Firepower distribution method and system based on double-layer decoupling and multistage penalty genetic algorithm

Abstract

The invention belongs to the technical field of weapon target distribution, and particularly relates to a firepower distribution method and system based on a double-layer decoupling and multistage penalty genetic algorithm. Constructing a firepower distribution primary decoupling model comprising a threat matrix and a firepower distribution membership degree, constructing a firepower distribution secondary optimization model oriented to an objective function, and fusing hard constraint, soft constraint, a multi-stage penalty mechanism and a self-adaptive penalty factor; and adopting an MLP-GA optimization method fusing a multilayer perceptron and a genetic algorithm to iteratively solve the secondary firepower distribution model. The firepower distribution method based on the optimization mechanism of double-layer decoupling and multi-stage penalty has the capabilities of structural decomposition, intelligent optimization and environmental adaptability, solves the technical problems that an existing firepower distribution method is slow in response and difficult to meet the requirements of a complex dynamic battlefield, and improves the real-time performance and robustness of firepower resource allocation in the complex battlefield.

Description

Technical Field

[0001] The present invention belongs to the technical field of weapon target allocation technology, and in particular relates to a firepower allocation method and system based on a double-layer decoupling and multi-level penalty genetic algorithm. Background Art

[0002] In modern naval warfare, efficient deployment of firepower resources and precise strikes are crucial for improving operational effectiveness. Weapon-Target Assignment (WTA), a core issue in decision support systems, involves complex matching between multiple attack platforms, missile types, and targets, and is a typical multi-constrained combinatorial optimization problem. Traditional WTA models typically tightly couple firepower allocation with route planning, attempting to simultaneously improve mission execution paths and strike effectiveness through joint optimization. However, this strong coupling approach neglects the relative independence and interaction between the two, resulting in a slow response to complex battlefield dynamics and difficulties in achieving optimal resource utilization.

[0003] From an algorithmic perspective, the firepower allocation problem is a classic NP-hard problem, with its solution space exponentially increasing due to the sheer number of targets, platform types, and weapon types. While traditional exact algorithms (such as branch-and-bound and dynamic programming) can achieve optimal solutions, their computational complexity is extremely high, making them difficult to apply in real-time battlefield environments. To improve solution efficiency, researchers have introduced intelligent optimization methods such as particle swarm optimization (PSO) and genetic algorithms (GA). While these methods alleviate the computational burden to some extent, they generally suffer from insufficient ability to handle complex constraints and a tendency to fall into local optimal solutions, making them difficult to adapt to the complex and dynamic demands of actual naval warfare.

[0004] Furthermore, the high complexity of the combat environment presents a significant challenge for current firepower allocation research. Modern naval warfare not only involves electromagnetic interference, complex terrain, and weather conditions, but also requires coping with the enemy's advanced multi-layered defense systems and tactical deception tactics. The combination of these factors significantly complicates modeling and decision-making in the combat environment. Existing research, most of which is based on idealized or simplified scenarios for modeling and testing, lacks effective simulation and adaptation to the complexity of the real battlefield, making it difficult to support the demands of high-intensity, highly confrontational combat. Therefore, how to construct a firepower allocation model that can adapt to changing battlefield situations and possesses high real-time performance and strong robustness has become a core issue that needs to be addressed in this field. Summary of the Invention

[0005] To address the aforementioned technical issues, the present invention provides a firepower allocation method and system based on a dual-layer decoupling and multi-level penalty genetic algorithm. These methods aim to address the problems of traditional firepower allocation models, such as severe decision-making coupling, insufficient ability to handle complex constraints, and the tendency of existing algorithms to fall into local optimality and struggle to adapt to complex battlefield environments. By proposing a solution based on dual-layer decoupling and multi-level penalty, this approach enables highly flexible and efficient firepower allocation for multi-platform anti-ship missiles in complex battlefield environments, thereby improving the overall effectiveness of the combat system.

[0006] In one aspect, the present invention provides a firepower allocation method based on a double-layer decoupling and multi-level penalty genetic algorithm, the method comprising:

[0007] Step S1: Based on the threat relationship and spatial distribution characteristics between the attack platform and the target platform, a first-level decoupling model of firepower allocation is constructed, which includes a threat matrix and firepower allocation membership.

[0008] Step S2: construct a two-level optimization model for firepower allocation oriented to the objective function, integrating hard constraints and soft constraints, multi-level penalty mechanism, adaptive penalty factor and fitness function;

[0009] Step S3: The MLP-GA optimization method that integrates the multi-layer perceptron and the genetic algorithm is used to iteratively solve the secondary firepower allocation model.

[0010] In a preferred implementation, step S1 further includes: step S11: calculating the threat matrix between the attack platform and the target platform to quantify the threat level of each attack platform to each target platform; step S21: determining the objective function based on the combat purpose, and determining the fitness function corresponding to the objective function.

[0011] In a preferred implementation, step S11 further includes:

[0012] Step S11.1: Calculate the estimated range distance from each attack platform to each target platform;

[0013]

[0014] Where: d ij represents the predicted range between the i-th attack platform and the j-th target platform; i represents the number index of the attack platform, and its value range is i=1,2,…,m; j represents the number index of the target platform, and its value range is j=1,2,…,n; x i 、y i represents the two-dimensional coordinate position of the i-th attack platform; x j 、y j Indicates the two-dimensional coordinate position of the j-th target platform;

[0015] Step S11.2: Calculate the threat factor of each target platform relative to each attack platform based on the estimated range;

[0016]

[0017] Where: t ij represents the comprehensive threat index of attack platform i to target platform j; ω1 and ω2 represent weight coefficients; d ij_target represents the distance between attack platform i and target platform j; d ij_max v represents the maximum range of the weapon system of attack platform i on target platform j; j_target represents the protection capability value of target platform j; v j_max Indicates the maximum reference value of protection capability; It means the attack platform is closer to the target.

[0018] In a preferred implementation, step S21 further includes:

[0019] Step S12.1: Calculate the mean coordinates of each attack platform and each target platform, and obtain the center coordinates of the attack platform group and the target platform group respectively;

[0020] Step S12.2: Using the center coordinates of the attack platform as the origin, the direction connecting the center coordinates of the target platform and the center coordinates of the attack platform is used as the initial x-axis. The x-axis is rotated 90 degrees counterclockwise to construct a firepower allocation coordinate system. The unit vectors of the x-axis and y-axis are defined in the firepower allocation coordinate system. Based on the unit vectors, the original two-dimensional coordinates of each attack platform and target platform are translated into the firepower allocation coordinate system to obtain the new coordinates of the attack platform and target platform in the firepower allocation coordinate system.

[0021] Step S12.3: In the fire distribution coordinate system, a set of dividing lines parallel to the x-axis is constructed. The new coordinates of the target platform in the y-axis direction are divided based on these dividing lines to form multiple fire distribution areas. The fire distribution area assigned to each attacking platform is determined based on the mapping relationship between the attacking platform and the fire distribution area.

[0022] Step S12.4: Based on the target platform's position in the firepower allocation coordinate system and its firepower allocation area, a fuzzy membership function is used to calculate the firepower allocation membership of each target platform to different attack platforms to optimize the matching of firepower resources;

[0023] The firepower distribution membership is determined by the following formula:

[0024]

[0025] Where: represents the firepower subordination of target platform j to attack platform i; represents the Y-axis coordinate of target platform j in the firepower allocation coordinate system; represents the Y-axis coordinate of attack platform i in the firepower allocation coordinate system; L k , L k-1 Indicates the coordinates of the dividing line between adjacent fire areas (vertical); i = k-1, k, k+1 represent the coordinates of Z k-1 、Z k 、Z k+1 The index of the attack platform in the region corresponds to the target; exp(·) represents the exponential function, which is used to construct a nonlinear weight distribution mechanism so that the targets far away from the region boundary have lower contributions; Indicates the target platform's membership to the attack platform in the previous partition; Indicates the target platform to L k The vertical distance of the dividing line boundary; |L k - Indicates attack platform i to L k The longitudinal distance of the dividing line boundary; Indicates the target platform's degree of affiliation to the attack platform in the current area; Indicates the y coordinate of the target platform j and the current area Z k The average distance between the upper and lower boundaries of |L k-1 -L k | indicates the current firepower allocation area Z k The vertical height of Indicates the target platform's membership to the next partition attack platform; Indicates the target platform j to the previous dividing line L k-1 The longitudinal distance of the boundary; Indicates the distance between attack platform i and the dividing line L in the firepower distribution coordinate system k-1 The vertical distance of the border.

[0026] In a preferred implementation, step S2 further includes:

[0027] Step S21: determining an objective function based on the combat purpose, and determining a fitness function corresponding to the objective function;

[0028] Step S22: By distinguishing the constraints in the firepower allocation process into hard constraints and soft constraints, a multi-level penalty mechanism and an adaptive penalty factor are introduced for the soft constraints;

[0029] Step S23: Based on the multi-level penalty mechanism and the adaptive penalty factor, a total fitness function is constructed that integrates the strike benefit, speed-distance adaptation, resource cost, and multi-level soft constraints;

[0030] The overall fitness function is:

[0031]

[0032] Where: represents the benefit term, which is used to guide resources to concentrate on high-value and attackable targets; C represents the normalized resource consumption cost of all allocation schemes; λ1P1, λ2P2, and λ3P3 represent multi-level penalty terms, corresponding to membership violation, firepower balance violation, and priority deviation, respectively; 1 represents a constant, which is used to ensure that the fitness is non-negative and is convenient for the use of the genetic algorithm sorting mechanism; i represents the i-th attack platform, with a total of n attack platforms; j represents the j-th target platform, with a total of m target platforms; t ij represents the comprehensive threat index of attack platform i to target platform j; q j represents the target damage benefit factor; M ij represents the speed-distance adaptation factor; α ij represents the firepower allocation variable, which is 1 if attack platform i is assigned to target j, otherwise it is 0;

[0033] The penalty factor function is:

[0034]

[0035] Where: k0 represents the initial penalty factor of the k-th penalty term; kmax represents the maximum penalty value of the k-th penalty item; t represents the current iteration number; T represents the maximum number of iterations; pk represents the exponent that controls the growth rate of the k-th penalty; k∈(1,2,3) represents the penalty items of 3 penalty levels.

[0036] In a preferred implementation, further in step S21, the combat objectives include but are not limited to pursuing maximum damage effect, prioritizing cost reduction, and striking key targets;

[0037] Soft constraints include but are not limited to firepower allocation affiliation, firepower allocation balance, and target priority requirements;

[0038] The hard constraints include, but are not limited to, hard constraint variables including the number of missiles launched by the i-th attack platform at the j-th target platform, the total inventory of missiles available to the attack platform i, the inventory of missiles of type t in the attack platform i, missiles of type t, the number of missiles allocated to the target platform j, and the value of the firepower allocation membership is not 0;

[0039] The multi-level penalty mechanism has at least 3 levels, among which level 1 is a light penalty, corresponding to the target priority requirement; level 2 is a moderate penalty, corresponding to the balance of firepower distribution; level 3 is a heavy penalty, corresponding to the degree of firepower distribution.

[0040] In a preferred implementation, further, step S3 includes:

[0041] Step S31: Determine the dimensional structure of the firepower task allocation matrix and the number of initial solution individuals Y based on the number of attacking platforms and the number of target platforms. Based on the matrix dimensional structure and the number of individuals, construct Y initial feasible solution populations that meet the hard constraints through multiple random generation methods, and normalize each firepower task allocation matrix in the initial feasible solution population.

[0042] Step S32: After completing the initial population construction and normalization, the firepower task allocation problem is iteratively solved using a method that integrates a multi-layer perceptron and a genetic algorithm to obtain the final firepower task allocation solution.

[0043] In a preferred implementation, step S31 further includes:

[0044] Step S31.1: Define a combat operation as including n attack platforms for executing the mission and m target platforms to be attacked. Based on this, set the task allocation matrix structure corresponding to each initial solution individual to n×m, and determine the number of initial solution individuals.

[0045] Step S31.2: Based on the number of initial solution individuals determined in step S31.1 and the dimensions of the firepower strike task allocation matrix, when constructing the initial solution individuals, use a column-by-column task allocation method. Under the premise of satisfying the hard constraints of task coverage, platform capability, and platform adaptability, randomly generate the task allocation matrix until Y feasible initial solution populations that meet the hard constraints are obtained;

[0046] Step S31.3: After the initial feasible solution population that satisfies the hard constraints is constructed, each firepower task allocation matrix in the initial feasible solution population is normalized.

[0047] In a preferred implementation, step S32 further includes:

[0048] Step S32.1: Using the normalized initial feasible solution population from step S31 as input to the optimization algorithm, an initial population consisting of multiple individuals is constructed based on a genetic algorithm. Each individual is represented by a fire task assignment matrix. The fire task assignment matrix is ​​an integer matrix or array that represents the mapping relationship between tasks and attack platforms.

[0049] Step S32.2: In each iteration, a combination of roulette wheel selection and tournament selection is used to select some individuals from the current population as parent individuals. The selected parent individuals are used in subsequent crossover and mutation operations.

[0050] Step S32.3: Perform a two-point crossover operation on the selected parent individuals to generate new offspring individuals. Then, perform a random mutation operation on the gene loci of the new offspring individuals based on the set probability. Simultaneously, perform a hard constraint check on the new offspring individuals after crossover and mutation, and remove individuals that violate the hard constraints to maintain population feasibility.

[0051] Step S32.4: Construct a fitness function based on the modeling objective function and fuse it with the MLP model's prediction function for the individual allocation structure to form a fused total fitness function. The fused total fitness function is then used to perform model fitness scoring and MLP prediction scoring on each individual.

[0052] Step S32.5: Directly copy the individuals with the highest fitness scores in the current population into the next generation population, and merge the offspring individuals generated through crossover and mutation to form the new generation complete population;

[0053] Step S32.6: When the maximum number of iterations is reached or the population fitness converges, the optimization process is terminated and the individual with the highest fitness score in the current population is output as the final firepower task allocation plan;

[0054] In step S32.4, the fusion fitness function F 总 :

[0055] F 总 =ω1·F 适应度 +ω2·F MLP ,ω1+ω2=1

[0056] Where: ω1, ω2 represent weighting parameters; F 适应度 represents the fitness scoring function based on the benefit term, resource consumption cost, and multi-level penalty term; F MLP Represents the prediction scoring function for the individual distribution structure.

