Radar interference resource allocation method based on improved grey wolf algorithm

Abstract

The invention discloses a radar interference resource allocation method based on a grey wolf algorithm. The method mainly solves the problems that in the prior art, interference resource allocation efficiency is low, combination explosion occurs, and engineering implementation is not facilitated. The scheme comprises the following steps: 1) constructing an interference task scene, and constraining a solution space through a coding strategy optimization method; 2) constructing an interference resource allocation objective function, and initializing an allocation scheme according to a good point set theory; 3) on the basis of the grey wolf algorithm, a nonlinear convergence factor, a dynamic weight and a reverse learning method are introduced to complete updating of a grey wolf position, namely updating of a distribution scheme is completed; and 4) repeating the iterative updating process in the step 3) until the algorithm converges, and taking the wolf pack position corresponding to the currently obtained interference benefit as a final interference resource allocation result. The method can effectively improve the optimization speed in the resource allocation process, avoids falling into a local optimal solution, and can be used for improving the resource allocation task efficiency in a radar cooperative interference scene.

Description

Technical Field

[0001] This invention belongs to the field of radar technology, and further relates to jamming resource allocation technology, specifically a radar air jamming resource allocation method based on an improved gray wolf algorithm, which can be used to improve resource allocation efficiency in cooperative jamming scenarios. Background Technology

[0002] Radar jamming resource allocation refers to allocating jammer beams within the current jammer's capability range, based on the threat level of incoming targets and the benefits that jammers can gain from jamming targets. Jamming resource allocation is actually a nonlinear integer combinatorial optimization problem. As the number of radars and jammers increases, the computational complexity also increases accordingly. It is a class of NP-hard (Non-deterministic Polynomial-hard) problems. For example, the improved ant colony algorithm proposed by He Fan et al. is used to solve the optimal allocation of multi-target radar jamming resources [J]. Firepower and Command Control, 2014, 39(06):111-114. Applying traditional methods to jamming resources can achieve good results in small-scale scenarios, but as the processing scale increases, it is often difficult to find the global optimal solution and has poor real-time performance. Optimization algorithms provide a new approach to the jamming resource allocation problem. The gray wolf algorithm has few core parameters and a simple principle. Unlike genetic algorithms and particle swarm algorithms, it does not require additional manually set parameters and is widely used in various fields such as power grid energy storage optimization and powerless optimization. It is also applicable to jamming resource allocation schemes.

[0003] In their patent document titled "A Method for Cooperative Jamming Resource Allocation of Networked Radars Based on Gray Wolf Algorithm," Li Chao et al. established a distance matrix to determine the radar number of each jammer, thereby constructing an optimal jamming resource allocation model. Based on the actual number of jammers, the number of jamming patterns, and the number of radars in the network, they encoded the individual positions in the gray wolf population and initialized the population. An improved gray wolf optimization algorithm was then used to solve the optimal jamming resource allocation model. After iteration, the position vector of the gray wolf corresponding to the maximum fitness value in the last generation of the gray wolf population was recorded to achieve the optimal jamming resource allocation. This method is applicable to scenarios involving cooperative jamming of networked radars. However, the proposed algorithm still suffers from problems such as being prone to getting trapped in local optima, having weak local search capabilities, and slow convergence speed in later stages. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of existing technologies by proposing a radar jamming resource allocation method based on an improved GreyWolf Optimizer (IGWO). This method solves the technical problems of low resource allocation efficiency and combinatorial explosion in cooperative jamming scenarios, which are detrimental to engineering implementation. The proposed Improved GreyWolf Optimizer (IGWO) effectively improves the convergence speed and makes it easier to obtain the global optimum by introducing coding strategy optimization, optimal point set theory, nonlinear convergence factor, dynamic weight mechanism, and back-learning theory strategy. Simulations verify the correctness and superiority of the IGWO algorithm, demonstrating its ability to significantly improve resource allocation efficiency in cooperative jamming scenarios.

