A particle swarm optimization method for area defense interception decision

Abstract

The application discloses a particle swarm optimization method for regional defense interception decision, and comprises the following steps: firstly, acquiring the current situation of regional defense, obtaining the threat coefficient of an attacking target and the defense interception coefficient of a weapon platform launching a missile, setting the population size and the maximum iteration number of the particle swarm and initializing the population particles; obtaining the interception efficiency of all the current particles according to the threat coefficient of the attacking target and the success coefficient of the defense interception; finally, outputting the particle with the maximum fitness in all the particles, taking the particle vector coordinates of the particle as the current particle population optimum, and comparing the particle with the optimal particle found so far to update the global optimal vector coordinates. The application can effectively solve the particle swarm optimization method for regional defense interception target distribution into local optimum, slow convergence speed in the late iteration, low solution accuracy and other defects, constantly reach the global optimal solution of the particle, improve the convergence speed, ensure the stability of the convergence, and meet the real-time requirement of the auxiliary decision in the modern local battlefield.

Description

Technical Field

[0001] This invention relates to the field of computer simulation and method optimization technology, and in particular to a particle swarm optimization method for a regional defense interception strategy. Background Technology

[0002] The area defense interception strategy problem primarily stems from the needs of classic military operations. It is a fundamental area of ​​defense-related military operations research. This problem is a strictly constrained combinatorial optimization problem, proven to be nondeterministic polynomial-time complete, and its research is of significant importance. The area defense interception problem refers to multiple incoming targets attacking valuable facilities within a friendly area, with the targets dispersing their firepower to strike different facilities during the attack. With a sharp increase in the number of incoming targets, the friendly forces also need to simultaneously launch a large number of missiles and other interceptor aircraft to intercept them, thus forming a target allocation and interception strategy problem involving multiple weapon platforms. The key to intercepting multiple incoming targets is target allocation based on the interception capabilities of friendly weapon platforms and missile resources. Area defense situation assessment and threat analysis are the foundation of target allocation. Therefore, area defense situation assessment, threat analysis, and target allocation together constitute the core content of area defense, with interception strategy being the most critical component.

[0003] Current regional defense interception strategies primarily rely on basic empirical formulas to calculate the interception coefficients of weapon platforms. Target allocation methods mainly include particle swarm optimization (PSO), genetic algorithms, and ant colony optimization (ACO). However, most basic swarm intelligence algorithms suffer from low efficiency and poor convergence. Kennedy et al. proposed the Particle Swarm Optimization (PSO) method in 1995 due to its simple concept, ease of operation, and wide search space. However, PSO also suffers from drawbacks such as convergence to local optima, slow convergence speed in later iterations, and low accuracy. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of particle swarm optimization (PSO) methods for target allocation in weapon platforms used for intercepting incoming targets in area defense, such as being prone to getting trapped in local optima, slow convergence speed in the later stages of iteration, and low solution accuracy. This invention proposes a novel PSO optimization method for interception strategy decision-making. Utilizing the basic principles of PSO, the method adjusts particle coordinates based on these principles and applies a new search algorithm to invalid particle coordinates. This allows particles to continuously reach the global optimum while improving convergence speed and ensuring convergence stability. The objective of this invention is achieved through the following technical solution: a PSO optimization method for area defense interception decision-making, comprising the following steps:

[0005] Step 1: Obtain the current situation of regional defense from the decision-making command center;

[0006] This includes the number and location of our defensive weapon platforms, the number of missiles each platform can launch, the number and location of enemy incoming targets, enemy air strike targets, and the type and performance of the incoming targets.

[0007] Step 2: Based on the current regional defense situation, obtain the threat coefficient of the incoming target and the defense interception coefficient of the missiles launched by the weapon platform using empirical formulas;

[0008] The threat level of an incoming target is the value of that target in attacking our facilities.

