An efficient task allocation method based on an improved genetic algorithm

Abstract

This invention discloses an efficient task allocation method based on an improved genetic algorithm, comprising the following steps: establishing a fire allocation model under joint strikes by multiple missile types; solving the multi-missile fire allocation model using an improved genetic algorithm based on Monte Carlo simulation; and obtaining strategy optimization results that satisfy a predetermined heavy damage effect. The method proposes an improved genetic algorithm combined with Monte Carlo simulation, capable of rapidly generating optimal fire allocation strategies in dynamic enemy-friendly combat environments, to solve missile fire allocation problems in large-scale, highly dynamic battlefields. The method has good versatility and scalability, and can be integrated as a standalone module into specific applications such as system simulation, red-blue force-on-force exercises, and wargaming to play a wider role.

Description

Technical Field

[0001] This invention belongs to the field of operations research and optimization technology, specifically relating to an efficient task allocation method based on an improved genetic algorithm. Background Technology

[0002] In recent years, research on using heuristic algorithms to solve the fire allocation problem has mainly included two categories: one is from the perspective of algorithm design, which is to avoid the algorithm getting stuck in local optima by designing different heuristic search strategies; the other is from the perspective of problem modeling, which is to improve the optimization model of the fire allocation problem, consider the fire allocation problem in the battlefield environment from different angles and levels, and improve the model's adaptability to dynamic environments.

[0003] In terms of algorithm design, the most common improvement approach is to design different encoding rules for different problems to better adapt to problem solving. For example, Zhang Ying et al. designed an integer encoding rule based on resource constraints based on the characteristics of the static fire allocation model, successfully solving the multi-target fire allocation problem; Zhu Weiliang et al. designed a unique sequence encoding rule for the genetic algorithm based on the special characteristics of the anti-ship missile fire allocation problem, significantly improving the algorithm's solution speed; Wang Bo et al. adopted a simple and intuitive decimal encoding strategy in the genetic algorithm, which facilitates the design of crossover and mutation operators; Wang Guangyuan et al. introduced the new element of population diversity measurement, designed an improved particle swarm optimization algorithm with dynamically adjusted inertia weights, and constructed a corresponding problem model for the fire allocation of shore-based missiles against naval vessels.

[0004] In addition, another approach to improvement is to design new heuristic algorithms using novel heuristic rules or to integrate existing heuristic algorithms to compensate for their shortcomings. For example, Liu Hao et al. designed a particle swarm optimization algorithm based on the foraging behavior of bird flocks and improved it by introducing the survival-of-the-fittest mechanism from genetic algorithms, effectively enhancing the algorithm's iterative performance and the accuracy of the global optimum. Regarding the design of new heuristic algorithms, Zhai Longgang et al. designed an artificial immune system algorithm based on the theory of artificial immune systems and applied it to missile fire allocation. Similarly, Xie Junjie used the Q-learning algorithm from reinforcement learning to solve the fire allocation problem, thereby improving the algorithm's solution efficiency.

[0005] In terms of problem modeling, the current common approach is to introduce new constraints or adopt different tactical strategies to address specific problems. For example, Zeng Jiayou et al. analyzed in detail the operational characteristics of shore-to-ship missiles and constructed a penetration probability model for a single ship within a multi-site shore-to-ship missile strike fleet; Wang Minle et al. considered the element of firing advantage and established an optimal fire allocation model for conventional missiles based on the effect-based combat mode; Zhu Chuanwei et al. used factors such as commander decisions and the effective range of the ship-to-air missile weapon system's illumination radar as constraints to establish a fire allocation model for the weapon system's illumination radar; Liu Xiaolei et al. constructed an optimization model for multi-target fire allocation of anti-tank missiles based on principles such as prioritizing key targets, maximizing mission objectives, and avoiding crossfire.

