A Method for Extracting Spectral Parameters of DFB Lasers

Abstract

The present invention relates to the field of extracting spectral parameters of lasers, and discloses a method for extracting spectral parameters of a DFB laser, comprising the following steps: constructing a deep learning model to train the corresponding relationship between spectral parameters and spectral extraction information; using a spectrometer to test the DFB laser with parameters to be extracted, and taking the measured spectrum as the target spectral extraction information; inputting the initialized spectral parameters into the learning model to predict the spectral extraction information, performing error analysis on the spectral extraction information output by the model and the target spectral extraction information, using the differential evolution algorithm for population evolution, and inputting the evolved parameters into the model until the target accuracy or the number of iterations is reached, thereby completing the extraction of spectral parameters. The method disclosed by the present invention greatly reduces the time for parameter extraction and the calculation cost; can quickly extract spectral parameters and avoid falling into the situation of local optimum; and realizes batch extraction of spectral parameters of DFB lasers in a short time.

Description

Technical Field

[0001] The present invention relates to the field of extracting spectral parameters of lasers, and particularly to a method for extracting spectral parameters of a DFB laser. Background Art

[0002] With the advantages of low threshold current, small size, and low power consumption, DFB lasers have been widely used in fields such as high-speed optical communication systems, sensing systems, and medical applications. However, in the actual production process, due to the influence of manufacturing processes, manufacturing equipment, and even different batches, there will be deviations between the material parameters and geometric dimensions of the lasers and the design values. These deviations will lead to inconsistencies between the test results and simulation results of the devices. Therefore, it is necessary to extract actual physical parameters based on performance tests. Parameter extraction is a key method for identifying defects in the process, improving laser design, and verifying theoretical models.

[0003] Currently, parameter extraction methods usually combine traditional optimization algorithms with spectral numerical calculation methods. Through the optimization algorithm, the parameters related to the spectrum are gradually iteratively modified and simulated until the error between the calculated spectrum and the target spectrum meets the requirements or reaches the number of iterations. If the traditional optimization algorithm runs based on iteration, in order to obtain the interaction of multiple physical states and the internal trends of the device, it is very time-consuming and requires high computational costs. It is difficult to achieve large-scale parameter extraction based on this method. Summary of the Invention

[0004] To solve the above technical problems, the present invention provides a method for extracting spectral parameters of a DFB laser to solve the problems of time-consuming and high computational costs of existing parameter extraction methods.

[0005] To achieve the above object, the technical solution of the present invention is as follows:

[0006] A method for extracting spectral parameters of a DFB laser, comprising the following steps:

[0007] Step 1, constructing a data set by using spectral parameters and corresponding spectral extraction information, and constructing a deep learning model. Using the spectral parameters as the input of the model and the spectral extraction information as the output of the model, training and testing the model with the data set; the spectral parameters include grating period, effective refractive index, coupling coefficient, phase, and group refractive index; the spectral extraction information includes the wavelength coordinates and amplitudes of the peak and valley values of the spectrum;

[0008] Step 2: Use a spectrometer to test the DFB laser for the parameters to be extracted, obtain spectral extraction information, and use it as the target spectral extraction information; use the differential evolution algorithm to extract the spectral parameters of the DFB laser. First, initialize the population, input the initialized spectral parameters into the qualified model to predict the spectral extraction information, perform error analysis on the spectral extraction information output by the model and the target spectral extraction information, and then drive the population to continuously evolve through the processes of mutation, crossover, and selection. Input the evolved parameters into the model to predict the spectral extraction information, and then perform error analysis on the spectral extraction information output by the model and the target spectral extraction information until the target accuracy or the number of iterations is reached, and complete the extraction of the spectral parameters.

[0009] In the above solution, in Step 1, when constructing the dataset, first set the range of the spectral parameters, then uniformly sample each parameter based on the set range, and then randomly combine the 5 spectral parameters to obtain several groups of spectral parameters. For each group of spectral parameters, use the transfer matrix method to calculate the spectrum of the DFB laser; according to the calculated spectrum, extract the wavelength coordinates and amplitudes of the peak and valley values of the spectrum to obtain the corresponding spectral extraction information.

[0010] In the above solution, in Step 1, when constructing the dataset, perform standardized preprocessing on the spectral parameters and min-max normalization preprocessing on the spectral extraction information. Construct the dataset with the preprocessed spectral parameters and spectral extraction information, and divide the dataset into a training set, a validation set, and a test set.

