Feature selection method based on multi-objective genetic algorithm

Abstract

This invention discloses a feature selection method based on a multi-objective genetic algorithm, comprising: S1, inputting a dataset and calculating relevance and redundancy using the mRMR algorithm; S2, storing the weight information of each feature after scoring using a feature weight vector fw; S3, initializing a population P containing N individuals according to the feature weights fw and generating H reference points; S4, crossover mutation to form a new population; S5, non-dominated sorting; S6, population normalization; S7, associating reference points; S8, elite selection; S9, repeating steps S4-S8 until the maximum number of iterations is reached. This method incorporates a filtered mRMR algorithm in the population initialization stage, combined with an encapsulated algorithm to form a hybrid feature selection method. It utilizes the internal information of the dataset to assist in population initialization, introducing maximum relevance and minimum redundancy to score the features of the original dataset, providing direction for population initialization and making it more directional.

Description

Technical Field

[0001] This invention belongs to the field of genetic algorithm technology and relates to a feature selection method based on a multi-objective genetic algorithm. Background Technology

[0002] In the medical field, DNA (Deoxyribonucleic acid) microarray technology can simultaneously collect large amounts of gene expression data, aiding in disease diagnosis and treatment strategy development. Although this technology yields a vast number of gene signatures, only a small fraction can be used to characterize disease specificity and serve as biomarkers for diagnosis or efficacy evaluation. Therefore, selecting relevant genes to determine disease-related characteristics is crucial.

[0003] Feature selection is an important data preprocessing technique. Its main goal is to identify the optimal subset of original features, remove irrelevant and redundant attributes, and ultimately reduce feature dimensionality. In recent years, evolutionary algorithms have attracted much attention due to their powerful optimization capabilities and have been applied to many practical problems, including genetic algorithms that simulate biological evolution, particle swarm optimization (PSO) and ant colony optimization (ACO) that simulate animal predation. Among these, genetic algorithms can use binary encoding to represent feature selection and non-selection, thus having an advantage in solving feature selection problems. Although genetic algorithms have proven effective in feature selection, the randomness of population initialization can hinder convergence. Furthermore, not all gene mutation operators produce consistently favorable results. Summary of the Invention

[0004] To address the aforementioned problems, this invention proposes a feature selection method based on a multi-objective genetic algorithm, which effectively solves the problems in the prior art.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] Feature selection methods based on multi-objective genetic algorithms include:

[0007] S1. Input dataset, use the maximum correlation minimum redundancy algorithm to calculate the correlation between features and labels and the redundancy between features;

[0008] S2. Use the feature weight vector fw to store the weight information after each feature is scored;

[0009] S3. Initialize a population P containing N individuals based on the feature weights fw, and generate H reference points;

[0010] S4. Assume that the current population of generation t is Pt. Perform crossover mutation on Pt to produce offspring Qt. Then combine Pt and its offspring Qt to form a new population Rt.

[0011] S5. Non-dominated ranking: The new population Rt is divided into different non-dominated levels F1, F2, F3..., where individuals at the higher level will dominate individuals at the lower level, and no individual will be dominated by other individuals at the same level.

[0012] S6. Population normalization: The target value of all individuals in the population is scaled to near the hyperplane of the reference point distribution to complete the population normalization.

[0013] S7. Associate reference points: Extract a reference line from the origin to each reference point, and associate each individual in the population with the reference point corresponding to the nearest reference line.