[0005] To achieve the above objectives, the technical solution of the present invention includes the following:

[0006] (1) Construct a jamming mission scenario, including jammers and radars with quantities of M and N, respectively, where M and N are positive integers. Set the multi-beam constraint condition for the jammers as L = [L1, L2, ..., L...]. k ,...,L M ];

[0007] (2) Encoding strategy optimization is achieved by introducing vector constraint method. The interference task scenario constraints are determined according to the optimized encoding strategy, and the spatial dimension d and the upper and lower bounds of each dimension are set according to the scenario constraints; at the same time, the maximum number of iterations t is set. max The population size is n;

[0008] (3) Construct the objective function for allocating interference resources, and set constraints based on the interference machine's capabilities, by introducing the optimal point set P. m (i) Determine the initialization strategy:

[0009] The position Z of the i-th individual gray wolf in the j-th dimension can be obtained from the following formula. i,j :

[0010] Z i,j =lb j +P m (i)(ub j -lb j ), 1≤i≤m, 1≤j≤d

[0011] In the formula, d represents the spatial dimension, and its value is the number of radar targets; ub j and lb j The upper and lower bounds of the dimension of the space are represented by a d×1 vector, and their values ​​are the same as the upper and lower bounds of the jammer number.

[0012] (4) In the current round t, calculate the benefit value corresponding to each individual gray wolf according to the interference benefit function, and introduce a nonlinear convergence factor g on the basis of the traditional gray wolf algorithm. At the same time, use the dynamic weight strategy to balance and limit the local optimization and global optimization capabilities of the gray wolf algorithm to complete the update of α wolf, β wolf and δ wolf.

[0013] (5) Randomly select a portion of the wolf pack and obtain the inverse solution Z for the location of the gray wolves in that portion. i,j The system updates and re-evaluates the position based on reverse learning theory to obtain the optimal value f'(Z). i );

[0014] (6) Determine whether the current iteration count has reached the maximum iteration count t. max If the condition is met, the iterative update process ends and step (7) is executed; otherwise, let t = t + 1 and return to step (4).

[0015] (7) End the iterative update process and take the wolf pack position corresponding to the current interference benefit as the final interference resource allocation result.

[0016] Compared with the prior art, the present invention has the following advantages:

[0017] First, because the present invention introduces an encoding strategy in the model building and initialization stages, considering that traditional methods for solving objective functions do not impose restrictions on the solution space, it effectively improves the algorithm's optimization ability. At the same time, the theory of optimal point sets is introduced to optimize the population initialization position, which significantly improves the quality of the final solution compared to traditional methods.

[0018] Secondly, in the iterative process, this invention introduces a nonlinear convergence factor into the traditional Grey Wolf algorithm, which improves the global search efficiency in the early stage and makes the local search more thorough in the later stage. In addition, a dynamic weight strategy is introduced to balance and limit the local and global optimization capabilities of the Grey Wolf algorithm. Finally, the reverse solution theory is used to avoid the algorithm from getting trapped in local optima.

[0019] The improved gray wolf algorithm proposed in this invention has lower time complexity than traditional methods, meets real-time requirements, and thus improves the optimization rate in resource allocation; it can effectively avoid getting trapped in local optima and is easy to implement in engineering; the method has strong robustness and can meet the multi-beam constraint requirements of jammers. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the implementation of the method of the present invention;

[0021] Figure 2 A comparison of the convergence speed of the algorithm before and after adopting a nonlinear convergence factor;

[0022] Figure 3 A comparison chart showing the solution quality and optimization efficiency curves of solving the objective function using the method of this invention and existing methods;

[0023] Figure 4 The figures show a comparison of the convergence error of the method of the present invention and the existing method when solving the objective function using Monte Carlo experiments in different scenarios; where (a)-(d) correspond to the simulation scenarios 1-4 in Table 2 provided in the embodiments of the present invention, respectively. Detailed Implementation

[0024] The present invention will now be further described with reference to the accompanying drawings.

[0025] Example 1: Refer to Appendix Figure 1 The present invention proposes a radar jamming resource allocation method based on an improved gray wolf algorithm, which specifically includes the following steps:

[0026] Step 1) Construct a jamming mission scenario, including M and N jammers and radars, where M and N are positive integers. Set the multi-beam constraint condition for the jammers as L = [L1, L2, ..., L k ,...,L M ];

[0027] Step 2) Optimize the encoding strategy by introducing vector constraints. Determine the interference task scenario constraints based on the optimized encoding strategy, and set the spatial dimension d and the upper and lower bounds of each dimension according to the scenario constraints; at the same time, set the maximum number of iterations t. max The population size is n. The above encoding strategy is optimized in this embodiment, and the specific process is as follows:

[0028] The solution vector is obtained by representing radar numbers using one-dimensional vector indices and jammer numbers using vector values: i k ∈{1,2,...,M}; This solution represents the following meaning: Radar 1 is jammed by jammer i1, Radar 2 is jammed by jammer i2, and so on; and due to the influence of the number of jamming beams, the jammer i in the solution vector... k The frequency of occurrence cannot exceed Second-rate.

