A two-dimensional MUSIC spectrum peak searching method based on improved archimedes algorithm

Abstract

The application discloses a two-dimensional MUSIC spectrum peak searching method based on an improved Archimedes algorithm, which comprises the following steps: firstly, one-dimensional MUSIC spatial spectrum function derivation is performed on a signal model, and the one-dimensional MUSIC spatial spectrum function is extended to a two-dimensional MUSIC spatial spectrum function; secondly, the two-dimensional MUSIC spatial spectrum function is taken as a target function of the Archimedes optimization algorithm; then, the target function is combined, a chaos algorithm strategy is introduced to initialize a population, a mutation algorithm is introduced to disturb a position, and the Archimedes optimization algorithm is improved; finally, two-dimensional MUSIC spectrum peak searching is performed through the improved Archimedes optimization algorithm, and the direction of arrival, i.e. the pitch angle and the azimuth angle, obtained through the maximum value seeking mode of the target function is the spectrum peak value. The application has a faster optimization speed, higher optimization precision and better robustness, and can quickly and accurately perform two-dimensional MUSIC spectrum peak searching.

Description

Technical Field

[0001] The invention belongs to the technical field of sound source localization, and in particular relates to a two-dimensional MUSIC spectrum peak search method based on an improved Archimedean algorithm. Background Art

[0002] To address the computational complexity of the MUSIC algorithm, researchers have conducted relevant research and achieved a lot of progress and results. One of these results is the idea of ​​introducing swarm intelligence algorithms into the spectrum peak search to reduce the algorithm's computational complexity.

[0003] Based on this, the Archimedean algorithm (AOA) was introduced to accelerate the peak search process. However, the AOA performs poorly during global exploration and tends to converge prematurely. Therefore, while the AOA has good optimization accuracy, it is prone to being trapped in local extremes and lacks stability. Summary of the Invention

[0004] To overcome the limitations of the MUSIC algorithm, which relies on peak search, traditional methods employ a grid search method. While this method offers high accuracy, it suffers from significant computational overhead and poor real-time performance. Therefore, an improved Archimedean algorithm is introduced to accelerate the peak search process. This algorithm is based on a fusion of a chaos algorithm and a Gaussian-Cauchy hybrid mutation algorithm. The chaotic algorithm is used during population initialization to mitigate the problem of low population diversity. Furthermore, the Gaussian-Cauchy hybrid mutation algorithm is used to randomly mutate individuals in each iteration, preventing the algorithm from falling into local optima and improving its stability.

[0005] In order to achieve the above tasks, the present invention adopts the following technical solutions:

[0006] A two-dimensional MUSIC spectrum peak search method based on an improved Archimedean algorithm comprises the following steps:

[0007] S1. The signal model is derived, and then the one-dimensional MUSIC spatial spectrum function is derived, and the one-dimensional MUSIC spatial spectrum function is extended to the two-dimensional MUSIC spatial spectrum function.

[0008] S2. The spatial spectrum function of two-dimensional MUSIC is used as the objective function of the Archimedean optimization algorithm.

[0009] S3. Combined with the objective function, the fusion chaos algorithm strategy is introduced to initialize the population, the mutation algorithm is introduced to perturb the position, and the Archimedean optimization algorithm AOA is improved.

[0010] Improved Archimedean Optimization Algorithm: To ensure that the initial population of the Archimedean algorithm has good traversability, a fusion chaos algorithm strategy is introduced to initialize the population. A hybrid map combining the circle chaos map and the Chebyshev chaos map is introduced to initialize the population, thereby improving the algorithm's convergence speed and solution accuracy. To prevent the Archimedean algorithm from falling into local optimal solutions, a Gauss-Cauchy hybrid mutation algorithm is introduced to perturb the position, allowing the population to escape local optimal solutions and expand the population's search space for solutions.

[0011] S4. Perform a two-dimensional MUSIC spectrum peak search using the improved Archimedean optimization algorithm. The two-dimensional MUSIC spectrum peak search obtains the direction of arrival (DOA), i.e., the elevation angle and azimuth angle, as the spectrum peak by maximizing the objective function. Compare the DOA estimation results for different azimuths and the time required for the spectrum peak search.