[0057] On the other hand, the present invention also provides a firepower allocation system based on a double-layer decoupling and multi-level penalty genetic algorithm, the firepower allocation system comprising:

[0058] A first-level decoupling modeling module is used to construct a first-level decoupling model of firepower tasks based on the threat relationship and spatial distribution characteristics between the attacking platform and the target platform. The first-level decoupling model includes a threat matrix and firepower allocation membership, which is used to characterize the target's counter-attack capability against the attacking platform and the platform's strike intent against the target.

[0059] A secondary optimization modeling module is used to construct a secondary optimization model for firepower task allocation based on the objective function. The secondary optimization model integrates hard and soft constraints, adopts a multi-level penalty mechanism and an adaptive penalty factor to adjust the degree of constraint violation, and is used to characterize multiple optimization indicators such as mission strike effectiveness, firepower balance, and target priority;

[0060] An intelligent optimization solution module is used to call the MLP-GA optimization method constructed by integrating the multi-layer perceptron and the genetic algorithm to iteratively solve the secondary optimization model. The intelligent optimization solution module includes:

[0061] Initial population generation submodule: used to construct multiple firepower task allocation initial solution individuals that meet hard constraints according to task scale;

[0062] Genetic evolution submodule: used to perform operations such as crossover, mutation, and constraint detection on the population;

[0063] Fitness fusion evaluation submodule: used to jointly calculate the model fitness score and the MLP network prediction score, construct the fusion fitness function and perform iterative screening;

[0064] Optimal solution output submodule: used to output the optimal fitness individual after meeting the convergence conditions as the final firepower task allocation plan.

[0065] The beneficial effects of the present invention are:

[0066] First, the present invention's firepower allocation method, based on a dual-layer decoupling and multi-level penalty genetic algorithm, structurally decomposes the threat assessment and firepower decision-making processes between attacking and target platforms in the firepower allocation problem by constructing a "first-level decoupling + second-level optimization" model. This effectively mitigates the strong coupling between mission paths and firepower configuration in traditional WTA models. The first-level model utilizes a threat matrix and spatial distribution characteristics to quantitatively describe target threat levels, providing accurate input for second-level decision-making. This results in a logically clear and responsive dynamic firepower allocation mechanism, enhancing the system's practicality and real-time performance in complex battlefield situations. A strategy for integrating soft and hard constraints is introduced into the second-level optimization model, hierarchically regulating model constraints through a multi-level penalty mechanism and adaptive penalty factors. This not only improves the model's compatibility with complex tactical requirements such as weapon payload, strike time window, and attack priority, but also effectively avoids the inadequate handling of infeasible solutions by traditional intelligent algorithms, ensuring the tactical feasibility of the optimization results and the rationality of resource allocation. The multi-layer perceptron (MLP) is introduced to assist in initialization and fitness evaluation, and combined with the global search characteristics of the genetic algorithm (GA), the learning and judgment capabilities of local structural information are enhanced while maintaining the global search capability. The MLP-GA optimization mechanism improves the problem of premature algorithm and falling into local optimality, accelerates the convergence speed in complex search spaces, and improves the solution quality and computational stability of the model. In response to multi-source heterogeneous environments such as dynamic threats, complex electromagnetic interference, terrain constraints and deception tactics in modern naval warfare, the present invention constructs a dynamic adaptation model based on threat level and spatial layout, and introduces a robustness enhancement strategy in the optimization process, so that the proposed method has good environmental adaptability and anti-interference ability. The method has good scalability and computability, and can be widely used in the optimal allocation of firepower resources in many-to-many and high-density combat scenarios. It supports high-dimensional decision spaces composed of large-scale platforms, targets and multiple types of ammunition, and provides efficient and intelligent decision support for complex joint combat missions.

[0067] Second, in a preferred implementation, the present invention improves the geometric representation and allocation accuracy of target threat levels by introducing a firepower allocation strategy based on two-dimensional coordinate system transformation and regional subdivision. It employs a two-layer decoupled modeling approach based on the relative range between the attacking and target platforms, the threat matrix, and the firepower membership factor. This model can meticulously depict the physical distance and defense capability differences between platforms, enhancing the modeling's real-world fit. During the firepower allocation phase, by constructing a firepower allocation coordinate system and performing dynamic coordinate transformation, the firepower resource distribution mapping in the new coordinate space is made more directional and hierarchical, helping to improve the clarity of attack priority sorting. Furthermore, this method introduces a piecewise membership function based on a power exponential function to finely model the firepower coverage interval, effectively enhancing the ability to identify target platform distance sensitivity, thereby achieving the coordinated optimization of firepower strike effectiveness and allocation fairness while meeting tactical constraints.

[0068] Third, in a preferred implementation, the present invention enhances the firepower allocation model's compatibility with resource benefit maximization and mission risk constraints by constructing a comprehensive fitness function that integrates benefit evaluation with multi-level penalty factors. This constructed objective function not only comprehensively considers the threat matching between the attacking and target platforms, the weight of firepower resource consumption, and the strike benefit, but also introduces three types of progressively increasing penalty mechanisms, implementing differentiated penalty controls for unmet strike priorities, payload constraints, and mission completion requirements, thereby achieving unified modeling and dynamic regulation of soft and hard constraints. Furthermore, by employing an exponential, nonlinear, dynamic penalty factor function, the model is given the ability to flexibly adjust penalty intensity, which not only speeds up optimization convergence, but also avoids falling into local optima and improves global search stability. Furthermore, through the hierarchical evaluation of the mission objective function, this method effectively identifies resource allocation priorities and balances conflicts between multi-objective tasks.

[0069] Fourth, in a preferred implementation, the present invention achieves rapid initialization and high-quality solution generation for complex firepower task matrices by constructing a hierarchical, iterative mechanism for generating and evolving feasible solution populations. This method employs matrix splitting to construct a task allocation matrix, combining task progress boundaries with platform loading capacity to form a multidimensional task-platform matching constraint space, ensuring that each feasible solution possesses engineering feasibility. A hierarchical, boundary-constrained approach to generating feasible solutions is introduced during the population initialization phase, expanding the coverage of the solution space and enhancing the diversity and convergence guidance capabilities of the optimization algorithm in the early search phase.

[0070] Fifth, the firepower allocation system based on a dual-layer decoupling and multi-level penalty genetic algorithm, provided by the present invention, adopts a modular design with a clear overall architecture and efficient functional collaboration. The first-level decoupling modeling module achieves structured abstraction of battlespace information and threat relationships, enhancing the model's ability to analyze and express complex battlefield factors. The second-level optimization modeling module integrates multiple tactical constraints and multi-objective evaluation indicators, introducing a multi-level penalty and adaptive adjustment mechanism, enhancing the system's optimization compatibility and control flexibility under multi-constraint conflict conditions. The system's intelligent optimization solution module, by integrating a multi-layer perceptron and a genetic algorithm, combines heuristic search with data-driven prediction methods, effectively improving the model's efficiency in solving complex firepower tasks and the global quality of the solution. Its evolutionary strategy, combining adaptive population construction, constraint manipulation, and a fusion scoring mechanism, not only improves the algorithm's ability to identify infeasible solutions but also enhances its robust retention of high-quality solutions. The overall system boasts high intelligence, excellent real-time performance, and strong operational adaptability, providing a scientific, efficient, and reconfigurable solution for firepower resource allocation in a wide range of complex combat scenarios. BRIEF DESCRIPTION OF THE DRAWINGS

[0071] Figure 1 The figure is an overall flow chart of the firepower allocation method based on double-layer decoupling and multi-level penalty genetic algorithm of the present invention;

[0072] Figure 2 This is a logical structure relationship diagram of the firepower allocation method based on double-layer decoupling and multi-level penalty genetic algorithm of the present invention;

[0073] Figure 3 A schematic diagram of the new coordinate system conversion in the firepower allocation method based on double-layer decoupling and multi-level penalty genetic algorithm of the present invention;

[0074] Figure 4 A schematic diagram of firepower allocation area division in the firepower allocation method based on double-layer decoupling and multi-level penalty genetic algorithm of the present invention;

[0075] Figure 5 This is a flow chart of the MLP-GA algorithm in the firepower allocation method based on double-layer decoupling and multi-level penalty genetic algorithm of the present invention;

[0076] Figure 6 Schematic diagram of a two-point crossover operation in the firepower allocation method based on a double-layer decoupling and multi-level penalty genetic algorithm of the present invention;

[0077] Figure 7 This is a schematic diagram of firepower allocation area division in a 10-on-10 combat scenario in Example 1 of the present invention;

[0078] Figure 8This is a diagram showing the calculation results of the threat matrix of each target platform against each attack platform in a 10-on-10 combat scenario in Example 1 of the present invention;

[0079] Figure 9 This is a comparison chart of the fitness values ​​and fitness standard deviations of seven algorithms in a 10-on-10 combat scenario in Example 1 of the present invention;

[0080] Figure 10 This is a radar chart comparison of seven algorithms in a 10-on-10 combat scenario in Example 1 of the present invention;

[0081] Figure 11 This is a comparison chart of the fitness values ​​and fitness standard deviations of seven algorithms in a 20-on-20 combat scenario in Example 2 of the present invention;

[0082] Figure 12 This is a radar chart comparison of seven algorithms in a 20-on-20 combat scenario in Example 2 of the present invention;

[0083] Figure 13 This is a comparison chart of the fitness values ​​and fitness standard deviations of seven algorithms in a 50-on-50 combat scenario in Example 2 of the present invention;

[0084] Figure 14 This is a radar chart comparison of seven algorithms in a 50-on-50 combat scenario in Example 2 of the present invention. DETAILED DESCRIPTION

[0085] In order to enable those skilled in the art to better understand the technical solution of the present application, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments.

[0086] The terms "up", "down", "left", "right", "front", and "back" in this application are based on the positional relationships shown in the accompanying drawings. The corresponding positional relationships may vary depending on the drawings, and should not be construed as limiting the scope of protection.

[0087] In this application, the terms "installed," "connected," "connected," "connected," "fixed," etc. should be understood in a broad sense. For example, they can refer to fixed connection, detachable connection, integral connection, mechanical connection, electrical connection, or mutual communication. They can also be directly connected or indirectly connected through an intermediate medium. They can also refer to internal communication between two components or interaction between two components. For those skilled in the art, the specific meanings of the above terms in this application can be understood according to specific circumstances.

[0088] This paper describes a firepower allocation method and system based on a double-layer decoupling and multi-level penalty genetic algorithm. This method cleverly decouples anti-ship missile mission planning into two relatively independent stages: firepower allocation and coordinated route planning, by setting an estimated range and constructing a firepower allocation membership. In the firepower allocation stage, a firepower allocation model that comprehensively considers multiple factors is constructed and accurately solved using a genetic algorithm (MLP-GA) based on a multi-level penalty mechanism. In the route planning stage, the firepower allocation results are fully utilized to reduce planning complexity and achieve efficient mission planning.

[0089] As the instruction manual Figure 1-2 ,The firepower allocation method based on double-layer decoupling and multi-level penalty genetic algorithm, the specific steps are as follows:

[0090] Step S1: Based on the threat relationship and spatial distribution characteristics between the attack platform and the target platform, a first-level decoupling model of firepower allocation is constructed, which includes a threat matrix and firepower allocation membership.

[0091] The purpose of step S1 is to establish a unified threat perception and assessment framework for fire strike missions. By constructing a first-level firepower allocation model, it provides quantitative support for subsequent mission scheduling, resource optimization, and attack decision-making. In combat decision-making, firepower resources are limited and target platforms are variable. Therefore, a model that comprehensively considers multiple factors such as distance, weapon performance, and target defense capabilities is urgently needed to quantify the strike effect and threat level of different attack platforms on the target, thereby achieving scientific and reasonable initial allocation.

[0092] In step S1, the core structure of the model is implemented by establishing the following sub-steps. Step S1 specifically includes:

[0093] Step S11: Calculate the threat matrix between the attacking platform and the target platform to quantify the threat level of each attacking platform to each target platform.

[0094] This sub-step builds a threat matrix based on the spatial relationship and operational parameters between the attacking and target platforms. It includes the following three steps:

[0095] Step S11.1: Calculate the estimated range distance from each attack platform to each target platform.

[0096] In a combat mission, our side dispatches n attack platforms and k types of missiles, while the target side has m target platforms. The coordinates of the attack platforms can be obtained based on the existing inertial navigation system (INS) and global positioning system (GPS) fusion positioning technology. For example, our ships are usually equipped with Beidou / GPS receivers and inertial measurement units, which can determine their positions in real time on the battlefield situation map (x i ,y iThe coordinates of the target platform are obtained by our sensor system. For example, the shipborne radar measures the azimuth and distance of the target and converts it into the two-dimensional coordinates of the target based on our known position. In addition, electronic reconnaissance and satellite remote sensing and other comprehensive detection methods are used, as well as multi-source sensor information through data fusion algorithms (such as Kalman filtering and multi-sensor joint positioning) to generate the current coordinate estimate of the enemy ship (x j ,y j ). According to the spatial coordinates of the attack platform (x i ,y i ) and the spatial coordinates of the target platform (x j ,y j ), and the Euclidean distance model is used to calculate the expected flight distance d ij , d ij The value represents the path distance required for the platform to launch a missile to the target. It is a key parameter for the subsequent evaluation of the weapon's strike possibility and success probability and is determined by the following formula:

[0097]

[0098] Where: d ij represents the straight-line distance (predicted range) between the i-th attack platform and the j-th target platform; i represents the number index of the attack platform (e.g., missile boat, carrier-based aircraft, shore-based launch system, etc.), and the value range is i = 1, 2, ..., m; j represents the number index of the target platform (e.g., enemy ship, landing craft, command center, etc.), and the value range is j = 1, 2, ..., n; x i 、y i represents the two-dimensional coordinate position of the i-th attack platform; x j 、y j Represents the two-dimensional coordinate position of the j-th target platform.