[0009] Defense Interception Coefficient

[0010] P = F(V) a V t ,θ,φ,σ) (1)

[0011] Where V a Accelerating the incoming target, V t Let be the velocity of the incoming target, θ, φ, and σ be the angles of the incoming target and our missile launch, respectively, and σ be two parameters following a normal distribution. F is an interception coefficient calculation function, and P is the obtained defensive interception value.

[0012] Step 3: Set the particle swarm size and maximum number of iterations;

[0013] The population size of the particle swarm is the number of particles, representing the number of different interception strategy schemes contained in the interception strategy set; the maximum number of iterations represents the number of times the strategy set is continuously modified, that is, how many times the interception strategy set is modified: the interception strategy set refers to the set of interception targets and the number of interception missiles launched by each weapon platform under all feasible solutions.

[0014] Step 4: Initialization of population particles;

[0015] Each particle is represented by an N-dimensional vector coordinate, where N is the number of weapon platforms, and the vector coordinate represents the aircraft designation of the incoming target that our weapon platform will intercept, along with the number of interceptor missiles launched against that target. The vector coordinates are represented as follows:

[0016]

[0017] Where i is the i-th particle in the particle swarm, and d is the n-th dimension of the particle. The integer part of the particle coordinates represents the incoming target number intercepted by the weapon platform. The fractional part of the particle coordinates represents the number of interceptor missiles the weapon platform used to intercept the target.

[0018] Step 5: Based on the threat coefficient of the incoming target and the success coefficient of the defense and interception, obtain the interception effectiveness of all particles according to the empirical formula (3) for interception effectiveness.

[0019] Empirical formula for interception effectiveness;

[0020]

[0021]

[0022] f = max{f 1 / f 2} (4)

[0023] Where f 1 To maximize the enemy's loss function, f 2 To minimize our loss function, f maximizes the interception efficiency. j p represents the threat coefficient of the j-th incoming target. kj Let x be the defensive interception coefficient of the k-th weapon platform against the j-th incoming target. kj Let q be the number of interceptor missiles of the k-th weapon platform against the j-th incoming target. k Let be the missile value coefficient of the k-th weapon platform.

[0024] Step Six: The interception efficiency of all particles is used as the fitness of the particles as the historical best coordinates of the individual particles. The particles with the highest fitness are selected, and their coordinates are used as the historical best coordinates of the population.

[0025] Step 7: Change the vector coordinates of the particles, update the historical best coordinates of the particle swarm and the best coordinates of the individual particles, use the interception efficiency as the fitness of the particle swarm algorithm, find the particle with the maximum fitness among all particles, take its particle vector coordinates as the current best of the particle swarm, and compare it with the best particle found so far to update the global best vector coordinates.

[0026] The vector coordinates of each particle are changed according to the following rules and steps:

[0027] (1) The best historical coordinates of the particle population and the vector coordinates of the current particle, the best individual coordinates of the particle, and the vector coordinates of the current particle are updated according to formula (4) to update the particle's update speed.

[0028] (2) Update the new coordinates of the particle according to formula (5).

[0029] (3) According to formula (6), make the coordinates of the new particle satisfy the search space required by the algorithm and use it as a feasible solution for the interception strategy.

[0030] (4) Recalculate the fitness of the particle according to formula (3).

[0031] Particle velocity update formula:

[0032]

[0033] Particle coordinate update formula:

[0034]

[0035] Where w is the inertia weight; c1 and c2 are acceleration factors; 1,2 A random number in the interval [0, 1] Let gbest be the optimal coordinates experienced by the i-th particle up to generation G. G It is the optimal coordinate found by the entire particle swarm up to generation G. V represents the position of the i-th particle in the (G+1)-th generation. i G+1 Let be the velocity of the i-th particle in the (G+1)-th generation.