[0012] Furthermore, the step S1 specifically includes:

[0013] S11. Derive the signal model:

[0014] For two-dimensional DOA estimation, an L-shaped array or a uniform planar array is generally used. Here, a uniform planar array is used. Assume that the number of planar array elements is M×P and the number of signal sources is K. Assume that the direction of arrival of each signal source in space is represented by (θ1, φ1), (θ2, φ2)…, (θ K ,φ K ) where θ k 、φ K are the elevation angle and azimuth angle of the kth signal source respectively. The uniform array can be divided into several sub-arrays according to rows or columns, where each sub-array is a uniform linear array. Taking the row as an example, the mathematical model of the sub-array m can be expressed as:

[0015] A m =A x D m (A y ),m=1,2,…,M

[0016] Where: A x and A y is the L-type array response matrix corresponding to the subarray, D m (.) represents a diagonal matrix consisting of m rows of the matrix in the brackets. Then the received signal of the uniform plane array is:

[0017]

[0018] Among them, S is the signal emitted by the signal source, and N is the noise.

[0019] S12. Derivation of one-dimensional MUSIC is performed and extended to the spatial spectrum function of two-dimensional MUSIC as the objective function:

[0020] The covariance matrix is ​​obtained based on the uniform planar array receiving signal. The array covariance matrix R can be divided into two spaces, signal subspace and noise subspace, by eigendecomposition, namely:

[0021]

[0022] Where: s is the diagonal matrix consisting of the larger K eigenvalues ​​in the eigendecomposition of R, U s is the signal subspace spanned by the corresponding eigenvector. Similarly, ∑ N is a diagonal matrix consisting of NK eigenvalues, U N is the spanned noise subspace. Since the noise subspace is orthogonal to the signal subspace, we can get:

[0023]

[0024] According to the above formula, we can get:

[0025] A(θ)R s A H (θ)U N =0

[0026] Where: Matrix R s is a full rank matrix, non-singular, so it has an inverse matrix. So formula (5) can be transformed into: A H (θ)U N =0, this formula shows that the matrix A H Each vector in (θ) is orthogonal to the noise subspace, so:

[0027] U N a(θ i )=0,i=1,2,…,K

[0028] Where: a(θ i ) is A(θ i ), the spatial spectrum function is obtained from the orthogonal relationship between the noise characteristic vector and the signal characteristic vector:

[0029]

[0030] Where a(θ) is the vector of the array response matrix, U N is the noise subspace, a H (θ) is the conjugate transpose of a(θ), For U N The conjugate transpose of .

[0031] Two-dimensional MUSIC is similar to one-dimensional MUSIC, except that the direction matrix is ​​expanded. The spatial spectrum function of two-dimensional MUSIC is:

[0032]

[0033] Where: where a x (θ,φ) and a y (θ, φ) is the quality of the L-type array response matrix corresponding to the subarray, is the tensor product, E N is the noise feature vector, For E N The conjugate transpose of . Then the angle where the spectrum peak of the spectrum function is located is the spatial wave arrival direction, and the spatial spectrum function of the above two-dimensional MUSIC is the target function.

[0034] Furthermore, the step S3 specifically includes:

[0035] S31. To ensure that the initial population of the Archimedean algorithm has good ergodicity, a fusion chaos algorithm strategy is introduced to initialize the population. A hybrid map combining the circle chaos map and the Chebyshev chaos map is introduced to initialize the population, thereby improving the convergence speed and solution accuracy of the algorithm:

[0036] Furthermore, the step S31 specifically includes:

[0037] The S311.Circle chaotic map is defined as follows:

[0038]

[0039] Among them, x n is the input value at time n;

[0040] The S312.chebyshev chaotic map is defined as follows:

[0041] x n+1 =cos(φcos -1 x n )

[0042] The value of Φ is a constant.

[0043] S313. Random position parameter fusion of two chaotic maps:

[0044] Each individual in the population generates a random number between (0,1) as the position parameter of the individual. The position parameters of all individuals form the position parameter matrix Pt, where N is the population size and D is the spatial dimension.

[0045] Pt(i,j)=randi=1,2,…,Nj=1,2,…,D.

[0046] Set the selection probability to 0.5 and update the individual positions of the population as follows.

[0047]

[0048] in, is the position of an individual in a population with a population size of i and a spatial dimension of j at time n.

[0049] The generated initial population is checked for boundary constraints, and positions exceeding or falling below the upper and lower bounds are assigned as boundary values.

[0050] Perform bounds constraint checks on the generated initial population:

[0051]

[0052] S32. Introduce the number of iterations into the mutation probability Rand, where Rand is a random value between 0 and 1:

[0053]

[0054] Where CurrentGen is the current iteration number and Gen is the maximum iteration number.

