High-dimensional feature selection method of evolutionary multi-task optimization algorithm based on proxy assistance

Abstract

The invention discloses a high-dimensional feature selection method of an evolutionary multitask optimization algorithm based on proxy assistance, and mainly relates to the field of feature selection and intelligent optimization. The invention designs a novel evolutionary multi-task optimization technical scheme for solving three defects of an existing evolutionary multi-task optimization algorithm for solving high-dimensional feature selection. In the task generation stage, a task generation strategy considering linear and nonlinear correlation at the same time is provided, and diversity is improved; in the knowledge migration stage, an agent-assisted knowledge migration strategy is provided for the farmer particles, and forward knowledge is migrated by evaluating aggregated knowledge and non-aggregated knowledge through agent assistance; in addition, a bidirectional asymmetric flipping strategy is provided for winner particles to improve the classification accuracy. By carrying out feature selection on a small-sample high-dimension biological data set, experiments show that compared with other feature selection methods based on an evolutionary multi-task optimization algorithm, the method can obtain a better feature subset.

Description

Technical Field The present invention belongs to the technical field of feature selection and intelligent optimization, and particularly relates to a high-dimensional feature selection method based on a proxy-assisted evolutionary multi-task optimization algorithm. Background Art Feature selection is a key issue in multiple fields such as pattern recognition, machine learning, and data mining. It involves selecting the most informative or relevant feature subset from the original feature set to improve model performance, reduce computational costs, and solve the curse of dimensionality problem. Evolutionary computing algorithms can find high-quality solutions for feature selection problems. However, due to the "curse of dimensionality" and the complex interactions between features, feature selection for high-dimensional datasets remains a challenging problem. Existing evolutionary computing algorithms still face challenges of high computational costs and being prone to falling into local optima when solving high-dimensional feature selection problems. Evolutionary multi-task optimization algorithms can effectively narrow the search space of problems, thereby reducing computational costs and quickly obtaining high-quality solutions through knowledge transfer. Although feature selection algorithms based on evolutionary multi-task optimization algorithms have been proposed, they still have three deficiencies. First, in terms of task generation, most existing algorithms only consider the linear correlation between features and labels, while ignoring the non-linear correlation. However, capturing the non-linear correlation between features and labels is also important for constructing high-quality tasks. Second, in terms of knowledge transfer between tasks, these algorithms usually encounter the problem of negative knowledge transfer due to limited ability to adaptively transfer knowledge. Existing algorithms use aggregated knowledge from other tasks for knowledge transfer. However, using only the aggregated knowledge from other tasks for knowledge transfer may lose the specific knowledge from other tasks, making the aggregated knowledge unable to effectively guide evolution. Third, when searching the solution space, it is difficult for existing algorithms to achieve the best balance between global search ability and computational efficiency. Existing research solves the feature selection problem by generating a high-dimensional task that selects features from all features and multiple low-dimensional related tasks. The existence of the high-dimensional task allows the algorithm to search for solutions globally, but too many features will increase computational costs. In addition, there is also research that solves the high-dimensional feature selection problem by generating multiple low-dimensional related tasks. Although the reduction of feature dimensions reduces computational costs, the algorithm loses the ability to comprehensively consider all features, which may lead to the loss of the global optimal solution. Therefore, in order to better solve the high-dimensional feature selection problem, it is necessary to design an effective and efficient evolutionary multi-task optimization algorithm to avoid the above defects. Summary of the Invention The main objective of the present invention is to overcome the drawbacks and deficiencies of the prior art and provide a high-dimensional feature selection method based on an agent-assisted evolutionary multi-task optimization algorithm. In the task generation stage, a task generation strategy that simultaneously considers linear and non-linear correlations is proposed to improve diversity. In the knowledge transfer stage, an agent-assisted knowledge transfer strategy is proposed for the losing particles. By using the agent to assist in evaluating the aggregated knowledge and non-aggregated knowledge, it helps to transfer positive knowledge to explore high-quality features. In addition, a two-way asymmetric flipping strategy is proposed for the winning particles to improve the classification accuracy. To achieve the above objective, the present invention adopts the following technical solutions: A high-dimensional feature selection method based on an agent-assisted evolutionary multi-task optimization algorithm, where the high-dimensional features are taken from the feature data in the fields of leukemia, face images, text, genes, tumors, and lung cancer. The high-dimensional feature selection method includes the following steps: S1. Divide the high-dimensional data set into a training set and a test set using ten-fold cross-validation; S2. For the training set, use the task generation strategy to generate 4 low-dimensional related tasks. The process of the task generation strategy is as follows: S201. Calculate the feature weights using two filtering methods, namely the Pearson correlation coefficient and the maximum information coefficient; S202. Use the inflection point selection strategy to distinguish high-correlation features and low-correlation features, and select features in the low-correlation feature subset with probability p, and combine them with all the features in the high-correlation feature subset to construct tasks; S3. Initialize 4 particle swarm populations with a population size of M according to the 4 tasks. Each population corresponds to the optimization of a low-dimensional feature selection task; S4. For each particle swarm population, use the supervised learning method k-NN as the classifier, and evaluate the fitness of the particles according to the training set. The objective function of the fitness is as follows: where AC(x) represents the classification accuracy of the classifier based on the features selected by x. The classification accuracy is calculated using the balanced accuracy algorithm. NS(x) and NT represent the