[0099] It should be noted that this model is applied to typical maritime combat scenarios, primarily involving offensive and defensive engagements between surface ships. In such missions, the various platforms involved (such as destroyers, frigates, and landing ships) are essentially on the same horizontal plane, with minimal or negligible vertical variations. The target platforms of the fire distribution model are primarily enemy surface vessels, and the primary means of attack are anti-ship missiles. The flight pattern of anti-ship missiles dictates that altitude is unnecessary. During their mid- and terminal flight phases, anti-ship missiles typically fly sea-skimming, typically at altitudes between 5 and 15 meters. This extremely low trajectory enhances radar concealment and penetration capabilities. Given target ranges often exceeding tens or even hundreds of kilometers, vertical variations of a few meters contribute minimally to the overall Euclidean distance calculation. Therefore, the z-axis can be ignored in the modeling and threat assessment process, and the two-dimensional Euclidean distance calculation method meets operational accuracy requirements.

[0100] Step S11.2: Based on the estimated range, calculate the threat factor of each target platform relative to each attack platform.

[0101] Based on formula (1), a comprehensive threat factor model t is established based on key indicators such as the target platform's defense capability and weapon penetration performance. ij :

[0102]

[0103] Where: t ij represents the comprehensive threat index of attack platform i to target platform j. The larger the value, the higher the threat level. ω1 and ω2 represent weight coefficients, which are used to balance the weights of distance factor and performance factor in the threat level, satisfying ω1+ω2=1. ij_target represents the distance between attack platform i and target platform j, corresponding to the calculation result in formula (1); d ij_max v represents the maximum range of the weapon system of attack platform i on target platform j; j_target represents the protection capability value of the target platform j (such as armor strength, interference capability, maneuverability and other comprehensive indicators); v j_max Indicates the maximum reference value of protection capability; The closer the attack platform is to the target, the higher the threat level of the attack. ij_target =0, the threat level is the highest; The higher the protection capability of the target platform, the lower the corresponding threat level.

[0104] It should be noted that d ij_max It is usually set based on the maximum possible engagement distance between the attacking platform and the target platform in the combat mission scenario, such as the maximum detection distance of radar, the maximum range of missiles, or the maximum range of drones; or based on empirical values ​​or combat exercise data, such as the maximum contact distance between platforms in previous exercises and combat simulations; and using battlefield simulation systems (such as STK and MATLAB simulation) to evaluate the maximum possible distance between all platforms. j_target The method of obtaining the value can be based on the performance evaluation of the target platform's weapon system and protection system, such as the target platform's passive protection (such as armor and stealth), active protection (such as interception systems and electronic countermeasures equipment), and maneuverability and evasion capabilities. Alternatively, platform performance data can be retrieved from defense and aerospace databases, or extracted from public papers and technical specifications. Alternatively, military experts can score the target platform based on the mission scenario, such as a 1-10 score system, and then normalize it. Alternatively, modeling tools (such as Arena, AnyLogic, and STK) can be used to evaluate the target platform's survivability probability and convert it into a protection capability value. j_maxThe acquisition of v can be achieved by collecting the protection performance indicators of all attack platforms (such as stealth capability, anti-interference capability, maneuverability and avoidance capability, etc.), and selecting the largest one as v through weighted comprehensive scoring. j_max Or, by establishing a protection capability scoring model, normalizing the scores of each indicator and taking the maximum value as v j_max , for example: v j_max =α1·Indicator 1 (Radar Cross Section RCS) + α2·Indicator 2 (Anti-interference performance) + α2·Indicator 3 (Maneuverability score)... (α1, α2, α2... represent the weights of the corresponding indicators in the protection capability); if the platform information is incomplete, a constant (such as 100) can be set using the theoretical value or standard model.

[0105] Formula (2) achieves a quantitative assessment of strike effectiveness by introducing two key factors: attack range and target defense capability. This model takes into account both combat geometry and platform performance factors, providing support for the prioritization and scheduling of firepower resources.

[0106] Step S11.3: Summarize all threat factors to construct a two-dimensional threat matrix to characterize the threat relationship between the attack platform and the target platform.

[0107] Threat Matrix:

[0108]

[0109] Among them, each element t ij Represents the comprehensive threat degree of attack platform i to target platform j; the matrix dimension is m×n.

[0110] By establishing a threat matrix, we can intuitively and systematically reflect who poses a threat to whom and to what extent, achieve comprehensive "many-to-many" modeling, clarify threat relationships, assist in target protection / strike priorities, and provide a clear basis for subsequent decision-making analysis, combat deployment, resource allocation, etc.

[0111] Step S12: Based on the spatial distribution relationship between the attack platform and the target platform, a firepower allocation coordinate system is constructed and the firepower allocation area is divided to calculate the firepower allocation membership of each target platform to each attack platform.

[0112] Firepower allocation subordination is an indicator that measures the adaptability or effectiveness of an attack platform against a target platform. It is used to quantify the spatial "rationality" and "attack compatibility" of firepower resources. A higher firepower allocation subordination indicates that the attack platform is more suitable for striking the target platform and has a higher priority.

[0113] Step S12.1: Calculate the mean coordinates of each attack platform and each target platform, and obtain the center coordinates of the attack platform group and the target platform group respectively.

[0114] The calculation formula for the center coordinates of the attack platform is as follows:

[0115]

[0116] Where: Indicates the coordinates of the center point (geometric center) of the attack platform group; represents the geometric center coordinates of all attack platforms, that is, the center point of the attack platform group; i represents the index variable used to traverse all attack platforms, with a value range of i=1,2,...,n; x i 、y i represents the coordinate component of the i-th attack platform in two-dimensional space, where x i Indicates the horizontal coordinate of the i-th attack platform, y i represents the vertical coordinate of the i-th attack platform; n represents the total number of all attack platforms.

[0117] The geometric center (center of mass) coordinates of the attack platform group are calculated by formula (3) in order to divide the battle zone and guide direction planning in firepower distribution.

[0118] Corresponding to the attacking platform, the geometric center of the target platform group is used for fire strike sector planning, matching strategy and central axis distribution analysis. The formula for calculating the center coordinates of the target platform is as follows:

[0119]

[0120] Where: Indicates the coordinates of the center point of the target platform; Represents the geometric center coordinates of all target platforms; j represents the index variable used to traverse all target platforms, with a value range of j = 1, 2, ..., m; x j 、y j Represents the two-dimensional coordinates of the j-th target platform, where x j Indicates the horizontal coordinate of the j-th target platform, y j represents the ordinate of the jth target platform; m represents the total number of all target platforms.

[0121] Step S12.2: Take the center coordinate of the attack platform as the origin, connect the direction of the center coordinate of the target platform and the center coordinate of the attack platform as the initial x-axis, and rotate the x-axis 90 degrees counterclockwise to construct a fire distribution coordinate system. Define the unit vectors of the x-axis and y-axis in the fire distribution coordinate system, and based on the unit vectors, translate the original two-dimensional coordinates of each attack platform and target platform into the fire distribution coordinate system to obtain the new coordinates of the attack platform and target platform in the fire distribution coordinate system.

[0122] First, establish the firepower distribution coordinate system and define the direction basis of the firepower distribution coordinate system. Figure 2 , Figure 2 The red dots in the middle represent multiple attack platforms, and the blue dots represent multiple target platforms. is the geometric center of all attack platform groups, is the geometric center of all target platform groups. As an endpoint in the firepower distribution coordinate system, As another endpoint in the fire distribution coordinate system, the platform center of the target platform Attack Platform Center The connection, serving as the x-axis of the firepower allocation coordinate, effectively reflects the "primary attack direction" of the current combat operation, i.e., the direction of alignment. All firepower platforms and target platforms can be uniformly projected, compared, and allocated within this coordinate system. Rotating the x-axis counterclockwise by 90° creates a new y-axis, forming an orthogonal coordinate system, the firepower allocation coordinate system.

[0123] Through coordinate system transformation, the firepower distribution problem is converted into a structural modeling method of "advancing along the attack direction (x-axis) and distributing along the flank (y-axis)", thereby improving the uniformity of the attack, regional control capabilities and algorithm feasibility.

[0124] Secondly, the x-axis and y-axis direction vectors are normalized to form a standard rectangular coordinate system. After the new coordinate system is established, in order to perform subsequent coordinate transformations of the target point and the attack platform (especially projection calculations), a clear and standard coordinate axis direction must be defined first. In the newly constructed rectangular coordinate system, the direction basis of the firepower distribution coordinate system is established according to formulas (3) and (4). Specifically, the difference vector between the center coordinates of the target platform and the center coordinates of the attack platform is defined as the new x-axis direction, and the vector is normalized to obtain a unit x-axis direction vector. Subsequently, the unit x-axis vector is rotated 90 degrees counterclockwise to obtain a new y-axis direction vector. It should be noted that these two unit vectors only represent directional attributes and do not contain length scales. The unit vectors in the x-axis and y-axis directions in the coordinate system are calculated separately to describe their respective directional information:

[0125]

[0126] In formula (5), Indicates the assist direction of the attack platform; Right now The new x-axis direction represents the direction from the center of the attack platform group Point to the target platform group center The direction vector of . In formula (6), Indicates the direction of flank expansion; Right now The new y-axis direction indicates that The vector after rotating 90 degrees counterclockwise. In formulas (5) and (6), Represents the length of the original direction vector, which is used for normalization to ensure that both direction vectors are unit vectors.

[0127] Finally, coordinate transformation, vector translation + projection, is performed. The original coordinates of each attack platform and target platform are uniformly translated into a firepower allocation coordinate system with the center of the attack platform as the new origin. Vector projections are then performed based on the newly constructed x-axis and y-axis vectors. Using the vector dot product method, the new coordinates of each platform in the firepower allocation coordinate system are accurately calculated.

[0128] The new coordinates of each attack platform in the firepower allocation coordinate system are:

[0129]

[0130] In formulas (7) and (8), Represents the projection value of the attack platform along the main attack direction (x-axis) in the new coordinate system; represents the projection value of the attack platform along the wing direction (y axis) in the new coordinate system; i represents the horizontal coordinate of the i-th attack platform in the original coordinate system; y i represents the ordinate of the i-th attack platform in the original coordinate system; Represents the value of the geometric center of all attack platforms on the horizontal axis (refer to Formula 3); Represents the value of the geometric center of all attack platforms on the vertical axis (refer to Formula 3); Represents the coordinate difference vector of the i-th attack platform relative to the center of the attack platform group, which can also be called the position offset vector or relative position vector; The unit vector representing the main attack direction (x-axis direction) in the new coordinate system for firepower distribution (refer to Formula 5); Represents the unit vector in the flank direction (y-axis direction) in the new fire distribution coordinate system (see Formula 6).

[0131] The new coordinates of each target platform in the firepower distribution coordinate system are:

[0132]

[0133] In formulas (9) and (10), represents the new coordinates of the j-th target platform in the firepower allocation coordinate system; x j 、y j represents the two-dimensional coordinates of the j-th target platform in the original global coordinate system; Represents the center coordinates of the attack platform group, which is defined as the origin of the firepower distribution coordinate system; The unit vector representing the main attack direction (x-axis direction) in the new coordinate system for firepower distribution (refer to Formula 5); Represents the unit vector in the flank direction (y-axis direction) in the new fire distribution coordinate system (see Formula 6).

[0134] Step S12.3: In the firepower distribution coordinate system, construct a set of dividing lines parallel to the x-axis, and divide the new coordinates of the target platform in the y-axis direction based on the dividing lines to form multiple firepower distribution areas, and determine the firepower distribution area under the jurisdiction of each attack platform based on the mapping relationship between the attack platform and the firepower distribution area.

[0135] After establishing the firepower allocation reference coordinate system and converting the attack and target platform coordinates, considering that this application involves firepower allocation within a decoupled mission plan, avoiding route intersections is crucial for ensuring the safety and efficiency of subsequent route planning. Furthermore, reducing the computational complexity of firepower allocation membership is essential for shortening solution time. To address these challenges, the firepower allocation area must be divided to determine the firepower allocation range for each platform.

[0136] The firepower distribution coordinate system includes the entire firepower distribution area. The range of the entire firepower distribution area refers to the maximum interval covered by the projection coordinates of all attack platforms and all target platforms in the y-axis direction in the firepower distribution coordinate system.

[0137] Use a set of dividing lines L parallel to the x-axis k (k=i-1) Divide the entire firepower distribution area into several areas Z k+1 The number of dividing lines is determined by the number of attack platforms, and the position of each dividing line is determined by calculating the weighted average ordinate of two adjacent attack platforms along the y-axis:

[0138]

[0139] Where: β i ∈[0,1], represents the weight coefficient of a platform on the i-th attack platform in the position determination, Among them S i is the number of weapons / firepower intensity of the i-th attack platform, S i-1 is the number of weapons / firepower intensity of the i-1th attack platform; represents the coordinate of the i-1th attack platform in the y-axis direction in the firepower allocation coordinate system; represents the coordinate of the ith attack platform in the y-axis direction in the firepower distribution coordinate system; (1-β i )Right now Represents the weight coefficient of the current i-th attack platform in position determination.

[0140] β iIt is determined based on the weapon inventory loaded on the attack platform and is used to adjust the influence of two adjacent attack platforms on the position of the dividing line. The larger the inventory of the attack platform, the greater the β i The smaller it is, the farther the dividing line is from the attack platform, and the larger the firepower distribution area to which the attack platform belongs.

[0141] Each firepower allocation sub-area is Z k ∈(L k ,L k-1 ), satisfying L k-1 >L k The increasing relationship is from top to bottom along the y-axis. k Belongs to the two sides of the area, that is, belongs to Z k and Z k+1 The common boundary of each fire distribution sub-area can represent the "lateral attack coverage section of the attack platform during the main attack direction advancement process". k In the , ensure that there is at least one area with a width (i.e. vertical length) equal to the maximum width value as a reference for the boundary limit.