[0006] In fact, heuristic algorithms have achieved fruitful results in the study of fire allocation problems, but existing research still has certain limitations. Most algorithms lack generality, only addressing specific problem types and difficult to extend to other problems. Furthermore, most missile fire allocation models are built on the premise that the enemy's interception strategy is known or predetermined, without considering changes in that strategy. However, in actual battlefield environments, it is difficult for our side to obtain detailed enemy interception strategies. This necessitates thorough simulation of the enemy's interception strategy before missile launch, and based on this simulation, evaluating the mission success rate of our missile fire allocation strategy. Summary of the Invention

[0007] To address one or more technical problems in existing technologies, this invention provides an efficient task allocation method based on an improved genetic algorithm. The method proposes an improved genetic algorithm combined with Monte Carlo simulation, capable of rapidly generating optimal fire allocation strategies in dynamic combat environments, thus solving the missile fire allocation problem in large-scale, highly dynamic battlefields. This method possesses good versatility and scalability, and can be integrated as a standalone module into specific applications such as system simulation, red-blue force-versus-force exercises, and wargaming, thereby playing a wider range of roles.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] An efficient task allocation method based on an improved genetic algorithm includes the following steps:

[0010] Step 1: Establish a mission planning model for multiple types of missile-strike surface ships;

[0011] Step 2: Use an improved genetic algorithm based on Monte Carlo simulation to solve the multi-missile fire allocation model;

[0012] Step 3: Obtain the strategy optimization results that satisfy the given damage effect conditions.

[0013] Specifically, the fire allocation model under the joint strike of multiple missile types includes the objective function: This represents minimizing the cost of a fire strike, with the following constraints: Indicates missile stockpile constraints; X mij (D mj -L i )≤0, This indicates missile range constraints; This represents the target damage probability constraint, where M is the set of fire units, for any fire unit m∈M, I is the set of anti-ship missile types, for any missile i∈I, J is the set of enemy destroyers, for any enemy ship j∈J, C ij The cost required for anti-ship missile i to strike an enemy destroyer j, Q ij L represents the probability of anti-ship missile i damaging enemy destroyer j. i For the range of anti-ship missile i, D mj U represents the distance between fire unit m and enemy destroyer j. mi The number of anti-ship missiles i equipped for fire unit m, ε j X represents the probability of severely damaging enemy destroyer j. mij This represents the number of anti-ship missiles i required for fire unit m to strike enemy destroyer j.

[0014] Specifically, the improved genetic algorithm based on Monte Carlo simulation uses the improved Monte Carlo method to simulate the enemy's interception strategy, uses the genetic algorithm to perform the strategy search task, and uses a breadth-first search strategy to optimize our firepower allocation strategy.

[0015] Specifically, in the improved Monte Carlo method, an optimized random number generation algorithm, Sobol, is used to recursively generate random numbers, and historical sample data from the experience replay pool is used to dynamically adjust the number and location of sampling points to improve sampling efficiency.

[0016] Furthermore, the input to the improved genetic algorithm based on Monte Carlo simulation is the missile penetration probability P. ki Minimum number of missiles d min and the success rate of the predetermined task γ θ The output is our optimal firepower allocation strategy s g and maximum task success rate γ m Specifically, it includes the following steps:

[0017] Step 201, Initialize parameters: P0, ψ, σ, S B γ m P0 represents the initial population size, ψ represents the number of iterations, σ represents the mutation rate, and SB Indicates the size of the experience replay pool, γ m This represents the maximum task success rate in the iteration rounds;

[0018] Step 202: Generate an enemy destroyer air defense missile interception strategy based on the improved Monte Carlo simulation and put it into experience replay pool B;

[0019] Step 203, Initialize the population d = 1, 2, ..., P0;

[0020] Step 204, when γ m ≤γ θ hour:

[0021] Step 20401, repeat the following steps from n=1 to ψ:

[0022] Step 2040101: Read samples from experience replay pool B;

[0023] Step 2040102, adjust the missile penetration probability P. k ' i ;

[0024] Step 2040103, calculate each individual Task success rate γ d And select the task with the highest success rate.

