Spectrum prediction method of snow ablation optimization algorithm based on chaotic mapping good point set initialization and simulated annealing, program, equipment and storage medium

Abstract

The invention provides a spectrum prediction method of a snow ablation optimization algorithm based on chaotic mapping good point set initialization and simulated annealing, a program, equipment and a storage medium. The improved snow ablation optimization algorithm is adopted to optimize key parameters in the spectrum prediction model, the positions of individuals in the population are initialized based on the chaotic mapping good point set, and the uniformity and randomness of the initial population are effectively improved; on the basis of a double-population mechanism of the snow ablation optimization algorithm, one population keeps an original individual position updating mode, the other population introduces a probability acceptance mechanism of simulated annealing, a neighborhood solution is accepted at a certain probability to update the position of an individual, and the global search ability of the algorithm is enhanced; the disturbance amplitude in the search process is controlled by using a temperature attenuation mechanism, the convergence speed is improved, the optimization precision is improved, and the robustness of the algorithm is enhanced. Compared with other algorithms, the method is better in effect, the prediction performance is greatly improved, and the method can be suitable for different channel environments.

Description

Technical Field

[0001] The present invention belongs to the technical field of spectrum prediction, and in particular relates to a spectrum prediction method, program, device and storage medium of a snow melting optimization algorithm based on chaos mapping good point set initialization and simulated annealing. Background Art

[0002] Metaheuristic algorithms are a class of advanced optimization algorithmic frameworks used to solve complex combinatorial and continuous optimization problems. Metaheuristic algorithms are highly abstract optimization strategies that often mimic natural population behavior, biological evolution, and physical processes. They are used to search for globally optimal or suboptimal solutions in complex search spaces. While these algorithms are not guaranteed to find the optimal solution, they can typically find high-quality approximate solutions within a reasonable timeframe. Due to their global search capabilities, metaheuristic algorithms are widely used in combinatorial optimization, machine learning, and industrial scheduling.

[0003] Extensive research has been conducted on metaheuristic algorithms. The Snow Ablation Optimizer (SAO) is a metaheuristic optimization algorithm based on the natural snow ablation process. It simulates the morphological changes and energy transfer of snow during ablation. It was proposed by Deng et al. in 2023. This algorithm simulates the ablation, flow, and refreezing of snow, performing global and local searches within the solution space to find the optimal solution.

[0004] Metaheuristic algorithms typically do not rely on the problem's gradient information and can therefore be used to solve complex, nonlinear, nonconvex, high-dimensional, and multimodal problems that are difficult to model. Applying metaheuristic algorithms to neural network spectrum prediction not only overcomes some of the limitations of traditional methods but also significantly improves the model's prediction accuracy and reliability, especially when dealing with complex and dynamically changing spectrum environments. Furthermore, spectrum data in wireless communications often exhibits strong nonlinear characteristics. When combined with neural networks, metaheuristic algorithms can more effectively capture these nonlinear relationships, improving the model's performance in complex pattern recognition tasks. Consequently, spectrum prediction improved with metaheuristic algorithms has become increasingly popular. Summary of the Invention

[0005] The purpose of the present invention is to improve the limitations of snow ablation optimizers in the prior art in performing spectrum prediction, and to provide a spectrum prediction method, program, device and storage medium for a snow ablation optimization algorithm based on chaos mapping good point set initialization and simulated annealing.

[0006] A spectrum prediction method based on a snow melting optimization algorithm using chaos mapping good point set initialization and simulated annealing includes the following steps:

[0007] Get the training set and test set, the sample data includes time and power spectrum density values;

[0008] Construct a spectrum prediction model and combine all key parameters of the spectrum prediction model into a parameter vector;

[0009] An improved snowmelt optimization algorithm is used to optimize the parameter vector. The position of individuals in the population represents a set of parameter vector solutions. The spectrum prediction model corresponding to the parameter vector solution is trained using the training set, and the average absolute percentage error of the spectrum prediction is obtained using the test set. The average absolute percentage error of the spectrum prediction model corresponding to the individual position in the population is used as the fitness value. The position of individuals in the population is initialized based on the chaotic mapping good point set. Based on the dual-population mechanism of the snowmelt optimization algorithm, one population maintains the original individual position update mode, and the other population introduces a simulated annealing probabilistic acceptance mechanism to accept the neighborhood solution with a certain probability to update the individual position. The temperature decay mechanism is used to control the disturbance amplitude during the search process. Finally, the optimal parameter vector corresponding to the global optimal position with the lowest fitness value is output.

[0010] A spectrum prediction model is constructed based on the optimal parameter vector, and after training with the training set, the spectrum prediction task is performed.

[0011] Furthermore, the spectrum prediction model adopts a CNNBiGRU neural network, including an input unit, a CNN feature extraction unit, a BIGRU unit, a fusion and output unit;

[0012] The input unit is used to transform the input data to obtain a three-dimensional tensor;

[0013] The CNN feature extraction unit is used to extract local spatial features from the original input, including convolutional layer, Relu layer and maximum pooling layer; the convolutional layer performs convolution operation on the input data to extract low-level features; the Relu layer introduces the Relu function to enhance the expression ability of the model, and the maximum pooling layer compresses the extracted feature dimensions to retain the main information;

[0014] In the BIGRU unit, the forward GRU branch receives the local spatial features output by the CNN feature extraction unit, uses GRU to capture its forward temporal dependency, and outputs the hidden state of each time step; the reverse GRU branch performs reverse processing by flipping the input sequence to capture reverse temporal information;

[0015] After obtaining the output of the forward and reverse GRUs, the fusion and output unit further fuses the information of the two and introduces a multi-head self-attention mechanism to make the model focus on key time points, keep the input and output dimensions consistent, and finally denormalize the output data and output the results.