[0055] When the above conditions are met, the Gauss-Cauchy hybrid mutation algorithm is introduced to perturb the position.

[0056] In order to prevent the Archimedean algorithm from falling into the local optimal solution, the Gauss-Cauchy hybrid mutation algorithm is introduced to perturb the position, so that the population can jump out of the local optimal solution and expand the population search solution space:

[0057] Furthermore, the step S32 specifically includes:

[0058] S321. Gaussian mutation algorithm:

[0059] Gaussian mutation was originally used to change the local search performance of the genetic algorithm in the key search area. It replaces the original gene value with a random number that conforms to the normal distribution with mean μ and variance σ. The following is the Gaussian mutation formula:

[0060]

[0061] Gaussian i (x) = N(x best ,δ)

[0062] x is the position of the individual, x bestis the current global optimal individual, and delta is the standard deviation of Gaussian distribution, and the Gaussian mutation makes the population escape from the limitation of local optimal solution.

[0063] S322.Cauchy mutation algorithm:

[0064] Cauchy mutation has very strong global disturbance ability and better global search ability, and the Cauchy mutation formula is as follows:

[0065]

[0066] x is the position of the population.

[0067] S323.Gaussian-Cauchy hybrid mutation algorithm:

[0068] On the basis of combining the characteristics of Gaussian mutation and Cauchy mutation, a Gaussian-Cauchy hybrid mutation mechanism is proposed, and the formula is as follows:

[0069] Mutation i (x)=α·Gaussian i (x)+β·Cauthy i (x)

[0070]

[0071] Since in the whole population iteration process, the initial population is usually far away from the actual optimal solution, with the increase of iteration times, the number of individuals close to the actual optimal solution will be more and more, and the number of individuals needing mutation will also decrease, in order to make more individuals with better fitness not to be mutated, the iteration times are introduced into the mutation probability Rand, Rand is a random value between 0 and 1, CurrentGen is the current iteration times, Gen is the maximum iteration times, alpha is the Gaussian mutation coefficient, and beta is the Cauchy mutation coefficient, since the fixed Cauchy mutation coefficient is not conducive to solving the optimal individual in the whole iteration process, in the early and middle stages of the algorithm, a larger coefficient is needed to make the algorithm jump out of the local optimum, and in the later stage of the algorithm, a smaller coefficient is needed to make the algorithm complete convergence, therefore, the iteration times are introduced to match the sine function, so that the Cauchy mutation coefficient is limited in the range of 0-1 and decreases with the increase of iteration times.

[0072]

[0073] The present application has the beneficial effects that:

[0074] The two-dimensional MUSIC spectrum peak search based on the improved Archimedes algorithm has the two-dimensional MUSIC spectrum peak function as a target function, has faster optimization speed, higher optimization precision and better robustness than the original Archimedes optimization algorithm, improves the optimization precision while accelerating the speed, and can quickly and accurately perform two-dimensional MUSIC spectrum peak search. BRIEF DESCRIPTION OF DRAWINGS

[0075] Figure 1 is a flow chart of the two-dimensional MUSIC spectrum peak search based on the improved Archimedes algorithm of the application;

[0076] Figure 2 is a two-dimensional MUSIC spectrum peak graph with an azimuth angle and an elevation angle of [25, 15];

[0077] Figure 3 is a two-dimensional MUSIC spectrum peak graph with an azimuth angle and an elevation angle of [85, 35];

[0078] Figure 4 is a two-dimensional MUSIC spectrum peak graph with an azimuth angle and an elevation angle of [-45, -30]. DETAILED DESCRIPTION

[0079] The technical idea of the application is: first, derive the two-dimensional MIUSIC spatial spectrum function as a target function; then introduce a fusion chaos algorithm strategy to initialize the population, introduce circle and chebyshev hybrid mapping for population initialization, expand the search range of the algorithm, and thus improve the convergence speed and solution accuracy of the algorithm; finally, introduce a Gaussian-Cauchy hybrid mutation algorithm to make the population jump out of the local optimum and expand the population search solution space.

[0080] The embodiment provides a two-dimensional MUSIC spectrum peak search method based on an improved Archimedes algorithm, as shown in Figure 1 The method comprises the following steps:

[0081] S1. Derive the signal model, then derive the one-dimensional MUSIC spatial spectrum function, and extend to the two-dimensional MUSIC spatial spectrum function.

[0082] S2. Take the two-dimensional MUSIC spatial spectrum function as a target function of the Archimedes optimization algorithm.