[0025] Step 2040104: Mutation, selection, and crossover produce the next generation population. d = 1, 2, ..., P0;

[0026] Step 2040105: Dynamically adjust the enemy destroyer's air defense missile interception strategy and update the experience replay pool B;

[0027] Step 2040106, if Then Assigned to γ m ,Will Assigned to s g ;

[0028] Step 205, end the algorithm.

[0029] Specifically, the chromosome encoding method in the improved genetic algorithm adopts a decimal encoding mode, and different chromosomes correspond to different missile fire allocation methods: different gene segments on the chromosome correspond to different fire launch units, and the code value of the gene position on each gene segment represents the corresponding missile type.

[0030] Specifically, the formula for calculating the corrected missile penetration probability is as follows:

[0031]

[0032] The aforementioned calculation formula is based on the assumption that an enemy destroyer uses m type k anti-aircraft missiles to intercept n type i anti-ship missiles, and that the penetration probability P of each anti-ship missile against this batch of anti-aircraft missiles can be calculated. k ' i The Bernoulli binomial distribution model was established, and the results were obtained by modeling the saturated and unsaturated cases of the air defense channel.

[0033] Specifically, in the improved genetic algorithm, the task success rate is used as the fitness value of an individual. Selection, crossover, and mutation operations are performed based on the task success rate to evolve into better individuals.

[0034] Specifically, a breadth-first search strategy is used to optimize the fire allocation strategy. The depth of the breadth search is determined by the minimum number of missiles required to achieve the desired strike effect. The air defense missile interception strategy is dynamically adjusted during the selection, mutation, and crossover operations of the genetic algorithm to find the optimal fire allocation scheme more quickly. Attached Figure Description

[0035] Figure 1 This is a flowchart illustrating an embodiment of the present invention;

[0036] Figure 2 This is a schematic diagram of a width-first search according to an embodiment of the present invention;

[0037] Figure 3 This illustrates how the mission success rate varies with the minimum number of missiles launched in this embodiment of the invention. Detailed Implementation

[0038] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings. Obviously, the described embodiments are merely some, not all, of the embodiments of this invention. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.

[0039] The multi-missile firepower allocation problem is a type of firepower strike operation that studies how to inflict effective damage on the enemy while minimizing the loss of friendly firepower resources. It requires, at a specific operational moment and based on a given operational objective, coordinating various combat platforms to rationally allocate combat resources and achieve a predetermined destructive strike against the enemy target. Among these, the multi-missile joint strike against surface ships is a typical problem in this research, involving multiple missile types, multiple launch platforms, and multiple targets, among other multi-dimensional variables. In this embodiment, this problem can be defined as:

[0040] We need to formulate a firepower allocation plan so that, regardless of the interception strategy adopted by the enemy destroyer, the probability of severely damaging the enemy destroyer when we launch a simultaneous attack is no less than that of the designated target, and the missile launch cost should be kept as low as possible.

[0041] Based on the above requirements, the problem constraints can be set as follows:

[0042] (1) It is essential to ensure that our firepower launch platforms can carry out the assigned firepower strike missions;

[0043] (2) We must achieve the goal of inflicting heavy damage by carrying out a simultaneous strike;

[0044] (3) The effectiveness of the fire strike plan must be ensured under any enemy air defense strategy.

[0045] Assume we have M missile launch platforms, equipped with I different types of anti-ship missiles, which will launch a simultaneous attack on J enemy ships from different positions. To construct a fire planning model for a multi-missile joint strike, the model parameters are defined in Table 1.