[0011] In the above solution, in Step 1, during the model training process, use the loss function to quantify the difference between the spectral extraction information predicted by the model and the spectral extraction information in the training set; during the training process, use the data in the validation set to measure whether overfitting occurs during the training process; after the model training is completed, use the data in the test set to test the model. If it passes the test, proceed to the next step. If it fails, retrain the model.

[0012] In the above solution, in Step 1, the constructed deep learning model includes an input layer, 5 hidden layers, and an output layer; the input layer includes 5 neurons, corresponding to 5 spectral parameters respectively; the output layer includes 22 neurons, corresponding to the wavelength coordinates and amplitudes of 22 spectral peaks and valleys respectively; the number of neurons in the 5 hidden layers is 100, 200, 300, 200, and 100 respectively; batch normalization is introduced before each hidden layer to adjust the feature distribution and improve the convergence stability.

[0013] In a further technical solution, the activation function used in the deep learning model is the ReLu activation function.

[0014] In a further technical solution, during the model training process, the loss functions adopted are the mean squared error and the mean absolute error, and the formulas are as follows:

[0015] ;

[0016] ;

[0017] Among them, is the mean squared error, is the mean absolute error, n is the total number of samples, is the theoretical value of the th sample, is the predicted value of the th sample.

[0018] In a further technical solution, the method of batch normalization is as follows:

[0019] In the training batch of the th dimension, there are A samples, is the th sample in the th training dimension of the training batch B; perform normalization processing on :

[0020] ;

[0021] Among them, is the data after normalizing ; is a very small constant used to prevent the denominator from being 0, is the mean of this training batch , is the variance of this training batch;

[0022] ;

[0023] ;

[0024] After the scaling and shifting factors:

[0025] ;

[0026] Among them, is the data after the value range of is transformed by the scaling and shifting factors, and is the input of the hidden layer, and represent the parameter vectors of scaling and shifting respectively.

[0027] In the above solution, in step 2, the spectral extraction information of the target test is the lasing spectrum of the DFB laser near the threshold measured by a spectrometer.

[0028] In the above solution, in step 2, the differential evolution algorithm includes four steps: initialization, mutation, crossover, and selection. The specific process is as follows:

[0029] (1) Initialization

[0030] For a 5-dimensional search space, the population initialization is expressed as:

[0031] ;

[0032] where is the th candidate solution in the Gth generation. Each candidate solution contains 5 spectral parameters, namely a set of numerical values of grating period, effective refractive index, phase, coupling coefficient, and group refractive index. N is the size of the population, represents the value of the candidate solution in the jth dimension;

[0033] Randomly initialize the initial value of the candidate solution in the th dimension within the search space, where and are the minimum and maximum values of the search range in the th dimension respectively, and is a uniformly random number in the range from 0 to 1;

[0034] After population initialization, input the initialized spectral parameters into the deep learning model, and then calculate the error between the actually measured spectral extraction information and the spectral extraction information predicted by the model using the mean square error;

[0035] (2) Mutation

[0036] The mutation operation is used to generate a new candidate solution:

[0037] ;

[0038] where is the mutation vector corresponding to the th candidate solution, , and are 3 different candidate solutions in the population, and F is a scaling factor used to control the scale of the differential vector;

[0039] (3) Crossover

[0040] The mutated candidate solution and the original candidate solution are subjected to a binomial crossover operation to generate a trial individual, expressed as:

[0041] ;

[0042] Among them, is the crossover probability, is a randomly selected dimension, ensuring that at least one dimension changes; represents the value of the th candidate solution at the th dimension when the generation number of evolution is G;

[0043] (4) Selection

[0044] Finally, a selection operation is performed between the candidate solution after mutation and the original candidate solution. The specific formula is as follows:

[0045] ;

[0046] Among them, is the objective function, represents the th candidate solution in the parental population when the generation number of evolution is G + 1, represents the th candidate solution in the crossover population when the generation number of evolution is G. If has better fitness, it enters the next generation; otherwise, the original candidate solution is retained.