[0083] Further, the step S2 specifically comprises:

[0084] S21. Archimedes optimization algorithm original algorithm flow:

[0085] The Archimedean optimization algorithm is a population-based optimization algorithm inspired by Archimedes' principle. It treats all objects immersed in a liquid as a population. Through collisions and the buoyancy of the objects, the objects continuously adjust their density, volume, and acceleration to achieve equilibrium. It consists of three phases: initialization, global exploration (where collisions occur between objects), and local development (where collisions are avoided).

[0086] Furthermore, the step S21 specifically includes:

[0087] S211. Initialization phase:

[0088] In the initialization phase, AOA initializes the population position by the following formula

[0089] X i =lb i +rand×(ub i -lb i )

[0090] where [lb i ,ub i ] represents the search space, and rand∈(0,1) is a random number.

[0091] The density (den), volume (vol) and acceleration (acc) of each individual are randomly initialized by the following formula:

[0092] den i =rand

[0093] vol i =rand

[0094] acc i =lb i +rand×(ub i -lb i )

[0095] At this stage, AOA will evaluate the population and select the current best individual (x best ), the density of the optimal individual (den best ), volume (vol best ) and the acceleration of the optimal individual (acc best ). And update the volume and density of other individuals with the density and volume of the optimal individual:

[0096]

[0097] Next, set the transfer algorithm TF and density factor d according to the following two formulas:

[0098]

[0099] Among them, t represents the current iteration number, t max Represents the maximum number of iterations.

[0100] S212. Global exploration phase (collision between objects):

[0101] If TF < 0.5, AOA performs global exploration and updates the individual acceleration according to the following formula:

[0102]

[0103] in, Indicates that in generation t+1, i th Individual acceleration, den mr and vol mr is the density and volume of the randomly selected individual in the current iteration. AOA normalizes the acceleration of each individual according to the following formula and is used to update the individual position:

[0104]

[0105] in is i in generation t+1 th The normalized acceleration of the individual; u and l are used to adjust the normalization range.

[0106] At this stage, the individual positions are updated as follows:

[0107]

[0108] Where C1 is a fixed constant and rand∈(0,1) is a random number.

[0109] S213. Local development stage (no collision between objects):

[0110] If TF>0.5, AOA performs local transmission, updates the individual acceleration according to formula (9), and normalizes the acceleration according to formula (7):

[0111]

[0112] At this stage, the individual positions are updated as follows:

[0113]

[0114] Where C2 is a fixed constant; T = C3 × TF, and T∈[C3 × 03, 1]; F is a direction factor used to determine the direction of the iterative position update, defined as follows:

[0115]

[0116] Wherein, P = 2 × rand - C4, where C4 is a fixed constant.

[0117] S3. Improved Archimedean Optimization Algorithm: To ensure that the initial population of the Archimedean algorithm has good traversability, a fusion chaos algorithm strategy is introduced to initialize the population. A hybrid map combining the circle chaos map and the Chebyshev chaos map is introduced to initialize the population, thereby improving the algorithm's convergence speed and solution accuracy. To prevent the Archimedean algorithm from falling into local optimal solutions, a Gauss-Cauchy hybrid mutation algorithm is introduced to perturb the position, allowing the population to escape local optimal solutions and expand the population's search space for solutions.

[0118] S4. The improved Archimedean optimization algorithm is used to verify the two-dimensional MUSIC spectrum peak search effect. The two-dimensional MUSIC spectrum peak search obtains the direction of arrival (DOA), i.e., the elevation angle and azimuth angle, as the spectrum peak value by finding the maximum value of the objective function. The DOA estimation results for different azimuths and the peak search time are compared.

[0119] In step S1 , a signal model is derived, and then a one-dimensional MUSIC spatial spectrum function is derived, and then expanded to a two-dimensional MUSIC spatial spectrum function as a target function.

[0120] S11. Derive a signal model of a uniform planar array to obtain a received signal model.

[0121] S12. Derive the one-dimensional MUSIC spatial spectrum function and generalize it to the two-dimensional MUSIC spatial spectrum function as the target function.

[0122] In step S2, the spatial spectrum function of the two-dimensional MUSIC in step S12 is used as the objective function of the Archimedean optimization algorithm.

[0123] S21. Initialize the original Archimedean algorithm, randomly initialize the density (den), volume (vol), and acceleration (acc) of each individual and update the transfer algorithm TF and density factor d. Use TF to determine whether to proceed to the global exploration phase (collision between objects) or the local development phase (no collision between objects).