[0036] A novel semi-random search algorithm formula:

[0037] 'a' is a random number from Generate a positive integer

[0038] To randomly select from [0, LOAD d Generate a positive integer (7)

[0039]

[0040] in express The interception target does not satisfy the algorithm's validity correction within the search space, i.e., the position of the i-th particle in the j-th dimension after G+1 generation correction. Similarly... The number of missiles launched against the intercept target, radius r = (*M / 2) The underscore indicates the rounding symbol, coff = 1 - tanh( / ), G is the current iteration number, MaxIter is the maximum number of iterations for the particle swarm, tanh is the tangent function, M is the number of incoming enemy targets, and LOaD is the maximum number of missiles that the weapon platform can launch. The novel semi-random search algorithm formula described above in this invention ensures that the solution avoids getting trapped in local optima through randomness and also fully considers historical optimal information. Therefore, this novel search algorithm can ensure the global optimum and stability of the solution.

[0041] Changing the historical best coordinates of the particle population and the individual historical best coordinates of a particle involves the following steps:

[0042] 1) Compare the fitness of all the modified particles according to formula (9), find the maximum fitness, and compare it with the fitness of the best historical coordinate of the population recorded up to now. If it is greater than the fitness of the best historical position of the population, replace the previously recorded best historical coordinate of the population and obtain the new best historical coordinate of the population.

[0043] 2) According to formula (10), the fitness of each particle’s own historical best coordinates and the changed coordinates are compared. If the new coordinates are better than the historical best coordinates of the individual particle, then the new coordinates are taken as the best coordinates of the individual particle.

[0044]

[0045]

[0046] Let gbest be the optimal coordinates experienced by the i-th particle up to generation G. G It is the optimal coordinates found by the entire particle swarm up to generation G, which is the fitness function, i.e., maximizing interception efficiency.

[0047] Step 8: Repeat step 7, continuously updating the particle coordinates until the maximum number of iterations is reached.

[0048] Step 9: Output the vector coordinates of the globally optimal particle, which is the best interception strategy.

[0049] The resulting interception strategy is an optimized allocation scheme in the regional interception process under the condition that the information of the incoming target is known, which allocates the incoming targets on the battlefield to weapon platforms for interception.

[0050] The effective effects of this invention are as follows: 1. It models a real-world regional defense interception scenario, achieving a near-realistic interception of incoming targets. 2. The improved search algorithm avoids the particle swarm optimization algorithm getting stuck in local optima and premature convergence due to the manual allocation of targets using invalid particle coordinates. It semi-randomly selects new valid coordinate values ​​based on historical coordinate information to ensure that particles with high local fitness are selected, guaranteeing population diversity. It intelligently selects interception strategies that satisfy constraints, ensuring optimal interception strategies and maximizing the interception effectiveness of the regional defense interception strategy. 3. The formula of the semi-random search algorithm uses randomness to ensure that the solution avoids getting stuck in local optima and also fully considers historical optimal information, ensuring the global optimality and stability of the solution. Attached Figure Description

[0051] Figure 1 This is the method flow of the present invention;

[0052] Figure 2 This is a schematic diagram illustrating the principle of the search algorithm. Detailed Implementation

[0053] The present invention will now be described in further detail with reference to the accompanying drawings and embodiments.

[0054] This invention discloses a particle swarm optimization method for area defense interception decision-making, the process of which is as follows: Figure 1 As shown, it includes the following steps: Step 1: The decision-making command center obtains the current situation of regional defense;

[0055] Obtain the current regional defense situation from the decision-making command center, including: the number and location of our defensive weapon platforms and the number of missiles each platform can launch; the number and location of incoming enemy targets; enemy air strike targets; and the type and capabilities of the incoming targets. Step Two: Based on the current regional defense situation, use empirical formulas to obtain the threat coefficient of the incoming targets and the defensive interception coefficient of the missiles launched by the weapon platforms.

[0056] The empirical formula for the interception coefficient of our weapon platform k against the incoming target j is:

[0057] P = F(V) a V t ,θ,φ,σ) (1)

[0058] Where V a Accelerating the incoming target, V t Let θ be the velocity of the incoming target, φ be the angle between the incoming target and our missile launcher, and σ be two parameters of the normal distribution. F is an interception coefficient calculation function, and P is the obtained defense interception value.