[0046] Table 1 Explanation of Parameter and Variable Consistency

[0047]

[0048] Given limited firepower resources, maximizing firepower damage is a crucial aspect of operational command, while maximizing operational benefits with minimal operational costs is the ultimate goal of optimization theory. With minimizing the cost of firepower strikes as the objective, the model's objective function is designed as follows:

[0049]

[0050] Considering the limited number of ammunition in the actual fire launch phase, for any fire unit m, the total number of Type i anti-ship missiles launched cannot exceed the upper limit of the number of ammunition in that unit, that is:

[0051]

[0052] Simultaneously, it is necessary to determine whether fire unit m can effectively strike the enemy pursuing ship j, that is, to determine whether the range of anti-ship missile i matches the distance between fire unit m and the enemy destroyer j. If an effective strike cannot be achieved, this situation needs to be reasonably considered, and the missile range constraint should be established as follows:

[0053]

[0054] From the attacker's perspective, its aim is to achieve a target destruction probability against the enemy pursuing ship at minimal cost, which can be specifically described as:

[0055]

[0056] like Figure 1 As shown, this embodiment provides an efficient task allocation method based on an improved genetic algorithm, including the following steps:

[0057] Step 1: Establish a mission planning model for multiple types of missile-strike surface ships;

[0058] Step 2: Use an improved genetic algorithm based on Monte Carlo simulation to solve the multi-missile fire allocation model;

[0059] Step 3: Obtain the strategy optimization results that satisfy the given damage effect conditions.

[0060] Enemy strategy simulation based on Monte Carlo method

[0061] Assume the enemy destroyer j∈J is equipped with T types of k anti-aircraft missiles. jk Let k ∈ K, and K be the set of anti-aircraft missiles k. The penetration probability of anti-aircraft missile k against anti-ship missile i is denoted as P. ki ∈[0,1]. During the interception process, an anti-aircraft missile can only intercept one anti-ship missile i, and once launched, its interception target cannot be changed.

[0062] The Monte Carlo method, originally proposed by John von Neumann and Ulam, is also known as the stochastic simulation method. It's a method based on random sampling that uses random or pseudo-random numbers to solve complex mathematical problems. The Monte Carlo method is frequently used in simulation experiments to solve various uncertainties, such as in finance, physics, statistics, computer science, and biology. By inputting the distribution and relationships of some random variables, the Monte Carlo method can estimate the probability of certain events and calculate their expected values, yielding results with high accuracy and reliability.

[0063] While the Monte Carlo method is a commonly used numerical method, it has some drawbacks and limitations in simulating missile interception strategies. The Monte Carlo method requires generating and evaluating a large number of random samples; as the number of samples increases, the computational complexity grows exponentially. Simultaneously, the simulation requires storing and processing a large number of random numbers, which consumes significant storage and computational resources. Furthermore, insufficient random numbers increase the error of the estimation, affecting the reliability of the results. Finally, the convergence speed of the estimation is an unpredictable factor, typically requiring multiple experiments to obtain reliable results, further increasing the demand for computational and storage resources.

[0064] Therefore, in order to address the problem of excessive waste of computational and storage resources in the Monte Carlo method when simulating missile interception strategies, this embodiment considers adopting the following effective method:

[0065] (1) Optimize the random number generator

[0066] The quality and efficiency of the random number generator are key factors affecting the computational resources of the Monte Carlo method. Optimized random number generation algorithms, such as the Las Vegas method and Sobol sequences, can be used to reduce the computational and storage requirements. Here, we primarily use the Sobol recursive method to generate random numbers, and its specific implementation steps are as follows:

[0067] Enemy destroyers j∈J are equipped with n types of anti-aircraft missiles. Based on the Sobol sequence formula, n random sequences are generated, each with a real number between 0 and 1. The Sobol sequence formula is:

[0068] v[d]=2 -d ,d=1,2,...,n,

[0069]

[0070] Where, x j,k This represents the generated Sobol sequence, where v[d] is the binary encoding of the generated random number. During the random generation of air defense missile strategies, random sequences are generated recursively, and the number of generated sequences is determined by the Monte Carlo method.

[0071] This will generate a Sobol sequence x. j,k Same as 2 n-k Multiplying and rounding down yields a rounded sequence, which is the random generation sequence for the anti-aircraft missiles. Furthermore, the number of anti-aircraft missiles must satisfy a corresponding storage constraint; that is, the number of randomly generated anti-aircraft missiles cannot exceed the number of type k anti-aircraft missiles equipped on the enemy destroyer j∈J. jk Therefore, this step can be specifically represented as:

[0072]

[0073]

[0074] (2) Optimize the sampling strategy using the experience replay pool.