[0047] Through the above technical solutions, the method for extracting spectral parameters of a DFB laser provided by the present invention has the following beneficial effects:

[0048] The parameter extraction method provided by the present invention can quickly extract spectral parameters in the case of having a laser spectrum, avoiding a large number of numerical simulation operations required by traditional optimization methods when extracting parameters, greatly reducing the time for parameter extraction and the calculation cost; compared with traditional optimization algorithms, the fusion of deep learning and differential evolution algorithms can quickly extract spectral parameters and avoid falling into the local optimum; batch extraction of spectral parameters of DFB lasers can be achieved in a short time. Description of the Drawings

[0049] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art.

[0050] Figure 1 is a schematic flow chart of extracting spectral parameters of a DFB laser using a differential evolution algorithm disclosed in an embodiment of the present invention;

[0051] Figure 2 is a schematic structural diagram of a uniform grating DFB laser;

[0052] Figure 3Schematic diagram for comparing the spectral extraction information predicted based on two sets of parameters in the test set with the spectral extraction information in the test set in the embodiments of the present invention; (a) is the schematic diagram for parameter sample 1, and (b) is the schematic diagram for parameter sample 2;

[0053] Figure 4 Comparison between the spectral extraction information predicted based on the spectral extraction parameters and the spectral extraction information in the test spectra in the embodiments of the present invention;

[0054] Figure 5 Schematic diagram for comparison between the spectrum calculated by using the transfer matrix method based on the extraction parameters and the test spectrum in the embodiments of the present invention. Detailed implementation manners

[0055] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying drawings in the embodiments of the present invention.

[0056] The present invention provides a method for extracting spectral parameters of a DFB laser, including the following steps:

[0057] 1. Set the range of spectral parameters, where the spectral parameters include grating period, effective refractive index, coupling coefficient, phase, and group refractive index; then uniformly sample each parameter based on the set range, and then randomly combine these 5 parameters to obtain several sets of spectral parameters. For each set of spectral parameters, calculate the spectrum of the DFB laser by using the transfer matrix method; the specific method for calculating the spectrum of the DFB laser by using the transfer matrix method can be seen in Patent CN 119358427 A, which will not be elaborated here.

[0058] 2. According to the calculated spectrum of the DFB laser, extract the wavelength coordinates and amplitudes of the peak and valley values of the spectrum, and then preprocess the spectral parameters and the corresponding spectral extraction information respectively; construct a data set from the preprocessed spectral parameters and spectral extraction information, and divide the data set into a training set, a validation set, and a test set;

[0059] The method for preprocessing the spectral parameters is standardization, and the method for preprocessing the spectral extraction information is min-max normalization. The specific method is as follows:

[0060] The standardization processing of the input data (spectral parameters) is to adjust each feature dimension to have a mean of 0 and a variance of 1. Suppose there are samples , for each dimension of feature , first calculate its mean and variance:

[0061] ;

[0062] ;

[0063] Subtract the mean and divide by the standard deviation of the feature to obtain a new feature value :

[0064] ;

[0065] Performing min - max normalization on the output data (spectral extraction information) normalizes the value range of each feature to . Suppose there are samples , for each dimension of the feature , the new feature obtained after normalization is:

[0066] ;

[0067] where and are the minimum and maximum values in this dimension respectively

[0068] 3. Build a deep learning model and use the data in the training set to train the model. The spectral parameters are used as the model input, and the spectral extraction information is used as the model output. During the model training process, a loss function is used to quantify the difference between the predicted spectral extraction information of the model and the spectral extraction information in the training set; during the training process, the data in the validation set is used to measure whether overfitting occurs

[0069] The built deep learning model includes an input layer, 5 hidden layers, and an output layer; the input layer contains 5 neurons, corresponding to 5 spectral parameters respectively; the output layer contains 22 neurons, corresponding to the wavelength coordinates and amplitudes of 22 spectral peaks and valleys respectively; the number of neurons in the 5 hidden layers are 100, 200, 300, 200, and 100 respectively; batch normalization is introduced before each hidden layer to adjust the feature distribution and improve the convergence stability. The activation function used in the deep learning model is the ReLu activation function

[0070] 60000 samples are used to build the deep learning model. During the model parameter optimization process, the Nadam optimizer is used to adjust the weights and biases of the neurons to minimize the loss function, and the learning rate of the optimizer is 0.001. The loss functions used during the optimization process are the mean squared error and the mean absolute error, and both are used together to quantify the difference between the predicted wavelength coordinates and amplitudes of spectral peaks and valleys in the model and the training set data. The formulas are as follows

[0071] ;

[0072] ;

[0073] where is the mean squared error is the mean absolute error, and n is the total number of samples. is the theoretical value of the th sample, is the th sample's predicted value.

