] Suppose that m self - detonating drones form a drone cluster to jointly execute a strike mission, striking n targets scattered at different positions on the battlefield, and there are t threat sources with threat radius sets of R = {R1, R 2, R3...R t}, and the coordinates are {(x t1 , y t1 ), (x t2 , y t2 )...(x tt , y tt )}, and ensure that each self - detonating drone can execute the mission at most once and strike one target; among them, initially define the self - detonating drone cluster M = {M1, M2,..., M m}, the ground target set N = {N1, N2,..., N n}, set the initial position of the target as (x i , y j ), the value of target N j is Q j ; to successfully implement the strike mission, during the process of executing the collaborative strike mission, the self - detonating drones need to avoid the threat sources that appear in the battlefield and finally reach the target mission point to implement the strike. And according to the target type, the upper limit of the number of times each target can be struck is D jmax pieces, that is, the number of drones assigned to each target should be less than or equal to D jmax pieces;

[0008] Step 2: Use the grid method to design a two - dimensional battlefield simulation model to describe the battlefield space in detail;

[0009] In the two - dimensional battlefield simulation model, each grid represents a coordinate point, used to represent the positions of drones, targets, and obstacles; the planning space is represented as a set Ω, (x, y) represents the horizontal and vertical coordinates of a certain position point in the space Ω, x max and y max respectively represent the maximum distance positions specified by the horizontal and vertical coordinates, as shown in the following formula:

[0010] Ω = {(x, y)|0 ≤ x ≤ x max , 0 ≤ y ≤ y max}

[0011] Step 3: Model the battlefield threat sources, select radar threat, anti - aircraft gun threat, and terrain threat as threat source parameters and calculate the threat degree of the threat sources;

[0012] Step 3.1: Calculate the radar threat degree within the battlefield range;

[0013] The radar echo signal power is expressed by the formula:

[0014]

[0015] Wherein, P t is the transmission power, G is the transmission antenna gain, σ is the radar cross section, R is the distance from the target to the radar in meters, and λ is the electromagnetic wave wavelength; for a determined UAV, the radar cross section is constant, and the above formula is simplified to:

[0016]

[0017] Wherein, K is a constant; when the radar is not interfered, the probability of detecting a target is related to the quality of the received signal. Assuming that the radar can detect in all directions and the maximum detection radius of the radar is R max , then the detection probability of the radar for the UAV is expressed as:

[0018]

[0019] Step 3.2, calculate the threat level of the anti-aircraft gun;

[0020] When the enemy radar detects the UAV, the anti-aircraft missile will attack according to the target information. The kill probability of the anti-aircraft missile is:

[0021] P m = T·Y·Z[1-(1 - A·E·W) Q

[0022] Wherein, T is the radar detection probability of the surface-to-air missile, Y is the radar interception guidance probability, Z is the information transmission conversion probability, A is the missile successful launch probability, E is the missile flight reliability probability, W is the missile kill probability, and Q is the number of missiles launched at one time.

[0023] Step 3.3, calculate the terrain threat level;

[0024] Calculate the height threat and size of the terrain:

[0025]

[0026] Wherein, T h represents the terrain altitude threat size, h m represents the altitude of the current terrain, and h u represents the upper limit altitude of the UAV flight. If the terrain altitude exceeds the low-altitude flight upper limit of the UAV, the UAV terrain threat is set to the maximum value;

[0027] When the real-time flight altitude of the UAV is h real , the threat of different altitude obstacles to the UAV is expressed as:

[0028] ​

[0029] Step 4: Establish a reasonable optimization target allocation model, and define the target optimization function according to the constraint conditions of the optimization model;

[0030] Step 4.1: Calculate the voyage cost;

[0031] Step 4.1.1: Calculate the track distance in each track segment;

[0032] l MS To represent the track length of the Mth UAV in the kth track segment, S is the number of track segments:

[0033]

[0034] In the formula, represents the starting point coordinates of the Mth UAV in the kth track segment.

[0035] Step 4.1.2: Calculate the voyage cost of each strike plan;

[0036] The strike plan is as follows: Suppose the first UAV among m UAVs attacks the first target among n targets, then it is a strike plan. If the first UAV among m UAVs attacks the second target among n targets, then it is another strike plan. If it attacks the nth target among n targets, then it is the nth strike plan; Each UAV has the same number of strike plans. In each strike plan, one UAV only attacks one target.

[0037] During the track planning process, a track is divided into S track segments. The track distance L of the Mth UAV attacking the Nth target MN is expressed by the formula:

[0038]

[0039] Step 4.1.3: Normalize the voyage cost value;

[0040] The voyage cost F after being unified to the same order of magnitude l is expressed by the formula:

[0041]

[0042] In the formula, L MN represents the track distance of the Mth UAV attacking the Nth target, and L Nmax represents the maximum value of the flight distances when all UAVs conduct attacks. The ratio of the two can obtain the voyage cost of each strike plan.

[0043] Step 4.2: Calculate the threat cost within the battlefield;

[0044] The threat cost is inversely proportional to the distance from the threat source to the track. The whole track is divided into S track segments, and the threat cost values of each track segment are calculated. Then the overall threat cost is the sum of the threat costs of the S track segments.

[0045] Step 4.2.1: Calculate the threat cost value generated in each track segment;

[0046] Suppose there is the Mth unmanned aerial vehicle attacking the Nth target in the battlefield. First, each track is divided into S track segments, and two adjacent track points of the unmanned aerial vehicle are denoted as L k and L k+1 , and the threat source coordinates are denoted To obtain the threat cost of each track segment, each track segment is equally divided into C parts, and the threat cost is indirectly calculated by obtaining the distances from the threat source to the C track points, which is specifically expressed as:

[0047]

[0048] In the formula, N Th is the number of threat sources, C is the number of equal parts of each track segment, is the coordinate of each track point, t = 1, 2,..., N Th , c = 1, 2,..., C;

[0049] Step 4.2.2: Calculate the overall threat cost in each track;

[0050] Sum up the threat costs of the S track segments to obtain the total threat cost F of the track t as:

[0051]

[0052] Step 4.2.3: Normalize the threat cost for calculation under a unified scale;

[0053] Normalize the threat cost to a unified scale. The threat cost F t is expressed by the formula as:

[0054]

[0055] In the formula, F t MN represents the threat cost of the track where the Mth unmanned aerial vehicle attacks the Nth target, and F tmax represents the track with the maximum total threat cost among all tracks;

[0056] Step 4.3: Calculate the overall attack benefit;

[0057] Step 4.3.1: Calculate the overall attack benefit in each strike plan;

[0058] Use the target residual value to evaluate the attack benefit cost of the target. The attack benefit generated by the Mth drone attacking the Nth target is expressed as:

[0059] F v =V N ·P MN ·x ij

[0060] In the formula, V N is the target value of the Nth target, P MN is the damage probability of the Mth drone hitting the Nth target, and x ij is a decision variable;

[0061] Step 4.3.2: Normalize the attack benefit;

[0062] Unify the attack benefit F v to the same order of magnitude, which is expressed by the formula:

[0063]

[0064] In the formula, represents the attack benefit of the Mth drone attacking the Nth target, and F vmax represents the maximum attack benefit that can be obtained in all strike plans.

[0065] Step 4.4: Calculate the enemy target value;

[0066] Combined with different types of each weapon device and its attack range, set different threat levels I typ from 0 to 1 for the target to clearly evaluate and distinguish the strike value degree of each target in the battlefield environment.

[0067] Step 4.5: Analyze the constraint conditions generated in the target assignment;

[0068] The constraint conditions are as follows:

[0069] (1) Range constraint

[0070] The distance traveled by each self-destruct drone should be less than its range, which is expressed as:

[0071]

[0072] In the formula, is the maximum range of the self-destruct drone, is the actual distance traveled by the self-destruct drone,

[0073] N v is the maximum flight height constraint.