[0075] In Monte Carlo simulations, dynamically adjusting the sampling strategy can significantly improve efficiency and accuracy. Historical sample data from the experience replay pool can be used to adjust the sampling strategy; for example, the number and location of sampling points can be dynamically adjusted based on the distribution of historical samples to improve sampling efficiency. In this embodiment, the enemy destroyer's anti-aircraft missiles are encoded in decimal. Therefore, under given constraints, the enemy destroyer's interception strategy can be dynamically adjusted by changing the number of k-type anti-aircraft missiles, significantly reducing computational storage. The dynamic adjustment of the enemy interception strategy is mainly reflected in the heuristic search iteration process. Using the prior distribution of the enemy interception strategy from the previous iteration, interception strategies with high success rates are selected to dynamically generate new strategies and update the experience replay pool. Furthermore, when dynamically adjusting the number of k-type anti-aircraft missiles, the adjustment step size—the number added or subtracted from the original number of anti-aircraft missiles—significantly affects the algorithm's computational complexity. To balance the accuracy of the Monte Carlo method with computational complexity, the adjustment step size is set to 5 in this embodiment. Similarly, the adjusted number of anti-aircraft missiles must satisfy given constraints such as natural numbers and the total number of missiles.

[0076] Improved Genetic Algorithm Design

[0077] The improved genetic algorithm based on Monte Carlo simulation first encodes the friendly fire launch strategy and the enemy destroyer's air defense missile interception strategy. Second, for the friendly fire launch strategy, an initial population conforming to predetermined constraints is initialized, while the enemy destroyer's air defense missile interception strategy is generated based on the improved Monte Carlo simulation described in the previous section and placed into an experience replay pool. Considering the accuracy of the Monte Carlo algorithm, this embodiment sets the size of the experience replay pool to 10,000. Next, during the iterative search process of the genetic algorithm, the minimum number of missiles launched is taken as the objective, the maximum mission success rate during the iteration is calculated, and all anti-ship missile launch strategies with mission success rates satisfying the predetermined strike requirements are selected. If no anti-ship missile launch strategy satisfying the predetermined strike requirements exists in the current iteration round, the anti-ship missile launch strategy with the highest mission success rate is selected. Among all selected anti-ship missile launch strategies, the one with the lowest launch cost is considered the optimal missile launch strategy in the current iteration round. Finally, the next generation population is generated based on the optimal missile launch strategy in the current round, and the enemy missile interception strategy and experience replay pool are dynamically updated.

[0078] Based on the above analysis, the input to the improved genetic algorithm based on Monte Carlo simulation is the missile penetration probability P. ki Minimum number of missiles d min and the success rate of the predetermined task γ θ The output is our optimal firepower allocation strategy s g and maximum task success rate γ m Specifically, it includes the following steps:

[0079] Step 201, Initialize parameters: P0, ψ, σ, S B γ m P0 represents the initial population size, ψ represents the number of iterations, σ represents the mutation rate, and S B Indicates the size of the experience replay pool, γ m This represents the maximum task success rate in the iteration rounds;

[0080] Step 202: Generate an enemy destroyer air defense missile interception strategy based on the improved Monte Carlo simulation and put it into experience replay pool B;

[0081] Step 203, Initialize the population

[0082] Step 204, when γ m ≤γ θ hour:

[0083] Step 20401, repeat the following steps from n=1 to ψ:

[0084] Step 2040101: Read samples from experience replay pool B;

[0085] Step 2040102, adjust the missile penetration probability P. k ' i ;

[0086] Step 2040103, calculate each individual Task success rate γ d And select the task with the highest success rate.

[0087] Step 2040104: Mutation, selection, and crossover produce the next generation population.