[0142] The width constraint of the fire distribution area is determined by the following formula:

[0143] L0-L1=L k -L k-1 =max(L k -L k+1 ) (10)

[0144] Where: L0 represents the topmost dividing line position, corresponding to the upper boundary of the first firepower distribution area Z1; L1 represents the second dividing line position, corresponding to the lower boundary of Z1 or the upper boundary of Z2; L k L represents the longitudinal coordinate of the kth dividing line, corresponding to the upper or lower boundary of a certain firepower area; k-1 Indicates that L k The adjacent previous dividing line constitutes area Z k ∈(L k ,L k-1 );(L k -L k+1 ) represents the longitudinal height (width) of the k+1th firepower area, indicating the coverage of the firepower allocation sub-area in the y-axis direction; max(·) means taking the maximum value of all area widths.

[0145] As the instruction manual Figure 3 , Figure 3This is a diagram of the firepower distribution area division. The figure is based on the firepower distribution coordinate system constructed with the center of the attack platform as the origin. A set of dividing lines (dashed lines) L1-L4 parallel to the attack direction (x-axis) divides the target area into multiple longitudinal firepower distribution sub-areas Z2, Z3, and Z4. The position of the dividing lines is calculated based on the longitudinal weighted average coordinates of adjacent attack platforms, and the weight β is determined based on their weapon resources. i In the figure, the white triangles represent attack platforms (A, B, C), the black inverted triangle represents the target platform (D), and the gray blocks are the various firepower sub-regions. The target platform belongs to a specific region based on its projected position in the new coordinate system, which is used for subsequent firepower affiliation allocation and resource scheduling.

[0146] After dividing the firepower distribution area, the firepower distribution area under the jurisdiction of each platform is clarified, and the basic basis for firepower distribution is constructed. However, allocating all target platforms to the attack platform corresponding to their firepower distribution area may not be the best effect. Therefore, it is necessary to provide a more direct basis for firepower distribution, that is, to calculate the firepower distribution affiliation of each target platform to each attack platform.

[0147] Step S12.4: Based on the position of the target platform in the firepower allocation coordinate system and the firepower allocation area to which it belongs, a fuzzy membership function is used to calculate the firepower allocation membership of each target platform to different attack platforms to optimize the matching of firepower resources.

[0148] The purpose of calculating the firepower allocation membership in this step is to measure the "adaptability" or "allocation priority" of a target platform to the attack platform in the adjacent firepower allocation area, which is used for the subsequent weight decision of firepower allocation resources.

[0149] Assume that the current target platform j is located in the fire distribution area Z k Inside, that is, Then we need to calculate the Z of the area k and its two adjacent regions Z k-1 and Z k+1 The firepower adaptability of the attack platform is given by the three-stage membership function, which gives the membership degree of the target platform in each direction.

[0150] The firepower distribution membership is determined by the following formula:

[0151]

[0152] Where: represents the firepower subordination of target platform j to attack platform i; represents the Y-axis coordinate of target platform j in the firepower allocation coordinate system; represents the Y-axis coordinate of attack platform i in the firepower allocation coordinate system; L k , Lk-1 Indicates the coordinates of the dividing line between adjacent fire areas (vertical); i = k-1, k, k+1 represent the coordinates of Z k-1 、Z k 、Z k+1 The index of the attack platform in the region corresponds to the target; exp(·) represents the exponential function, which is used to construct a nonlinear weight distribution mechanism so that the targets far away from the region boundary have lower contributions; Indicates the target platform's membership to the attack platform in the previous partition; Indicates the target platform to L k The longitudinal distance of the dividing line boundary; Indicates attack platform i to L k The longitudinal distance of the dividing line boundary; Indicates the target platform's degree of affiliation to the attack platform in the current area; Indicates the y coordinate of the target platform j and the current area Z k The average distance between the upper and lower boundaries of |L k-1 -L k | indicates the current firepower allocation area Z k The vertical height of Indicates the target platform's membership to the next partition attack platform; Indicates the target platform j to the previous dividing line L k-1 The longitudinal distance of the boundary; Indicates the distance between attack platform i and the dividing line L in the firepower distribution coordinate system k-1 The vertical distance of the border.

[0153] from It can be seen that The index value is large, This indicates that the target platform has a low degree of subordination to the attacking platform's firepower allocation; on the contrary, This indicates that the target platform has a high degree of subordination to the attacking platform’s firepower allocation. It can be seen that This means that the target platform has a low degree of subordination to the attacking platform’s firepower allocation; conversely, the target platform has a high degree of subordination to the attacking platform’s firepower allocation. It can be seen that The index value is large, This indicates that the target platform has a low degree of subordination to the attacking platform in terms of firepower allocation; conversely, the target platform has a high degree of subordination to the attacking platform in terms of firepower allocation.

[0154] Through the three-segment function of formula (11) Calculate and compare these three values ​​to find the largest one, which means which area's attack platform is most suitable for attacking target platform k, and then assign the target platform j to the area with the largest membership value. > a certain threshold (e.g. 0.6), it is classified as a joint strike by multiple regions, which can be applied to the “fuzzy attribution” or coordinated strike strategy.

[0155] By constructing the threat matrix in step S11 and the firepower allocation membership in step S12, a first-level decoupled model for firepower allocation is constructed. The threat matrix focuses on mission rationality, determining attack worthiness and priority targets; while the firepower allocation membership focuses on spatial geometric adaptability, measuring the spatial fit of the attacking platform and determining attack targets. However, within the overall firepower allocation model, they serve the same goal: providing multi-dimensional support for attack decision-making.

[0156] Step S2: Construct a two-level optimization model for firepower allocation oriented to the objective function, integrating hard constraints and soft constraints, multi-level penalty mechanism, adaptive penalty factor and fitness function.

[0157] The purpose of step S2 is to further introduce battlefield tactical objectives and resource constraints based on the first-level decoupling model to establish a practical firepower allocation optimization model. Its key tasks are: optimizing firepower resources under the guidance of objective functions (such as maximizing combat effectiveness and minimizing costs); addressing multiple constraints to ensure that the allocation solution is executable within the capabilities of weapon resources; and guiding the optimization algorithm to a feasible solution within the search space through a soft constraint penalty mechanism, thereby improving computational efficiency and convergence.

[0158] Specifically, step S2 includes:

[0159] Step S21: Determine the objective function based on the combat purpose, and determine the fitness function corresponding to the objective function.

[0160] Fitness function = objective function ± penalty term

[0161] The objective function determines the direction of optimization, and the fitness function is used to quantify the pros and cons of individual solutions. It needs to be flexibly set in combination with the mission scenario. Operational objectives include, but are not limited to, pursuing maximum damage effect, prioritizing cost reduction, and striking key targets. For example, when pursuing maximum damage effect, the objective function is directed towards maximizing the probability of complete target destruction, and the fitness function focuses on the missile kill probability and the number of strikes; when prioritizing cost reduction, the objective function is directed towards minimizing the cost of weapon use, and the fitness function focuses on the unit price of ammunition and weapon consumption; when the goal is to strike key targets, the objective function is directed towards increasing the strike ratio of high-value targets, and the fitness function focuses on adjusting the weight coefficient.

[0162] Without considering the cost priority, maximize the overall killing probability or damage effectiveness. The fitness function for pursuing the maximum damage effect is:

[0163] Fitness function 1 = objective function 1 - λ1 · penalty term 1 = ∑ j t ij ·q j α ij -λ1·Penalty term 1(12)

[0164] Where: t ij represents the comprehensive threat index of attack platform i to target platform j; q j =w j ·P j represents the probability of complete destruction of the jth target platform, w j represents the value weight of target platform j, P j represents the probability of target platform j being destroyed; α ij Indicates whether the i-th attack platform attacks the j-th target platform (0 or 1, 0 means no attack assignment, 1 means weapon assignment); λ1 represents the penalty factor; penalty term 1 represents the weighted sum of the degree of constraint violation.

[0165] The optimization goal of the fitness function that pursues the maximum damage effect is that the larger the objective function value, the better, and the smaller the penalty, the better.

[0166] Under the constraints of the firepower strike mission, the cost of the weapon resources used should be minimized. The fitness function that prioritizes cost reduction is:

[0167] Fitness function 3 = - objective function 2 - λ2 Penalty term 2 = -∑ i c i ·x ij -λ2·Penalty term 2(13)

[0168] Where: c i represents the unit cost of the i-th attack platform; x ij represents the number of attacks executed by the i-th attack platform on the target platform j; λ2 represents the penalty factor; and the penalty term 2 represents the weighted sum of the degree of constraint violation.

[0169] Formula (13) uses a negative sign to transform the "minimum cost" problem into a "maximum negative benefit" form. The penalty term is used to limit violations of soft / hard constraints (such as excessive weapon inventory, mismatched membership, etc.).

[0170] Targets are prioritized according to their tactical value weights, with high-value targets being hit first. The fitness function for hitting key targets is:

[0171]

[0172] Where: t ij It represents the comprehensive threat index of attack platform i to target platform j; represents the firepower affiliation of target platform j to attack platform i; α ij Indicates whether the i-th attack platform attacks the j-th target platform (0 or 1, 0 means no attack assignment, 1 means weapon assignment); λ3 represents the penalty factor; penalty term 3 represents the weighted sum of the degree of constraint violation.

[0173] It should be noted that if Even if α ij = 1, the weapons cannot be effectively attacked and are considered invalid attacks. Therefore, whether allocation is allowed is controlled by hard constraints. Then α ij =0.

[0174] Step S22: By differentiating the constraints in the firepower allocation process into hard constraints and soft constraints, a multi-level penalty mechanism and an adaptive penalty factor are introduced for the soft constraints.

[0175] It's important to note that in complex combinatorial problems like firepower allocation and multi-objective optimization, constraints are often categorized as hard constraints and soft constraints. Hard constraints are rigid restrictions that must always be satisfied; any violation will result in the solution being deemed infeasible. Soft constraints are constraints that can be temporarily violated during the solution process. Violation does not invalidate the solution, but it will affect its quality (the objective function value).

[0176] The comparison of hard constraints and soft constraints is shown in Table 1:

[0177] Table 1

[0178]

[0179]

[0180] Therefore, the treatment of soft constraints is to improve the comprehensive benefits of allocation while satisfying the feasible solution.

[0181] In the firepower allocation problem, hard constraints must always be satisfied; violations result in an infeasible solution. The hard constraints include the number of missiles launched by the i-th attack platform at the j-th target platform, the total missile inventory available to attack platform i, the inventory of type t missiles on attack platform i, missiles of type t, the number of missiles allocated to target platform j, and a non-zero firepower allocation membership. Therefore, hard constraints include, but are not limited to, the total number of missiles launched by each platform ≤ the platform's inventory; the number of missiles of a certain type used by each platform ≤ the inventory of that type of missile; each target must be struck by at least one missile and a maximum of two; and target combinations with a firepower allocation membership of 0 are not allowed to be allocated.

[0182] Soft constraints include, but are not limited to, firepower allocation affiliation: prioritizing missiles to targets with high compatibility; firepower distribution balance: ensuring that target platforms receive a balanced amount of firepower, avoiding overloading some and leaving others uncovered; and target priority requirements: prioritizing critical targets and allocating more attack resources. Violations of these constraints are reflected in the objective function through a "penalty function."

[0183] It's important to note that firepower allocation membership bridges the gap between mission feasibility and optimality, playing a dual role in the constraint model. In the hard constraint dimension, it ensures that "only capable targets are attacked," serving as a foundation; in the soft constraint dimension, it ensures that "suitable targets are attacked first," serving as an optimization. For example, in the hard constraint, only combinations with a firepower allocation membership greater than 0 are allowed. A hard constraint greater than 0 takes effect, while a value of 0 indicates that attack platform i cannot effectively attack target j. In the soft constraint, firepower allocation membership is between 0 and 1, and the soft constraint takes effect. However, if 0 < firepower allocation membership < a certain threshold (e.g., 0.4), the system penalizes such low-fitting attacks. A firepower allocation membership of 1 indicates a very good attack match.

[0184] Furthermore, in response to the priority requirements of soft constraints, a multi-level penalty mechanism is introduced, which is divided into three penalty levels according to the importance and violation degree of different constraints. The firepower allocation membership target of the soft constraint is defined as a high priority and used for the three-level penalty. Assuming the goal is to maximize the firepower matching degree, the ideal matching degree target value is 1, and the penalty term function is:

[0185]

[0186] Where: P1 represents the penalty term for violation of firepower allocation membership; x ij represents the number of missiles launched by the i-th attack platform at the j-th target platform; represents the firepower affiliation of target platform j to attack platform i, The greatest punishment.

[0187] The target priority of the soft constraint is defined as medium priority for level 2 penalty. Let each target platform j have a priority weight w j ∈[0,1], ideally, higher priority targets should be allocated more resources, and the penalty function is:

[0188]

[0189] Where: P2 represents the penalty term for deviation from the target priority; L j represents the number of missiles actually received by the jth target platform; w jrepresents the priority weight of the jth target platform (range [0,1]); α represents the normalization factor so that the expected attack volume is proportional to the priority; m represents the total number of target platforms.

[0190] The soft-constrained firepower allocation balance target is defined as medium priority, which is used for level 1 penalty. Assume that the number of attack platforms received by each target platform should be average. The firepower distribution balance penalty function is:

[0191]

[0192] Where: P3 represents the penalty term for firepower distribution balance; L j represents the number of missiles actually received by the jth target platform; represents the average distribution of missiles among all target platforms (ideal balance); m represents the total number of target platforms.

[0193] According to formulas (15)-(17), for individuals that slightly violate the firepower balance, a smaller penalty (level 1 penalty) is imposed, allowing the algorithm to explore the solution space within a certain range and find a better solution; for individuals that moderately violate the target priority, a moderate penalty (level 2 penalty) is imposed to prevent the solution from deviating too far from the feasible domain; for individuals that seriously violate the firepower allocation membership, a larger penalty (level 3 penalty) is imposed to directly eliminate solutions that significantly violate the constraints.