[0029] Step 3) Construct the objective function for allocating interference resources, and set constraints based on the interference machine's capabilities, by introducing the optimal point set P. m (i) Determine the initialization strategy:

[0030] The position Z of the i-th individual gray wolf in the j-th dimension can be obtained from the following formula. i,j :

[0031] Z i,j =lbj +P m (i)(ub j -lb j ), 1≤i≤m, 1≤j≤d

[0032] In the formula, d represents the spatial dimension, and its value is the number of radar targets; ub j and lb j The upper and lower bounds of the dimension of the space are represented by a d×1 vector, and their values ​​are the same as the upper and lower bounds of the jammer number.

[0033] The above set of best points P m (i) is determined as follows:

[0034] Assume G d Let be a unit cube in d-dimensional Euclidean space, in which there exists a set of points:

[0035] P m (i)={({r1i},{r2i},…,{r k i},…,{r d i}), 1≤i≤m}

[0036] In the formula, {·} represents taking the decimal part of the ·. If P m The deviation of (i) satisfies Where ε is any positive integer, C(r) k ,ε) is only related to r k A constant related to ε is called P. m (i) is the set of best points, r k This is called the optimal point; take r k ={2cos(2πk / p)}, where p is the smallest prime number that satisfies d≤(p-3) / 2.

[0037] Step 4) In the current round t, calculate the benefit value corresponding to each individual gray wolf based on the interference benefit function, and introduce a nonlinear convergence factor g on the basis of the traditional gray wolf algorithm. At the same time, use a dynamic weight strategy to balance and limit the local optimization and global optimization capabilities of the gray wolf algorithm, and complete the update of α wolf, β wolf and δ wolf.

[0038] The nonlinear convergence factor g introduced in this step of this embodiment is expressed as follows:

[0039]

[0040] In the formula g start and g end This represents the initial and final values ​​of the convergence factor.

[0041] The dynamic weighting strategy introduced in this step of the embodiment is as follows:

[0042]

[0043] Z(t+1)=W1Z1+W2Z2+W3Z3

[0044] In the formula, f(Z1), f(Z2), and f(Z3) represent the optimal interference benefits achieved by α wolf, β wolf, and δ wolf in the current round, respectively; Z1, Z2, and Z3 represent the positions of α wolf, β wolf, and δ wolf when they achieve their optimal values ​​in the current round; W1, W2, and W3 represent the learning rates of w wolf on α wolf, β wolf, and δ wolf, respectively; and Z(t+1) is the position of the w wolf group in the next round.

[0045] Step 5) Randomly select a portion of the wolf pack and obtain the inverse solution Z for the positions of these gray wolves. i,j The system updates and re-evaluates the position based on reverse learning theory to obtain the optimal value f'(Z). i The reverse solution Z for the location of the individual gray wolf described in this embodiment. i,j The result is obtained from the following formula:

[0046] Z i,j '=lb j +(ub j -Z i,j ), 1≤i≤m, 1≤j≤d.

[0047] The method of updating and re-judging the position of individual gray wolves based on reverse learning theory is implemented as follows:

[0048]

[0049] Where f(·) represents the interference benefit value corresponding to ·; Z i Z i 'These are the solutions and inverse solutions for when gray wolf i achieves the optimal value for f(·), respectively.

[0050] Step 6) Determine if the current iteration count has reached the maximum iteration count t. max If the condition is met, end the iterative update process and execute step 7); otherwise, let t = t + 1 and return to execute step 4).

[0051] Step 7) End the iterative update process and take the wolf pack position corresponding to the current interference benefit as the final interference resource allocation result.