[0124] S22. When TF < 0.5, the global exploration phase is carried out (collision occurs between objects).

[0125] S23. When TF>0.5, proceed to the local development phase (no collision between objects).

[0126] In step S3, an improved Archimedean optimization algorithm is implemented. To ensure that the initial population of the Archimedean algorithm has good ergodicity, a fusion chaos algorithm strategy is introduced to initialize the population. A hybrid mapping combining the circle chaos map and the Chebyshev chaos map is introduced to initialize the population, thereby improving the algorithm's convergence speed and solution accuracy. To prevent the Archimedean algorithm from falling into a local optimal solution, a Gauss-Cauchy hybrid mutation algorithm is introduced to perturb the position, allowing the population to escape the local optimal solution and expand the population's search space.

[0127] S31. In order to provide the Archimedean algorithm with better ergodicity for the initialized population, a fusion chaos algorithm strategy is introduced to initialize the population.

[0128] S32. In order to prevent the Archimedean algorithm from falling into a local optimal solution, the Gauss-Cauchy hybrid mutation algorithm is introduced to perturb the position, so that the population can jump out of the local optimal solution and expand the population search space:

[0129] Step S31 specifically includes:

[0130] S311.Circle chaos map definition.

[0131] S312. Chebyshev chaotic map definition, where the experimental effect is best when the Φ value is 4.5.

[0132] S313. Initialize the Archimedean method in S21 to fuse the two chaotic maps, and determine which chaotic map to use by judging the random position parameter Pt.

[0133] Step S32 specifically includes:

[0134] S321. List the expression of Gaussian mutation algorithm.

[0135] S322. List the expression of the Cauchy mutation algorithm.

[0136] S323. Through the mixed expression, the Gauss-Cauchy mixed mutation algorithm is obtained. Taking into account the specific change process, a smaller coefficient is required in the later stage of the algorithm in order to complete the convergence of the algorithm. Therefore, the number of iterations is introduced here with the sine function to limit the Cauchy variation coefficient to the range of 0 to 1, and decreases with the increase of the number of iterations.

[0137] In step S4, the improved Archimedean optimization algorithm is used to verify the effectiveness of the two-dimensional MUSIC spectrum peak search. The two-dimensional MUSIC spectrum peak search obtains the direction of arrival (DOA), i.e., the elevation angle and azimuth angle, as the spectrum peak value by maximizing the objective function. The DOA estimation results for different azimuths and the peak search time are compared.

[0138] The following is an experiment and its effect of two-dimensional MUSIC spectrum peak search by improving the Archimedean algorithm in a specific embodiment.

[0139] In order to verify the performance of the hybrid strategy to improve the Archimedean optimization algorithm in this example, the two-dimensional MUSIC spectrum peak search based on the improved Archimedean algorithm was tested. The experimental results are as follows: Figure 2 、 Figure 3 and Figure 4 The search results of the traditional MUSIC algorithm and the improved algorithm in this paper are shown in and The measurement errors of the two algorithms are expressed as and Table 1 compares the DOA estimation results of the improved algorithm and the traditional MUSIC algorithm at different azimuths. Table 2 compares the peak search time of the improved algorithm and the traditional MUSIC algorithm.

[0140] The number of array elements is M=N=8, which is an 8×8 uniform array. The array element spacing is half a wavelength, the number of snapshots is SNAP=500, the noise is Gaussian white noise, the signal-to-noise ratio is 10dB, and the number of signal sources is M=1. The angle search range is (-90°, 90°), and the improved algorithm and the traditional grid search method are used for spectrum peak search respectively. The maximum number of iterations is iter max =100, the population size is 50, and the step size Δ of the traditional grid search method is 0.1.

[0141] Table 1 Comparison of DOA estimation results at different orientations

[0142]

[0143] Table 2 Comparison of peak search time

[0144]