[0016] Furthermore, the key parameters of the spectrum prediction model include CNN learning rate, CNN convolution kernel, BiGRU layer neurons, and the number of attention heads in the self-attention layer.

[0017] Furthermore, the positions of individuals in the population are initialized based on the chaotic mapping good point set, specifically:

[0018] For the position X of an individual in the population i (t) = {x i1 (t),x i2 (t),...,x iA (t)}, t is the number of iterations, X i (t) is the position of the i-th individual in the population at the t-th iteration, i = 1, 2, ..., N, N is the total number of individuals in the population; x ij (t) is X i (t) The value of the jth parameter in the corresponding parameter vector solution, j = 1, 2, ..., A, A is the total number of parameters to be optimized;

[0019] Set the chaotic mapping parameter r, the random initial value y0∈(0,1], and generate N chaotic values ​​y1,...,y according to the nonlinear recursive equation of the chaotic mapping. N , and all chaotic values ​​y i Mapped to [0,1];

[0020] y i+1 =ry i (1-y i )

[0021] According to the upper bound lb of each parameter j and the lower bound ub j , generate the GPS initialization result X of each individual position in the population iL (1);

[0022] X iL (1) = {x iL1 (1),x iL2 (1),...,x iLA (1)}

[0023] x iLj (1) = lb j +(ub j -lb j )×y i

[0024] For each parameter, choose an irrational number p j , generate the initialization result X of the good point set for each individual position in the population iGPS (1);

[0025] X iGPS (1) = {x iGPS1 (1),x iGPS2 (1),...,x iGPSA (1)}

[0026] x iGPSj (1) = lb j +(ub j -lb j )×f(i×p j )

[0027] Among them, the function f(·) represents the decimal part of the input value;

[0028] Set the amplitude control parameter μ of the chaotic perturbation to generate the initialization result X based on the chaotic mapping good point set for each individual position in the population iCG (1);

[0029] X iCG (1) = X iGPS (1)+μX iL (1)

[0030] X iCG (1) = {x iCG1 (1),x iCG2 (1),...,x iCGA (1)}

[0031] X iCG (1) Mapping to the search space, generating the initialization result X for each individual position in the population i (1);

[0032] X i (1) = {x i1 (1),x i2 (1),...,x iA (1)}

[0033] x ij (1) = lb j +(ub j -lb j )×x iCGj (1).

[0034] Furthermore, based on the dual population mechanism of the snow melt optimization algorithm, one population maintains the original individual position update mode, specifically:

[0035] The total population N is randomly divided into two sub-populations, and the number of individuals in the two sub-populations is N / 2;

[0036] The first subpopulation updates the individual positions according to the original update mode of the snowmelt optimization algorithm;

[0037]

[0038] Among them, Elite(t)∈[G(t),X second (t),X third (t),X c (t)], Elite(t) is the second (t), X third (t), X c (t) is randomly selected; G(t), X second (t), X third (t) are the positions of the individuals with the smallest, second smallest, and third smallest fitness values ​​in the t-th iteration respectively; X c (t) is the centroid of the top 50% of individual positions with the smallest fitness value in the t-th iteration, JY(t) is the index set of the top 50% individuals with the smallest fitness value in the tth iteration; bm i (t) is the Brownian motion vector of the i-th individual in the t-th iteration, BM i (t)=[bm1(t),...,bm N (t)] T , bm i (t) is the Brownian motion matrix BM i The i-th row vector in (t), BM i (t) is an N×A matrix, bm i (t) is a 1×A row vector, and the Brownian motion matrix BM i All elements in (t) obey the normal distribution with mean 0 and variance 1; θ 1i is a random number between [0,1]; X(t) is the centroid position of the population in the tth iteration,

[0039] Furthermore, based on the dual population mechanism of the snow melting optimization algorithm, another population introduces a simulated annealing probability acceptance mechanism to update the position of the individual by accepting the neighborhood solution with a certain probability, specifically:

[0040] The second subpopulation introduces the simulated annealing probability acceptance mechanism and accepts the neighborhood solution with a certain probability:

[0041] For all individuals in the second subpopulation, calculate the initial updated solution X iM1 (t+1);

[0042]

[0043] Among them, Mt is the snow melting rate, M t =DDF×(T t -T c );T t is the daily average temperature in the tth iteration; T c is the basic temperature; DDF(t) is the melting factor, t max is the maximum number of iterations; θ 2i is a random number between [-1,1];

[0044] For each individual's initial update solution X iM1 (t+1) Add random perturbation to generate a new solution X iM2 (t+1); calculate the initial updated solution X respectively iM1 The fitness value S(X iM1 (t+1)) and the new solution X iM2 The fitness value S(X iM2 (t+1));

[0045] If S(X iM2 (t+1))<S(X iM1 (t+1)), then accept the new solution and the position of the individual is updated to X i (t+1)=X iM2 (t+1);

[0046] If S(X iM2 (t+1))≥S(X iM1 (t+1)), then according to the acceptance probability P it Decide whether to accept the new solution;

[0047]

[0048] Furthermore, the improved snow melting optimization algorithm is used to optimize the parameter vector, specifically including the following steps:

[0049] Step 1: Initialize t = 1, the daily average temperature T1, and initialize the position X of the individual in the population based on the chaotic mapping good point set i (1), calculate the fitness values ​​of all individuals in the population, and obtain the individual positions G(1), X(2) with the smallest, second smallest, and third smallest fitness values. second (1) X third (1), and obtain the indexes of the top 50% of individuals with the smallest fitness values, and construct the index set JY(1); initialize G(1) as the global optimal position;

[0050] Step 2: Calculate the population centroid , melting factor DDF(t) and snow melting rate M t ;

[0051] Step 3: Randomly divide the total population N into two sub-populations, and the number of individuals in each sub-population is N / 2;

[0052] Step 4: The first subpopulation updates the individual positions according to the original update mode of the snowmelt optimization algorithm;

[0053] Step 5: The second subpopulation introduces the simulated annealing probability acceptance mechanism, accepts the neighborhood solution with a certain probability, and updates the individual's position:

[0054] Step 6: Calculate the fitness value based on the updated positions of all individuals and update the elite pool [G(t+1), X second (t+1),X third (t+1),X c (t+1)]: If there is an individual updated position X i If the fitness value corresponding to (t+1) is less than the fitness value corresponding to the global optimal position, the global optimal position is updated;

[0055] Step 7: Use the temperature attenuation mechanism to control the disturbance amplitude during the search process and update the daily average temperature T t+1 ;

[0056] T t+1 =α×T t

[0057] Step 8: If T t+1 <T min or t>t max , then stop the iteration and output the optimal parameter vector corresponding to the global optimal position; otherwise, let t = t + 1 and return to step 2.

[0058] A computer device / equipment / system includes a memory, a processor, and a computer program stored in the memory, wherein the processor executes the computer program to implement the steps of the spectrum prediction method of the snow ablation optimization algorithm based on chaotic mapping good point set initialization and simulated annealing.

[0059] A computer-readable storage medium stores a computer program / instruction thereon, which, when executed by a processor, implements the steps of the spectrum prediction method of the snow ablation optimization algorithm based on chaos mapping good point set initialization and simulated annealing.

[0060] A computer program product includes a computer program / instruction, which, when executed by a processor, implements the steps of the spectrum prediction method of the snow ablation optimization algorithm based on chaos mapping good point set initialization and simulated annealing.

[0061] The beneficial effects of the present invention are:

[0062] This invention uses an improved snowmelt optimization algorithm to optimize key parameters in the spectrum prediction model. It initializes the positions of individuals in a population based on a chaotic mapping optimal point set, effectively improving the uniformity and randomness of the initial population. Building on the dual-population mechanism of the snowmelt optimization algorithm, one population maintains the original individual position update pattern, while the other population introduces a simulated annealing probabilistic acceptance mechanism, accepting neighborhood solutions with a certain probability to update individual positions, enhancing the algorithm's global search capabilities. Furthermore, a temperature attenuation mechanism is used to control the perturbation amplitude during the search process, improving convergence speed, enhancing optimization accuracy, and enhancing the robustness of the algorithm. Compared to other algorithms, this invention achieves superior results, significantly improving prediction performance, and is applicable to diverse channel environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0063] Figure 1 This is a flow chart of the improved snow melting optimization algorithm in the present invention.

[0064] Figure 2 This is a description diagram of the CEC2022 function parameter space.

[0065] Figure 3 Comparison of the convergence curves of the eight algorithms when using the 10-dimensional CEC2022 test function.

[0066] Figure 4 Explore and develop scale maps for populations.

[0067] Figure 5 This is the structural diagram of the CNNBiGRU neural network model.

[0068] Figure 6 This is the overall architecture diagram of the present invention.

[0069] Figure 7 The determination coefficient R of spectrum prediction in ten channels by different methods 2 picture

[0070] Figure 8 The mean absolute percentage error (MAPE) of spectrum prediction for different methods in ten channels

[0071] Figure 9 This is a data set partitioning table in an embodiment of the present invention.

[0072] Figure 10 This is a table of simulation experiment parameter settings in an embodiment of the present invention. DETAILED DESCRIPTION

[0073] The present invention will be further described below with reference to the accompanying drawings.

[0074] This paper proposes an improvement method to address the limitations of the snowmelt optimizer, addressing its low initial population quality and its susceptibility to local optima. This improves optimization efficiency, further enhances the algorithm's search and development capabilities, and achieves a certain degree of balance. This algorithm addresses the difficulty in improving the accuracy of neural network-based spectrum predictions and improves prediction results.

[0075] The present invention first improves the population initialization method of the snow melting optimizer, including Logistic chaotic map initialization and Good Point Set (GPS) initialization.

[0076] Logistic chaos map is a classic nonlinear recursive equation that is often used to study chaotic behavior. Its mathematical expression is as follows:

[0077] y n+1 =ry n (1-y n )

[0078] Where: y n represents the value of the nth generation; r represents the control parameter, usually r∈(3,4].

[0079] Although the logistic map is a deterministic equation without random numbers, it can still exhibit random-like behavior. Initially used to study population growth models, it was later discovered that chaotic behavior could be generated under the control of control parameters, thus becoming one of the foundations of commonly used chaotic maps. The logistic map is primarily determined by the control parameter r. When r = 3.57, the population enters a chaotic range, exhibiting extreme sensitivity to initial values. This means that even a very small change in y0 can result in two completely different long-term trajectories. Around r ≈ 3.83, a periodic window appears, where the population briefly returns to a periodic state before re-entering a chaotic state. When r = 4, the population becomes completely chaotic, exhibiting pseudo-randomness.