[0014] S8. Elite selection: Individuals ranked after non-dominance are progressively incorporated into the new population P. t+1 In, until there is a non-dominated level Fl such that |P t+1 |≥N;

[0015] If |P t+1 |=N,P t+1 As the next generation of population, execute the next cycle, repeating steps S4-S8;

[0016] If |P t+1 |>N, select K individuals from Fl, where K=N-|P t+1 |;

[0017] When selecting K individuals, first calculate the reference point at P. t+1 The number of associated individuals in Fl is then selected, and those associated with at least one reference point are included in P. t+1 In the middle, repeat K times until |P is obtained. t+1 |=N;

[0018] S9. Repeat steps S4-S8 until the maximum number of iterations Tmax is reached;

[0019] In the S4 population initialization, a binary string is used to represent a chromosome, where 1 indicates that the feature is selected, and 0 indicates otherwise. In a D-dimensional dataset, the i-th chromosome in the population will be encoded by a D-bit string:

[0020] X i (t)=(x i,1 ,x i,2 ,...,x i,j )

[0021] x i,j ∈{0,1},j=1,2,...,D,i=1,2,...,N

[0022] The population initialization includes: in a population with population size N, original number of features D, and feature weight fw, a random number M is selected, 1 < M < D, and M index positions mr_idx are selected based on the feature weight fw. This process is repeated N times to complete the initialization of all individuals, forming an initialized population Pt.

[0023] Optionally, the S4 feature selection algorithm includes a fast bit mutation operator, which includes:

[0024] Set a mutation probability μ, and then...

[0025] G=μ×min(count(0),count(1))

[0026] Calculate the number of genes to be flipped. Randomly select G genes that are encoded as 0 or 1, and flip their values. count(0) and count(1) represent the number of genes encoded as 0 and 1, respectively.

[0027] Optionally, during the S4 mutation process, the new individual is compared with individuals in the last layer of non-dominated sorting, and if the individual is dominant, there are k opportunities to retries the mutation.

[0028] Optionally, a fitness function may be included, which includes a classification error rate, a distance metric, and a feature selection ratio.

[0029] Optionally, the classification error rate is the balanced error rate, calculated using the following formula:

[0030]

[0031] balanced_err = 1 - balanced_acc

[0032] Where c is the number of classes of samples in the dataset, and TPR i represents the proportion of correctly predicted samples in class i, balanced_cc represents the average balanced accuracy of correctly predicted samples, and balanced_rr represents the average balanced accuracy of incorrectly predicted samples.

[0033] Optionally, the distance metric formula is:

[0034]

[0035] Where M is the number of samples in the training data, Dis(S i ,S j) is the distance between two samples Si and Sj, calculated using Manhattan distance. -5 is used to narrow the effective range of the Sigmoid function, which scales the training data to the range [0,1]. class(S i ) and class(S j ) represents S i S j The categories of the two samples.

[0036] Optionally, the feature selection ratio formula is:

[0037]

[0038] D represents the number of features in the original dataset, feature_proportion represents the feature selection ratio, and numberof selected features represents the number of features selected.

[0039] Compared with the prior art, the present invention has the following beneficial effects:

[0040] 1. Effectively solves the problem that current algorithms only use a single mutation operator when solving the feature selection problem, resulting in a slow feature reduction speed and uncertain population initialization direction when applied to high-dimensional datasets;

[0041] 2. In the population initialization stage, the maximum relevance and minimum redundancy are introduced to score the features of the original dataset, providing direction for population initialization;

[0042] 3. Furthermore, a fast bit mutation operator and a mutation retry operator are introduced during the population mutation stage to increase the number of mutations in the population and reduce the fitness differences among the populations, thereby avoiding the algorithm from getting stuck in the search and causing overfitting. Attached Figure Description

[0043] Figure 1 This is a schematic diagram of the overall process of an embodiment of the present invention;

[0044] Figure 2 This is a schematic diagram of a fast bit mutation according to an embodiment of the present invention;

[0045] Figure 3 This is a radar chart comparing the accuracy of the genetic algorithm in an embodiment of the present invention;

[0046] Figure 4 This is a comparison chart of the algorithm running time of embodiments of the present invention;

[0047] Figure 5 This is a comparison chart of the accuracy of the same particle swarm algorithm according to an embodiment of the present invention;

[0048] Figure 6This is a heatmap of the algorithm simplicity in an embodiment of the present invention;

[0049] Figure 7 This is a comparison chart of the average results of rapid bit mutation and basic bit mutation in an embodiment of the present invention. Detailed Implementation

[0050] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0051] Please see Figure 1 The feature selection method based on a multi-objective genetic algorithm disclosed in this embodiment of the invention includes:

[0052] S1. Input dataset and use the Maximum Relevance Minimum Redundancy (mRMR) algorithm to calculate the correlation between features and labels and the redundancy between features.