[0088] Step 2040105: Dynamically adjust the enemy destroyer's air defense missile interception strategy and update the experience replay pool B;

[0089] Step 2040106, if Then Assigned to γ m ,Will Assigned to s g ;

[0090] Step 205, end the algorithm.

[0091] Encoding scheme

[0092] The number of missiles of various types is encoded, generating random permutations of the number of each type, such that the sum of the numbers of all types of missiles equals a predetermined minimum number of missiles to be launched. Simultaneously, constraints such as missile reserves and missile range must be satisfied. Based on this, the chromosome encoding method adopts a decimal encoding mode, with different chromosomes corresponding to different missile fire allocation methods. Different gene segments on the chromosome correspond to different fire launch units, and the code value of the gene position in each gene segment represents the corresponding missile type. The most obvious advantage of using an integer encoding mode is its intuitiveness and improved algorithm efficiency.

[0093] Penetration probability correction

[0094] Based on the characteristics of missile interception and air defense firepower allocation, if an enemy destroyer uses m type k air defense missiles to intercept our n type i anti-ship missiles, the penetration probability P of each anti-ship missile against this batch of air defense missiles can be calculated. k ' i By establishing a Bernoulli binomial distribution model and then modeling the saturated and unsaturated cases of the air defense passage separately, we can obtain:

[0095]

[0096] Fitness function design

[0097] The mission success rate is used as the fitness value of an individual. Mission success rate is a crucial indicator for evaluating the effectiveness of our firepower allocation strategy. It is defined as follows: Under the current anti-ship missile firepower allocation strategy, if there are N1 possible enemy air defense missile interception strategies, and N2 of these strategies prevent the current anti-ship missile firepower allocation strategy from achieving the intended heavy damage, let the mission success rate be γ. Its specific expression is as follows:

[0098]

[0099] Crossover and mutation operators

[0100] The mission success rate, acting as an individual's fitness value, determines the direction of the evolutionary algorithm. Therefore, operations such as selection, crossover, and mutation are needed based on the mission success rate to evolve superior individuals. In the selection operation, individuals with high mission success rates are chosen as parents. In the crossover operation, the missile allocation numbers of the parents are swapped, but constraints must be carefully considered to ensure that the crossover individuals meet the missile quantity limit. The mutation operation generates new firepower allocation strategies with a certain probability to increase population diversity.

[0101] Breadth-first search strategy

[0102] like Figure 2 As shown, to accelerate the convergence speed of the algorithm, we improve the traditional genetic algorithm by adopting a breadth-first search strategy to optimize our firepower allocation strategy. Specifically, the minimum number of missiles required to achieve the desired strike effect is used as the depth of the breadth search. During the selection, mutation, and crossover operations of the genetic algorithm, the air defense missile interception strategy is dynamically adjusted to find the optimal firepower allocation scheme more quickly.

[0103] Instance verification

[0104] To verify the feasibility and effectiveness of the improved genetic algorithm, this embodiment uses a red-blue opposing force scenario as a backdrop. From the red team's perspective, a coordinated attack is launched on the blue team's destroyer, with the goal of severely damaging it. The missile performance parameters for both sides are shown in Table 2, and the penetration probabilities of various red team missiles against different blue team air defense methods are shown in Table 3. The number of missiles required to severely damage a ship refers to the number of missiles hitting the ship that results in severe damage. It is important to emphasize that, for ease of description and to reduce computational complexity, this embodiment assumes that the launch cost of all missile types is the same.

[0105] Table 2 Performance parameters of missiles from both sides (Red and Blue)

[0106] Missile Name Quantity / piece The number of explosive shells that severely damaged the Blue Force destroyer A-1 24 2.5 A-2 16 2 A-3 12 1.8 A-4 16 3

[0107] (a) Performance parameters of the Red Force's missiles

[0108]

[0109]

[0110] (b) Performance parameters of Blue Force missiles

[0111] Table 3. Penetration Probability of Red Force's Various Missile Types Against Blue Force's Different Air Defense Methods

[0112]

[0113] To test the algorithm's performance, experiments were conducted on a computer configured with an Nvidia GeForce RTX 3060, using the PyCharm compiler in a Python 3.7 environment. The relevant parameters used in the improved genetic algorithm are shown in Table 4.