[0080] The good point set is a uniform sampling method based on number theory, which makes the generated point set more evenly distributed in the high-dimensional search space. The formula is as follows:

[0081] z i ={i×p},i=1,2,…,N

[0082] Among them, z i represents the i-th point in the good point set; p represents an irrational number, usually the reciprocal of a prime number (e.g. ); {·} indicates taking the decimal part.

[0083] Combining a chaotic map to generate a good point set can effectively improve the uniformity and randomness of the initial population. This is particularly true in high-dimensional spaces, where chaotic systems can generate a well-distributed initial population. The logistic chaotic map provides ergodicity, ensuring a uniform distribution of the population within the search space, avoiding over-concentration or over-sparseness of individuals, thereby improving global search capabilities. The good point set exhibits excellent uniform distribution, ensuring uniform coverage of individuals across the search space, reducing search blind spots and enhancing the search efficiency and stability of the optimization algorithm. The combination of these two methods ensures population diversity while improving distribution uniformity, enhancing the algorithm's global search capabilities and making optimization results more accurate and stable.

[0084] Next, we improved the population update of the snowmelt optimizer, specifically the simulated annealing (SA) algorithm. The core idea of ​​SA is to introduce a probabilistic acceptance mechanism, which allows for the acceptance of inferior solutions to escape local optima. The probabilistic acceptance mechanism works as follows: if a new solution is better than the current one, it is accepted; if a new solution is worse than the current one, it is accepted with a certain probability.

[0085] The position update formula of the Snow Melt Optimizer mainly relies on the elite group (the best, second best, third best and the top 50% of the fitness group) to search, so it is easy to fall into the local optimum in high-dimensional situations with greater complexity and affect the global exploration ability. b There are some problems in the population (development population) exploration process:

[0086] 1. Falling into local optimum: Due to N b The population mainly relies on local search strategies, and its search direction is easily restricted by the current optimal solution, thereby limiting the expansion of the search space and making the algorithm easily fall into local optimality on complex problems.

[0087] 2. Decreased exploration efficiency: As the number of iterations increases, the individuals in the population tend to converge and the degree of variation decreases, resulting in a decrease in search ability, which in turn affects the final optimization accuracy.

[0088] 3. Insufficient diversity: During the local development process, the similarity between individuals gradually increases, resulting in a decrease in population diversity, which in turn reduces the global optimization ability of the algorithm.

[0089] The simulated annealing algorithm can accept poor solutions according to probability, jump out of the local optimal solution during the exploration process, and improve the global search capability. To solve the above problems, the present invention uses the N b The simulated annealing algorithm is introduced into the population optimization process, and the random perturbation characteristics of the Metropolis criterion are used to enhance N bThe search capability of the population can be improved, thereby improving the optimization effect of the algorithm and enhancing the global search capability and convergence rate of the algorithm.

[0090] The core idea of ​​the improved method is as follows: b The simulated annealing mechanism is introduced in the population development process, which allows the acceptance of variant solutions with a certain probability to enhance the global search capability of the algorithm. The temperature attenuation mechanism is used to control the disturbance amplitude during the search process, so that the algorithm can conduct a large-scale exploration in the early stage and gradually converge to the optimal solution in the later stage. b The population search method dynamically adjusts the search step size in each iteration to further improve the convergence speed and optimization accuracy.

[0091] In order to ensure that the dual population mechanism unique to the SAO algorithm is not destroyed, one population is selected to combine with the SA mechanism while the other population maintains the original update mode. This not only retains the characteristics of SAO but also obtains the advantages of SA. b The population is combined with the SA mechanism. The steps are as follows: First, the current solution is generated according to the original position update formula; then, the simulated annealing inner loop is entered, and a new solution is generated by adding random perturbations (the range of random perturbations is set to -1% to 1%) to the current solution; then, the fitness of the current solution and the new solution are calculated and compared, and the acceptance of the new solution is determined according to the acceptance method described in Chapter 2; then, the temperature is lowered until the SA inner iteration is exited.

[0092] The spectrum prediction model of the present invention adopts a CNNBiGRU neural network, including an input unit, a CNN feature extraction unit, a BIGRU unit, a fusion and output unit;

[0093] (1) Input unit: The normalized input data is transformed to obtain a three-dimensional tensor suitable for input into the neural network. The shape is [20, 1, 1], representing a one-dimensional time series signal. This signal is organized into a two-dimensional image format and enters the subsequent convolution operation.

[0094] (2) CNN feature extraction unit: This unit is responsible for extracting local spatial features from the raw input. It consists of the following layers: The convolution layer performs convolution operations on the input data to extract low-level features. Parameters include the convolution kernel size KerlSize and the number of channels (32). Next, the Relu layer introduces the Relu function to enhance the model's expressiveness. The max pooling layer compresses the extracted feature dimensions, retaining the main information. The window size is set to [3×3] to keep the output size unchanged. Finally, the above process is repeated to increase the number of output channels to 64. KerlSize is the parameter to be optimized.

[0095] (3) BIGRU unit: The forward GRU branch receives the [20,1] sequence output by CNN as input and uses GRU to capture its forward temporal dependency. number GRU units, outputting the hidden state of each time step, with an output size of [20, GRU number ]. The reverse GRU branch performs reverse processing by flipping the input sequence, thereby capturing reverse timing information. number GRU units, the output size is [20,GRU number ]. Among them GRU number is the parameter to be optimized.