[0194] In order to improve the search adaptability of the firepower allocation optimization model at different stages, an adaptive penalty factor λ is designed, and its nonlinear growth function that changes with time is constructed. In the initial stage of the algorithm (such as genetic algorithm, particle swarm, etc.), the solution space has not yet converged. If the penalty is too strong, it is easy to cause local convergence in the early stage of the algorithm and limit the feasible solution space, thereby missing the potential global optimal area. Therefore, it is necessary to set the penalty factor to a lower value (such as 0.01-0.1) to encourage the algorithm to conduct extensive searches in a larger solution space, discover more potential feasible solutions, and enhance the global search capability of the algorithm. As the iteration proceeds, the penalty factor is gradually increased according to the convergence of the solution and the degree of constraint violation, guiding the algorithm to converge to a feasible solution space that satisfies the constraints and ultimately approaches the global optimal solution. In order to adapt to different optimization strategies from the initial search stage to the end of convergence, the penalty factor λ is set as a time-increasing function:

[0195]

[0196] Where: k0 represents the initial penalty factor of the k-th penalty term (small); λ kmaxrepresents the maximum penalty value of the k-th penalty item; t represents the current iteration number; T represents the maximum number of iterations; pk represents the exponent that controls the growth rate of the k-th penalty (such as p = 2 represents accelerated increase); k∈(1,2,3) represents the penalty items of 3 penalty levels.

[0197] Step S23: Based on the multi-level penalty mechanism and the adaptive penalty factor, a total fitness function is constructed that integrates the strike benefit, speed-distance adaptation, resource cost, and multi-level soft constraints.

[0198] Based on the penalty mechanism, the speed and distance factors are combined to form a firepower adaptation weight, taking into account their impact. The speed factor measures whether the target platform is within the attack platform's effective intercept capability in its current state, primarily reflecting the target's "hitability" and "struggle." The distance factor measures whether the target is within the attack platform's effective firepower range, primarily reflecting the physical limitations of "reachability" and "ability to hit."

[0199] Speed ​​factor f speed,j for:

[0200]

[0201] Distance factor f dist,ij for:

[0202]

[0203] Where: v target,j represents the actual speed of the jth target platform; v max represents the maximum attack speed of the jth target platform or the maximum interceptable speed of the target platform weapon system; d ij represents the actual distance between the i-th attack platform and the j-th target platform; d max represents the maximum threat distance between the i-th attack platform and the j-th target platform.

[0204] It should be noted that v target,j Through real-time battlefield situation systems (such as radar and satellite monitoring), or historical target behavior patterns + predictive modeling obtained from intelligence systems; max Determined by the weapon system design (such as the maximum tracking speed of the interceptor missile against the ballistic missile). For a combined platform, the upper limit of the minimum interceptable speed of the weapons currently equipped on the platform is used. ij The three-dimensional or two-dimensional geographic coordinates of the attacking platform and the target platform are as shown in formula (1); d max It is usually determined by the type of weapons such as missiles and artillery (e.g., the range of a cruise missile is 1,500 km). If the platform carries multiple weapons, the "shortest effective range of weapons available for this type of target" is used as a conservative estimate.

[0205] The combination is firepower adaptation weight M ij for:

[0206] M ij =f speed,j ·f dist,ij (twenty one)

[0207] Where M ij ∈[0,1], the closer the value is to 1, the more it means that it can both hit and stop. ij =0, it means that the current target platform i cannot effectively attack the attack platform j (the speed is too fast or the distance is too far).

[0208] At the same time, combined with formulas (12)-(21), the total objective function is used as the total fitness function to evaluate the pros and cons of each candidate solution (i.e., firepower allocation scheme) in the heuristic algorithm (such as genetic algorithm, particle swarm optimization, ant colony algorithm, etc.).

[0209] The overall fitness function is:

[0210]

[0211] Where: represents the benefit term, which is used to guide resources to concentrate on high-value and viable targets; C represents the normalized resource consumption cost of all allocation schemes, and C is the ∑ i c i ·x i ; λ1P1, λ2P2, and λ3P3 represent multi-level penalty terms, corresponding to membership violation, firepower balance violation, and priority deviation, respectively; 1 represents a constant, which is used to ensure that the fitness is non-negative and is convenient for the use of the genetic algorithm sorting mechanism; i represents the i-th attack platform, with a total of n attack platforms; j represents the j-th target platform, with a total of m target platforms; t ij represents the comprehensive threat index of attack platform i to target platform j; q j represents the target damage benefit factor; M ij represents the speed-distance adaptation factor; α ij Represents the firepower allocation variable, which is 1 if attack platform i is assigned to target j, otherwise it is 0 (whether to attack or not).

[0212] Formula (22) combines soft constraints and hard constraints. Although hard constraints do not appear directly in the objective function, they are reflected in the overall structure of the model. By limiting the legality of variable combinations, if a solution violates these constraints, it will not be included in the fitness calculation or genetic reproduction. The constraints of hard constraints are as follows:

[0213] Among them, α iIndicates the maximum number of targets allowed to be attacked by the attack platform, that is, the upper limit of the attack mission. Among them, x ij W represents the number of attacks performed by the i-th attack platform on the target platform j; i represents the maximum available weapon resources of attack platform i, that is, the attack platform resource load limit. Among them, b j Indicates the maximum allowable overlap of strikes on target platforms (to avoid excessive concentration of firepower and waste), and is often used to control mission density, save resources or ensure target dispersion. Here, 1 represents the minimum number of strikes, which must be carried out by at least one attack platform. Among them, 0 means that the attack is absolutely prohibited and the mission avoids constraints. Among them, α ij =1 means that attack platform i is assigned to target platform j, α ij =0 means no task is assigned.

[0214] The fitness function in formula (22) is based on minimizing the cost and violation of soft constraints while maximizing the effective strike benefit. It is a typical "benefit-cost" model. This fitness function integrates task orientation (maximum damage, key targets), resource constraints (cost), feasibility control (speed / distance), structural rationality (multi-level soft constraints), and search guidance (dynamic penalty factor). It can be directly used in heuristic optimization frameworks such as genetic algorithms, ant colony algorithms, and particle swarm algorithms to evaluate the quality of firepower allocation solutions. In genetic algorithms, the larger the fitness function, the better the individual.

[0215] Step S3: The MLP-GA optimization method that integrates the multi-layer perceptron and the genetic algorithm is used to iteratively solve the secondary firepower allocation model.

[0216] The purpose of step S3 is to use the firepower allocation secondary optimization model constructed in step S2, which takes the objective function as the core and integrates hard and soft constraints, multi-level penalty mechanism, adaptive penalty factor and the fitness function of the candidate firepower allocation scheme, to achieve efficient search for optimal / near-optimal solutions through the joint solution method of hybrid linear programming (MLP) and genetic algorithm (GA), and obtain a feasible firepower allocation scheme that meets the mission objectives and constraints.

[0217] Step S31: Determine the dimensional structure of the firepower task allocation matrix and the number of initial solution individuals Y based on the number of attack platforms and the number of target platforms. Based on the matrix dimensional structure and the number of individuals, construct Y initial feasible solution populations that meet the hard constraints through multiple random generation methods, and normalize each firepower task allocation matrix in the initial feasible solution population.

[0218] It should be noted that the number of initial solution individuals refers to the number of feasible solutions (task allocation plans) randomly generated at the beginning of the algorithm's iterative optimization. In the firepower allocation problem, one individual equals one firepower task allocation matrix (i.e., the specific allocation plan for a group of attacking platforms to target platforms). The number of initial solution individuals equals the number of initially generated firepower task allocation matrices, and the initial feasible solution equals the firepower task allocation matrix constructed based on the hard constraints. These individuals serve as the "initial population" for the genetic algorithm or other optimization methods, used for subsequent iterations, crossover, mutation, and other operations.

[0219] Step S31 specifically includes:

[0220] Step S31.1: Define that a combat operation includes n attack platforms for performing tasks and m target platforms to be attacked, and based on this, set the task allocation matrix structure corresponding to each initial solution individual to n×m, and determine the number of initial solution individuals.

[0221] The initial number of solutions Y can be set in two ways: fixed scale and dynamic scale. When the task complexity is medium or the computing resources are controllable, a fixed scale method can be used, that is, the number of initial solutions can be set using conventional empirical values:

[0222] Y=P,P∈[50,200] (23)

[0223] Among them, P is the preset individual number parameter, which is flexibly set according to the task scale, experience value and computing resources.

[0224] For example, suppose a fire strike mission involves 8 attack platforms and 12 target platforms. Based on experience, a fixed number of initial solution individuals P = 100 is selected. That is, in the population initialization stage, 100 task assignment matrices that meet hard constraints are generated as individuals.

[0225] To further improve the quality of individual initialization, the number of individuals can be dynamically set based on the structural characteristics of the firepower task allocation matrix. The dynamic proportional setting method takes into account the effective allocation possibility between platforms and targets and the sparsity of tasks, specifically including:

[0226] Calculate the candidate allocation matrix a that satisfies the firepower task ij Total number of combinations >0:

[0227]

[0228] Calculate the average number of assignable platforms for a single target:

[0229]

[0230] Combined with the task dimension and structural complexity, determine the number of initial solution individuals Y:

[0231]

[0232] Where: μ1 and μ2 represent the experience adjustment coefficients (such as μ1∈[2,5], μ2∈[1,3]). This setting method can flexibly expand the population size according to the task adaptation structure.

[0233] For example, if there are 10 attack platforms in the mission, attacking 15 target platforms, and the number of feasible allocation combinations S=90, then Assuming the empirical coefficients μ1=3 and μ2=2, the number of initial solution individuals Y=3·(10+15)+2·6=87, that is, 87 initial solution individuals are generated and enter the optimized population.

[0234] Step S31.2: According to the number of initial solution individuals determined in step S31.1 and the dimension of the fire strike task allocation matrix, when constructing the initial solution individuals, the task allocation method is adopted column by column. Under the premise of satisfying the hard constraints of task coverage constraints, platform capability constraints and platform adaptability, the task allocation matrix is ​​randomly generated until Y feasible initial solution populations that meet the hard constraints are obtained.

[0235] Specifically, based on the known number of initial solution individuals Y and the dimension n×m of the task allocation matrix, according to the preset hard constraints, a random method is used to generate task allocation matrix individuals that meet the constraints one by one, and their collection constitutes an initial population. The hard constraint conditions have been specified in step S22. When generating matrix individuals, the following three types of non-violable task allocation hard constraints must be met: Task coverage constraint: Each task must be executed by at least one attack platform, that is, each row of the matrix has at least one value of 1. Resource upper limit constraint: The number of tasks that can be assigned to each attack platform shall not exceed its maximum available resources, that is, the number of missiles launched by each attack platform shall not exceed the number it carries. Adaptability constraint: If the attack platform i cannot effectively strike the target j (that is, the firepower adaptability Then α ij =0), the corresponding allocation is prohibited.

[0236] According to the above constraints, the process of constructing the initial matrix individuals includes: building a matrix of size n×m, selecting only one type of attack platform i (such as drone, missile, artillery, etc.) for each strike mission, and applying the attack platform i to the strike behavior of the entire row.

[0237] Firepower task allocation matrix A ij for:

[0238]

[0239] In this allocation matrix, each row (n rows) represents a fire strike mission, with a total of n strike missions, and the fire strike mission is executed by attack platform i. Each column (m columns) represents a target platform j, with a total of m target platforms. ij Indicates whether the strike mission of the i-th attack platform attacks the j-th target platform.

[0240] To construct the firepower task allocation matrix A ij , initialized by traversing row by row. For each row (representing a strike mission), a number of targets that meet the firepower membership are randomly assigned from the target platform. The number of attack platforms and missiles launched by attack platform i is sufficient, and it is necessary to ensure that the row contains at least one element with a value of 1, that is, the task is performed by at least one attack platform. If this condition cannot be met in a row, the current matrix is ​​considered invalid and regenerated. Repeat this process until each row meets the requirements, and the initial feasible solution construction is completed. For example, in the first row, if a 11 If it is 1, it means that attack platform 1 is assigned to target platform 1. If the rest of the values ​​in row 1 are 0, it means that the rest of target platforms 2 to m in row 1 are not assigned to attack platform 1, indicating that there is at least one value a in row 1. 11 is 1, otherwise it is an illegal solution.

[0241] Each attack platform may be attacked by multiple target platforms. Under the premise of meeting the hard constraints, multiple attack platforms are further added to the fire strike mission with redundant qualifications to improve the diversity of the search space. At this time, the fire task allocation matrix A ij for:

[0242]

[0243] In the first row of tasks, if a 11 and a 21 If all are 1, it means that attack platform 1 and attack platform 2 are assigned to target platform 1 at the same time. If the rest of the values ​​in row 1 are 0, it means that the rest of target platforms 2 to m in row 1 are not assigned to attack platform 1, indicating that there are at least a 11 、a 21 Both values ​​must be 1, otherwise the solution is illegal. If there is over-allocation (for example, the hard constraint setting condition is that each row of attack platforms cannot have more than 2 assigned attack platforms) or non-coverage (each row of attack platforms is 0 or 1), you can perform a deletion / replacement operation (such as deleting excessive allocations or replacing them with other attack platforms). If the problem cannot be fixed, the matrix individual is invalidated and regenerated. Repeat the above operation until Y matrix individuals that meet the hard constraints are generated as the initial feasible solution population.

[0244] This step is based on the firepower adaptability matrix, combined with the task-platform mapping relationship and the platform capability upper limit, and generates an initial task allocation solution set that meets the task feasibility through the "column priority + constraint detection + random enhancement" method. It has rationality, legality and a certain diversity of solutions.

[0245] Step S31.3: After the initial feasible solution population that satisfies the hard constraints is constructed, each firepower task allocation matrix in the initial feasible solution population is normalized.

[0246] Specifically, traverse each firepower task allocation matrix A ij , extract the minimum value among all nonzero elements:

[0247] Min=min{a ij |a ij >0} (29)

[0248] Then check the firepower task allocation matrix A row by row ij , confirm whether each row of tasks has at least one non-zero value, that is, at least one target platform is attacked by the attack platform. Perform the following unification operation:

[0249]

[0250] In the formula, Max represents the maximum value in the matrix.