[0074] (2) Decision variable constraints

[0075]

[0076] In the formula, the decision variable x ij is a 0-1 variable. When the UAV i acts on the target j, x ij = 1 indicates an attack is carried out, and x ij = 0 indicates that no attack is carried out. The decision variable is represented as x ij ∈(0,1), i = 1,..., M, j = 1,..., N, indicating that at least one UAV executes a task once, and at most the number of UAVs assigned does not exceed D jmax aircraft; indicating that one UAV can execute at most one task;

[0077] Step 4.6. According to the target assignment optimization index, construct the objective function and describe each cost function therein;

[0078] The target assignment optimization index requires minimizing the attack cost of the UAV and maximizing the attack benefit.

[0079] The optimization objective function of multi-UAV cooperative target assignment is expressed as:

[0080] F = λ1F l + λ2F t - λ3F v

[0081] In the formula, λ = (λ1, λ2, λ3) is the weight vector of each factor in the optimization objective function, indicating different degrees of influence of each factor on the target assignment result, and at the same time satisfying λ i ∈(0,1); F l is the range cost, F t is the threat cost, F v is the attack benefit. When the range cost and threat cost are minimized and the attack benefit reaches the maximum, the optimal solution of the final target assignment is output.

[0082] Step 5. Use the improved genetic algorithm based on the idea of adaptive penalty function and the greedy algorithm switching mechanism to perform target assignment, perform algorithm switching operations on the two algorithms in different combat environments, and the genetic algorithm based on the penalty function idea is improved on the traditional genetic algorithm to solve the optimization problem of the objective function with multiple sets of constraints;

[0083] Step 5.1. Initialize the battlefield environment, and set the number of suicide UAVs, strike targets, and threat sources;

[0084] Step 5.2: Set the initial population size, the number of iterations, the initial values of the selection rate, the crossover rate, and the mutation rate;

[0085] Step 5.3: Set the encoding operation method for the initial population;

[0086] Step 5.3.1: Perform the encoding operation using the binary encoding method. Take the correspondence between the suicide drones and the targets, that is, each possible allocation plan represents a chromosome, and each gene in the chromosome represents whether a specific drone is assigned to a certain target;

[0087] Step 5.3.2: Perform binary encoding on m suicide drones and n targets in the battlefield environment. Use 1 to represent that the suicide drone strikes the target, and 0 represents no strike. Then each chromosome has m×n numbers, that is, "genes";

[0088] Step 5.3.3: Group every n genes into a group, and arrange each group of genes vertically to obtain the multi-suicide drone target allocation matrix C m×n ;

[0089] Step 5.3.4: It is stipulated that the i-th row of the matrix represents the suicide drone, i = 1, 2, 3......, m, the j-th column of the matrix represents the target, and c ij represents the strike situation of the suicide drone on the target. If c ij = 0, it means that the suicide drone M i does not strike the target N j . If c ij = 1, it means that the suicide drone M i strikes the target N j ;

[0090] Step 5.4: Initialize the population and generate N individuals;

[0091] Step 5.5: Determine the constraint conditions of the suicide drones according to Step 4.5;

[0092] Step 5.6: Construct a penalty function. For individuals that violate the constraint conditions, subtract the penalty function when calculating the fitness value to reduce the fitness value;

[0093] Step 5.6.1: Use the two constraint conditions in Step 4.5 as the penalty terms in the penalty function, and select the penalty factor, that is, the weight coefficient; construct the penalty function p(x) = f(x) + h(x)G(x), where f(x) is the objective function value, h(x) is the penalty factor, and G(x) is the penalty term.

[0094] Step 5.6.2: Substitute the constraint conditions. The penalty function is expressed as p(x) = f(x) + η(n + m). According to the cumulative penalty principle, it is stipulated that the greater the number of violated overall constraint terms of an individual, the greater the penalty intensity; where 0 < η ≤ 1, and it can be adaptively adjusted according to the number of feasible solutions.

[0095] Step 5.7: Construct the fitness function, and the formula is as follows: Fitness(x) = C max -p(x)

[0096]

[0097] where f(x) is the objective function value, and C max is the maximum estimated value of the objective function, which is obtained through estimation.

[0098] Step 5.8: Perform selection, crossover, and mutation operations on the population;

[0099] After constructing the fitness function and the penalty function, perform genetic operations such as selection, crossover, and mutation on the population, and iterate successively.

[0100] Step 5.8.1: According to the principle of survival of the fittest, measure the fitness of an individual to the environment through the individual fitness function value, and sort the individuals in the initial population;

[0101] Step 5.8.2: Use the roulette wheel method to select the chromosomes in the population that meet the fitness standard value, and then use the elite selection and retention strategy to select and retain the excellent individuals in the sorting result;

[0102] Step 5.8.3: Perform crossover and mutation operations on the retained excellent individuals to generate an offspring population, and combine the two populations to form a new offspring population R with a size of 2N t .

[0103] Step 5.9: Generate an adaptive fitness function value;

[0104] Let the number of feasible solutions after each iteration be P1, the total number be N, and the penalty factor That is, the penalty term weight changes proportionally with the increase or decrease of the feasible solutions. When there are too many feasible solutions, the penalty factor also increases accordingly in the next iteration, and vice versa;

[0105] Step 6: When the genetic algorithm with the improved adaptive penalty function idea fails to meet the combat requirements, the distribution algorithm uses the greedy algorithm to continue solving the algorithm.

[0106] Step 6.1. Parameter initialization: Given that there are n objectives as inputs for solving the problem, set the solution set J of the problem to be empty; initialize the parameters of the maximum allowable iteration times, end flag threshold, and the number of objectives for the greedy algorithm.

[0107] Step 6.2. Define the objective function: According to the problem requirements, randomly generate the task pairings of suicide drones and strike targets, and calculate the objective evaluation function. Select a metric standard and sort the n inputs according to this metric standard;

[0108] Step 6.3. Traverse all the strike plans of m suicide drones and n targets, and calculate the corresponding cost values through the cost function formula;

[0109] Step 6.4. Based on the absolute value of the objective function, establish a cost matrix, where A 11 , A 12 , A 13... A 1m is defined as the cost value of the strike plan composed of the target 1 to be struck and M drones, and the remaining row elements A mn all represent the attack cost values of the strike plan where the M-th drone strikes the N-th target. Finally, a cost matrix containing N×M cost value elements is formed.

[0110]

[0111] Step 6.4.1. Use the comparison method to find the maximum element in the cost matrix A and record its position at the same time;

[0112] Step 6.4.2. Assume that the maximum element in the cost matrix A is A 00 , which means that after considering the comprehensive target cost and flight path cost of our drones, the maximum benefit for the enemy target N0 to be struck by M0 is achieved, so implement the strike plan of M0 on N0;

[0113] Step 6.4.3. Since N0 has become the target of M0, set the row and column where A 00 is located to ∞;

[0114] Step 6.4.4. After setting the row and column where A 00 is located to ∞, A 00 will no longer participate in the subsequent task allocation. Then return to Step 6.3 to continue the loop iteration to find the next optimal solution for state update;

[0115] Step 6.4.5. After completing all one-to-one allocations, restore to the original cost matrix composition, set all the already allocated plans to ∞ to avoid searching again. For the other remaining elements in the matrix, re-search for the multi-to-one allocation results;

[0116] Step 6.5. Output the optimal solution: When all n inputs have been searched, if the task conditions are met, the search stops, that is, the current solution set is the global optimal solution, and the search result is output.

[0117] Step 7. Set the main switching mechanism of the target allocation algorithm.

[0118] Step 7.1. Initialize the global battlefield variable information according to the battlefield environment requirements.