[0053] S2. Use the feature weight vector fw to store the weight information after each feature is scored;

[0054] S3. Initialize a population P containing N individuals based on the feature weights fw, and generate H reference points;

[0055] S4. Assume that the current population of generation t is Pt. Perform crossover mutation on Pt to produce offspring Qt. Then combine Pt and its offspring Qt to form a new population Rt.

[0056] S5. Non-dominated ranking: The new population Rt is divided into different non-dominated levels F1, F2, F3..., where individuals at the higher level will dominate individuals at the lower level, and no individual will be dominated by other individuals at the same level.

[0057] S6. Population normalization: The target value of all individuals in the population is scaled to near the hyperplane of the reference point distribution to complete the population normalization.

[0058] S7. Associate reference points: Extract a reference line from the origin to each reference point, and associate each individual in the population with the reference point corresponding to the nearest reference line.

[0059] S8. Elite selection: Individuals ranked after non-dominance are progressively incorporated into the new population P. t+1 In, until there is a non-dominated level Fl such that |P t+1 |≥N;

[0060] If |P t+1 |=N,P t+1 As the next generation of population, execute the next cycle, repeating steps S4-S8;

[0061] If |P t+1 |>N, select K individuals from Fl, where K=N-|P t+1 |;

[0062] When selecting K individuals, first calculate the reference point at P. t+1 The number of associated individuals in Fl is then selected, and those associated with at least one reference point are included in P. t+1 In the middle, repeat K times until |P is obtained. t+1 |=N;

[0063] S9. Repeat steps S4-S8 until the maximum number of iterations Tmax is reached;

[0064] In the S4 population initialization, a binary string is used to represent a chromosome, where 1 indicates that the feature is selected, and 0 indicates otherwise. In a D-dimensional dataset, the i-th chromosome in the population will be encoded by a D-bit string:

[0065] X i (t)=(x i,1 ,x i,2 ,...,x i,j )

[0066] x i,j ∈{0,1},j=1,2,...,D,i=1,2,...,N

[0067] The population initialization includes:

[0068] In a population with population size N, number of original features D, and feature weights fw, a random number M is selected, 1 < M < D. Based on the feature weights fw, M index positions are selected. This process is repeated N times until all individuals are initialized, forming an initialized population Pt.

[0069] Specifically, to address the issues of random population initialization and limited search capabilities in feature selection in current genetic algorithms, a filtered mRMR algorithm is added to the population initialization stage. This is combined with an encapsulated algorithm to form a hybrid feature selection method. This method utilizes the internal information of the dataset to assist in population initialization and introduces maximum relevance and minimum redundancy to score the features of the original dataset, providing direction for population initialization and making it more directional.

[0070] For a specific implementation of the feature selection method based on multi-objective genetic algorithm provided in the application, please refer to [link / reference]. Figure 2 The S4 feature selection algorithm includes a fast bit mutation operator, which includes:

[0071] Define a mutation probability μ, using the formula:

[0072] G=μ×min(count(0),count(1))

[0073] Calculate the number of genes to be flipped. Randomly select G genes that are encoded as 0 or 1, and flip their values. Here, Count(0) represents the number of genes encoded as 0, and Count(1) represents the number of genes encoded as 1.

[0074] In general, in traditional genetic algorithms, when the population mutates, the algorithm randomly selects some genes to mutate. However, in feature selection algorithms, using traditional mutation operators slows down the rate at which the number of features decreases, and the proportion of selected features remains at a balanced level. If the proportion of selected features is relatively low, genes encoding 0 will occupy most of the chromosomes, making randomly selected genes more likely to be 0, and mutations in this case will increase the feature size. If the rate of feature reduction slows down, the feature selection process will also slow down.