[0052] Example 2: Refer to Figure 1-2 The overall implementation steps of the interference resource allocation method proposed in this embodiment are the same as those in Embodiment 1. Now, a scenario is built to further describe the implementation process of the present invention in detail with specific examples:

[0053] If we select five dimensions—time domain, spatial domain, frequency domain, energy domain, and jamming pattern—to measure the overall effectiveness, then the jamming effectiveness of jammer n against radar m can be expressed as:

[0054]

[0055] In the formula, λ1, λ2, λ3, λ4, and λ5 represent the weights of the five indicators, and their importance can be analyzed based on the actual battlefield situation; e t e θ e f e p e s These are the benefit values ​​for five indicators. Λ represents the Zadeh operator, indicating the minimum value operation. When any benefit is 0, the interference fails. Specific weights are assigned by experts, and these weights satisfy the following:

[0056]

[0057] In a combat situation, when there are N jammers and M airborne radar sources, the comprehensive benefit matrix can be expressed as:

[0058]

[0059] When each jammer has L jamming beams, the upper limit for the number of airborne radar sources that can be jammed is N·L. If M > N·L, jamming resources are limited and cannot jam all airborne radar sources. In this case, jammers should be allocated to radars with higher threat levels. If M ≤ N·L, jamming resources are sufficient, and they can be allocated according to predetermined principles. Based on the content and actual situation, the objective function is summarized as follows:

[0060]

[0061] In the formula, w m denoted as the threat level coefficient for radar m.

[0062] The interference allocation principle, i.e., the constraints, are as follows:

[0063]

[0064] The constraints are explained as follows:

[0065] Constraint (1): x nm =0 indicates that the jammer n does not interfere with m, x nm =1 indicates that jammer n interferes with m;

[0066] Constraint (2): Since the jammer has the capability of multi-beam jamming, and one jamming beam is directed at one radar, the jammer n can jam a maximum of L. nEach radar is jammed by a specific jamming pattern.

[0067] Constraint (3): Under this model, each radar will be jammed by a jammer.

[0068] Although the GWO algorithm is simple and computationally inexpensive, it suffers from poor population diversity, susceptibility to local optima, weak local search capability, and slow convergence speed in later stages. To address these issues, this invention proposes an improved IGWO algorithm. A special encoding strategy is designed for this scenario to significantly reduce the solution space. The population is initialized using optimal point set theory to achieve a more uniform distribution. A convergence factor with nonlinear variation is used to balance the global and local search capabilities of the GWO algorithm. A dynamic weight strategy and back-learning theory are introduced to avoid the algorithm getting trapped in local optima. The improvements to the algorithm in this embodiment are mainly reflected in the following aspects:

[0069] (I) Encoding Strategy Design:

[0070] Common encoding methods used in swarm intelligence algorithms include binary encoding, real number encoding, and integer encoding. When using binary encoding, the encoding length becomes excessively long as the allocation scale increases. Real number encoding faces the problem that, given the discrete nature of the problem, a special discretization process is required for the obtained real number solutions. However, this approach may introduce computational errors, affecting the accuracy and efficiency of the algorithm.

[0071] To address the problem of assigning jamming targets, under the constraints of this scenario, a one-dimensional vector can be used. The vector index represents the radar number, and the vector value represents the jammer number, thus reducing the solution space. For example, the optimal solution α = [i1, i2, ..., i...] can be calculated. k ,...,i N ],i1,i2...,i N The solution ∈{1,2,...,M} represents the following: Radar 1 is jammed by jammer i1, Radar 2 is jammed by jammer i2, and so on; due to the influence of the number of jamming beams, the jammer i in the solution vector... k The frequency of occurrence cannot exceed This design significantly reduces the scope of the understanding space and enhances the algorithm's optimization capabilities.

[0072] (II) Theory of Best Point Sets:

[0073] In swarm intelligence algorithms, the initialization position of the population plays a direct and crucial role in finding the optimal solution and the quality of the solution. The GWO algorithm uses random numbers for population initialization, which to some extent limits the algorithm's performance. To address this issue, this invention introduces the theory of optimal point sets into swarm intelligence algorithms. The following is a detailed introduction to the theory of optimal point sets to provide a theoretical basis for subsequent algorithm improvements.

[0074] In a unit cube in d-dimensional Euclidean space, there exists a set of points:

[0075] P m (i)={({r1i},{r2i},…,{r d i}),1≤i≤m}<1-6>

[0076] In the formula, {r k i} is r k The decimal part of i, if P m The deviation of (i) satisfies Where ε is any positive integer, C(r) k ,ε) is only related to r k A constant related to ε is called P. m (i) is the set of best points, r k This is called the optimal point, and we take r. k ={2cos(2πk / p), 1≤k≤d}, where p is the smallest prime number satisfying d≤(p-3) / 2. Therefore, based on the theory of optimal point sets, the new initialization strategy is:

[0077] Z i,j =lb j +P m (i)(ub j -lb j ), 1≤i≤m, 1≤j≤d<1-7>

[0078] In the formula, Z i,j This represents the value of the i-th individual in the j-th dimension; lb j and ub j Let d×1 vector represent the upper and lower bounds of the spatial dimension. Based on the improved coding strategy, the spatial dimension d represents the number of radar targets, and the upper and lower bounds are the same as the upper and lower bounds of the jammer number.