[0074] The method of batch normalization is as follows:

[0075] In the training batch of the th dimension, there are A samples. is the rd sample in the th training dimension of training batch B. Standardize :

[0076] ;

[0077] Among them, is the data after standardizing ; is a very small constant used to prevent the denominator from being 0. is the mean of this training batch , is the variance of this training batch;

[0078] ;

[0079] ;

[0080] After the scaling and shifting factors:

[0081] ;

[0082] Among them, is the data after transformed by the scaling and shifting factors, which is the input of the hidden layer. and represent the parameter vectors of scaling and shifting respectively.

[0083] 4. After the model training is completed, use the data in the test set to test the model. If the test is qualified, proceed to the next step; if not, retrain the model.

[0084] Apply the method provided by the present invention to a uniform grating DFB laser, and its structural schematic diagram is as shown in Figure 2 . The range of the spectral parameters given when generating the data set is shown in Table 1.

[0085] Table 1 Range of Spectral Parameters

[0086]

[0087] Under the parameter ranges in Table 1, uniform sampling is performed for each parameter, and then these 5 parameters are randomly combined to obtain several groups of spectral parameters. Then, 78000 spectral samples are calculated by the transfer matrix method. The wavelength coordinates and amplitudes of the peaks and valleys of the spectra and the relevant parameters of the spectra are jointly used to construct a dataset. A deep learning model is constructed based on 60000 of these samples, 9000 samples are used to verify the model, and 9000 samples are used to evaluate the generalization ability of the constructed model. Randomly select 2 parameter samples from the test set and input them into the constructed deep learning model to predict the wavelength coordinates and amplitudes of the spectral peaks and valleys. The results are as Figure 3 shown in (a) and (b) below. The spectral information in the test set is the dashed line, and the prediction information of the model is the solid line. From Figure 3 it can be seen that the spectral extraction information predicted by the constructed model is highly consistent with the data in the dataset, intuitively indicating the accuracy and reliability of the model in predicting spectra. The specific values of the two parameter samples selected from the test set are shown in Table 2.

[0088] Table 2 Values of Two Parameter Samples

[0089]

[0090] 5. Use a spectrometer to test the DFB laser of the parameter to be extracted to obtain spectral extraction information, and use it as the target spectral extraction information; use the differential evolution algorithm to extract the spectral parameters of the DFB laser. As Figure 1 shown, first initialize the population, input the initialized spectral parameters into the qualified model to predict the spectral extraction information, perform error analysis on the spectral extraction information output by the model and the target spectral extraction information, and then drive the population to continuously evolve through the processes of mutation, crossover, and selection. Input the evolved parameters into the model to predict the spectral extraction information, and then perform error analysis on the spectral extraction information output by the model and the target spectral extraction information until the target accuracy or the number of iterations is reached, and complete the extraction of spectral parameters.

[0091] The target spectral extraction information is the lasing spectrum of the DFB laser near the threshold tested by the spectrometer.

[0092] The differential evolution algorithm includes four steps: initialization, mutation, crossover, and selection. The specific process is as follows:

[0093] (1) Initialization

[0094] For a 5-dimensional search space, the population initialization is expressed as:

[0095] ;

[0096] Among them, is the th candidate solution in the G-th generation. Each candidate solution contains 5 spectral parameters, namely a set of numerical values of grating period, effective refractive index, phase, coupling coefficient, and group refractive index. N is the size of the population, represents the value of the candidate solution in the j-th dimension;

[0097] Given the upper and lower limits of the parameters, randomly initialize the initial value of the candidate solution in the th dimension in the search space, where and are the minimum and maximum values of the search range in the th dimension respectively, is a uniform random number in the range from 0 to 1;

[0098] After the population is initialized, input the initialized spectral parameters into the deep learning model, and then calculate the error between the actually measured spectral extraction information and the spectral extraction information predicted by the model using the mean square error;

[0099] (2) Mutation

[0100] The mutation operation is used to generate new candidate solutions:

[0101] ;

[0102] Among them, is the mutation vector corresponding to the th candidate solution, , and are 3 different candidate solutions in the population, and F is a scaling factor used to control the scale of the difference vector;