[0075] By setting a fast mutation operator, the survival pressure on genes in the chromosome is increased. Even if many genes encode 0, genes encoding 1 are easily selected for inversion. This means that genes associated with important traits have a greater chance of survival during mutation. A mutation probability μ that is too high or too low is detrimental to the algorithm's operation. When the mutation probability μ is too low, the mutation rate slows down, affecting the algorithm's efficiency. When μ is too high, it is easy to generate an individual with better fitness than others, affecting the evolution of the population and causing the algorithm to get stuck in a local optimum. The mutation probability is generally set to 1 / L to 1 / 2, where L is the number of genes on the chromosome.

[0076] By setting mutation operations, mutation information can be generated, thereby avoiding the algorithm from getting trapped in local optima during the search process, improving the algorithm's search ability, and ensuring population diversity. However, if the mutation rate is too high, prominent individuals and their offspring will eliminate other individuals, controlling the evolutionary direction of the population and hindering population diversity. Therefore, in step S8, a selection process of K individuals is set as a mutation retry operator. In the non-dominated sorting, if a newly mutated individual is dominated by any individual in the last layer, it will be eliminated in the subsequent elite selection. During the mutation process, the new individual is compared with individuals in the last layer of the non-dominated sorting. If the individual is dominant, it has k opportunities for mutation retry. Therefore, by using the mutation retry operator, the number of mutations is randomly increased, reducing the fitness differences in the population.

[0077] Meanwhile, a fast bit mutation operator and a mutation retry operator are introduced during the population mutation stage to increase the number of mutations in the population and reduce the fitness differences in the population, thereby avoiding the algorithm from getting stuck in the search and causing overfitting.

[0078] As a specific implementation of the feature selection method based on multi-objective genetic algorithm provided in the application, it includes a fitness function, which includes classification error rate, distance metric and feature selection ratio.

[0079] It should be understood that the choice of fitness function directly affects the convergence speed of the genetic algorithm and whether it can find the optimal solution. This is because the genetic algorithm basically does not utilize external information in the evolutionary search, relying solely on the fitness function and using the fitness of each individual in the population for the search. Using classification error rate, distance metric, and feature selection ratio as the algorithm's three fitness functions facilitates the combination of the advantages of filtering and encapsulation feature selection methods, ensuring that the selected dataset still has good classification performance.

[0080] Furthermore, the classification error rate is the balanced error rate, and the formula is:

[0081]

[0082] balanced_err = 1 - balanced_acc

[0083] Where c is the number of classes of samples in the dataset, and TPR i represents the proportion of correctly predicted samples in class i, balanced_cc represents the average balanced accuracy of correctly predicted samples, and balanced_rr represents the average balanced accuracy of incorrectly predicted samples.

[0084] It should be understood that setting a balanced error rate addresses the problem of data imbalance in high-dimensional, small-sample datasets.

[0085] Furthermore, the distance metric formula is:

[0086]

[0087] Where M is the number of samples in the training data, Dis(S i ,S j ) is the distance between two samples Si and Sj, calculated using Manhattan distance. -5 is used to narrow the effective range of the Sigmoid function, which scales the training data to the range [0,1]. class(S i ) and class(S j ) represents S i S j The categories of the two samples.

[0088] It should be understood that the classification error rate, as an optimization objective, is calculated for a specific classifier. Therefore, the solution obtained may achieve high accuracy on that classifier, but may not achieve the desired results on other classifiers. Furthermore, since classifiers may suffer from overfitting, the accuracy of a single classification method is unreliable. Therefore, adding a distance metric as a second optimization objective reflects the similarity between features.

[0089] Furthermore, the feature selection ratio formula is as follows:

[0090]

[0091] D represents the number of features in the original dataset, feature_proportion represents the feature selection ratio, and numberof selected features represents the number of features selected.

[0092] It should be understood that using the feature selection ratio as an optimization objective is to select fewer features to achieve a better dimensionality reduction effect.