Claims

1. A two-dimensional MUSIC spectrum peak search method based on an improved Archimedean algorithm, characterized in that: The following steps are involved: S1. Derivation of the signal model, and then derivation of the one-dimensional MUSIC spatial spectrum function, the one-dimensional MUSIC spatial spectrum function is extended to the two-dimensional MUSIC spatial spectrum function. The specific implementation process is as follows: S11. Derive the signal model: A uniform planar array is used for two-dimensional DOA estimation. Assume that the number of planar array elements is M×P and the number of signal sources is K. Assume that the direction of arrival of each signal source in space is represented by (θ1, φ1), (θ2, φ2)…, (θ K ,φ K ) where θ k 、φ K are the elevation angle and azimuth angle of the kth signal source respectively; the uniform array is divided into several sub-arrays according to rows or columns, where each sub-array is a uniform linear array, and the mathematical model of sub-array m is expressed as: A m =A x D m (A y ),m=1,2,…,M Where: A x and A y is the L-type array response matrix corresponding to the subarray, D m (.) represents a diagonal matrix consisting of m rows of the matrix inside the brackets; then the uniform plane array receives the signal: Among them, S is the signal emitted by the signal source, and N is the noise; S12. Derivation of one-dimensional MUSIC is performed and extended to the spatial spectrum function of two-dimensional MUSIC: The covariance matrix is ​​obtained based on the uniform planar array receiving signal. The array covariance matrix R is divided into signal subspace and noise subspace by eigendecomposition. According to the orthogonal relationship between the noise eigenvector and signal eigenvector of the noise subspace and the signal subspace, the spatial spectrum function is obtained as follows: Where a(θ) is the vector of the array response matrix, U N is the noise subspace, a H (θ) is the conjugate transpose of a(θ), For U N The conjugate transpose of Then the spatial spectrum function of two-dimensional MUSIC is: Where: where a x (θ,φ) and a y (θ, φ) is the quality of the L-type array response matrix corresponding to the subarray, is the tensor product, E N is the noise feature vector, For E N The conjugate transpose of , then the angle where the spectrum peak of the spectrum function is located is the spatial wave arrival direction; S2. The spatial spectrum function of two-dimensional MUSIC is used as the objective function of the Archimedean optimization algorithm; S3. Combined with the objective function, the fusion chaos algorithm strategy is introduced to initialize the population, the mutation algorithm is introduced to perturb the position, and the Archimedean optimization algorithm (AOA) is improved. The specific implementation process is as follows: S31. Introduce a hybrid map combining the chaotic map circle and the chaotic map Chebyshev to initialize the population. The specific implementation is as follows: The S311.Circle chaotic map is defined as follows: Among them, x n is the input value at time n; The S312.chebyshev chaotic map is defined as follows: x n+1 =cos(Φcos -1 x n ) Where Φ is a constant; S313. Random position parameter fusion of two chaotic maps: Each individual in the population generates a random number between (0, 1) as the location parameter of the individual. The location parameters of all individuals form the location parameter matrix Pt, where N is the population size and D is the spatial dimension. Pt(i,j)=Randi=1,2,…,Nj=1,2,…,D. Set the selection probability to 0.5 and update the individual positions of the population as follows: in, is the position of an individual in a population with a population size of i and a spatial dimension of j at time n; Perform boundary constraint checks on the generated initial population, and assign boundary values ​​to positions that exceed or fall below the upper and lower bounds; S32. Introduce the number of iterations into the mutation probability Rand, where Rand is a random value between 0 and 1. Where CurrentGen is the current number of iterations, and Gen is the maximum number of iterations; When the above conditions are met, the Gauss-Cauchy hybrid mutation algorithm is introduced to perturb the position; S4. A two-dimensional MUSIC spectrum peak search is performed using an improved Archimedean optimization algorithm. The two-dimensional MUSIC spectrum peak search obtains the direction of arrival, i.e., the elevation angle and the azimuth angle, as the spectrum peak by finding the maximum value of the objective function.

2. The two-dimensional MUSIC spectrum peak search method based on the improved Archimedean algorithm according to claim 1, characterized in that: The specific implementation process of step S32 is as follows: S321. Gaussian mutation algorithm: Replace the original gene value with a random number that conforms to the normal distribution with mean μ and variance σ. The following is the Gaussian mutation formula: Gaussiaa i (x)=N(x best ,δ) x is the position of the individual, x best is the current global optimal individual, δ is the standard deviation of the Gaussian distribution, and the Gaussian mutation limits the population from escaping the local optimal solution; S322. Cauchy mutation algorithm: The following is the Cauchy variation formula: S323. Gauss-Cauchy hybrid mutation algorithm: Based on the characteristics of Gaussian mutation and Cauchy mutation, a Gaussian-Cauchy hybrid mutation mechanism is proposed. The formula is as follows: Mutation i (x)=α·Gaussian i (x)+β·Cauthy i (x) Among them, α is the Gaussian coefficient of variation, and β is the Cauchy coefficient of variation. The number of iterations is combined with the sine function to limit the Cauchy coefficient of variation to the range of 0 to 1, and decreases with the increase of the number of iterations.

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