[0119] Step 7.2. Define different-scale combat scenarios according to different quantity levels of combat weapons, and clarify the completion time T of each target allocation task. c , where the number of self-destructing drones participating in the battle on our side is m, and the number of enemy combat weapons is n. It is stipulated that m > n under each battlefield scale. The following are the three defined combat scales, and subsequent actual battlefields are also classified according to this definition;

[0120] When the number of our drones' targets m ≤ 20 and the number of enemy targets n ≤ 20, it belongs to a small-scale conflict;

[0121] When 20 < m ≤ 50 of our drones' targets and 20 < m ≤ 50 of the enemy targets, it belongs to a medium-scale combat;

[0122] When 50 < m ≤ 100 of our drones' targets and 50 < m ≤ 100 of the enemy targets, it belongs to a large-scale battle;

[0123] Other situations are not considered.

[0124] Step 7.3. According to the requirements of task nature, planning time, and optimization performance, clarify the goals and conditions of the switching algorithm, and clarify the completion time T of each target allocation task. f .

[0125] Step 7.4. Establish a task planning model database. Conduct comparative experiments on the two algorithms with different combat scales respectively, and continuously increase the experimental scale to obtain the calculation time and the change values of the objective function under multiple different combat postures. Store the experimental results to form a database and establish a historical target allocation model;

[0126] Step 7.5. Input the actual battlefield combat parameters into the system.

[0127] Step 7.6. Identify the characteristic indicators of the actual battlefield situation and make a similarity judgment; including the number of weapons in the battle between both sides, the combat scale, and the completion time T of the order issuance. f as the main characteristic judgment indicators;

[0128] Step 7.7. Develop a switching strategy;

[0129] Step 7.7.1: Compare the case data including the calculation time and the change value of the objective function in the existing historical database with the actual combat conditions, search in the database, and select the target allocation model with the highest similarity as the matching object.

[0130] Step 7.7.2: Using the target allocation time T specified in the combat mission as the benchmark, complete the similarity judgment through Step 7.6, and select the case with the same scale as the actual battlefield and the highest similarity. c

[0131] Step 7.7.3: Extract the comparison of the optimization performance of the genetic algorithm and the greedy algorithm and the algorithm decision results within the benchmark time range of the case with the highest similarity. According to the comparison results, due to the high consistency of similarity, match the battlefield environment in the database with the actual combat scenario, and feedback and output the algorithm decision in this case as the optimal decision result under the current situation.

[0132] Step 7.8: Monitor and evaluate the effect; if there are new changes in the battlefield situation, it is necessary to identify the characteristic indicators under the new situation again, return to Step 7.6, and make a new algorithm planning decision result to ensure the real-time and accuracy of target allocation.

[0133] The beneficial effects of adopting the above technical solutions are as follows:

[0134] The present invention provides a rapid target allocation method for UAV cooperative attack based on case-based reasoning. Compared with other mission planning algorithms, the optimization model algorithm provided by the present invention mainly solves the problems of too long calculation time for target allocation in traditional combat mission scenarios and the increase of result deviation with the increase of battlefield complexity; at the same time, a large-scale combat mission scenario is set, and simulation is carried out in combination with a switchable control target allocation algorithm. The results show that the optimization algorithm model has excellent adaptability to the target allocation task of large-scale strike missions, and at the same time, the optimality of the solution is also guaranteed to a certain extent. Brief Description of the Drawings

[0135] Figure 1 It is the flow chart of the rapid target allocation method for UAV cooperative attack in the embodiment of the present invention;

[0136] Figure 2 It is the schematic diagram of grid method battlefield modeling in the embodiment of the present invention;

[0137] Figure 3 It is the flow chart of the improved genetic algorithm in the embodiment of the present invention;

[0138] Figure 4 It is the flow chart of the greedy algorithm in the embodiment of the present invention;

[0139] Figure 5 ​Flowchart of the algorithm switching mechanism in the embodiments of the present invention;

[0140] Figure 6 Performance comparison chart of algorithm optimization in the embodiments of the present invention. Detailed implementation manners

[0141] The following further describes in detail the specific implementation manners of the present invention in conjunction with the accompanying drawings and embodiments. The following embodiments are used to illustrate the present invention, but not to limit the scope of the present invention.

[0142] A method for rapid target allocation of cooperative attacks of unmanned aerial vehicles based on case-based reasoning, as Figure 1 shown, the present invention mainly uses a cooperative target allocation algorithm based on a switching mechanism to calculate reasonable target allocation results, determines the optimization function through battlefield modeling, constraint condition analysis, cost function calculation, etc., and uses the improved adaptive penalty function genetic algorithm or greedy algorithm to solve the scheme under different combat scenarios. The specific steps are as follows:

[0143] Step 1: Uniformly model the battlefield space environment according to the requirements of the cluster combat strike mission and the battlefield environment;

[0144] Suppose that m self-destruct unmanned aerial vehicles form an unmanned aerial vehicle cluster to jointly execute a strike mission, strike n targets scattered at different positions on the battlefield, and there are t threat sources with threat radius sets R = {R1, R2, R3... R t}, and the coordinates are {(x t1 , y t1 ), (x t2 , y t2 )... (x tt , y tt )}, and ensure that each self-destruct unmanned aerial vehicle executes at most one mission and strikes one target; among them, initially define the self-destruct unmanned aerial vehicle cluster M = {M1, M2,..., M m}, the ground target set N = {N1, N2,..., N n}, set the initial position of the target as (x i , y j ), the value of the target N j is Q j ; to successfully implement the strike mission, during the process of executing the cooperative strike mission, the self-destruct unmanned aerial vehicle needs to avoid the threat sources that appear on the battlefield and finally reach the target mission point to implement the strike. And according to the target type, the upper limit of the number of strikes for each target is specified as D jmax pieces, that is, the number of unmanned aerial vehicles assigned to each target should be less than or equal to D jmax pieces;

[0145] Step 2: Use the grid method to design a two-dimensional battlefield simulation model to describe the battlefield space in detail; for example Figure 2 The following figure shows the schematic diagram of the battlefield modeling by the grid method of the present invention. The two-dimensional simulated battlefield environment mainly includes the position of the unmanned aerial vehicle on the left, the position of the threat sources in the battlefield and their threat ranges, which are all represented by blank circles for simplified illustration, the position of the target on the right, and key information such as the attackable range, etc.

[0146] Taking into account the actual requirements of the cooperative attack mission planning, the grid map method that is suitable for large-scale battlefield modeling and has good visualization performance is adopted to model the battlefield space. In the two-dimensional battlefield simulation model, each grid represents a coordinate point, which is used to represent the positions of unmanned aerial vehicles, targets, and obstacles; the planning space is represented as a set Ω, and (x, y) represents the horizontal and vertical coordinates of a certain position point in the space Ω. x max and y max respectively represent the maximum distance positions specified by the horizontal and vertical coordinates, as shown in the following formula:

[0147] Ω = {(x, y)|0 ≤ x ≤ x max , 0 ≤ y ≤ y max}

[0148] Step 3: Model the battlefield threat sources, select radar threat, anti-aircraft gun threat, and terrain threat as threat source parameters and calculate the threat degree of the threat sources;

[0149] Step 3.1: Calculate the radar threat degree within the battlefield range;

[0150] During the flight, the unmanned aerial vehicle needs to take a series of measures to avoid the detection area of the radar, thereby reducing the risk of being detected by the radar. The radar echo signal power is expressed by the formula:

[0151]

[0152] In the formula, P t is the transmitting power, G is the transmitting antenna gain, σ is the radar cross section, R is the distance from the target to the radar, the unit is m, and λ is the electromagnetic wave wavelength; for a determined unmanned aerial vehicle, the radar cross section is certain, and the above formula is simplified to:

[0153]

[0154] In the formula, K is a constant; when the radar is not interfered, the probability of detecting the target is related to the quality of the received signal. Assuming that the radar can detect omnidirectionally and the maximum detection radius of the radar is R max , then the detection probability of the radar for the unmanned aerial vehicle is expressed as:

[0155]

[0156] Step 3.2. Calculate the threat level of anti-aircraft guns;

[0157] When the enemy radar detects the UAV, the anti-aircraft missile will attack according to the target information. It is an important fire threat to low-altitude UAVs. The kill probability of the anti-aircraft missile is:

[0158] P m = T·Y·Z[1-(1 - A·E·W) Q

[0159] In the formula, T is the radar detection probability of the surface-to-air missile, Y is the radar interception and guidance probability, Z is the information transmission and conversion probability, A is the missile successful launch probability, E is the missile flight reliability probability, W is the missile kill probability, and Q is the number of missiles launched at one time.