[0093] In one feasible approach, this embodiment selects 15 publicly available benchmark genomic datasets from the University of California, Irvine (UCI) for experiments. Table 3.1 shows the number of features, number of samples, number of classes, and the percentage of samples in the largest and smallest classes for each of the 15 datasets. The number of features in these datasets is far greater than the number of samples, and the difference between the largest and smallest classes is significant, indicating a highly imbalanced dataset, typical of high-dimensional, small-sample datasets.

[0094] Table 3.1 Dataset Description

[0095]

[0096]

[0097] In some feasible approaches, 10-fold cross-validation is used to generate training and test sets, with one fold serving as the test set and the remaining nine folds as the training set for feature selection training. After feature selection training is complete, the optimal feature subset is obtained. Then, the training and test sets are modified by eliminating unselected features, and the results from the test set are used to evaluate the algorithm. During feature selection, 10-fold cross-validation is used to calculate the fitness of individuals, and a k=1 kNN is used as the classifier to calculate the classification error rate. Due to the high dimensionality and small sample size of the dataset, hierarchical 10-fold cross-validation is used to sample the data.

[0098] The dataset contains between 2000 and 13000 features. The population size is set to 1 / 20 of the number of features, with a maximum of 300. During the reference point association process, each candidate solution is associated with a reference point, and this association affects the elimination probability of the candidate solution. Therefore, the number of reference points is greater than the population size. Setting the number of reference point partitions along each axis to 27 yields 406 reference points, exceeding the maximum population size. The number of mutations and crossovers are both set to the same as the population size. The mutation probability is set to 0.1, allowing two mutations to increase the number of mutations. Ten independent feature selections are performed on each dataset. After feature selection, the optimal solution is selected. One 10-fold cross-validation generates 10 solutions, and ten executions yield 100 solutions. The performance evaluations of the 100 solutions are averaged to obtain the final result, which is then compared with other algorithms. Specific experimental parameters are shown in Table 3.2.

[0099] Table 3.2 Experimental Parameter Settings

[0100]

[0101]

[0102] In evaluating the effectiveness of the feature selection algorithm presented in this method, five feature selection algorithms were compared. These algorithms were categorized into two types: feature selection based on genetic algorithms and feature selection based on particle swarm optimization. The results were also compared with those obtained by directly classifying the original dataset.

[0103] During the evaluation process, the experimental parameters of the third-generation non-dominated sorting genetic algorithm (NSGA-III) and the problem-specific non-dominated sorting genetic algorithm (PS NSGA) were kept consistent with those of our proposed method, and binary encoding was used to represent chromosomes. The Particle Swarm Optimization-Feature Selection (PSO-FS) algorithm first discretizes features using the minimum description length, and then performs feature selection using the standard PSO algorithm. Furthermore, our method maintains consistency with particle swarm-based feature selection methods in terms of population size and number of iterations.

[0104] For ease of evaluation, three metrics were used to assess the performance of feature selection: classification accuracy (AvgACC), time, and parsimony. Time, measured in seconds, quantifies the computation time required for a single feature selection operation; a higher time indicates a longer algorithm runtime and lower execution efficiency. Since different types of algorithms have varying execution efficiencies, only the runtime of genetic algorithm-based feature selection algorithms was compared.

[0105] Classification accuracy (AvgACC):

[0106] Simplicity of Parsimony:

[0107] In the comparison between our method and feature selection based on genetic algorithms, we selected the NSGA-III feature selection method and the PS NSGA feature selection method. The results are shown in Table 3.3, where the results of our method are represented by mRNSGA.

[0108] Table 3.3 Comparison of results with methods based on genetic algorithms

[0109]

[0110]

[0111] Across all datasets, the feature subset selected by this method is consistently several orders of magnitude smaller than the full feature set. In 11 datasets, the number of selected features represents less than 1% of the total features, thus improving accuracy. Overall, this method achieves an average accuracy improvement of 10.08% across all datasets by selecting only 0.98% of the features.