[0114] Table 4 Algorithm Parameters

[0115] Parameter name symbol numerical size Variation rate σ 0.1 Number of iterations ψ 100 Initial population size <![CDATA[P0]]> 50 Experience replay pool size <![CDATA[S B ]]> 1000

[0116] In actual combat, mission success rate represents the certainty of completing the fire strike mission. According to the system-breaking strategy, the goal is to destroy the target as much as possible. In this embodiment, the predetermined mission success rate is set to 99%. Using an improved genetic algorithm in this example, the mission success rate achievable with the minimum number of missiles launched by the Red Force is shown in Table 5. The table also illustrates how the mission success rate changes with the minimum number of missiles required for the Red Force to launch. Figure 3 As shown.

[0117] Table 5. Mission success rate corresponding to the minimum number of missiles for the Red Team.

[0118] Red team's minimum number of missiles Task success rate Red team's minimum number of missiles Task success rate 10 0.2255 21 0.8067 11 0.3055 22 0.9228 12 0.3867 23 0.8901 13 0.4701 24 0.9799 14 0.4989 25 0.9757 15 0.5769 26 0.98 16 0.6509 27 0.9887 17 0.6513 28 0.9974 18 0.715 29 0.9957 19 0.6713 30 0.9998 20 0.8516 31 0.9998

[0119] Therefore, when the Red Force launches 28 anti-ship missiles, it can meet the problem constraint of a 99% mission success rate, and the Blue Force destroyer is severely damaged. The optimal firepower allocation result for the Red Force at this time is shown in Table 6.

[0120] Table 6 Optimal Firepower Allocation Strategy for the Red Team

[0121] A-1 A-2 A-3 A-4 24 2 0 2

[0122] Similarly, once the optimal firepower allocation strategy for the Red Team is determined, the optimal interception strategy for the Blue Team is calculated using an improved genetic algorithm to minimize the damage it suffers. The corresponding Blue Team air defense missile interception strategies are shown in Table 7.

[0123] Table 7: Blue Team's Most Effective Interception Strategy

[0124] FK-2 FK-2 FK-2 A-1 9 12 1 A-2 17 11 29 A-3 23 1 11 A-4 5 5 2

[0125] Finally, the improved genetic algorithm based on Monte Carlo simulation was compared with traditional classical algorithms and computer numerical simulation methods on the same computing platform. The results are shown in Table 8.

[0126] Table 8: Summary of Algorithm Comparison Results

[0127] Algorithm Name Runtime Number of solutions Properties of solutions An improved genetic algorithm based on Monte Carlo simulation Approximately 27 minutes 6 More accurate Traditional genetic algorithm Approximately 96 minutes 4 More accurate Computer numerical simulation Approximately 258 minutes 1 accurate

[0128] By comparing the improved genetic algorithm based on Monte Carlo simulation with the traditional genetic algorithm and pure computer simulation, it is easy to see that the improved genetic algorithm has a much shorter running time than other algorithms, can find most feasible solutions that meet the constraints, and the properties of the solutions are more accurate, providing a reference for commanders in fire command decisions on the battlefield.