[0096] (4) Fusion and output unit: After obtaining the output of the forward and reverse GRU, the model further fuses the information of the two and generates the final prediction result. The introduction of the multi-head self-attention mechanism enables the model to focus on key time points, enhance the modeling ability, and keep the input and output dimensions consistent. Finally, the output data is denormalized and the result is output. The number of self-attention heads is self number is the parameter to be optimized.

[0097] In the present invention, a training set and a test set are first obtained, and the sample data includes time and power spectral density values; a spectrum prediction model is constructed, and all key parameters of the spectrum prediction model are combined into a parameter vector; an improved snow melting optimization algorithm is used to optimize the parameter vector, and the position of the individual in the population represents a set of parameter vector solutions. For the spectrum prediction model corresponding to the parameter vector solution, the spectrum prediction model is trained using the training set, and the average absolute percentage error of the spectrum prediction is obtained using the test set. The average absolute percentage error of the spectrum prediction model corresponding to the individual position in the population is used as the fitness value, and the position of the individual in the population is initialized based on the chaotic mapping good point set. On the basis of the dual-population mechanism of the snow melting optimization algorithm, one population maintains the original individual position update mode, and the other population introduces a simulated annealing probability acceptance mechanism to accept the neighborhood solution with a certain probability to update the individual position. The temperature attenuation mechanism is used to control the disturbance amplitude in the search process, and finally the optimal parameter vector corresponding to the global optimal position with the lowest fitness value is output; the spectrum prediction model is constructed according to the optimal parameter vector, and after training with the training set, the spectrum prediction task is performed.

[0098] The improved snow melting optimization algorithm is used to optimize the parameter vector, which includes the following steps:

[0099] Step 1: Set the chaotic mapping parameter r, the random initial value y0∈(0,1], the amplitude control parameter μ of the chaotic perturbation, μ can be [0.05,0.2], the base temperature T c , temperature attenuation parameter α, minimum temperature threshold T min , the total number of individuals in the population N, the maximum number of iterations tmax , the random number θ for each individual 1i ∈[0,1] and θ 2i ∈[-1,1];

[0100] For the position X of an individual in the population i (t) = {x i1 (t),x i2 (t),...,x iA (t)}, t is the number of iterations, X i (t) is the position of the i-th individual in the population at the t-th iteration, i = 1, 2, ..., N, N is the total number of individuals in the population; x ij (t) is X i (t) The value of the jth parameter in the corresponding parameter vector solution, j = 1, 2, ..., A, A is the total number of parameters to be optimized;

[0101] Initialize t = 1, the daily average temperature T1, and initialize the position X of the individual in the population based on the chaotic mapping good point set i (1), comprising the following steps:

[0102] Step 1.1: Generate N chaotic values ​​y1,...,y according to the nonlinear recursive equation of chaotic mapping N , and all chaotic values ​​y i Mapped to [0,1];

[0103] y i+1 =ry i (1-y i )

[0104] Step 1.2: According to the upper bound lb of each parameter j and the lower bound ub j , generate the GPS initialization result X of each individual position in the population iL (1);

[0105] X iL (1) = {x iL1 (1),x iL2 (1),...,x iLA (1)}

[0106] x iLj (1) = lb j +(ub j -lb j )×y i

[0107] Step 1.3: For each parameter, choose an irrational number p j , generate the initialization result X of the good point set for each individual position in the populationiGPS (1);

[0108] X iGPS (1) = {x iGPS1 (1),x iGPS2 (1),...,x iGPSA (1)}

[0109] x iGPSj (1) = lb j +(ub j -lb j )×f(i×p j )

[0110] Among them, the function f(·) represents the decimal part of the input value;

[0111] Step 1.4: According to the amplitude control parameter μ of the chaotic perturbation, generate the initialization result X of the optimal point set based on the chaotic mapping for each individual position in the population. iCG (1);

[0112] X iCG (1) = X iGPS (1)+μX iL (1)

[0113] X iCG (1) = {x iCG1 (1),x iCG2 (1),...,x iCGA (1)}

[0114] Step 1.5: Place the X iCG (1) Mapping to the search space, generating the initialization result X for each individual position in the population i (1);

[0115] X i (1) = {x i1 (1),x i2 (1),...,x iA (1)}

[0116] x ij (1) = lb j +(ub j -lb j )×x iCGj (1)

[0117] Calculate the fitness values ​​of all individuals in the population and obtain the individual positions G(1), X(2) with the smallest, second smallest, and third smallest fitness values. second (1) X third(1), and obtain the indexes of the top 50% of individuals with the smallest fitness values, and construct the index set JY(1); initialize G(1) as the global optimal position;

[0118] Step 2: Calculate the population centroid , melting factor DDF(t) and snow melting rate M t ;

[0119]

[0120] M t =DDF×(T t -T c )

[0121] Step 3: Randomly divide the total population N into two sub-populations N a and N b , the number of individuals in the two subpopulations is N / 2;

[0122] Step 4: First subpopulation N a Update the individual's position according to the original update mode of the snow melt optimization algorithm;

[0123]

[0124] Among them, Elite(t)∈[G(t),X second (t),X third (t),X c (t)], Elite(t) is the second (t), X third (t), X c (t) is selected randomly;

[0125] X c (t) is the centroid of the top 50% of individual positions with the smallest fitness value in the t-th iteration:

[0126]

[0127] bm i (t) is the Brownian motion vector of the i-th individual in the t-th iteration, BM i (t)=[bm1(t),...,bm N (t)] T , bm i (t) is the Brownian motion matrix BM i The i-th row vector in (t), BM i (t) is an N×A matrix, bm i (t) is a 1×A row vector, and the Brownian motion matrix BM iAll elements in (t) follow a normal distribution with mean 0 and variance 1;

[0128] Step 5: Second subpopulation N b The simulated annealing probability acceptance mechanism is introduced to accept the neighborhood solution with a certain probability and update the individual position:

[0129] For the second subpopulation N b For all individuals in, calculate the initial update solution X iM1 (t+1);

[0130]

[0131] Among them, M t is the snow melting rate, M t =DDF×(T t -T c );T t is the daily average temperature in the tth iteration; T c is the basic temperature; DDF(t) is the melting factor, t max is the maximum number of iterations; θ 2i is a random number between [-1,1];

[0132] For each individual's initial update solution X iM1 (t+1) Add random perturbation to generate a new solution X iM2 (t+1); calculate the initial updated solution X respectively iM1 The fitness value S(X iM1 (t+1)) and the new solution X iM2 The fitness value S(X iM2 (t+1));

[0133] If S(X iM2 (t+1))<S(X iM1 (t+1)), then accept the new solution and the position of the individual is updated to X i (t+1)=X iM2 (t+1);

[0134] If S(X iM2 (t+1))≥S(X iM1 (t+1)), then according to the acceptance probability P it Decide whether to accept the new solution;

[0135]

[0136] Step 6: Calculate the fitness value based on the updated positions of all individuals and update the elite pool [G(t+1), X second (t+1),Xthird (t+1),X c (t+1)]: If there is an individual updated position X i If the fitness value corresponding to (t+1) is less than the fitness value corresponding to the global optimal position, the global optimal position is updated;

[0137] Step 7: Use the temperature attenuation mechanism to control the disturbance amplitude during the search process and update the daily average temperature T t+1 ;

[0138] T t+1 =α×T t

[0139] Step 8: If T t+1 <T min or t>t max , then stop the iteration and output the optimal parameter vector corresponding to the global optimal position; otherwise, let t = t + 1 and return to step 2.

[0140] Example 1:

[0141] The program is implemented in MATLAB, and the performance is verified using the CEC test function and compared with other metaheuristic algorithms. The following are specific experiments: First, this embodiment uses the public classic benchmark test set "IEEECEC2022" to verify the performance advantages of the method of the present invention compared with the currently available advanced or mature optimization methods in terms of convergence speed. The test suite includes unimodal functions, basic functions, hybrid functions, and combination functions. Secondly, in order to further verify the excellent performance of the method of the present invention, this embodiment compares it with several other advanced or mature optimization methods, including BOA algorithm, DBO algorithm, SSA algorithm, SABO algorithm, PSO algorithm, GWO algorithm and SAO algorithm. The four benchmark functions involved in the test are all configured as 10 dimensions. Each optimization method executes each benchmark function 30 times. The maximum number of iterations for each test is 1000 times, and the initial population size is set to 100.

[0142] CGSSAO is used to optimize the spectrum prediction algorithm based on the CNNBiGRU neural network. The parameters to be optimized of the optimized CNN network are CNN learning rate, CNN convolution kernel, BiGRU layer neurons, and the number of self-attention layer attention heads. The spectrum data is 510MHz-530MHz, the frequency resolution is 2MHz, and the time resolution is 15min. In the data used in the article, channel X refers to a 2MHz frequency bandwidth. Figure 9 The data set partition table is shown as follows: Figure 10 Shown is the simulation experiment parameter setting table.

[0143] Before conducting the experiment, the spectrum data needs to be normalized. As shown in the following formula, the minimum-maximum normalization is used to preprocess the data.

[0144]

[0145] Figure 2 The figure in the figure describes the parameter space of the CEC2022 function. It shows the smooth structure of the single-peak function F1, and at the same time shows a large number of local optimal solutions on the function and the complex structure of the function, which accurately simulates the real function solution space structure.

[0146] Figure 3 The convergence curves of eight algorithms are compared using the 10-dimensional CEC2022 test function. Compared with other algorithms, the proposed method achieves the best convergence results in most cases and has a faster convergence speed. In most cases, the algorithm converges to the optimal solution within 1000 iterations without stagnation, demonstrating its excellent global exploration and local development capabilities.

[0147] Figure 4 is the exploration-exploitation ratio of the population, with blue representing the exploitation ratio and green representing the exploration ratio. We can see that a high exploration ratio is maintained in the early stages of the iteration. As the iteration progresses, the exploitation ratio gradually increases while the exploration ratio decreases. This ratio is also maintained appropriately even when faced with complex hybrid and combinatorial functions.

[0148] Figure 7 is the determination coefficient R of spectrum prediction in ten channels by different methods 2 Fig. In the comparison of the coefficient of determination, the present invention is the best. Figure 7 In the channels shown, the coefficient of determination R in channels 1-10 is 2 Both are greater than 0.91.

[0149] Figure 8 The figure is the mean absolute percentage error (MAPE) of spectrum prediction in ten channels by different methods. Figure 8 Among the channels shown, the MAPE in channels 1-10 are all below 0.0140.