[0112] Please see Figure 3 Compared to the NSGA-III feature selection algorithm, this method achieves higher classification accuracy across all datasets while selecting fewer feature subsets. On average, this method improves accuracy by 1.85% across all datasets and reduces the number of selected features by 11.82.

[0113] Please see Figure 4 Compared to the PS NSGA algorithm, the running time for single feature selection operations on different datasets is significantly shorter. The results show that the proposed method requires less time than the PS NSGA algorithm.

[0114] In comparing this method with feature selection based on particle swarm optimization, PSO-FS, Potential Particle Swarm Optimization (PPSO), Variable Length Particle Swarm Optimization (VLPSO), and Flexible Cut-point Particle Swarm Optimization (FCPSO) were selected, and the results are shown in Table 3.4.

[0115] Table 3.4 Comparison of results with particle swarm optimization methods

[0116]

[0117] This method outperforms the PSO-FS algorithm on all datasets, achieving higher classification accuracy while selecting fewer features. On the 9Tumor dataset, the accuracy of this method is improved by 14.39%, while the selected feature subset is only 1 / 5 of that selected by the PSO-FS algorithm.

[0118] Compared to the PPSO algorithm, this method selects fewer feature subsets across 13 datasets and achieves higher classification accuracy on 14 datasets (excluding the SRBCT dataset). Furthermore, on the SRBCT dataset, this method achieves only a 0.85% difference in classification accuracy while selecting only 5.6% of the features used in the PPSO algorithm. Compared to the VLPSO algorithm, this method selects fewer feature subsets across 12 datasets and achieves higher classification accuracy on 11 datasets. Although the VLPSO algorithm outperforms this method by 4.36% on the Leukemia2 dataset, this method selects less than a quarter of the features used in the VLPSO algorithm. Compared to the FCPSO algorithm, this method selects fewer features across 10 datasets and achieves higher classification accuracy on 13 datasets. While the FCPSO algorithm has the smallest average feature selection size across all 15 datasets, this method achieves an average accuracy 4.11% higher.

[0119] Please see Figure 5 This method achieves the highest classification accuracy on almost all datasets, and also has the highest average classification accuracy across all datasets.

[0120] To assess the impact of feature dimension parsimony, please refer to [link / reference]. Figure 6 The figure illustrates the trend of feature size variation across different datasets after each method is applied. The results show that the parsimony of most methods does not increase with the increase of dataset feature dimensionality, exhibiting weak adaptability to different feature sets. Our proposed method demonstrates good adaptability to parsimony and its ability to remove features improves with increasing dataset dimensionality.

[0121] In several feasible approaches, we selected a subset of high-dimensional datasets to compare the performance of the fast bit mutation and basic bit mutation operators in our proposed method. The results are shown in Table 3.5. The method using the fast bit mutation operator resulted in fewer features in the feature subset across the five datasets, while also demonstrating a significant improvement in classification accuracy.

[0122] Table 3.5 Comparison of results between rapid mutations and basic mutations

[0123]

[0124] Please see Figure 7 This study compares classification accuracy across 15 datasets with average feature subset size over 70 iterations. After reaching the maximum number of iterations, the algorithm using the fast bit mutation operator outperforms the operator using the basic bit mutation operator in both accuracy and average feature size. The fast bit mutation operator breaks the limitation of random mutation probability, improves mutation efficiency, and also improves the final accuracy more quickly.

[0125] This method introduces a mutation retry operator to increase the number of mutations in the genetic code. Table 3.6 shows the comparison results of algorithms with and without the mutation retry operator. The results show that the algorithm achieves better results in terms of accuracy and average feature size after adding the mutation retry operator. Since the mutation operator and mutation probability are the same, the parsimony of the population is not significantly different without the mutation retry operator; however, the algorithm achieves higher accuracy after using the mutation retry operator. The mutation retry operator reduces the fitness differences between individuals in the population. Under the same mutation rate, adding the mutation retry operator can improve the overall fitness of the population and reduce the possibility of the algorithm getting trapped in local optima.