[0079] (III) Nonlinear convergence factor:

[0080] Reference Figure 2 The value of the coefficient G is influenced not only by the convergence factor g, but also by the hunting behavior of the wolf pack. The GWO algorithm's optimization process is not linear, and the linear change of the convergence factor g cannot accurately reflect the actual optimization search process. Therefore, a nonlinear convergence factor g is introduced:

[0081]

[0082] In the formula, g start and g end This represents the initial and final values ​​of the convergence factor g. In this embodiment, g is taken as... end =0, g start =2,t max This represents the maximum number of iterations.

[0083] To improve the algorithm's local search capability, the trend of the convergence factor g is changed from a linear decrease to a faster decrease in the early stages of iteration, followed by a faster decrease in the later stages. This change allows the algorithm to efficiently perform a global search and quickly narrow down the search range in the early stages of iteration, while enabling a more thorough local search in the later stages.

[0084] (iv) Dynamic weighting strategy:

[0085] To avoid getting trapped in local optima and to balance and limit the local and global optimization capabilities of the Grey Wolf algorithm, this invention proposes a proportional weighting based on fitness values, as shown in formulas <1-9>:

[0086]

[0087] Z(t+1)=W1Z1+W2Z2+W3Z3 <1-10>

[0088] In the formula, f(Z1), f(Z2), and f(Z3) represent the optimal interference benefits achieved by α wolf, β wolf, and δ wolf in the current round, respectively; Z1, Z2, and Z3 represent the positions of α wolf, β wolf, and δ wolf when they achieve the optimal values ​​in the current round; W1, W2, and W3 represent the learning rates of w wolf on α wolf, β wolf, and δ wolf, respectively; f(·) represents the interference benefit value corresponding to that wolf; and Z(t+1) is the position of the w wolf group in the next round. In this embodiment, W1, W2, and W3 are initialized to 1 / 3.

[0089] (V) Reverse Learning Theory:

[0090] Reverse learning theory introduces opposing solutions into the search space, effectively increasing the diversity of the population and facilitating escape from local optima. In the GWO algorithm, if α, β, and δ wolves get trapped in a local optimum, w wolf may also fall into a local optimum. Based on the idea of ​​mutation, during the algorithm iteration, solutions in the opposite direction for some individuals can be calculated. If, after comparison, the solution in the opposite direction is found to be better than the solution in the current direction, the solution in the opposite direction can replace the solution in the current direction for the next iteration. Therefore, the reverse solution corresponding to each gray wolf individual is...

[0091] Z i,j '=lbj +(ub j -Z i,j ), 1≤i≤m, 1≤j≤d <1-11>

[0092] In the formula, Z i,j 'Represents the position Z of individual gray wolf i i,j The reverse solution, at this point the optimal value expression can be modified to:

[0093]

[0094] In the formula Z i Z i 'These are the solutions and inverse solutions for when gray wolf i achieves the optimal value for f(·), respectively.

[0095] To avoid wasting too much time on reverse learning, this embodiment does not require reverse learning of all individuals in the population in this step; instead, it simply involves randomly selecting individuals based on a certain probability.

[0096] The effects of the present invention will be further explained below with reference to simulation experiments.

[0097] Simulation Experiment 1: Comparative Analysis of IGWO Algorithm with Other Optimization Algorithms

[0098] To test and compare the performance of the IGWO algorithm with other optimization algorithms, this invention selected the GWO, GA, PSO, HO, MPA, and CSO algorithms for comparison. The population size was set to 40, the number of iterations to 200, and the number of Monte Carlo iterations to 100. The average value of the 100 results was calculated, and the average performance value changed with the number of iterations as follows: Figure 3 As shown:

[0099] This demonstrates that the IGWO algorithm proposed in this invention has the fastest convergence speed and the best optimization ability. Other algorithms, to varying degrees, get trapped in local optima. The MPA algorithm experiences a sudden change in convergence speed after 50 iterations. According to the algorithm principle, in the early stages of iteration (t... max / 3) In the exploration phase, marine predators remain stationary while prey engage in random Brownian motion. Therefore, in the initial stages, individual prey only search for the optimal solution in their immediate vicinity, resulting in low efficiency. Increasing the proportion of global search in the later stages of iteration leads to a further improvement in convergence speed, but it still easily gets trapped in local optima. The HO and CSO algorithms continue to increase their average efficiency after 200 iterations, indicating that they possess a strong ability to escape local optima, but in this scenario, they are inferior to the GWO algorithm. In summary, the IGWO algorithm proposed in this invention maintains convergence accuracy while also accelerating the convergence speed.