[0160] Step 3.3. Calculate the terrain threat level;

[0161] When the UAV is flying at a normal altitude, it will face threats from obstacles such as mountains and slopes. When flying at a low altitude, it will face threats from heights such as high-altitude wires and chimneys. There may be mountains of different heights in the planned area, and the aircraft may collide with the ground due to insufficient flight altitude during flight. The higher the altitude, the greater the threat to the UAV. Calculate the height threat and size of the terrain:

[0162]

[0163] In the formula, T h represents the size of the terrain altitude threat, h m represents the altitude of the current terrain, h u represents the upper limit altitude of the UAV flight. If the terrain altitude exceeds the low-altitude flight upper limit of the UAV, the UAV terrain threat is set to the maximum value;

[0164] When the real-time flight altitude of the UAV is h real , the threat of obstacles at different altitudes to the UAV is expressed as:

[0165]

[0166] Step 4. Combine the specific mission requirements, establish a reasonable optimization target allocation model by detailed analysis of key elements such as cost or benefit indicators and collaborative constraint conditions, and define the target optimization function according to the optimization model constraint conditions;

[0167] Step 4.1. Calculate the range cost;

[0168] Step 4.1.1. Calculate the track distance in each track segment;

[0169] l MS ​To represent the track length of the Mth unmanned aerial vehicle (UAV) on the kth track segment, where S is the number of track segments:

[0170]

[0171] In the formula, represents the starting point coordinates of the Mth UAV on the kth track segment.

[0172] Step 4.1.2: Calculate the range cost of each strike plan;

[0173] The strike plan is as follows: Suppose the first UAV among m UAVs attacks the first target among n targets, then this is a strike plan. If this UAV (the first UAV among m UAVs) attacks the second target among n targets, then this is another strike plan. If it attacks the nth target among n targets, then this is the nth strike plan; each UAV has the same number of strike plans. In each strike plan, one UAV only attacks one target.

[0174] During the track planning process, a track is divided into S track segments. The track distance L of the Mth UAV attacking the Nth target MN is expressed by the formula:

[0175]

[0176] Step 4.1.3: Normalize the range cost value;

[0177] The range cost F after being unified to the same order of magnitude l is expressed by the formula:

[0178]

[0179] In the formula, L MN represents the track distance of the Mth UAV attacking the Nth target, and L Nmax represents the maximum value of the flight distances when all UAVs conduct attacks. The ratio of the two can obtain the range cost of each strike plan.

[0180] Step 4.2: Calculate the threat cost within the battlefield;

[0181] For the convenience of calculation, since it is found during threat modeling that the threat levels of threat sources are all related to distance and are inversely proportional, it is considered that the threat cost is inversely proportional to the distance from the threat source to the track. The entire track is divided into S track segments, and the threat cost values of each track segment are calculated. Then the overall threat cost is the sum of the threat costs of the S track segments.

[0182] Step 4.2.1: Calculate the threat cost value generated in each track segment;

[0183] Suppose there is a $M$-th unmanned aerial vehicle (UAV) attacking an $N$-th target in the battlefield. First, each flight path is divided into $S$ flight path segments, and two adjacent flight path points of the UAV are denoted as $L$ k and $L$ k+1 . The coordinates of the threat source are denoted as To calculate the threat cost of each flight path segment, each flight path segment is equally divided into $C$ parts. The threat cost is indirectly calculated by obtaining the distances from the threat source to $C$ flight path points, which is specifically expressed as:

[0184]

[0185] In the formula, $N$ Th is the number of threat sources, $C$ is the number of equal parts of each flight path segment, is the coordinate of each flight path point, $t = 1, 2, \cdots, N$ Th , $c = 1, 2, \cdots, C$;

[0186] Step 4.2.2: Calculate the overall threat cost in each flight path;

[0187] Sum up the threat costs of the $S$ flight path segments to obtain the total threat cost $F$ of the flight path t as:

[0188]

[0189] Step 4.2.3: Normalize the threat cost for calculation under a unified scale;

[0190] Normalize the threat cost to a unified scale. The threat cost $F$ t is expressed by the formula as:

[0191]

[0192] In the formula, $F$ t MN represents the threat cost of the flight path where the $M$-th UAV attacks the $N$-th target, and $F$ tmax represents the flight path with the maximum total threat cost among all flight paths;

[0193] Step 4.3: Calculate the overall attack benefit;

[0194] Step 4.3.1: Calculate the overall attack benefit in each strike plan;

[0195] Use the remaining value of the target to evaluate the attack benefit cost of the target. The attack benefit generated by the $M$-th UAV attacking the $N$-th target is expressed as:

[0196] $F$ v $ = V$ N $\cdot P$ MN $\cdot x$ ij

[0197] Wherein, V N is the target value of the Nth target, and P MN is the damage probability of the Mth UAV hitting the Nth target, and x ij is a decision variable;

[0198] Step 4.3.2: Normalize the attack benefit;

[0199] Similar to the above index normalization, the attack benefit F v is unified to the same order of magnitude, and is expressed by the formula:

[0200]

[0201] Wherein, represents the attack benefit of the Mth UAV attacking the Nth target, and F vmax represents the maximum attack benefit that can be obtained in all strike plans.

[0202] Step 4.4: Calculate the enemy target value;

[0203] Combined with different types of each weapon device and its attack range, different threat levels I of 0-1 are set for the target typ , which is used to clearly evaluate and distinguish the strike value degree of each target in the battlefield environment. During the execution of combat missions, combat strike objects are usually divided into individual soldier targets, ground targets, and air targets. Conventional combat targets can perform combat missions such as battlefield reconnaissance and fire strikes, and targets can communicate with each other and achieve combat coordination. Individual soldier targets rely on flexible battlefield movement characteristics and good concealment and camouflage capabilities; ground vehicle targets such as tanks, infantry fighting vehicles, and vehicle-mounted anti-tank missiles have different combat strike weapons and also undertake different combat missions; air targets such as armed helicopters can quickly strike ground armored equipment and other targets, with strong mobility, good penetration effect, and good damage effect.

[0204] In this embodiment, the specific value performance of each weapon is shown in Table 1.

[0205] Table 1 Target type level division

[0206]

[0207] Step 4.5: Analyze the constraint conditions generated in target allocation;

[0208] Cooperative target allocation involves task matching between multiple UAVs and multiple targets. In this process, a series of constraint conditions must be considered to ensure the effective execution of tasks and the safety of UAVs. Considering the actual combat requirements, the constraint conditions considered in this paper for target allocation are as follows:

[0209] (1) Range constraint

[0210] Consider the flight distance of the self - detonating drone before fuel exhaustion. The distance traversed by each self - detonating drone should be less than its range, expressed as:

[0211]

[0212] where is the maximum range of the self - detonating drone is the actual traversed distance of the self - detonating drone

[0213] N v is the maximum flight altitude constraint.

[0214] (2) Decision variable constraint

[0215] The constraint condition is a limitation on the decision variable, restricting the range of the decision variable to ensure that the solution is feasible in the actual situation. The constraint condition can be an equation or an inequality, depending on the nature of the problem. The constraint conditions in this paper are as follows:

[0216]

[0217] where the decision variable x ij is a 0 - 1 variable. When the drone i acts on the target j, x ij = 1 means an attack is carried out, and x ij = 0 means no attack is carried out. The decision variable is expressed as x ij ∈(0,1), i = 1,..., M, j = 1,..., N, means that at least one drone executes a task at least once, and at most the number of drones assigned does not exceed D jmax ; means that one drone can execute at most one task;

[0218] Step 4.6. According to the target assignment optimization index, construct the objective function and describe each cost function therein;

[0219] The target assignment optimization index requires minimizing the attack cost of the drone and maximizing the attack benefit.