[0126] Table 3.6 Comparison of results with the addition of the mutation retry operator

[0127]

[0128] Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A feature selection method based on a multi-objective genetic algorithm, characterized in that, include: S1. Input dataset, use the maximum correlation minimum redundancy algorithm to calculate the correlation between features and labels and the redundancy between features; S2. Use the feature weight vector fw to store the weight information after each feature is scored; S3. Initialize a population P containing N individuals based on the feature weights fw, and generate H reference points; S4. Assume that the current population of generation t is Pt. Perform crossover mutation on Pt to produce offspring Qt. Then combine Pt and its offspring Qt to form a new population Rt. The feature selection algorithm includes a fast bit mutation operator, which comprises: Set a mutation probability μ, and then... G=μ×min(count(0),count(1)) To calculate the number of genes to be flipped, randomly select G genes that are encoded as 0 or 1, and flip their values. count(0) represents the number of genes encoded as 0, and count(1) represents the number of genes encoded as 1. S5. Non-dominated ranking: The new population Rt is divided into different non-dominated levels F1, F2, F3..., where individuals at the higher level will dominate individuals at the lower level, and no individual will be dominated by other individuals at the same level. S6. Population normalization: The target value of all individuals in the population is scaled to near the hyperplane of the reference point distribution to complete the population normalization. S7. Associate reference points: Extract a reference line from the origin to each reference point, and associate each individual in the population with the reference point corresponding to the nearest reference line. S8. Elite selection: Individuals ranked after non-dominance are progressively incorporated into the new population P. t+1 In, until there is a non-dominated level Fl such that |P t+1 |≥N; If |P t+1 |=N,P t+1 As the next generation of population, execute the next cycle, repeating steps S4-S8; If |P t+1 |>N, select K individuals from Fl, where K=N-|P t+1 |; When selecting K individuals, first calculate the reference point at P. t+1 The number of associated individuals in Fl is then selected, and those associated with at least one reference point are included in P. t+1 In the middle, repeat K times until |P is obtained. t+1 |=N; S9. Repeat steps S4-S8 until the maximum number of iterations Tmax is reached; In the S4 population initialization, a binary string is used to represent a chromosome, where 1 indicates that the feature is selected, and 0 indicates otherwise. In a D-dimensional dataset, the i-th chromosome in the population will be encoded by a D-bit string: X i (t)=(x i,1 ,x i,2 ,...,x i,j ) x i,j ∈{0,1},j=1,2,...,D,i=1,2,...,N The population initialization includes: In a population with population size N, number of original features D, and feature weights fw, a random number M is selected, 1 < M < D. Based on the feature weights fw, M index positions are selected. This process is repeated N times until all individuals are initialized, forming an initialized population Pt.

2. The feature selection method based on a multi-objective genetic algorithm according to claim 1, characterized in that: It includes a fitness function, which comprises classification error rate, distance metric, and feature selection ratio.

3. The feature selection method based on a multi-objective genetic algorithm according to claim 2, characterized in that: The classification error rate is the balanced error rate, and the formula is: balanced_err = 1 - balanced_acc Where c is the number of classes of samples in the dataset, and TPR i represents the proportion of correctly predicted samples in class i, balanced_cc represents the average balanced accuracy of correctly predicted samples, and balanced_rr represents the average balanced accuracy of incorrectly predicted samples.

4. The feature selection method based on a multi-objective genetic algorithm according to claim 2, characterized in that: The distance metric formula is as follows: Where M is the number of samples in the training data, Dis(S i ,S j ) is the distance between two samples Si and Sj, calculated using Manhattan distance. -5 is used to narrow the effective range of the Sigmoid function, which scales the training data to the range [0,1]. class(S i ) and class(S j ) represents S i S j The categories of the two samples.

5. The feature selection method based on a multi-objective genetic algorithm according to claim 2, characterized in that: The formula for the feature selection ratio is: D represents the number of features in the original dataset, feature_proportion represents the feature selection ratio, and number of selected features represents the number of features selected.

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