[0100] Simulation Experiment 2: Verifying the impact of the number of interfering beams on the algorithm

[0101] To verify the robustness of the algorithm, different numbers of beam constraints were set in this scenario, and each jammer was configured with a different number of jamming beams. The number of beams was represented by a 1×N dimensional vector L. N The vector index subscript indicates the jammer number, and the specific value represents the number of jamming beams. Table 1 shows the average iterative value, optimization rate (defined as reaching a global optimum of 96% or higher), and average runtime of the IGWO, GWO, PSO, HO, and CSO algorithms after 200 iterations and 100 Monte Carlo experiments.

[0102] Table 1. Average interference effectiveness, optimization rate, and runtime for different numbers of interference beams under the same scenario.

[0103]

[0104]

[0105] As shown in Table 1, the IGWO algorithm achieved good results under different beam number constraints. With the increase in the number of beams, the number of feasible solutions in the population increases, thus gradually increasing the average interference benefit and optimization rate of each algorithm. In terms of time, the HO algorithm is the longest, with territory maintenance and competition mechanisms increasing the algorithm's running time. The CSO algorithm is the shortest, but its optimization performance deteriorates significantly with increasing constraints. Due to the introduction of back-learning theory during the iteration process, the IGWO algorithm has better optimization efficiency than the GWO algorithm, but at the cost of some time performance. In engineering applications, achieving better results is acceptable if the time loss is not significant. This verifies the algorithm's robustness under different beam number constraints.

[0106] Simulation Experiment 3: Demonstrating the universality of the algorithm in different scenarios

[0107] To verify the generalizability of the algorithm in different scenarios, different numbers of jammers N, number of airborne target radars M, and population size were set. The Monte Carlo iteration count was set to 100, and the number of iterations to 200. The parameters of the first 10 radars and the first 4 jammers remained unchanged, while the positions of the jammers and radars were randomly changed. The average jamming effectiveness, optimization rate, and average runtime of the IGWO, GWO, PSO, HO, and CSO algorithms in different scenarios are shown in the table below:

[0108] Table 2. Average interference effectiveness, optimization rate, and runtime of different algorithms in different scenarios.

[0109]

[0110]

[0111] The convergence errors of the IGWO, GWO, PSO, HO, and CSO algorithms in different scenarios are statistically analyzed as follows: Figure 4 As shown, from Figure 4 As can be seen from the content, by changing the number and location of jammers and radars, the IGWO algorithm has a higher average convergence gain and smaller convergence error compared with several existing algorithms. As the scale increases and the scene constraints become stronger, IGWO may still get trapped in local optima in some cases. However, overall, the performance and versatility of the IGWO algorithm are stronger than other algorithms in different scenarios.

[0112] It should be noted that the user information (including but not limited to user device information, user personal information, etc.) and data (including but not limited to data used for analysis, data stored, data displayed, etc.) involved in this application are all information and data authorized by the user or fully authorized by all parties. Furthermore, the collection, use and processing of the relevant data must comply with the laws, regulations and standards of the relevant countries and regions, and corresponding operation portals are provided for users to choose to authorize or refuse.

[0113] The above simulation analysis proves the correctness and effectiveness of the method proposed in this invention.

[0114] The parts of this invention not described in detail are common knowledge to those skilled in the art.

[0115] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Obviously, those skilled in the art, after understanding the content and principle of the present invention, may make various modifications and changes in form and detail without departing from the principle and structure of the present invention. However, these modifications and changes based on the concept of the present invention are still within the scope of protection of the claims of the present invention.