[0103] (3) Crossover

[0104] The mutated candidate solution and the original candidate solution perform a binomial crossover operation to generate a trial individual, expressed as:

[0105] ;

[0106] Among them, is the crossover probability, is a randomly selected dimension to ensure that at least one dimension changes; represents the value of the th candidate solution in the th dimension when the evolutionary generation is G;

[0107] (4) Selection

[0108] Finally, a selection operation is performed between the mutated candidate solution and the original candidate solution, and the specific formula is as follows:

[0109] ;

[0110] Among them, is the objective function, represents the th candidate solution in the parental population when the evolutionary generation is G + 1, represents the th candidate solution in the crossover population when the evolutionary generation is G. If has a better fitness, it enters the next generation; otherwise, the original candidate solution is retained.

[0111] Table 3 lists the spectral parameters of the laser extracted by using the differential evolution algorithm. Then, based on these parameters, the wavelength coordinates and amplitudes of the spectral peaks and valleys are predicted by using the constructed model and compared with the information extracted from the target spectrum to be tested. The results are as Figure 4 shown. Figure 5 Among them is the comparison between the spectrum calculated by using the transfer matrix method based on the extracted spectral parameters and the actually measured spectrum. It can be seen from Figure 4 and Figure 5 that the trends between the dotted line and the solid line are in good agreement, indicating that the method of fusing deep learning and the differential evolution algorithm can accurately and efficiently extract spectral parameters.

[0112] Table 3 Extracted parameter values

[0113]

[0114] The present invention provides a method for extracting spectral parameters of a DFB laser based on the fusion of deep learning and the differential evolution algorithm. A deep learning model is constructed through spectral parameters and spectral extraction information to characterize the mapping relationship of the transfer matrix, and the effectiveness of the constructed model is evaluated through a test set. The population is initialized by using the differential evolution algorithm, and the parameters are input into the constructed model to perform error analysis on the predicted spectral extraction information and the target spectral extraction information to be tested. Then, the population is driven to evolve continuously through the processes of crossover, mutation, and selection. The spectral parameters are input into the constructed model to perform error analysis on the predicted spectral extraction information and the target spectral extraction information to be tested. When the error reaches the target value or the target number of iterations, the parameters are output to complete the parameter extraction. The invention extracts spectral parameters from the tested spectrum and calculates the spectrum by using the transfer matrix method based on the extracted spectral parameters, which is highly consistent with the tested spectrum. The invention can effectively avoid a large number of numerical simulation operations required for parameter extraction by traditional optimization algorithms, reduce the time cost, and at the same time can also realize the parameter extraction of the spectra of a batch of DFB lasers.

[0115] The foregoing description of the disclosed embodiments enables those skilled in the art to practice or use the present invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Thus, the present invention is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for extracting spectral parameters of a DFB laser, characterized in that It includes the following steps: Step 1: Construct a data set using spectral parameters and corresponding spectral extraction information, and construct a deep learning model. Use the spectral parameters as the input of the model and the spectral extraction information as the output of the model, and use the data set to train and test the model; the spectral parameters include grating period, effective refractive index, coupling coefficient, phase, and group refractive index; the spectral extraction information includes the wavelength coordinates and amplitudes of the peaks and valleys of the spectrum. Step 2: Use a spectrometer to test the DFB laser with parameters to be extracted to obtain spectral extraction information, and use it as the target spectral extraction information; use the differential evolution algorithm to extract the spectral parameters of the DFB laser. First, initialize the population, input the initialized spectral parameters into the tested model to predict the spectral extraction information, perform error analysis on the spectral extraction information output by the model and the target spectral extraction information, and then drive the population to evolve continuously through the processes of mutation, crossover, and selection. Input the evolved parameters into the model to predict the spectral extraction information, and then perform error analysis on the spectral extraction information output by the model and the target spectral extraction information until the target accuracy or the number of iterations is reached to complete the extraction of spectral parameters. In Step 1, the constructed deep learning model includes an input layer, 5 hidden layers, and an output layer; the input layer contains 5 neurons, corresponding to 5 spectral parameters respectively; the output layer contains 22 neurons, corresponding to the wavelength coordinates and amplitudes of 22 spectral peaks and valleys respectively; the number of neurons in the 5 hidden layers is 100, 200, 300, 200, and 100 respectively; batch normalization is introduced before each hidden layer to adjust the feature distribution and improve the convergence stability.