[0251] Further, adjust the matrix A ij The allocation value of is selected so that at least one task is allocated on the most prioritized target platform, and its original allocation value is taken as the normalized minimum value (Min), which is returned to zero after normalization to determine a benchmark task.

[0252] For example, suppose we have three fire strike missions: Mission 1, Mission 2, and Mission 3, which need to be assigned to four target platforms A, B, C, and D. Using weighted assignment values, the initial mission assignment matrix is ​​as follows:

[0253]

[0254] Then extract all non-zero elements from the matrix and take the minimum value, Min = 0.3. Check each row. The first row is task 1, which has 3 non-zero allocation values. The second row is task 2, which has 2 non-zero allocation values. The third row is task 3, which has 3 non-zero allocation values. Each task has at least 1 target platform allocation, which meets the conditions and does not need to be patched. Further, from matrix A, ij Find the position of the minimum non-zero value 0.3 in the matrix, take the maximum value Max=0.9 in the matrix, and normalize all non-zero elements:

[0255]

[0256] Get the normalized matrix:

[0257]

[0258] Task 3-target platform A is set as the benchmark task and normalized to 0, representing the highest priority task-target pair in the current initial optimization. All non-zero allocation values ​​are compressed and mapped to a unified [0,1] interval, eliminating the deviation caused by inconsistent numerical scales between different tasks, making it easier to use in subsequent heuristic scheduling, roulette wheel selection, and fitness calculation.

[0259] Through the above normalization operation, the generated initial feasible solution individuals not only meet the basic feasibility, but also enable each individual to have task coverage, prevent task omissions, and avoid extreme deviations in the distribution structure (such as all firepower concentrated on a certain target). By setting a "benchmark task", a starting induction point for the optimization direction is provided, which improves the algorithm convergence efficiency, increases population diversity and comparability, and is conducive to evolutionary operations such as crossover / mutation.

[0260] Step S31 implements hard constraint control for platform resource limits, task coverage, and adaptability verification, rigorously screening legitimate initial individuals to ensure the availability of the initial solution. Further building on the technology used to initialize the legitimate population in step S31, soft constraint control is implemented through methods such as membership, priority, and balance (flexible fault tolerance). A penalty function is used to dynamically guide the solution toward the optimal solution, achieving full constraint coverage.

[0261] Step S32: After completing the initial population construction and normalization processing, the firepower task allocation problem is iteratively solved by using a method that integrates a multilayer perceptron (MLP) and a genetic algorithm (GA) to obtain a final firepower task allocation solution.

[0262] The GA plays a leading role in this optimization framework, primarily searching and optimizing the population through a bionic evolutionary mechanism. The MLP is used to predict and score the impact of the solution. Together, the two evaluate individual quality, improving search efficiency and convergence accuracy.

[0263] As the instruction manual Figure 5 , step S32 includes:

[0264] Step S32.1: Use the normalized initial feasible solution population in step S31 as the input of the optimization algorithm, and construct an initial population containing multiple individuals based on the genetic algorithm. Each individual is represented as a firepower task allocation matrix. The firepower task allocation matrix is ​​an integer matrix or array that represents the mapping relationship between tasks and attack platforms.

[0265] The initial population is constructed using the encoding concept of a general algorithm (GA). Each individual represents a set of fire task assignments, represented by an integer fire task assignment matrix that conforms to the structural definition of a GA individual. This fire task assignment matrix is ​​a two-dimensional integer matrix or an equivalent array structure, with its dimensions corresponding to the number of tasks and attack platforms. The integer values ​​of the matrix elements represent the specific task assignment relationships. Specifically, the value of the element in the i-th row and j-th column of the matrix defines whether the i-th target task is assigned to the j-th attack platform, or the priority / weight between the task and a platform, determined by the specific encoding method.

[0266] The encoding structure conforms to the individual representation model in the GA framework and meets the following characteristics: discrete representation: integer encoding is used instead of real numbers or floating-point types, which is suitable for describing problems with enumerable solution spaces such as task scheduling and resource matching; strong mappability: the matrix structure can be directly mapped to the task-platform binary relationship; easy to operate: the matrix structure is convenient for executing genetic operator operations such as crossover and mutation, and supports constraint detection; feasibility guarantee: the initial population is normalized and feasibility tested to ensure that each individual meets the hard constraints in the problem definition in the initial state, such as task uniqueness, resource capacity limitations, platform adaptability, etc.

[0267] Step S32.2: In each iteration, a combination of roulette wheel selection and tournament selection is used to select some individuals from the current population as parent individuals. The selected parent individuals are used for subsequent crossover and mutation operations.

[0268] During each genetic iteration, to complete the generation of the next generation of offspring individuals, some individuals must be selected from the current population as parents for subsequent genetic operations (such as crossover and mutation). In this step, a combination of roulette wheel selection and tournament selection is used to dynamically select parents from the current population.

[0269] The cyclical alternation of the tournament and roulette methods creates a dynamic equilibrium selection mechanism: the tournament method selects locally high-quality individuals by setting a specific competition scale. Its elite retention effectively maintains population diversity and prevents the algorithm from prematurely falling into a local optimum. The roulette method, on the other hand, uses probabilistic selection to give high-fitness individuals greater succession opportunities, ensuring the continued propagation of superior genes. The complementary switching between these two selection modes allows the algorithm to flexibly adjust the selection pressure at different evolutionary stages, expanding the global search space in the early stages of iteration while strengthening local, refined search capabilities in the later stages.

[0270] In each iteration, the roulette wheel and tournament selection methods are alternated according to a set period or probability, creating an adaptive dynamic selection pressure regulation mechanism that balances exploration and exploitation. This alternating strategy not only enriches the population's genetic diversity but also improves search stability and convergence efficiency. Based on the tournament selection mechanism, multiple individuals (with a set tournament size k) are randomly sampled from the population to form a candidate subset. Within each subset, the individual with the best fitness is selected as the winner and enters the parent generation. Based on the roulette wheel selection mechanism, selection probability is assigned based on the proportion of each individual's fitness to the total fitness, and individual sampling is performed using a roulette wheel simulation method. By integrating these two selection mechanisms in a rotating manner within each iteration, a dynamic balanced selection mechanism is constructed that balances local exploitation and global exploration. In the early iterations, roulette wheel selection dominates, facilitating global search and maintaining diversity. In the later iterations, tournament selection gradually increases, promoting the inheritance of high-quality genes and local convergence. This effectively mitigates the risk of premature maturation and falling into local optima, improving the overall optimization capability and stability of the algorithm.

[0271] As the instruction manual Figure 6 The two-point crossover operation is used in genetic algorithms to generate new individuals. It randomly selects two crossover points (cut-points) between two parent individuals and swaps the gene segments in the selected intervals, thus forming two new offspring individuals. The top two rows in the figure represent the two parent chromosome individuals. Each individual uses a one-dimensional encoding structure to represent the firepower task allocation scheme. White and gray cells represent the status of genes for different task allocations. The dotted box marks the crossover interval between the two cut points. The gene segments within the crossover interval are symmetrically exchanged between the two individuals. The bottom two rows show the two offspring individuals generated after the crossover operation.

[0272] Two-point crossover exchanges parental gene segments by randomly selecting two cut points. Compared to single-point crossover, this method is more effective in preserving the structural integrity of high-quality gene segments while also expanding the breadth of the solution space through gene block recombination. In firepower allocation scenarios, this crossover method can effectively exploit implicit relationships between weapon systems and targets, promoting the generation of cross-dimensional resource coordination solutions. This method strengthens the inheritance of excellent individuals while maintaining population diversity and reducing the risk of premature maturation.

[0273] Step S32.3: Perform a two-point crossover operation on the selected parent individuals to generate new offspring individuals, and perform a random mutation operation on the gene loci of the new offspring individuals based on the set probability. At the same time, perform hard constraint detection on the new offspring individuals after crossover and mutation, and eliminate individuals that violate the hard constraints to maintain the feasibility of the population.

[0274] First, for each pair of parent individuals, two different crossover cut points are selected based on a pseudo-random number generation mechanism to divide the parent chromosome into three segments. The structure of the first and last segments of the parent chromosome is retained, and only the gene segments in the middle segment are swapped to generate two new offspring. This operation preserves the high-quality gene block structure of the parent while expanding the scope of the solution space. It is particularly suitable for encoding structural variables involved in firepower task allocation problems (such as the task-platform allocation matrix), and can realize the reorganization of resource allocation relationships across tasks and platforms.

[0275] For the offspring individuals generated after the crossover operation, random perturbations are performed on several loci within the chromosomes based on a set mutation probability threshold (typically 5%-10%). The mutation method is designed based on the individual encoding method. For example, in integer encoding, the task of a locus may change from one platform to another; in permutation encoding, the positions of two tasks may be swapped. The mutation operation introduces a population perturbation mechanism, effectively increasing population diversity and preventing the search from falling into local optimal solutions (premature convergence).

[0276] To ensure the feasibility of the solution obtained by genetic operations, a hard constraint detection mechanism is implemented on all newly generated offspring individuals, mainly including but not limited to: task integrity constraint: each task must be executed by and only by one adaptation platform; platform capacity / load constraint: the resource allocation of the attack platform must not exceed its execution upper limit; adaptability constraint: there must be an execution adaptation relationship between the task and the platform.

[0277] If an offspring individual violates any of the above hard constraints after crossover or mutation, the individual will be eliminated or replaced to ensure that all individuals in the new generation population are legal solutions and maintain the feasibility boundary in the genetic search process.

[0278] Step S32.4: Construct a fitness function based on the modeling objective function, and fuse the prediction function of the MLP model on the individual allocation structure to form a fused total fitness function, and perform model fitness scoring and MLP prediction scoring on each individual through the fused total fitness function.

[0279] In this step, based on the multi-objective and multi-constrained nature of the firepower task allocation problem, a dual fitness evaluation mechanism is proposed that integrates the modeling objective function with the predictive capabilities of the machine learning model. This mechanism, by constructing a fused fitness function, comprehensively scores the optimization value of each individual solution, providing a precise evaluation basis for subsequent population screening.

[0280] First, according to the multi-objective optimization model constructed in step S2, the fitness function F is designed. 适应度, used to measure the overall quality of individual solutions. Metrics considered include, but are not limited to, the total effectiveness of firepower strikes (target hit score); firepower affiliation, target priority, attack balance, and soft constraint violation. A multi-level penalty factor mechanism is also introduced to impose adaptive penalties on solutions that violate soft constraints, dynamically adjusting the fitness of individuals in complex constraint scenarios.

[0281] Then, the trained multilayer perceptron (MLP) model is used to construct the individual structure prediction function F MLP :

[0282] F MLP (x) = f (L) (W (L) ·f (L-1 )(…f (1) (W (1) x+b (1) )+…)+b (L) ) (31)

[0283] Where: F MLP (x) represents the strike effect score predicted by the input individual coding structure based on the training data; x represents the input vector, that is, the coding representation of the firepower task allocation structure of a single genetic individual; W (L) represents the connection weight from the L-1th layer to the Lth layer, which is a two-dimensional real number matrix; b (L) represents the additive bias term corresponding to each neuron in the Lth layer; L represents the layer depth of the entire multilayer perceptron, that is, the total number of layers in the network; f (L) represents the activation function of the Lth layer.

[0284] It should be noted that formula (31) is a standard multi-layer perceptron output expression, which is widely used in machine learning and deep learning literature.

[0285] The individual task assignment structure is fed into the MLP network as encoded input. The MLP outputs a score of its potential impact, reflecting the predictive quality of the assignment structure in the training corpus. This score serves as an auxiliary signal in the fusion fitness calculation, improving the ability to identify high-quality structural solutions, especially providing directional guidance in the middle and late stages of the search.

[0286] The final fitness function is a combination of the weighted form of the above two types of scores to construct a fusion fitness function F 总 , the expression is as follows:

[0287] F 总 =ω1·F 适应度 +ω2·F MLP ,ω1+ω2=1(32)

[0288] Where: ω1, ω2 represent weighting parameters; F 适应度 represents the fitness scoring function based on the benefit term, resource consumption cost, and multi-level penalty term (Formula 22); F MLP Represents the prediction scoring function for the individual distribution structure.

[0289] The MLP prediction score is to input the current individual coding structure into the trained multi-layer perceptron (MLP) neural network. The MLP network outputs its predicted strike effect score, which reflects the potential quality of the solution and serves as an auxiliary evaluation indicator.

[0290] Step S32.5: Several individuals with the highest fitness scores in the current population are directly copied into the next generation population, and the offspring individuals generated by crossover and mutation are merged to form a new generation of complete population.

[0291] From the current population according to the fusion fitness function F 总 Based on the scoring results, several individuals with the highest fitness (e.g., the top k individuals) are selected. These high-quality individuals do not participate in the current round of crossover and mutation operations. Instead, they are directly retained and replicated to the next generation population, preventing the loss of high-quality genes during genetic operations. All viable offspring individuals generated by the previous generation through two-point crossover and mutation are merged with the retained elite individuals to form a new complete population, which serves as input for the next round of genetic iterations. The population size is kept constant to meet the iterative requirements of the genetic algorithm. This mechanism improves algorithm stability and accelerates global convergence.

[0292] Step S32.6: When the maximum number of iterations is reached or the population fitness converges, the optimization process is terminated, and the individual with the highest fitness score in the current population is output as the final firepower task allocation plan.

[0293] The maximum number of iterations has been reached, meaning the number of executed iterations has reached the preset upper limit, T. Population fitness convergence occurs when the improvement in the optimal fitness of the population over multiple consecutive generations falls below a threshold (e.g., <ε), indicating that the algorithm has converged to a stable region. The individual with the highest ensemble fitness score is selected from the current (last generation) population. The firepower task allocation matrix corresponding to this individual is the algorithm optimization result and output as the final firepower task allocation solution. This output solution satisfies the optimal (or near-optimal) modeling objective function and meets all constraints, and can be directly used for task scheduling or weapon resource allocation decisions.