[0220] Determine the relative importance of each target according to the strategic plan of the commander or the expert knowledge base, that is, assign different weights to it, and use the linear weighted method to simplify the complex multi - objective problem into a single - objective optimization problem for solution. The optimization objective function of multi - drone collaborative target assignment is expressed as:

[0221] F = λ1F l +λ2Ft -λ3F v

[0222] where λ = (λ1, λ2, λ3) is the weight vector in the optimization objective function, indicating different degrees of influence of each factor on the target allocation result, and simultaneously satisfying λ i ∈(0, 1); F l is the voyage cost, F t is the threat cost, F v is the attack benefit. When the voyage cost and the threat cost are minimized and the attack benefit reaches the maximum, the optimal solution of the final target allocation is output.

[0223] Step 5. Use an improved genetic algorithm based on the idea of adaptive penalty function and a greedy algorithm switching mechanism to perform target allocation, and perform algorithm switching operations on the two algorithms in different combat environments. The genetic algorithm based on the penalty function idea is improved on the traditional genetic algorithm to solve the optimization problem of the objective function with multiple sets of constraints; as Figure 3 shown in the flowchart of the target allocation algorithm of the improved genetic algorithm of the present invention. The improved genetic algorithm is mainly used for the allocation mode in small-scale or non-urgent tasks in the target allocation algorithm based on the switching mechanism. In the improved genetic algorithm, an adaptive penalty function is mainly introduced to control the number of feasible solutions, thereby changing the quality of the optimal solution and improving the accuracy of the algorithm.

[0224] Step 5.1. Initialize the battlefield environment and set the number of suicide drones, strike targets, and threat sources;

[0225] Step 5.2. Set the initial population size, the number of iterations, the initial sizes of the selection rate, crossover rate, and mutation rate;

[0226] Step 5.3. Set the encoding operation method for the initial population;

[0227] Step 5.3.1. Perform encoding operations using binary encoding. Taking the corresponding relationship between suicide drones and targets, that is, each possible allocation scheme represents a chromosome, and each gene in the chromosome represents whether a specific drone is assigned to a certain target;

[0228] Step 5.3.2. Perform binary encoding on m suicide drones and n targets in the battlefield environment. Use 1 to represent that the suicide drone strikes the target, and 0 means no strike. Then each chromosome has m×n numbers, that is, "genes";

[0229] Step 5.3.3. Group every n genes into a group, and arrange each group of genes vertically to obtain the multi-suicide drone target allocation matrix C m×n ;

[0230] Step 5.3.4: Let the \(i\)-th row of the matrix represent the suicide drone, where \(i = 1, 2, 3,\cdots,m\), and the \(j\)-th column of the matrix represent the target \(c\). ij represents the strike situation of the suicide drone against the target. If \(c\) ij = 0, it means that the suicide drone \(M\) i does not strike the target \(N\). j If \(c\) ij = 1, it means that the suicide drone \(M\) i strikes the target \(N\). j ;

[0231] Step 5.4: Initialize the population to generate \(N\) individuals in the population;

[0232] Step 5.5: Determine the constraint conditions of the suicide drone according to Step 4.5;

[0233] Step 5.6: Construct a penalty function. For individuals that violate the constraint conditions, subtract the penalty function when calculating the fitness value to reduce the fitness value;

[0234] Step 5.6.1: Take the two constraint conditions in Step 4.5 as the penalty terms in the penalty function, and select a penalty factor, that is, a weight coefficient; construct the penalty function \(p(x)=f(x)+h(x)G(x)\), where \(f(x)\) is the objective function value, \(h(x)\) is the penalty factor, which is a function or a constant, and \(G(x)\) is the penalty term.

[0235] Step 5.6.2: Substitute the constraint conditions. The penalty function is expressed as \(p(x)=f(x)+\eta(n + m)\), and according to the cumulative penalty principle, it is stipulated that the greater the number of violated overall constraint terms of an individual, the greater the penalty intensity; where \(0\lt\eta\leq1\), which can be adaptively adjusted according to the number of feasible solutions;

[0236] Step 5.7: Construct a fitness function;

[0237] To avoid the situation of not satisfying the collaborative constraint conditions between suicide drones in Step 5.6.1, add a penalty term to the fitness function to affect the future evolution direction of the population, find the global optimal solution, and reduce the generation of infeasible solutions.

[0238] Since the fitness function is positive or 0, its formula is constructed as follows: Fitness\((x)=C\) max -p(x)

[0239]

[0240] where \(f(x)\) is the objective function value, the fitness function is determined by the objective function, and \(C\) maxis the maximum estimated value of the objective function, obtained through estimation.

[0241] Step 5.8: Perform selection, crossover, and mutation operations on the population;

[0242] After constructing the fitness function and penalty function, perform genetic operations such as selection, crossover, and mutation on the population, and iterate in turn.

[0243] Step 5.8.1: According to the principle of survival of the fittest, measure the fitness of each individual in the initial population for the environment through the individual fitness function value, and sort the individuals in the initial population;

[0244] Step 5.8.2: Use the roulette wheel method to select the chromosomes in the population that meet the fitness standard value, and then use the elite selection retention strategy to select and retain the excellent individuals from the sorting results;

[0245] Step 5.8.3: Perform crossover and mutation operations on the retained excellent individuals to generate an offspring population, and combine the two populations to form a new offspring population R with a size of 2N t .

[0246] Step 5.9: Generate an adaptive fitness function value;

[0247] Let the number of feasible solutions after each iteration be P1, the total number be N, and the penalty factor That is, the penalty term weight changes proportionally with the increase or decrease of the feasible solutions. When there are too many feasible solutions, the penalty factor also increases in the next iteration, and vice versa; the penalty function can be adaptively adjusted according to the proportion of feasible solutions output by different population sizes in the genetic algorithm.

[0248] Step 6: When the genetic algorithm with the improved adaptive penalty function idea cannot meet the combat requirements, to ensure the quality and timeliness of the decision-making solution, the allocation algorithm uses the greedy algorithm to continue solving the algorithm. As Figure 4 Shown is the flowchart of the target allocation algorithm using the greedy algorithm of the present invention. The greedy algorithm is mainly used for the allocation mode under large-scale or urgent tasks in the target allocation algorithm based on the switching mechanism. The greedy algorithm can achieve fast allocation on the premise of ensuring the accuracy of the results.

[0249] Step 6.1: Parameter initialization: It is known that there are n targets as inputs for solving the problem, and the solution set J of the problem is set to be empty; initialize the parameters of the maximum allowable iteration times, end flag threshold, and target quantity of the greedy algorithm.

[0250] Step 6.2: Define the objective function: According to the problem requirements, randomly generate task pairings between self-destructing drones and strike targets, and calculate the objective evaluation function. Select a measurement criterion and sort the n inputs according to this measurement criterion;

[0251] Step 6.3: Traverse all the strike plans of m self - destructing drones and n targets, and calculate the corresponding cost values through the cost function formula;

[0252] Step 6.4: Based on the absolute value of the objective function, establish a cost matrix. Among them, define A 11 , A 12 , A 13... A 1m The value of is the cost value of the strike plan composed of the target 1 to be struck and M drones. The remaining row elements A mn all represent the attack cost values of the strike plan where the M - th drone strikes the N - th target. Finally, a cost matrix containing N×M cost value elements is formed.