2. The method for extracting spectral parameters of a DFB laser according to claim 1, characterized in that, In Step 1, when constructing the data set, first set the range of spectral parameters, then uniformly sample each parameter based on the set range, and then randomly combine the 5 spectral parameters to obtain several groups of spectral parameters. For each group of spectral parameters, calculate the spectrum of the DFB laser using the transfer matrix method. According to the calculated spectrum, extract the wavelength coordinates and amplitudes of the peaks and valleys of the spectrum to obtain the corresponding spectral extraction information.

3. The method for extracting the spectral parameters of a DFB laser according to claim 1, characterized in that, In Step 1, when constructing the data set, perform standardization preprocessing on the spectral parameters and perform maximum-minimum normalization preprocessing on the spectral extraction information. Construct a data set with the preprocessed spectral parameters and spectral extraction information, and divide the data set into a training set, a validation set, and a test set.

4. A method for extracting spectral parameters of a DFB laser according to claim 1, characterized in that, In Step 1, during the model training process, use a loss function to quantify the difference between the spectral extraction information predicted by the model and the spectral extraction information in the training set; during the training process, use the data in the validation set to measure whether overfitting occurs during the training process. After the model training is completed, use the data in the test set to test the model. If the test is qualified, proceed to the next step; if not, retrain the model.

5. The extraction method of the spectral parameters of a DFB laser according to claim 1, characterized in that The activation function used in the deep learning model is the ReLu activation function.

6. The method for extracting the spectral parameters of a DFB laser according to claim 1, wherein During the model training process, the loss functions used are mean squared error and mean absolute error, and the formulas are as follows: ； ； Among them, is the mean square error, is the mean absolute error, n is the total number of samples, is the theoretical value of the th sample, is the predicted value of the 7. The method for extracting spectral parameters of a DFB laser according to claim 1, characterized in that The method of the batch normalization is as follows: In the training batch of the th dimension, there are A samples. It is the th sample in the th training dimension of training batch B. Standardize it: ； Among them, is the data after standardizing ; is a very small constant used to prevent the denominator from being zero, is the mean of this training batch ; is the variance of this training batch. ； ； After the scaling and translation factors: ； Among them, is the data after the value range transformation of the scaling and translation factors, which is the input of the hidden layer, and respectively represent the parameter vectors of scaling and translation.

8. The method for extracting spectral parameters of a DFB laser according to claim 1, wherein, In step 2, the target spectral extraction information is the lasing spectrum of the DFB laser near the threshold measured by a spectrometer.

9. The method for extracting spectral parameters of a DFB laser according to claim 1, characterized in that In step 2, the differential evolution algorithm includes four steps: initialization, mutation, crossover, and selection. The specific process is as follows: (1) Initialization For a 5-dimensional search space, the population initialization is expressed as: ； Among them, is the th candidate solution in the G-th generation. Each candidate solution contains 5 spectral parameters, namely a set of numerical values of grating period, effective refractive index, phase, coupling coefficient, and group refractive index. N is the size of the population, represents the value of the candidate solution in the j-th dimension; Randomly initialize the candidate solution within the search space with the initial value at the -dimensional , where and are the minimum and maximum values of the search range at the -dimensional respectively, and is a uniform random number within the range of 0 to 1; After the population initialization, the initialized spectral parameters are input into the deep learning model, and then the mean square error is used to calculate the error between the actually measured spectral extraction information and the spectral extraction information predicted by the model. (2) Mutation The mutation operation is used to generate new candidate solutions: ； Among them, is the mutation vector corresponding to the th candidate solution, , and are three different candidate solutions in the population, and F is the scaling factor used to control the scale of the difference vector; (3) Crossover The mutated candidate solutions and the original candidate solutions are subjected to a binomial crossover operation to generate trial individuals, which is expressed as: ； Among them, is the crossover probability, is a randomly selected dimension, ensuring that at least one dimension changes; represents the value of the -th candidate solution at the -th dimension when the generation number of evolution is G; (4) Selection Finally, a selection operation is performed between the mutated candidate solutions and the original candidate solutions. The specific formula is as follows: ； Among them, is the objective function, represents the -th candidate solution in the parental population when the generation number of evolution is G + 1, represents the -th candidate solution in the crossover population when the generation number of evolution is G. If has better fitness, it enters the next generation; otherwise, the original candidate solution is retained.

Images