[0294] Step S32 constructs a hybrid optimization strategy based on GA evolutionary search and supplemented by MLP prediction and evaluation to achieve iterative solution of the multi-objective and multi-constraint firepower task allocation model, effectively improving the quality, feasibility and optimization efficiency of the solution.

[0295] Example 1

[0296] As the instruction manual Figure 7 Using steps S1-S3 above, a typical 10-on-10 weapon target engagement scenario is constructed: the combat space is set as a two-dimensional limited area with dimensions of 120 km × 400 km; a total of 10 attack platforms and 10 target platforms participate in the mission; the combat objective is to maximize the number of target platforms destroyed while minimizing the cost of weapon use; each attack platform is equipped with missile weapons of the same type but different numbers, possessing differentiated strike capabilities; each missile has a different probability of damage to different target platforms (i.e., heterogeneous firepower effectiveness); each target platform has a different threat factor value to different attack platforms, reflecting the attack risk and combat cost; each target platform has a predefined priority level, reflecting its tactical importance and the urgency of destruction.

[0297] As the instruction manual Figure 8 As shown in the figure, the threat matrix of the target platform to the attack platform is constructed. The matrix is ​​a 10×10 two-dimensional square matrix, and the horizontal axis represents the attack platform number (A1-A 10 ), the vertical axis represents the target platform number (T1-T 10 ), the value in each cell represents the threat posed by target platform i to attack platform j, expressed as a dimensionless risk factor. Higher values ​​indicate stronger countermeasure or defensive capabilities for the target and greater operational risk to the attacking platform. This matrix, as part of the soft constraint penalty factor, participates in the calculation of the genetic algorithm's fitness function. During the optimization process, if an attacking platform in an individual scenario frequently attacks high-threat targets, its fitness is penalized. This design helps guide the algorithm in generating firepower strike plans that balance benefits and risks, avoiding the tactical "high cost for low benefit."

[0298] For the aforementioned mission scenarios, seven different allocation algorithm models were designed and compared to evaluate the relative advantages of the proposed methods. Undecoupled methods (LP, GA, PSO) were used as baseline models to validate the improved performance of the decoupled methods. Linear programming (LP) is fast and efficient, but its effectiveness is limited in complex problems. Genetic algorithms (GA) and particle swarm optimization (PSO) provide global search capabilities, but can be inefficient due to the large search space. A multi-layer perceptron-based multi-level penalty genetic algorithm (MLP-GA) significantly improves the quality and stability of mission planning by combining decoupled models with multi-objective optimization. To ensure fairness and repeatability in the algorithm comparison, the following parameters were uniformly adopted: initial population size of 10, number of genetic iterations of 50, random seed of 1 (to ensure experimental reproducibility), upper limit of the number of attack platforms of 10, upper limit of the number of target platforms of 10, and number of missile types of 1. All platform coordinates and platform attributes were randomly generated using a uniform distribution to simulate the dynamics and uncertainty of a real battlefield. The experimental results are shown in Table 1.

[0299] Table 1:

[0300]

[0301]

[0302] As shown in Table 1, GA+MLP+GA performs well across all five dimensions, particularly in optimization effect (fitness) and robustness (standard deviation). Despite a slightly higher time consumption (15 seconds), it offers significant advantages under complex constraints and is suitable for high-precision mission planning scenarios. Decoupled combinations such as GA+GA and PSO+PSO generally outperform traditional GA and PSO in path distance and fitness, demonstrating that decomposing the task structure prior to optimization enhances the algorithm's expressive power. While LP takes the shortest time (1.5 seconds), it performs the worst in terms of optimization goal achievement and path safety, making it unsuitable for complex, multi-objective, and strongly constrained firepower allocation tasks. Overall, GA+MLP+GA performs best across all performance dimensions, validating the advantages of neural network-assisted genetic evolution in complex, multi-constrained scenarios.

[0303] As the instruction manual Figure 9-10 , Figure 9 This figure shows a performance comparison of different algorithms in a 10×10 firepower task allocation scenario, using two dimensions: fitness value and fitness standard deviation. The horizontal axis represents different algorithms, including LP (linear programming), GA (genetic algorithm), PSO (particle swarm optimization), LP-GA (linear initialization + GA), GA-MLP (genetic algorithm + multi-layer perceptron), GA-MLP-GA (prediction-assisted + evolutionary optimization), and PSO-PSO (adaptive particle swarm dual-layer collaboration). The left vertical axis in the figure represents fitness value (blue bar graph), and the right vertical axis represents fitness standard deviation (red broken line). Basic algorithms (such as LP, GA, and PSO) generally have lower fitness values, while fusion algorithms (such as GA-MLP, GA-MLP-GA, and PSO-PSO) achieve significantly higher fitness values, with GA-MLP-GA in particular reaching the highest level. This demonstrates that the combination of deep learning assistance and evolutionary optimization offers stronger problem-solving capabilities in complex scenarios. The red line shows the standard deviation gradually decreasing from LP to the right, indicating that the stability of the optimization results is gradually increasing. In particular, GA-MLP-GA and PSO-PSO have the smallest standard deviations, reflecting the algorithm's convergence stability and higher solution reliability. GA-MLP-GA achieves the best results in both fitness and standard deviation, verifying the effective guidance ability of the multilayer perceptron in optimizing firepower task allocation. Therefore, the fusion algorithm GA-MLP-GA of this application performs best in both indicators, demonstrating good solution quality and convergence stability.

[0304] Figure 10The paper presents a comprehensive comparison of various optimization algorithms across multiple performance indicators in a 10×10 firepower task allocation scenario, using a radar chart to display the distribution of algorithm scores across five dimensions. The algorithms included in the figure include LP (linear programming), GA (genetic algorithm), PSO (particle swarm optimization), LP+GA (linear initialization + genetic optimization), GA+MLP (perceptron-assisted genetic algorithm), GA+MLP+GA (multi-stage nested optimization), and PSO+PSO (two-layer particle swarm collaborative optimization). GA+MLP+GA approaches the outer boundary in core performance metrics such as fitness, stability, and success distance, demonstrating its outstanding performance in solution quality, stability, and strike accuracy. Traditional GA and PSO perform moderately, with LP exhibiting significant local disadvantages.

[0305] Example 2

[0306] This example verifies the performance advantages of the hybrid optimization strategy combining a multi-layer perceptron (MLP) and a genetic algorithm (GA) in a larger-scale combat context. The experimental scenario is further expanded compared to Example 1, constructing a firepower task allocation task with greater complexity and uncertainty. The operational objective of this example is to minimize weapon usage costs and maximize the number of target platforms destroyed while satisfying resource and mission constraints. To this end, the following task modeling elements are constructed: Attack platform configuration: 20 attack platforms are set, all carrying the same type of missiles but varying numbers, reflecting platform capability differences; Target platform configuration: 20 target platforms are set, each with a different importance level, reflected in a target priority value. Each target platform has a different threat factor value for different attack platforms, used to simulate countermeasure risk; Firepower effectiveness modeling: Each missile has a different probability of damage against the target platform, forming a heterogeneous strike network between platforms, weapons, and targets. The damage probability is modeled based on factors such as weapon hit capability and the platform's detection effectiveness against the target.

[0307] In this 20-on-20 scenario, the same optimization framework as in Example 1 was used, that is, the modeling and solution process was completed according to steps S1 to S3. To verify the optimization effect of the proposed method, seven algorithm models were constructed and compared. The experimental results are shown in Table 2:

[0308] Table 2

[0309]

[0310] As shown in Table 2, LP (linear programming) has the highest probability of damage (9000), but its cost is as high as 7000 and its fitness is only 0.68, indicating that while it is computationally fast, it struggles to balance resource consumption and optimal constraints. GA (standard genetic algorithm) has a fitness of 0.78 and a reduction in cost, outperforming LP, but with a slightly higher standard deviation and slightly less stable solutions. PSO (particle swarm optimization) has a moderate damage rate but a fitness of only 0.74, requiring less time but with limited convergence quality. LP+LP has a cost reduction of 4800 and a fitness increase of 0.82, with good stability (σ = 0.05), indicating that model structure optimization improves linear programming. GA+GA further reduces the damage / cost ratio, reaching a fitness of 0.84 and a time consumption of 25 seconds, demonstrating its practicality. GA+MLP-GA (the method of the present invention) achieved the best overall performance, with a damage rate of 5600, a cost of 4000, the highest fitness (0.89), and the lowest standard deviation (0.04), indicating a highly concentrated solution set and validating the effectiveness of integrating MLP guidance with a multi-level penalty mechanism for high-dimensional optimization problems. PSO+PSO achieved a slightly lower fitness than MLP-GA (0.86) and a cost of 4200, but took the longest time (28 seconds), suggesting that its convergence efficiency and local development capabilities are slightly weaker than the fusion model for this type of problem.

[0311] As the instruction manual Figure 11-12 , Figure 11 The comparison chart of fitness value and fitness standard deviation in 20 vs. 20 scenario is shown in Figure 2. Figure 11 As can be seen, the blue bar graph represents the average fitness value obtained by each algorithm over multiple trials, representing the overall quality of the optimized solution. The red line graph shows the standard deviation of the fitness of each algorithm, reflecting the stability of the algorithm's solution (the smaller the standard deviation, the smaller the solution fluctuation and the more concentrated the convergence). The coordinate axes are double-labeled: the left scale is for fitness value (range: approximately 0.68 to 0.89), and the right scale is for standard deviation (range: 0.02 to 0.06). Decoupled methods (LP, GA, PSO): Fitness values ​​are generally low (LP is the lowest, approximately 0.68), and standard deviations are high (GA > PSO); this indicates limited solution quality, large solution volatility, and insufficient convergence stability. Decoupled methods (LP+LP, GA+GA, GA+MLP-GA, PSO+PSO): The fitness values ​​are generally high, especially the GA+MLP-GA scheme, which reaches the highest value (close to 0.89). The standard deviation decreases significantly, and the GA+MLP-GA of the present invention reaches the lowest value (about 0.02), showing strong solution concentration and search stability. PSO+PSO is slightly inferior. Although the fitness is higher, the fluctuation is slightly larger.

[0312] Figure 12 This is a radar comparison chart in a 20 vs. 20 scenario. Figure 12As can be seen, GA+MLP-GA (black line) leads evenly across all metrics, particularly in fitness, standard deviation control, and damage capability, significantly outperforming other algorithms. While LP (blue) performs best in time consumption, it lags behind in fitness and damage capability. Other models, such as GA, PSO, and PSO+PSO, have advantages in certain metrics but fall slightly short in overall performance. This figure demonstrates the comprehensive optimization capabilities of the proposed fusion method from a multi-dimensional visualization perspective. In particular, when solving high-dimensional, complex, and multi-constrained firepower task allocation problems, the improved GA+MLP-GA model, which integrates the prediction mechanism of a multi-layer perceptron with a genetic algorithm, achieves efficient search for the optimal solution set.

[0313] Example 3

[0314] Compared to Examples 1 and 2, this example expands the combat scenario to a 50-50 weapon-target matching task to create a more challenging verification environment. The operational objectives of this example remain the same as those of the previous two examples: minimize weapon resource costs and maximize the number of target platforms destroyed, while satisfying mission constraints and platform requirements. To achieve these objectives, the combat model is configured as follows: Attack Platform Configuration: A total of 50 attack platforms are set, each carrying a varying number of missiles. All missiles are of the same type, but differ in firepower distribution and payload. Target Platform Configuration: A total of 50 target platforms are set, each with differentiated combat attributes. Each target platform has a different priority level to reflect tactical importance, and an asymmetric damage probability matrix and threat factor matrix exists between them and the attacking platform. Firepower Effectiveness Modeling Features: Each missile has a different damage probability against each target, and each target poses a different threat level to different attack platforms, reflecting operational risk. Missile strike effectiveness, target countermeasure capability, and priority are all embedded in the fitness function as optimization constraints or penalty terms.

[0315] In this 50×50 high-dimensional task scenario, the same modeling and optimization process as in Examples 1 and 2 was used, i.e., steps S1-S3 were followed. To evaluate the stability and scalability of the method of the present invention, the following seven algorithm models were selected for performance comparison. The experimental results are shown in Table 3:

[0316] Table 3

[0317]

[0318] As can be seen from Table 3, as the task scale expands, traditional algorithms face dual bottlenecks in efficiency and accuracy. However, the genetic algorithm (GA+MLP-GA) proposed in this paper, which integrates MLP and a multi-level penalty mechanism, shows optimal performance in terms of solution quality, solution stability, and constraint adaptability, verifying the engineering applicability and technological advancement of this method in complex, high-dimensional weapon target allocation problems.

[0319] As the instruction manual Figure 13-14 , Figure 13 This is a comparison chart of fitness value and fitness standard deviation in the 50-50 scenario. Figure 14 This is a radar comparison chart in a 50-50 scenario. Figure 13 It can be seen that the horizontal axis is the 7 algorithms involved in the comparison (LP, GA, PSO, LP+LP, GA+GA, GA+MLP-GA, PSO+PSO). The left vertical axis (blue) is the average fitness value, which indicates the comprehensive quality of the solution. The right vertical axis (red) is the standard deviation of fitness, which reflects the convergence stability and the degree of discreteness of the solution set distribution. The blue bar graph represents the fitness value of each algorithm, and the red line graph represents the corresponding fitness standard deviation. The GA+MLP-GA method of the present invention has the highest fitness value (0.93) and the lowest standard deviation (0.02), showing the best solution quality and the strongest convergence stability. The non-decoupled algorithms such as LP, GA, and PSO have low fitness and high standard deviation, and the solution volatility is large. Other decoupled algorithms (such as GA+GA, PSO+PSO) are close to the optimal in fitness value, but the standard deviation is slightly higher. From Figure 14 It can be seen that the GA+MLP-GA of the present invention has the largest overall area and the five performances are well balanced, indicating that the method of the present invention performs best in terms of solution quality, stability, efficiency and task benefit.