[0059] Step 3: Set the population size and maximum number of iterations for the particle swarm.

[0060] The population size of the particle swarm is the number of particles, representing the number of different interception strategy schemes contained in the interception strategy set; the maximum number of iterations represents the number of times the strategy set is continuously modified, that is, how many times the interception strategy set is modified: the interception strategy set refers to the set of interception targets and the number of interception missiles launched by each weapon platform under all feasible solutions.

[0061] Step 4: Initialization of population particles;

[0062] Each particle represents an N-dimensional vector coordinate, where N is the number of weapon platforms, and the vector coordinate represents the aircraft code of the incoming target that our weapon platform will intercept and the number of interceptor missiles launched against that target.

[0063] For example, if we currently have 4 weapon platforms, then each particle vector is 4-dimensional. The upper limit of missiles that the 4 weapon platforms can launch is (2,1,2,3). In the coordinates (2.1,3.1,1.2,4.2), the value 2.1 represents the first weapon platform intercepting the 2nd incoming target and launching 1 missile, the second value 3.1 represents the second weapon platform intercepting the 3rd incoming target and launching 1 missile, and so on. The last value 4.2 represents the coordinates of the fourth weapon platform intercepting the 4th incoming target and launching 2 missiles.

[0064] Step 5: Based on the threat coefficient of the incoming target and the success coefficient of the defense and interception, obtain the interception effectiveness of all particles according to the empirical formula (3) for interception effectiveness.

[0065] Empirical formula for interception coefficient;

[0066]

[0067]

[0068] f = max{f 1 / f 2} (4)

[0069] Among them, f 1 To maximize the enemy's loss function, f 2 To minimize our loss function, f maximizes the interception efficiency. j p represents the threat coefficient of the j-th incoming target. kj Let x be the defensive interception coefficient of the k-th weapon platform against the j-th incoming target. kj Let q be the number of interceptor missiles of the k-th weapon platform against the j-th incoming target. k Let be the missile value coefficient of the k-th weapon platform.

[0070] Step Six: The interception efficiency of all particles is used as the fitness of the particles as the historical best coordinates of the individual particles. The particles with the highest fitness are selected, and their coordinates are used as the historical best coordinates of the population.

[0071] Step 7: Change the vector coordinates of the particles, update the historical best coordinates of the particle swarm and the best coordinates of the individual particles, use the interception efficiency as the fitness of the particle swarm algorithm, find the particle with the maximum fitness among all particles, take its particle vector coordinates as the current best of the particle swarm, and compare it with the best particle found so far to update the global best vector coordinates.

[0072] The vector coordinates of each particle change according to Figure 2 To provide a more detailed description, please follow these rules and steps:

[0073] 1) The best historical coordinates of the particle population and the vector coordinates of the current particle, the best individual coordinates of the particle, and the vector coordinates of the current particle are updated according to formula (4) to update the particle's update speed.

[0074] Particle velocity update formula:

[0075]

[0076] Where w is the inertia weight; c1 and c2 are acceleration factors; 1,2 A random number in the interval [0, 1] Let gbest be the optimal coordinates experienced by the i-th particle up to generation G. G It is the optimal coordinate found by searching the entire particle swarm up to generation G.

[0077] (2) Update the new coordinates of the particle according to formula (5).

[0078] Particle coordinate update formula:

[0079]

[0080] V represents the position of the i-th particle in the (G+1)-th generation. i G+1 Let be the velocity of the i-th particle in the (G+1)-th generation.

[0081] (3) According to formula (6), make the coordinates of the new particle satisfy the search space required by the algorithm and use it as a feasible solution for the interception strategy.