Claims

1. An efficient task allocation method based on an improved genetic algorithm, characterized in that, Includes the following steps: Step 1: Establish a fire allocation model for joint strikes by multiple types of missiles; Step 2: Use an improved genetic algorithm based on Monte Carlo simulation to solve the multi-missile fire allocation model; Step 3: Obtain the strategy optimization results that satisfy the given damage effect conditions; The fire allocation model under the joint strike of multiple missile types includes the objective function: This represents minimizing the cost of a fire strike, with the following constraints: , This indicates a missile stockpile constraint. , This indicates a missile range constraint. , , represents the target damage probability constraint, where, For a set of firepower units, for any firepower unit , For a set of anti-ship missile types, for any missile , Assemble enemy destroyers, target any enemy vessel. , For anti-ship missiles Strike enemy destroyers Required costs For anti-ship missiles against enemy destroyers The probability of damage, For anti-ship missiles range, For firepower units With enemy destroyers distance, For firepower units Equipped with anti-ship missiles Quantity, To counter enemy destroyers The probability of a critical hit, and This is a firepower unit. Strike enemy destroyers Required anti-ship missiles Quantity required ; The corrected formula for calculating the probability of missile penetration is as follows: ； The aforementioned calculation formula is based on the enemy destroyer's... pieces Type of anti-aircraft missile intercepts our side pieces Type of anti-ship missile, which reduces the penetration probability of each anti-ship missile against this batch of air defense missiles. The Bernoulli binomial distribution model was established, and the results were obtained by modeling the saturated and unsaturated cases of the air defense channel.

2. The efficient task allocation method based on the improved genetic algorithm according to claim 1, characterized in that, The improved genetic algorithm based on Monte Carlo simulation uses an improved Monte Carlo method to simulate the enemy's interception strategy, uses a genetic algorithm to perform the strategy search task, and uses a breadth-first search strategy to optimize our firepower allocation strategy.

3. The efficient task allocation method based on the improved genetic algorithm according to claim 2, characterized in that, In the improved Monte Carlo method, an optimized random number generation algorithm, Sobol, is used to recursively generate random numbers, and historical sample data from the empirical replay pool is used to dynamically adjust the number and location of sampling points to improve sampling efficiency.

4. The efficient task allocation method based on the improved genetic algorithm according to claim 1, characterized in that, The improved genetic algorithm based on Monte Carlo simulation takes the missile penetration probability as input. Minimum number of missiles and the success rate of the established task The output is our optimal firepower allocation strategy. and maximum task success rate Specifically, it includes the following steps: Step 201, Initialize parameters: , , , , , Indicates the initial population size. Indicates the number of iterations. Indicates the rate of variation. Indicates the size of the experience replay pool. This represents the maximum task success rate in the iteration rounds; Step 202: Generate an enemy destroyer's air defense missile interception strategy based on the improved Monte Carlo simulation and put it into the experience replay pool. middle; Step 203, Initialize the population , ; Step 204, when hour: Step 20401, from arrive Repeat the following steps: Step 2040101, from the experience replay pool Read samples from the middle; Step 2040102, adjust the missile penetration probability. ; Step 2040103, calculate each individual Task success rate And select the task with the highest success rate. ; Step 2040104: Mutation, selection, and crossover produce the next generation population. , ; Step 2040105: Dynamically adjust the enemy destroyer's air defense missile interception strategy and update the experience replay pool. ; Step 2040106, if Then Assign to ,Will Assign to ; Step 205, end the algorithm.

5. The efficient task allocation method based on the improved genetic algorithm according to claim 1, characterized in that, In the improved genetic algorithm, the chromosomes are encoded in a decimal encoding mode. Different chromosomes correspond to different missile fire allocation methods: different gene segments on the chromosome correspond to different fire launch units, and the code value of the gene position on each gene segment represents the corresponding missile type.

6. The efficient task allocation method based on the improved genetic algorithm according to claim 1, characterized in that, In the improved genetic algorithm, the task success rate is used as the fitness value of an individual. Selection, crossover, and mutation operations are performed based on the task success rate to evolve into better individuals.

7. The efficient task allocation method based on the improved genetic algorithm according to claim 2, characterized in that, The fire allocation strategy is optimized using a breadth-first search strategy. Specifically, the depth of the breadth search is determined by the minimum number of missiles required to achieve the desired strike effect. The air defense missile interception strategy is dynamically adjusted during the selection, mutation, and crossover operations of the genetic algorithm to find the optimal fire allocation scheme more quickly.

Images