[0320] The present invention also provides a firepower distribution system based on a double-layer decoupling and multi-level penalty genetic algorithm, the firepower distribution system comprising:

[0321] A first-level decoupling modeling module is used to construct a first-level decoupling model of firepower tasks based on the threat relationship and spatial distribution characteristics between the attacking platform and the target platform. The first-level decoupling model includes a threat matrix and firepower allocation membership, which is used to characterize the target's counter-attack capability against the attacking platform and the platform's strike intent against the target.

[0322] A secondary optimization modeling module is used to construct a secondary optimization model for firepower task allocation based on the objective function. The secondary optimization model integrates hard and soft constraints, adopts a multi-level penalty mechanism and an adaptive penalty factor to adjust the degree of constraint violation, and is used to characterize multiple optimization indicators such as mission strike effectiveness, firepower balance, and target priority;

[0323] An intelligent optimization solution module is used to call the MLP-GA optimization method constructed by integrating the multi-layer perceptron and the genetic algorithm to iteratively solve the secondary optimization model. The intelligent optimization solution module includes:

[0324] Initial population generation submodule: used to construct multiple firepower task allocation initial solution individuals that meet hard constraints according to task scale;

[0325] Genetic evolution submodule: used to perform operations such as crossover, mutation, and constraint detection on the population;

[0326] Fitness fusion evaluation submodule: used to jointly calculate the model fitness score and the MLP network prediction score, construct the fusion fitness function and perform iterative screening;

[0327] Optimal solution output submodule: used to output the optimal fitness individual after meeting the convergence conditions as the final firepower task allocation plan.

[0328] The above is only an embodiment of the present invention, and common sense such as the specific structure and characteristics of the scheme are not described in detail here. For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic characteristics of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes that fall within the meaning and scope of the equivalent elements of the claims are included in the present invention. Any figure mark in the claims should not be regarded as limiting the claim involved.

Claims

1. A firepower allocation method based on double-layer decoupling and multi-level penalty genetic algorithm, characterized in that: The method comprises: Step S1: Based on the threat relationship and spatial distribution characteristics between the attack platform and the target platform, a first-level decoupling model of firepower allocation is constructed, which includes a threat matrix and firepower allocation membership. Step S2: construct a two-level optimization model for firepower allocation oriented to the objective function, integrating hard constraints and soft constraints, multi-level penalty mechanism, adaptive penalty factor and fitness function; Step S3: The MLP-GA optimization method that integrates the multi-layer perceptron and the genetic algorithm is used to iteratively solve the secondary firepower allocation model.

2. The firepower allocation method based on double-layer decoupling and multi-level penalty genetic algorithm according to claim 1 is characterized in that: Step S1 includes: Step S11: calculating the threat matrix between the attack platform and the target platform to quantify the threat level of each attack platform to each target platform; Step S21: determining the objective function based on the combat purpose, and determining the fitness function corresponding to the objective function.

3. The firepower allocation method based on double-layer decoupling and multi-level penalty genetic algorithm according to claim 2 is characterized in that: Step S11 includes: Step S11.1: Calculate the estimated range distance from each attack platform to each target platform; Where: d ij represents the predicted range between the i-th attack platform and the j-th target platform; i represents the number index of the attack platform, and its value range is i=1,2,…,m; j represents the number index of the target platform, and its value range is j=1,2,…,n; x i 、y i represents the two-dimensional coordinate position of the i-th attack platform; x j 、y j Indicates the two-dimensional coordinate position of the j-th target platform; Step S11.2: Calculate the threat factor of each target platform relative to each attack platform based on the estimated range; Where: t ij represents the comprehensive threat index of attack platform i to target platform j; ω1 and ω2 represent weight coefficients; d ij_target represents the distance between attack platform i and target platform j; d ij_max v represents the maximum range of the weapon system of attack platform i on target platform j; j_target represents the protection capability value of target platform j; v j_max Indicates the maximum reference value of protection capability; It means the attack platform is closer to the target.

4. The firepower allocation method based on double-layer decoupling and multi-level penalty genetic algorithm according to claim 2 is characterized in that: Step S21 includes: Step S12.1: Calculate the mean coordinates of each attack platform and each target platform, and obtain the center coordinates of the attack platform group and the target platform group respectively; Step S12.2: Using the center coordinates of the attack platform as the origin, the direction connecting the center coordinates of the target platform and the center coordinates of the attack platform is used as the initial x-axis. The x-axis is rotated 90 degrees counterclockwise to construct a firepower allocation coordinate system. The unit vectors of the x-axis and y-axis are defined in the firepower allocation coordinate system. Based on the unit vectors, the original two-dimensional coordinates of each attack platform and target platform are translated into the firepower allocation coordinate system to obtain the new coordinates of the attack platform and target platform in the firepower allocation coordinate system. Step S12.3: In the fire distribution coordinate system, a set of dividing lines parallel to the x-axis is constructed. The new coordinates of the target platform in the y-axis direction are divided based on these dividing lines to form multiple fire distribution areas. The fire distribution area assigned to each attacking platform is determined based on the mapping relationship between the attacking platform and the fire distribution area. Step S12.4: Based on the target platform's position in the firepower allocation coordinate system and its firepower allocation area, a fuzzy membership function is used to calculate the firepower allocation membership of each target platform to different attack platforms to optimize the matching of firepower resources; The firepower distribution membership is determined by the following formula: Where: represents the firepower subordination of target platform j to attack platform i; represents the Y-axis coordinate of target platform j in the firepower allocation coordinate system; represents the Y-axis coordinate of attack platform i in the firepower allocation coordinate system; L k , L k-1 Indicates the coordinates of the dividing line between adjacent fire areas (vertical); i = k-1, k, k+1 represent the coordinates of Z k-1 、Z k 、Z k+1 The index of the attack platform in the region corresponds to the target; exp(·) represents the exponential function, which is used to construct a nonlinear weight distribution mechanism so that the targets far away from the region boundary have lower contributions; Indicates the target platform's membership to the attack platform in the previous partition; Indicates the target platform to L k The vertical distance of the dividing line boundary; |L k - Indicates attack platform i to L k The longitudinal distance of the dividing line boundary; Indicates the target platform's degree of affiliation to the attack platform in the current area; Indicates the y coordinate of the target platform j and the current area Z k The average distance between the upper and lower boundaries of |L k-1 -L k | indicates the current firepower allocation area Z k The vertical height of Indicates the target platform's membership to the next partition attack platform; Indicates the target platform j to the previous dividing line L k-1 The longitudinal distance of the boundary; Indicates the distance between attack platform i and the dividing line L in the firepower distribution coordinate system k-1 The vertical distance of the border.

5. The firepower allocation method based on double-layer decoupling and multi-level penalty genetic algorithm according to claim 2 is characterized in that: Step S2 includes: Step S21: determining an objective function based on the combat purpose, and determining a fitness function corresponding to the objective function; Step S22: By distinguishing the constraints in the firepower allocation process into hard constraints and soft constraints, a multi-level penalty mechanism and an adaptive penalty factor are introduced for the soft constraints; Step S23: Based on the multi-level penalty mechanism and the adaptive penalty factor, a total fitness function is constructed that integrates the strike benefit, speed-distance adaptation, resource cost, and multi-level soft constraints; The overall fitness function is: Where: represents the benefit term, which is used to guide resources to concentrate on high-value and attackable targets; C represents the normalized resource consumption cost of all allocation schemes; λ1P1, λ2P2, and λ3P3 represent multi-level penalty terms, corresponding to membership violation, firepower balance violation, and priority deviation, respectively; 1 represents a constant, which is used to ensure that the fitness is non-negative and is convenient for the use of the genetic algorithm sorting mechanism; i represents the i-th attack platform, with a total of n attack platforms; j represents the j-th target platform, with a total of m target platforms; t ij represents the comprehensive threat index of attack platform i to target platform j; q j represents the target damage benefit factor; M ij represents the speed-distance adaptation factor; α ij represents the firepower allocation variable, which is 1 if attack platform i is assigned to target j, otherwise it is 0; The penalty factor function is: Where: k0 represents the initial penalty factor of the k-th penalty term; kmax represents the maximum penalty value of the k-th penalty item; t represents the current iteration number; T represents the maximum number of iterations; pk represents the exponent that controls the growth rate of the k-th penalty; k∈(1,2,3) represents the penalty items of 3 penalty levels.

6. The firepower allocation method based on double-layer decoupling and multi-level penalty genetic algorithm according to claim 5 is characterized in that: In step S21, the combat objectives include but are not limited to pursuing maximum damage effect, prioritizing cost reduction, and striking key targets; Soft constraints include but are not limited to firepower allocation affiliation, firepower allocation balance, and target priority requirements; The hard constraints include, but are not limited to, hard constraint variables including the number of missiles launched by the i-th attack platform at the j-th target platform, the total inventory of missiles available to the attack platform i, the inventory of missiles of type t in the attack platform i, missiles of type t, the number of missiles allocated to the target platform j, and the value of the firepower allocation membership is not 0; The multi-level penalty mechanism has at least 3 levels, among which level 1 is a light penalty, corresponding to the target priority requirement; level 2 is a moderate penalty, corresponding to the balance of firepower distribution; level 3 is a heavy penalty, corresponding to the degree of firepower distribution.

7. The firepower allocation method based on double-layer decoupling and multi-level penalty genetic algorithm according to claim 5 is characterized in that: Step S3 includes: Step S31: Determine the dimensional structure of the firepower task allocation matrix and the number of initial solution individuals Y based on the number of attacking platforms and the number of target platforms. Based on the matrix dimensional structure and the number of individuals, construct Y initial feasible solution populations that meet the hard constraints through multiple random generation methods, and normalize each firepower task allocation matrix in the initial feasible solution population. Step S32: After completing the initial population construction and normalization processing, the firepower task allocation problem is iteratively solved by using a method that integrates a multi-layer perceptron and a genetic algorithm to obtain the final firepower task allocation solution.

8. The firepower allocation method based on double-layer decoupling and multi-level penalty genetic algorithm according to claim 7 is characterized in that: Step S31 includes: Step S31.1: Define a combat operation as including n attack platforms for executing the mission and m target platforms to be attacked. Based on this, set the task allocation matrix structure corresponding to each initial solution individual to n×m, and determine the number of initial solution individuals. Step S31.2: Based on the number of initial solution individuals determined in step S31.1 and the dimensions of the firepower strike task allocation matrix, when constructing the initial solution individuals, use a column-by-column task allocation method. Under the premise of satisfying the hard constraints of task coverage, platform capability, and platform adaptability, randomly generate the task allocation matrix until Y feasible initial solution populations that meet the hard constraints are obtained; Step S31.3: After the initial feasible solution population that satisfies the hard constraints is constructed, each firepower task allocation matrix in the initial feasible solution population is normalized.

9. The firepower allocation method based on double-layer decoupling and multi-level penalty genetic algorithm according to claim 8, characterized in that: Step S32 includes: Step S32.1: Using the normalized initial feasible solution population from step S31 as input to the optimization algorithm, an initial population consisting of multiple individuals is constructed based on a genetic algorithm. Each individual is represented by a fire task assignment matrix. The fire task assignment matrix is ​​an integer matrix or array that represents the mapping relationship between tasks and attack platforms. Step S32.2: In each iteration, a combination of roulette wheel selection and tournament selection is used to select some individuals from the current population as parent individuals. The selected parent individuals are used in subsequent crossover and mutation operations. Step S32.3: Perform a two-point crossover operation on the selected parent individuals to generate new offspring individuals. Then, perform a random mutation operation on the gene loci of the new offspring individuals based on the set probability. Simultaneously, perform a hard constraint check on the new offspring individuals after crossover and mutation, and remove individuals that violate the hard constraints to maintain population feasibility. Step S32.4: Construct a fitness function based on the modeling objective function and fuse it with the MLP model's prediction function for the individual allocation structure to form a fused total fitness function. The fused total fitness function is then used to perform model fitness scoring and MLP prediction scoring on each individual. Step S32.5: Directly copy the individuals with the highest fitness scores in the current population into the next generation population, and merge the offspring individuals generated through crossover and mutation to form the new generation complete population; Step S32.6: When the maximum number of iterations is reached or the population fitness converges, the optimization process is terminated and the individual with the highest fitness score in the current population is output as the final firepower task allocation plan; In step S32.4, the fusion fitness function F 总 : F 总 =ω1·F 适应度 +ω2·F MLP ,ω1+ω2=1 Where: ω1, ω2 represent weighting parameters; F 适应度 represents the fitness scoring function based on the benefit term, resource consumption cost, and multi-level penalty term; F MLP Represents the prediction scoring function for the individual distribution structure.

10. The firepower distribution system based on double-layer decoupling and multi-level penalty genetic algorithm is characterized by: The firepower distribution system includes: A first-level decoupling modeling module is used to construct a first-level decoupling model of firepower tasks based on the threat relationship and spatial distribution characteristics between the attacking platform and the target platform. The first-level decoupling model includes a threat matrix and firepower allocation membership, which is used to characterize the target's counter-attack capability against the attacking platform and the platform's strike intent against the target. A secondary optimization modeling module is used to construct a secondary optimization model for firepower task allocation based on the objective function. The secondary optimization model integrates hard and soft constraints, adopts a multi-level penalty mechanism and an adaptive penalty factor to adjust the degree of constraint violation, and is used to characterize multiple optimization indicators such as mission strike effectiveness, firepower balance, and target priority; An intelligent optimization solution module is used to call the MLP-GA optimization method constructed by integrating the multi-layer perceptron and the genetic algorithm to iteratively solve the secondary optimization model. The intelligent optimization solution module includes: Initial population generation submodule: used to construct multiple firepower task allocation initial solution individuals that meet hard constraints according to task scale; Genetic evolution submodule: used to perform operations such as crossover, mutation, and constraint detection on the population; Fitness fusion evaluation submodule: used to jointly calculate the model fitness score and the MLP network prediction score, construct the fusion fitness function and perform iterative screening; Optimal solution output submodule: used to output the optimal fitness individual after meeting the convergence conditions as the final firepower task allocation plan.

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