[0082] A novel semi-random search algorithm formula:

[0083] 'a' is a random number from Generate a positive integer

[0084] b is a random number drawn from [0, LOAD] d Generate a positive integer (7)

[0085]

[0086] in express The interception target does not satisfy the algorithm's validity correction within the search space, i.e., the position of the i-th particle in dimension d after G+1 generation correction. Similarly... The number of missiles launched against the intercept target, radius r = (coff*M / 2)The underline indicates the rounding symbol, coff = 1 - tanh(G / MaxIter), where G is the current iteration number, MaxIter is the maximum number of iterations for the particle swarm, tanh is the tangent function, M is the number of enemy targets, and LOAD is the maximum number of missiles that the weapon platform can launch. The novel semi-random search algorithm formula of the present invention ensures that the solution avoids getting trapped in local optima through randomness and also fully considers the historical optimal information. Therefore, the novel search algorithm can ensure the global optimum and stability of the solution. (4) Recalculate the fitness of the particle according to formula (3).

[0087] Changing the historical best coordinates of the particle population and the individual historical best coordinates of a particle involves the following steps:

[0088] 1) Compare the fitness of all the modified particles according to formula (9), find the maximum fitness, and compare it with the fitness of the best historical coordinate of the population recorded up to now. If it is greater than the fitness of the best historical position of the population, replace the previously recorded best historical coordinate of the population and obtain the new best historical coordinate of the population.

[0089] 2) According to formula (10), the fitness of each particle’s own historical best coordinates and the changed coordinates are compared. If the new coordinates are better than the historical best coordinates of the individual particle, then the new coordinates are taken as the best coordinates of the individual particle.

[0090]

[0091]

[0092] Let gbest be the optimal coordinates experienced by the i-th particle up to generation G. G It is the optimal coordinates found by the entire particle swarm up to generation G, which is the fitness function, i.e., maximizing interception efficiency.

[0093] Step 8: Repeat step 7, continuously updating the particle coordinates until the maximum number of iterations is reached.

[0094] Step 9: Output the vector coordinates of the globally optimal particle, which is the best interception strategy.

[0095] The resulting interception strategy is an optimized allocation scheme in the regional interception process under the condition that the information of the incoming target is known, which allocates the incoming targets on the battlefield to weapon platforms for interception.

[0096] The obtained interception strategy is an optimized allocation scheme in the regional interception process under the condition that the information of the incoming target is known. It allocates the incoming targets on the battlefield to weapon platforms for interception, striving to achieve the best interception effect.