[0253]

[0254] Step 6.4.1: Use the comparison method to find the maximum element in the cost matrix A and record its position at the same time;

[0255] Step 6.4.2: Assume that the maximum element in the cost matrix A is A 00 , which means that after considering the comprehensive target cost and flight path cost of our drones, the enemy target N0 has the greatest benefit when struck by M0. Then implement the strike plan of M0 against N0;

[0256] Step 6.4.3: Since N0 has become the target of M0, to avoid subsequent repeated allocation and overly concentrated strikes, set the row and column where A 00 is located to ∞;

[0257] Step 6.4.4: After setting the row and column where A 00 is located to ∞, A 00 no longer participates in subsequent allocation tasks. Then return to Step 6.3 to continue cyclic iteration to find the next optimal solution for state update;

[0258] Step 6.4.5: After completing all one - to - one allocations, restore to the original cost matrix composition, set all the already allocated plans to ∞ to avoid searching again. For the remaining elements in the matrix, re - search for the many - to - one allocation results;

[0259] Step 6.5: Output the optimal solution: When all n inputs have been searched, if the task conditions are met, the search stops, that is, the current solution set is the global optimal solution, and output the search results;

[0260] Step 7: Set the main switching mechanism of the target allocation algorithm;

[0261] For the nature and complexity of different problems, if the solution space of the problem is large and the complexity is high, a genetic algorithm needs to be used for global search; if the solution space of the problem is small and the complexity is low, only a greedy algorithm needs to be switched to find a better solution; for the computational complexity and execution time of the algorithm, as well as the limitedness of computing resources, if time and resources are limited, a greedy algorithm needs to be used to quickly obtain a solution. As Figure 5 shown in the flowchart of the algorithm switching mechanism of the present invention, according to the requirements of the battlefield environment, the global battlefield environment variables are initialized. For the problem nature, time and resource limitations, and accuracy requirements, the goals and conditions for switching algorithms are clarified. It is set that when higher accuracy or a global optimal solution is required, switch to the genetic algorithm; when the solution space of the problem is large and the computing resources are insufficient, switch to the greedy algorithm. Using the switching mechanism for target allocation can select the most suitable algorithm for decision-making in the current situation, enhance combat flexibility, and improve the mission success rate.

[0262] Step 7.1: Initialize the information of the global battlefield variables according to the requirements of the battlefield environment;

[0263] Step 7.2: Define combat scenarios of different scales according to different quantity levels of the combat weapons, and clarify the completion time T of each target allocation task. c where the number of self-detonating drones participating in the combat on our side is m, and the number of enemy combat weapons is n, and it is stipulated that m > n under each battlefield scale. The following are the three defined combat scales, and the actual battlefield will also be classified according to this definition in the future;

[0264] When the number of our drones' targets m ≤ 20 and the number of enemy targets n ≤ 20, it belongs to a small-scale conflict;

[0265] When the number of our drones' targets 20 < m ≤ 50 and the number of enemy targets 20 < m ≤ 50, it belongs to a medium-scale combat;

[0266] When the number of our drones' targets 50 < m ≤ 100 and the number of enemy targets 50 < m ≤ 100, it belongs to a large-scale battle;

[0267] Other situations are not taken into consideration.

[0268] Step 7.3: According to the requirements of the task nature, planning time, and optimization performance, clarify the goals and conditions for switching algorithms, and clarify the completion time T of each target allocation task. f .

[0269] Step 7.4: Establish a task planning model database. Conduct comparative experiments of different combat scales for the two algorithms respectively, and continuously increase the experimental scale to obtain the computational time and the change values of the objective function under multiple different combat situations. Store the experimental results to form a database and establish a historical target allocation model;

[0270] Step 7.5: Enter actual battlefield combat parameters into the system.

[0271] Step 7.6: Identify the characteristic indicators of the actual battlefield situation and make similarity judgments, including the number of weapons in combat, the scale of operations, and the time T for the command to be issued. f As the main feature judgment indicator;

[0272] Step 7.7: Develop a switching strategy;

[0273] Step 7.7.1. Compare the case data including calculation time and target function change value in the existing historical database with the actual combat conditions, search in the database, and select the target allocation model with the highest similarity as the matching object.

[0274] Step 7.7.2: Allocate time T according to the target specified in the mission c As a benchmark, complete the similarity judgment through step 7.6 and select the case with the same scale as the actual battlefield and the highest similarity;

[0275] Step 7.7.3, extract the most similar case, compare the optimization performance of the genetic algorithm and the greedy algorithm within the benchmark time range, and compare the algorithm decision results. According to the comparison results, due to the high similarity, match the battlefield environment in the database with the actual combat scenario, and the algorithm decision in this case is fed back as the optimal decision result under the current situation.

[0276] Step 7.8, monitor and evaluate the results; if there are new changes in the battlefield situation, it is necessary to identify the characteristic indicators under the new situation again, return to step 7.6, and make new algorithm planning decision results to ensure the real-time and accuracy of target allocation.

[0277] like Figure 6 The figure shows the optimization performance comparison of the algorithm of the present invention. Through experimental comparison, it can be concluded that the switching mechanism proposed in this paper is effective and feasible. First, the specified execution time of the task is used as a benchmark to compare the optimization of the algorithm within this time range. In non-urgent tasks, that is, when there is ample time for task planning, the optimality of the algorithm is considered, and the algorithm with the best optimization performance is selected for decision-making; in urgent tasks, that is, when the task planning time is extremely short, the optimization should be abandoned, and reasonable task planning should be carried out based on the planning time. Under the premise of meeting different combat requirements, the decision-making algorithm that best suits the requirements can be selected to the greatest extent, which increases the flexibility of battlefield decision-making and improves the overall combat effectiveness.

[0278] The above description is only a preferred embodiment of the present disclosure and an explanation of the technical principles applied. Those skilled in the art should understand that the scope of the invention involved in the embodiments of the present disclosure is not limited to the technical solutions formed by the specific combination of the above technical features, and should also cover other technical solutions formed by any combination of the above technical features or their equivalent features without departing from the above inventive concept. For example, the technical solutions formed by mutually replacing the above features with the technical features (but not limited to) disclosed in the embodiments of the present disclosure that have similar functions.