[0150] This method uses a chaotic mapping-based optimal point set to initialize the positions of individuals in a population. This method is more uniform than random initialization and can reduce population clumping issues. It is more stable and has stronger search capabilities than a single logistic algorithm. It is more ergodic than a single GPS algorithm and is suitable for complex optimization problems. Therefore, it can improve the distribution quality of the population to a certain extent, thereby improving the performance of the algorithm.

[0151] The present invention can improve the global search capability of the snow melting algorithm. The probability acceptance mechanism of simulated annealing effectively avoids the population from falling into the local optimum, enabling the algorithm to explore a wider search space and improve the global optimization capability. Secondly, it can improve the convergence speed. The temperature control mechanism allows a larger step search in the early stage and converges to a better solution in the later stage, thereby improving the optimization accuracy. The robustness of the algorithm is enhanced. Finally, through the introduction of the SA mechanism, the algorithm has stronger adaptability to different optimization problems and can demonstrate better stability and solution capabilities in complex optimization tasks.

[0152] Compared with other algorithms, the present invention has better effects and greatly improves the prediction performance. In addition, the algorithm has achieved relatively good prediction results for different channel environments.

[0153] The foregoing description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Those skilled in the art will readily appreciate that various modifications and variations of the present invention are possible. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present invention are intended to be within the scope of protection of the present invention.

Claims

1. A spectrum prediction method based on a snow melt optimization algorithm using chaos map good point set initialization and simulated annealing, characterized by: Get the training set and test set, the sample data includes time and power spectrum density values; Construct a spectrum prediction model and combine all key parameters of the spectrum prediction model into a parameter vector; An improved snowmelt optimization algorithm is used to optimize the parameter vector. The position of individuals in the population represents a set of parameter vector solutions. The spectrum prediction model corresponding to the parameter vector solution is trained using the training set, and the average absolute percentage error of the spectrum prediction is obtained using the test set. The average absolute percentage error of the spectrum prediction model corresponding to the individual position in the population is used as the fitness value. The position of individuals in the population is initialized based on the chaotic mapping good point set. Based on the dual-population mechanism of the snowmelt optimization algorithm, one population maintains the original individual position update mode, and the other population introduces a simulated annealing probabilistic acceptance mechanism to accept the neighborhood solution with a certain probability to update the individual position. The temperature decay mechanism is used to control the disturbance amplitude during the search process. Finally, the optimal parameter vector corresponding to the global optimal position with the lowest fitness value is output. A spectrum prediction model is constructed based on the optimal parameter vector, and after training with the training set, the spectrum prediction task is performed.

2. The spectrum prediction method based on the snow melting optimization algorithm of chaos map good point set initialization and simulated annealing according to claim 1 is characterized by: The spectrum prediction model adopts a CNNBiGRU neural network, including an input unit, a CNN feature extraction unit, a BIGRU unit, and a fusion and output unit; The input unit is used to transform the input data to obtain a three-dimensional tensor; The CNN feature extraction unit is used to extract local spatial features from the original input, including a convolutional layer, a ReLU layer and a maximum pooling layer; the convolutional layer performs a convolution operation on the input data to extract low-level features; The Relu layer introduces the Relu function to enhance the expressiveness of the model, and the maximum pooling layer compresses the extracted feature dimensions and retains the main information; In the BIGRU unit, the forward GRU branch receives the local spatial features output by the CNN feature extraction unit, uses GRU to capture its forward temporal dependency, and outputs the hidden state of each time step; the reverse GRU branch performs reverse processing by flipping the input sequence to capture reverse temporal information; After obtaining the output of the forward and reverse GRUs, the fusion and output unit further fuses the information of the two and introduces a multi-head self-attention mechanism to make the model focus on key time points, keep the input and output dimensions consistent, and finally denormalize the output data and output the results.

3. The spectrum prediction method based on the snow melting optimization algorithm of chaos map good point set initialization and simulated annealing according to claim 2 is characterized by: The key parameters of the spectrum prediction model include CNN learning rate, CNN convolution kernel, BiGRU layer neurons, and the number of attention heads in the self-attention layer.