Claims

1. A particle swarm optimization method for regional defense interception decision-making, characterized in that, It includes the following steps: Step 1: Obtain the current situation of regional defense: including the number and location of our defensive weapon platforms and the number of missiles that the platforms can launch, the number and location of enemy incoming targets, enemy air strike targets, and the type and performance of incoming targets; Step 2: Based on the current regional defense situation, obtain the threat coefficient of the incoming target and the defense interception coefficient of the missiles launched by the weapon platform; The threat level of an incoming target is the value of that target in attacking our facilities; Defense Interception Coefficient: (1) in, Accelerate for incoming targets For the speed of the incoming target, These are two parameters: the angle of the incoming target and the angle of our missile launch, and the normal distribution. F is an interception coefficient calculation function, and P is the obtained defensive interception value. Step 3: Set the population size and maximum number of iterations for the particle swarm optimization. The population size of the particle swarm is the number of particles, representing the number of different interception strategy schemes contained in the interception strategy set; the maximum number of iterations represents the number of times the strategy set is continuously modified, that is, how many times the interception strategy set is modified: the interception strategy set refers to the set of interception targets and the number of interception missiles launched by each weapon platform under all feasible solutions. Step 4: Initialization of population particles; Each particle is represented by an N-dimensional vector coordinate, where N is the number of weapon platforms, and the vector coordinate represents the aircraft designation of the incoming target that our weapon platform will intercept, along with the number of interceptor missiles launched against that target. The vector coordinates are represented as follows: Where i is the i-th particle in the particle swarm, and d is the n-th dimension of the particle. The integer part of the particle coordinates represents the incoming target number intercepted by the weapon platform. The fractional part of the particle coordinates represents the number of interceptor missiles the weapon platform used to intercept the target. Step 5: Based on the threat coefficient of the incoming target and the success coefficient of the defense and interception, obtain the interception effectiveness of all particles according to the empirical formula (3) for interception effectiveness; Empirical formula for interception effectiveness; (2) (3) (4) in To maximize the enemy's loss function, To minimize our loss function, To maximize interception efficiency; Let be the threat coefficient of the j-th incoming target. Let be the defense interception coefficient of the k-th weapon platform against the j-th incoming target. Let be the number of interceptor missiles of the k-th weapon platform against the j-th incoming target. Let be the missile value coefficient of the k-th weapon platform; Step 6: The interception efficiency of all particles is used as the fitness of the particles as the historical best coordinates of the individual particles. The particles with the highest fitness are selected, and their coordinates are used as the historical best coordinates of the population. Step 7: Change the vector coordinates of the particles, update the historical best coordinates of the particle swarm and the best coordinates of the individual particles, use the interception efficiency as the fitness of the particle swarm algorithm, find the particle with the maximum fitness among all particles, take its particle vector coordinates as the current best of the particle swarm, and compare it with the best particle found so far to update the global best vector coordinates. Step 8: Repeat Step 7, continuously updating the particle coordinates, until the set maximum number of iterations is reached; Step 9: Output the vector coordinates of the globally optimal particle, i.e. the best interception strategy; the obtained interception strategy is an optimized allocation scheme in the regional interception process under the condition that the information of the incoming target is known, which allocates the incoming targets on the battlefield to weapon platforms for interception; Step seven, specifically changing the particle's vector coordinates, includes the following steps: (1) The best historical coordinates of the particle population and the vector coordinates of the current particle, the best individual coordinates of the particle and the vector coordinates of the current particle are updated according to formula (4) to update the particle's update speed; (2) Update the particle's new coordinates according to formula (5); (3) According to formula (6), make the coordinates of the new particle satisfy the search space required by the algorithm and use it as a feasible solution for the interception strategy; (4) Recalculate the fitness of the particle according to formula (3); Particle velocity update formula: (5) Particle coordinate update formula: (6) in, Inertial weights; It is an acceleration factor; A random number in the interval [0, 1] until The optimal coordinates experienced by the i-th particle. It is the optimal coordinate found by the entire particle swarm up to generation G. Let be the position of the i-th particle in the (G+1)-th generation. Let be the velocity of the i-th particle in the (G+1)-th generation; A novel semi-random search algorithm formula: (7) (8) in express The interception target does not satisfy the requirement that its position within the search space be corrected for validity by the algorithm, i.e., the position of the i-th particle in dimension d after G+1 generation correction; similarly... The number of missiles launched against the intercept target, radius The underscore indicates the rounding symbol. This represents the current iteration number. The maximum number of particle swarm optimizations. It is the tangent function. The number of enemy targets attacking. This represents the maximum number of missiles that the weapon platform can launch. Step seven, which involves updating the historical optimal coordinates of the particle population and the optimal coordinates of individual particles, includes the following steps: 1) Compare the fitness of all the modified particles according to formula (9), find the maximum fitness, and compare it with the fitness of the best historical coordinate of the population recorded up to now. If it is greater than the fitness of the best historical position of the population, replace the previously recorded best historical coordinate of the population and obtain the new best historical coordinate of the population. 2) According to formula (10), the fitness of each particle’s own historical best coordinates and the changed coordinates are compared. If the new coordinates are better than the historical best coordinates of the individual particle, then the new coordinates are taken as the best coordinates of the individual particle. (9) (10) until The optimal coordinates experienced by the i-th particle. It is the optimal coordinate found by the entire particle swarm up to generation G. The fitness function is used to maximize interception efficiency.

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