Claims

1. A rapid target assignment method for collaborative attacks of unmanned aerial vehicles based on case-based reasoning, characterized in that, It includes the following steps: Step 1: Uniformly model the battlefield space environment according to the requirements of cluster combat strike missions and the battlefield environment. Suppose that m self - detonating drones form a drone swarm to jointly execute a strike mission, targeting n targets scattered at different positions on the battlefield, and there are t threat sources distributed in the battlefield with threat radius sets \(R = \{R_1, R_2, R_3,\cdots,R\) t \}\), and coordinates \(\{(x\) t1 , y\) t1 ), (x\) t2 , y\) t2 ),\(\cdots,(x\) tt , y\) tt )\}. It is ensured that each self - detonating drone executes at most one mission and strikes one target. Among them, the self - detonating drone swarm is initially defined as \(M=\{M_1,M_2,\cdots,M\) m \}, the ground target set is \(N = \{N_1,N_2,\cdots,N\) n \}, the initial position of the target is set as \((x\) i , y\) j ), and the value of target \(N\) j is \(Q\) j ; To successfully implement the strike mission, during the process of executing the collaborative strike mission, the self - detonating drones need to avoid the threat sources that appear in the battlefield and finally reach the target mission point to carry out the strike; and according to the target type, the upper limit of the number of times each target can be struck is \(D\) jmax pieces, that is, the number of drones assigned to each target should be less than or equal to \(D\) jmax pieces; Step 2: Use the grid method to design a two-dimensional battlefield simulation model to describe the battlefield space in detail. In the two-dimensional battlefield simulation model, each grid represents a coordinate point, which is used to represent the positions of unmanned aerial vehicles, targets, and obstacles; the planning space is represented as a set Ω, and (x, y) represents the abscissa and ordinate of a certain position point in the space Ω, where x max and y max respectively represent the maximum distance positions specified by the abscissa and ordinate, as shown in the following formula: Ω={(x,y)|0≤x≤x max , 0≤y≤y max} Step 3: Model the battlefield threat sources, select radar threat, anti-aircraft gun threat, and terrain threat as threat source parameters, and calculate the threat degrees of the threat sources. Step 4: Establish a reasonable optimization target allocation model, and define the target optimization function according to the constraint conditions of the optimization model. Step 5: Use the improved genetic algorithm based on the idea of adaptive penalty function and the greedy algorithm switching mechanism for target allocation, perform algorithm switching operations on the two algorithms in different combat environments. The genetic algorithm based on the penalty function idea is improved on the traditional genetic algorithm to solve the optimization problem of the target function with multiple sets of constraint conditions. Step 6: When the genetic algorithm improving the idea of adaptive penalty function fails to meet the combat requirements, the allocation algorithm uses the greedy algorithm to continue solving the algorithm. Step 7: Set the main switching mechanism of the target allocation algorithm to achieve fast target allocation for UAV cooperative attacks. The specific steps of Step 3 include the following steps: Step 3.1: Calculate the radar threat degree within the battlefield range. The power of the radar echo signal is expressed by the formula: where P t is the transmit power, G is the transmit antenna gain, σ is the radar cross section, R is the distance from the target to the radar in meters, and λ is the electromagnetic wave wavelength; for a given UAV, the radar cross section is constant, and the above equation simplifies to: Where K is a constant; when the radar is not interfered, the probability of detecting a target is related to the quality of the received signal. Assuming that the radar can detect in all directions and the maximum detection radius of the radar is R max , the detection probability of the radar for the UAV is expressed as: Step 3.2: Calculate the anti-aircraft gun threat degree. When the enemy radar detects the UAV, the anti-aircraft missile will attack according to the target information. The kill probability of the anti-aircraft missile is: P m = T·Y·Z[1 - (1 - A·E·W) Q ​ In the formula, T is the radar detection probability of the surface-to-air missile, Y is the radar interception and guidance probability, Z is the information transmission conversion probability, A is the missile successful launch probability, E is the missile flight reliability probability, W is the missile kill probability, and Q is the number of missiles launched at one time. Step 3.3: Calculate the terrain threat degree. Calculate the height threat and size of the terrain: Where, T h represents the threat level of terrain altitude, h m represents the altitude of the current terrain, h u represents the upper limit altitude of the UAV flight. If the terrain altitude exceeds the low-altitude flight upper limit of the UAV, the UAV terrain threat is set to the maximum value; When the real-time flight altitude of the drone is h real the threat posed by obstacles at different altitudes to the drone is expressed as: The specific steps of Step 4 include the following steps: Step 4.1: Calculate the range cost. Step 4.1.1: Calculate the track distance in each track segment. l MS To represent the track length of the Mth UAV on the kth track segment, where S is the number of track segments: In the formula, represents the starting point coordinates of the Mth unmanned aerial vehicle on the kth track segment; Step 4.1.2: Calculate the range cost of each strike plan. The strike plan is as follows: Suppose the first UAV among m UAVs attacks the first target among n targets, then it is a strike plan. If the first UAV among the m UAVs attacks the second target among n targets, then it is another strike plan. If it attacks the nth target among n targets, then it is the nth strike plan; each UAV has the same number of strike plans. In each strike plan, one UAV only attacks one target. During the trajectory planning process, a trajectory is divided into S trajectory segments. The trajectory distance L for the Mth UAV to attack the Nth target MN is expressed by the formula: Step 4.1.3: Normalize the range cost value. The voyage cost F after being unified to the same order of magnitude l It is expressed by the formula as: where, L MN represents the track distance of the M-th UAV attacking the N-th target, and L Nmax represents the maximum value of the flight distances of all UAVs during the attack. The ratio of the two can be used to obtain the range cost of each strike plan; Step 4.2: Calculate the threat cost within the battlefield. The threat cost is inversely proportional to the distance from the threat source to the track. Divide the whole track into S track segments, calculate the threat cost values of each track segment, and the total threat cost is the sum of the threat costs of the S track segments. Step 4.2.1: Calculate the threat cost value generated in each track segment. Suppose there is the Mth unmanned aerial vehicle (UAV) attacking the Nth target in the battlefield. First, each flight path is divided into S flight path segments, and two adjacent flight path points of the UAV are represented as L k and L k+1 . The threat source coordinates are represented To calculate the threat cost of each flight path segment, each flight path segment is equally divided into C parts. The threat cost is indirectly calculated by obtaining the distances from the threat source to C flight path points, which is specifically expressed as: Where N Th is the number of threat sources, C is the number of equal parts into which each track is divided, is the coordinate of each track point, t = 1, 2, …, N Th , c = 1, 2, …, C; Step 4.2.2: Calculate the total threat cost in each track. Sum the threat costs of S track segments to obtain the total threat cost F in the track t It is as follows: Step 4.2.3: Normalize the threat cost to calculate under a unified scale. Normalize the threat cost to a unified scale, and the threat cost is F t It is expressed by the formula as follows: where F t MN represents the threat cost of the Mth UAV attacking the track where the Nth target is located, and F tmax represents the track with the maximum total threat cost among all tracks; Step 4.3: Calculate the overall attack benefit; Step 4.3.1: Calculate the overall attack benefit in each strike plan; The remaining value of the target is used to evaluate the attack benefit cost of the target. The attack benefit generated by the Mth UAV attacking the Nth target is expressed as: F v = V N · P MN · x ij where, V N is the target value of the Nth target, P MN is the damage probability of the Mth UAV hitting the Nth target, and x ij is the decision variable; Step 4.3.2: Normalize the attack benefit; Unify the attack benefit F v to the same order of magnitude, which is expressed by the formula: In the formula, represents the attack benefit of the Mth unmanned aerial vehicle attacking the Nth target, and F vmax represents the maximum attack benefit that can be obtained among all strike plans; Step 4.4: Calculate the value of the enemy target; Combined with different types of each weapon device and its attack range, set threat levels I of 0 - 1 with different degrees for the targets typ , which is used to clearly evaluate and distinguish the degree of strike value of each target in the battlefield environment; Step 4.5: Analyze the constraint conditions generated in target allocation; Step 4.6: Construct an objective function according to the target allocation optimization index and describe each cost function therein; The target allocation optimization index requires minimizing the attack cost of the UAV and maximizing the attack benefit; The optimization objective function of multi-UAV collaborative target allocation is expressed as: F = λ1F l + λ2F t - λ3F v where λ = (λ1, λ2, λ3) is the weight vector in the optimization objective function, representing the different degrees of influence of various factors on the target allocation result, and simultaneously satisfying F l is the voyage cost, F t is the threat cost, F v is the attack benefit. When the voyage cost and threat cost are minimized and the attack benefit reaches the maximum, the optimal solution of the final target allocation is output; The specific steps of Step 5 are as follows: Step 5.1: Initialize the battlefield environment and set the number of suicide UAVs, strike targets, and threat sources; Step 5.2: Set the initial population size, the number of iterations, and the initial sizes of the selection rate, crossover rate, and mutation rate; Step 5.3: Set the coding operation method for the initial population; Step 5.3.1: Use binary coding for the coding operation. The corresponding relationship between suicide UAVs and targets, that is, each possible allocation plan represents a chromosome, and each gene in the chromosome represents whether a specific UAV is assigned to a certain target; Step 5.3.2: Binary code the m suicide UAVs and n targets in the battlefield environment. Use 1 to represent that the suicide UAV strikes the target and 0 for no strike. Then each chromosome has m×n numbers, that is, "genes"; Step 5.3.3: Group every n genes into a set. When the genes in each set are arranged vertically, the multi-self-exploding drone target allocation matrix C is obtained. m×n ; Step 5.3.4: It is stipulated that the \(i\)-th row of the matrix represents the suicide drone, where \(i = 1, 2, 3,\cdots, m\), and the \(j\)-th column of the matrix represents the target \(c\). ij \(c\) represents the strike situation of the suicide drone against the target. If \(c\) ij \(= 0\), it means that the suicide drone \(M\) i does not strike the target \(N\). j If \(c\) ij \(= 1\), it means that the suicide drone \(M\) i strikes the target \(N\). j ​ Step 5.4: Initialize the population and generate N individuals; Step 5.5: Determine the constraint conditions of the suicide UAVs according to Step 4.5; Step 5.6: Construct a penalty function. For individuals that violate the constraint conditions, subtract the penalty function when calculating the fitness value to reduce the fitness value; Step 5.6.1: Use the two constraint conditions in Step 4.5 as penalty terms in the penalty function and select a penalty factor, that is, a weight coefficient; construct the penalty function p(x) = f(x) + h(x)G(x), where f(x) is the objective function value, h(x) is the penalty factor, and G(x) is the penalty term; Step 5.6.2: Substitute the constraint conditions. The penalty function is expressed as p(x) = f(x) + η(n + m), and according to the cumulative penalty principle, it is stipulated that the greater the number of individuals violating the overall constraint term, the greater the penalty; where 0 < η ≤ 1, and it can be adaptively adjusted according to the number of feasible solutions; Step 5.