4. The spectrum prediction method based on the snow melting optimization algorithm of chaos map good point set initialization and simulated annealing according to claim 1 is characterized by: The position of individuals in the population is initialized based on the chaotic mapping good point set, specifically: For the position X of an individual in the population i (t) = {x i1 (t),x i2 (t),...,x iA (t)}, t is the number of iterations, X i (t) is the position of the i-th individual in the population at the t-th iteration, i = 1, 2, ..., N, N is the total number of individuals in the population; x ij (t) is X i (t) The value of the jth parameter in the corresponding parameter vector solution, j = 1, 2, ..., A, A is the total number of parameters to be optimized; Set the chaotic mapping parameter r, the random initial value y0∈(0,1], and generate N chaotic values ​​y1,...,y according to the nonlinear recursive equation of the chaotic mapping. N , and all chaotic values ​​y i Mapped to [0,1]; yes i+1 =ry i (1-y i ) According to the upper bound lb of each parameter j and the lower bound ub j , generate the GPS initialization result X of each individual position in the population iL (1); X iL (1)={x iL1 (1),x iL2 (1),...,x iLA (1)} x iLj (1)=lb j +(ub j -lb j )×y i For each parameter, choose an irrational number p j , generate the initialization result X of the good point set for each individual position in the population iGPS (1); X iGPS (1)={x iGPS1 (1),x iGPS2 (1),...,x iGPSA (1)} x iGPSj (1)=lb j +(ub j -lb j )×f(i×p j ) Among them, the function f(·) represents the decimal part of the input value; Set the amplitude control parameter μ of the chaotic perturbation to generate the initialization result X based on the chaotic mapping good point set for each individual position in the population iCG (1); X iCG (1)=X iGPS (1)+μX iL (1) X iCG (1)={x iCG1 (1),x iCG2 (1),...,x iCGA (1)} X iCG (1) Mapping to the search space, generating the initialization result X for each individual position in the population i (1); X i (1)={x i1 (1),x i2 (1),...,x iA (1)} x ij (1)=lb j +(ub j -lb j )×x iCGj (1)。 5. The spectrum prediction method based on the snow melting optimization algorithm of chaos map good point set initialization and simulated annealing according to claim 4 is characterized by: Based on the dual population mechanism of the snow melt optimization algorithm, one population maintains the original individual position update mode, specifically: The total population N is randomly divided into two sub-populations, and the number of individuals in the two sub-populations is N / 2; The first subpopulation updates the individual positions according to the original update mode of the snowmelt optimization algorithm; Among them, Elite(t)∈[G(t),X second (t),X third (t),X c (t)], Elite(t) is the second (t), X third (t), X c (t) is randomly selected; G(t), X second (t), X third (t) are the positions of the individuals with the smallest, second smallest, and third smallest fitness values ​​in the t-th iteration respectively; X c (t) is the centroid of the top 50% of individual positions with the smallest fitness value in the t-th iteration, JY(t) is the index set of the top 50% individuals with the smallest fitness value in the tth iteration; bm i (t) is the Brownian motion vector of the i-th individual in the t-th iteration, BM i (t)=[bm1(t),...,bm N (t)] T , bm i (t) is the Brownian motion matrix BM i The i-th row vector in (t), BM i (t) is an N×A matrix, bm i (t) is a 1×A row vector, and the Brownian motion matrix BM i All elements in (t) obey the normal distribution with mean 0 and variance 1; θ 1i is a random number between [0,1]; The centroid position of the population in the tth iteration, 6. The spectrum prediction method based on the snow melting optimization algorithm of chaos map good point set initialization and simulated annealing according to claim 5 is characterized by: Based on the dual population mechanism of the snow melting optimization algorithm, another population introduces a simulated annealing probability acceptance mechanism to update the position of the individual by accepting the neighborhood solution with a certain probability. Specifically: The second subpopulation introduces the simulated annealing probability acceptance mechanism and accepts the neighborhood solution with a certain probability: For all individuals in the second subpopulation, calculate the initial updated solution X iM1 (t+1); Among them, M t is the snow melting rate, M t =DDF×(T t -T c );T t is the daily average temperature in the tth iteration; T c is the basic temperature; DDF(t) is the melting factor, t max is the maximum number of iterations; θ 2i is a random number between [-1,1]; For each individual's initial update solution X iM1 (t+1) Add random perturbation to generate a new solution X iM2 (t+1); calculate the initial updated solution X respectively iM1 The fitness value S(X iM1 (t+1)) and the new solution X iM2 The fitness value S(X iM2 (t+1)); If S(X iM2 (t+1))<S(X iM1 (t+1)), then accept the new solution and the position of the individual is updated to X i (t+1)=X iM2 (t+1); If S(X iM2 (t+1))≥S(X iM1 (t+1)), then according to the acceptance probability P it Decide whether to accept the new solution; 7. The spectrum prediction method based on the snow melting optimization algorithm of chaos map good point set initialization and simulated annealing according to claim 6 is characterized by: The improved snow melting optimization algorithm is used to optimize the parameter vector, specifically including the following steps: Step 1: Initialize t = 1, the daily average temperature T1, and initialize the position X of the individual in the population based on the chaotic mapping good point set i (1), calculate the fitness values ​​of all individuals in the population, and obtain the individual positions G(1), X(2) with the smallest, second smallest, and third smallest fitness values. second (1) X third (1), and obtain the indexes of the top 50% of individuals with the smallest fitness values, and construct the index set JY(1); initialize G(1) as the global optimal position; Step 2: Calculate the population centroid Melting factor DDF(t) and snow melting rate M t ; Step 3: Randomly divide the total population N into two sub-populations, and the number of individuals in each sub-population is N / 2; Step 4: The first subpopulation updates the individual positions according to the original update mode of the snowmelt optimization algorithm; Step 5: The second subpopulation introduces the simulated annealing probability acceptance mechanism, accepts the neighborhood solution with a certain probability, and updates the individual's position: Step 6: Calculate the fitness value based on the updated positions of all individuals and update the elite pool [G(t+1), X second (t+1),X third (t+1),X c (t+1)]: If there is an individual updated position X i If the fitness value corresponding to (t+1) is less than the fitness value corresponding to the global optimal position, the global optimal position is updated; Step 7: Use the temperature attenuation mechanism to control the disturbance amplitude during the search process and update the daily average temperature T t+1 ; T t+1 =α×T t Step 8: If T t+1 <T min or t>t max , then stop the iteration and output the optimal parameter vector corresponding to the global optimal position; otherwise, let t = t + 1 and return to step 2.

8. A computer device / apparatus / system comprising a memory, a processor, and a computer program stored in the memory, characterized in that: The processor executes the computer program to implement the steps of the method according to any one of claims 1 to 7.

9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

10. A computer program product comprising a computer program / instructions, characterized in that: When the computer program / instructions are executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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