Claims

1. A radar jamming resource allocation method based on an improved gray wolf algorithm, characterized in that, Includes the following steps: (1) Construct a jamming mission scenario, including jammers and radars with quantities of M and N, respectively, where M and N are positive integers. Set the multi-beam constraint condition for the jammers as L = [L1, L2, ..., L...]. k ,...,L M ]; (2) Encoding strategy optimization is achieved by introducing vector constraint method. The interference task scenario constraints are determined according to the optimized encoding strategy, and the spatial dimension d and the upper and lower bounds of each dimension are set according to the scenario constraints; at the same time, the maximum number of iterations t is set. max The population size is n; (3) Construct the objective function for allocating interference resources, and set constraints based on the interference machine's capabilities, by introducing the optimal point set P. m (i) Determine the initialization strategy: The position Z of the i-th individual gray wolf in the j-th dimension can be obtained from the following formula. i,j : Z i,j =lb j +P m (i)(ub j -lb j ),1≤i≤m,1≤j≤d In the formula, d represents the spatial dimension, and its value is the number of radar targets; ub j and lb j The upper and lower bounds of the dimension of the space are represented by a d×1 vector, and their values ​​are the same as the upper and lower bounds of the jammer number. (4) In the current round t, calculate the benefit value corresponding to each individual gray wolf according to the interference benefit function, and introduce a nonlinear convergence factor g on the basis of the traditional gray wolf algorithm. At the same time, use the dynamic weight strategy to balance and limit the local optimization and global optimization capabilities of the gray wolf algorithm to complete the update of α wolf, β wolf and δ wolf. (5) Randomly select a portion of the wolf pack and obtain the inverse solution Z for the location of the gray wolves in that portion. i,j The system updates and re-evaluates the position based on reverse learning theory to obtain the optimal value f'(Z). i ); (6) Determine whether the current iteration count has reached the maximum iteration count t. max If the condition is met, the iterative update process ends and step (7) is executed; otherwise, let t = t + 1 and return to step (4). (7) End the iterative update process and take the wolf pack position corresponding to the current interference benefit as the final interference resource allocation result.

2. The method according to claim 1, characterized in that: The specific process of optimizing the encoding strategy in step (2) is as follows: The solution vector is obtained by representing radar numbers using one-dimensional vector indices and jammer numbers using vector values: i1,i2...,i N ∈{1,2,...,M}; This solution represents the following meaning: Radar 1 is jammed by jammer i1, Radar 2 is jammed by jammer i2, and so on; and due to the influence of the number of jamming beams, the jammer i in the solution vector... k The frequency of occurrence cannot exceed Second-rate.

3. The method according to claim 1, characterized in that: The initialization strategy using optimal point set theory described in step (3) is as follows: Assume G d Let be a unit cube in d-dimensional Euclidean space, in which there exists a set of points: P m (i)={({r1i},{r2i},…,{r k i},…,{r d i}),1≤i≤m} In the formula, {·} represents taking the decimal part of the ·. If P m The deviation of (i) satisfies Where ε is any positive integer, C(r) k ,ε) is only related to r k A constant related to ε is called P. m (i) is the set of best points, r k This is called the optimal point, and we take r. k ={2cos(2πk / p)}, where p is the smallest prime number that satisfies d≤(p-3) / 2.

4. The method according to claim 1, characterized in that: The nonlinear convergence factor g mentioned in step (4) is expressed as follows: In the formula g start and g end This represents the initial and final values ​​of the convergence factor.

5. The method according to claim 4, characterized in that: The dynamic weighting strategy described in step (4) is implemented as follows: Z(t+1)=W1Z1+W2Z2+W3Z3 In the formula, f(Z1), f(Z2), and f(Z3) represent the optimal interference benefits achieved by α wolf, β wolf, and δ wolf in the current round, respectively; Z1, Z2, and Z3 represent the positions of α wolf, β wolf, and δ wolf when they achieve their optimal values ​​in the current round; W1, W2, and W3 represent the learning rates of w wolf on α wolf, β wolf, and δ wolf, respectively; f(·) represents the interference benefit value corresponding to that wolf; and Z(t+1) is the position of the w wolf group in the next round.

6. The method according to claim 1, characterized in that: The reverse solution Z for the location of the individual gray wolf in step (5) i,j The result is obtained from the following formula: Z i,j ’=lb j +(ub j -Z i,j ),1≤i≤m,1≤j≤d。 7. The method according to claim 6, characterized in that: The method of updating and re-judging the position of individual gray wolves based on reverse learning theory is implemented as follows: Among them, Z i Z i 'These are the solutions and inverse solutions for when gray wolf i achieves the optimal value for f(·), respectively.

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