7. Construct a fitness function, with the formula as follows: Fitness(x) = C max - p(x) Among them, f(x) is the objective function value, and C max is the maximum estimated value of the objective function, which is obtained through estimation; Step 5.8: Perform selection, crossover, and mutation operations on the population; After constructing the fitness function and penalty function, perform genetic operations such as selection, crossover, and mutation on the population and iterate in turn; Step 5.8.1: According to the principle of survival of the fittest, measure the fitness of each individual in the initial population by the individual fitness function value and sort the individuals in the initial population; Step 5.8.2: Use the roulette wheel method to select the chromosomes in the population with fitness values that meet the standard, and then use the elite selection and retention strategy to select and retain excellent individuals in the sorting results; Step 5.8.3: Perform crossover and mutation operations on the remaining excellent individuals to generate an offspring population, and combine the two populations to form a new offspring population R with a size of 2N t ; Step 5.9: Generate the adaptive fitness function value; Let the number of feasible solutions after each iteration be P1, the total number be N, and the penalty factor That is, the penalty term weight changes proportionally with the increase or decrease of the feasible solutions. When there are too many feasible solutions, the penalty factor also increases during the next iteration, and vice versa; The specific steps of step 6 are as follows: Step 6.1: Parameter initialization: It is known that there are n goals as inputs for solving the problem. Set the solution set J of the problem to be empty; initialize and set the parameters of the maximum allowable iteration times, end flag threshold, and the number of goals of the greedy algorithm. Step 6.2: Define the objective function: According to the problem requirements, randomly generate the task pairings between the suicide drones and the strike targets, and calculate the objective evaluation function; select a metric standard and sort the n inputs according to this metric standard. Step 6.3: Traverse all the strike plans of m suicide drones and n targets, and calculate the corresponding cost values through the cost function formula. Step 6.

4. Establish a cost matrix according to the absolute value of the objective function. Among them, define A 11 , A 12 , A 13... A 1m The value of is the cost value of the strike plan composed of the target to be struck 1 and M UAVs. The remaining row elements A mn All represent the attack cost value of the strike plan for the Mth UAV to strike the Nth target. Finally, a cost matrix containing N×M cost value elements is formed; Step 6.4.1: Use the comparison method to find the maximum element in the cost matrix A, and record its position at the same time. Step 6.4.

2. Assume that the maximum element in the cost matrix A is A 00 , which indicates that after considering the comprehensive target cost and the track cost of our UAV, the maximum benefit for the enemy's target N0 is achieved by implementing the strike by M0. Therefore, implement the strike plan of M0 on N0; Step 6.4.3: Since N0 has become the target of M0, set the row and column where A 00 is located to ∞; Step 6.4.

4. After setting the row and column where A is located to ∞, A 00 will no longer participate in subsequent allocation tasks, and then return to Step 6.3 to continue the loop iteration to find the next optimal solution for state update; 00 ​ Step 6.4.5: After completing all one-to-one allocations, restore to the original cost matrix composition, set all the already allocated plans to ∞ to avoid searching again. For the other remaining elements in the matrix, re-search for the many-to-one allocation results. Step 6.5: Output the optimal solution: When all n inputs have been searched, if the task conditions are met, the search stops, that is, the current solution set is the global optimal solution, and the search results are output. The specific steps of step 7 are as follows: Step 7.1: Initialize the battlefield global variable information according to the battlefield environment requirements. Step 7.2: Define combat scenarios of different scales according to different quantity levels of combat weapons, and clarify the completion time T for each target assignment task c , where the number of self - detonating drones participating in the combat on our side is m, and the number of enemy combat weapons is n, and it is stipulated that m > n for each battlefield scale. The following are the three defined combat scales, and the subsequent actual battlefields will also be classified according to this definition; When the number of our drones m ≤ 20 and the number of enemy targets n ≤ 20, it belongs to a small-scale conflict. When the number of our drones 20 < m ≤ 50 and the number of enemy targets 20 < m ≤ 50, it belongs to a medium-scale operation. When the number of our drones 50 < m ≤ 100 and the number of enemy targets 50 < m ≤ 100, it belongs to a large-scale campaign. Other situations are not considered. Step 7.3: According to the nature of the task, the planned time, and the requirements for optimizing performance, clarify the objectives and conditions of the handover algorithm, and clarify the completion time T for each assigned task of the objective f ; Step 7.4: Establish a task planning model database; conduct comparative experiments on the two algorithms with different combat scales respectively, and continuously increase the experimental scale to obtain the calculation time and the change values of the objective function under multiple different combat postures; store the experimental results to form a database and establish a historical target allocation model. Step 7.5: Input the actual battlefield combat parameters into the system. Step 7.6: Identify the characteristic indicators of the actual battlefield situation and make a similarity judgment; including the number of weapon confrontations between both sides, the scale of the operation, and the completion time T of order issuance f As the main characteristic judgment indicator; Step 7.7: Develop a switching strategy. Step 7.7.1: Compare the case data including the calculation time and the change values of the objective function in the existing historical database with the actual combat conditions, search in the database, and select the target allocation model with the highest similarity as the matching object. Step 7.7.2: Using the target allocation time T specified in the combat mission assignment as a reference, complete the similarity judgment through Step 7.6, and select the case with the same scale as the actual battlefield and the highest similarity; c ​ Step 7.7.3: Extract the comparison of the optimization performance of the genetic algorithm and the greedy algorithm and the algorithm decision results within the benchmark time range of the case with the highest similarity. According to the comparison results, due to the high consistency of similarity, match the battlefield environment in the database with the actual combat scenario, and use the algorithm decision in this case as the optimal decision result in the current situation for feedback output. Step 7.8: Monitor and evaluate the effects; if there are new changes in the battlefield situation, it is necessary to identify the characteristic indicators in the new situation again, return to step 7.6, and make new algorithm planning decision results to ensure the real-time and accuracy of target allocation. The constraint conditions described in step 4.5 are as follows: (1) Range constraint The distance traveled by each self - detonating drone should be less than its range, expressed as: In the formula, is the maximum range of the self-detonating drone, is the actual penetration distance of the self-detonating drone; (2) Decision variable constraint where the decision variable \(x\) ij is a 0-1 variable. When UAV \(i\) acts on target \(j\), \(x\) ij = 1 indicates an attack is carried out, and \(x\) ij = 0 indicates no attack is carried out; the decision variable \(x\) ij \(\in(0,1), i = 1,\cdots,M, j = 1,\cdots,N\), means that a task is carried out by at least one UAV at least once, and at most the number of UAVs assigned does not exceed \(D\) jmax aircraft; means that a UAV can carry out at most one task.

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