number of features selected by x and the number of features in the original feature set respectively, and α represents the weight of the classification error rate; S5. Establish a surrogate model based on the k-NN linear regression model, and train the surrogate model using the binary representation of all the population particles in the current generation and their corresponding true fitness values; S6. For each particle swarm population, randomly pair the particles, and these two particles will be compared through a competition mechanism, that is, by comparing the fitness values of the particles, the particle with the larger fitness value is called the losing particle, and the particle with the smaller fitness value is called the winning particle; S7. Update the loser particles using a proxy-assisted knowledge transfer strategy, which consists of two update rules: inter-task knowledge transfer and intra-task knowledge transfer. For the i-th loser particle If the random number drawn from [0, 1] is less than the knowledge transfer probability P k , then perform inter-task knowledge transfer; otherwise, perform intra-task knowledge transfer. S8. Update the winner particles using a bidirectional asymmetric flip strategy. S9. Each time the objective function is used to evaluate the particles, the fitness evaluation count will increase by one. When the total fitness evaluation count of the four low-dimensional tasks reaches the maximum fitness evaluation count MaxFEs, each of the four low-dimensional tasks will generate a feature subset with the highest fitness. Among the four feature subsets, select the one with the highest classification accuracy as the result. If the classification accuracies are the same, select the feature subset with the fewest features as the result. Otherwise, continue to execute steps S4 - S8 until the fitness evaluation count meets the pre-set maximum fitness evaluation count. Furthermore, the process of step S4 is as follows: S401. The balanced accuracy algorithm divides the training set into a training set and a validation set for training the k-NN classifier through five-fold cross-validation. Use the training set for training the k-NN classifier and calculate the classification error rate of the k-NN classifier using the validation set. Then calculate the classification accuracy, with the formula defined as follows: AC(x) = 1 - ER(x) where AC(x) represents the classification accuracy, ER(x) represents the classification error rate, c represents the number of classes in the data, and TPR k represents the true positive rate of class k, that is, among the samples that are actually class k, the proportion correctly predicted as class k by the model. To ensure that the balanced accuracy is not biased towards any class in the classification problem, the weight of each class is set to S402. For each particle swarm population, calculate the fitness of the particles according to the objective function f(x). Furthermore, the process of step S7 is as follows: S701. The knowledge transfer between tasks uses aggregated knowledge and non-aggregated knowledge as the transferred knowledge. The non-aggregated knowledge is to select a corresponding winner particle from each of the other three populations as the source knowledge, that is, for each of the other tasks, a non-aggregated knowledge can be obtained; the aggregated knowledge is to select three corresponding winner particles from the other three populations as the source knowledge, and then aggregate the knowledge in inverse proportion to the fitness values of the winner particles. The formula for aggregating knowledge from the winner particles of different tasks is defined as follows: where, μ k represents the aggregation weight of the k-th winner particle selected from the three tasks, A i represents the aggregated knowledge used to update the i-th loser particle , f(·) represents the objective function, represents the k-th winner particle; S702. The loser particle i for knowledge transfer between tasks learns the aggregated knowledge and non-aggregated knowledge. For each piece of knowledge, two possible candidate offspring are generated respectively. The update formula for generating candidate offspring is as follows: where, r1, r2, and r3 are three random numbers drawn from [0, 1], represents the j-th dimension of the velocity of the loser particle , represents the j-th dimension of the aggregated knowledge or non-aggregated knowledge obtained by the loser particle i; S703. For the 2 possible candidate offspring generated from the aggregated knowledge and the 6 possible candidate offspring generated from the non-aggregated knowledge, use the established k-NN linear regression proxy to assist in the evaluation, and select the candidate offspring with the smallest predicted fitness value obtained from the evaluation as the new loser particle; S704. The knowledge transfer within a task adopts the update method of the original competitive particle swarm algorithm, that is, learning the winner particle in the current population. Furthermore, the process of the two-way asymmetric flipping strategy in step S8 is as follows: S801. For the i-th winner particle in the current population First, calculate the binary representation of the i-th winner particle For each dimension in , if its value is greater than the given threshold δ, then the corresponding dimension in f is set to 1; otherwise, the corresponding dimension is set to 0; S802. According to the flipping probability P new, if the random number drawn from [0, 1] is less than P f , then the bit with a random 1-bit dimension value of 1 is flipped to 0, that is, the selected feature is flipped to an unselected feature; otherwise, the bit with a random 1-bit dimension value of 0 is flipped to 1, that is, the unselected feature is flipped to a selected feature; S803. Calculate the fitness of x new . If its fitness is smaller than the fitness of the winner particle , then change the corresponding dimension of the winner particle according to the flipped dimension in x new . Furthermore, in the step S2, the probability p is 0.1. Due to the complex interactions between features, not all features in low-correlation features are useless. Therefore, some low-correlation features are selected to construct the task together with high-correlation features. Furthermore, in the step S3, the population size M is 50. A smaller population size converges quickly and has a low computational cost.

[0043] Furthermore, in the step S4, the nearest neighbor k of the k-NN classifier is 5, and the weight α of the classification error rate is 0.9. The selection of the nearest neighbor k is consistent with the comparison algorithm to ensure the fairness of the experiment. Since the feature selection problem pays more attention to the classification error rate, in the objective function, the weight of the classification error rate should be set to a larger value. Therefore, in the experimental design, the weight α of the classification error rate is set to 0.9. Furthermore, in the step S5, the nearest neighbor k of the k-NN linear regression model is 3. The value of the nearest neighbor k is obtained based on the experience of existing research. Under this value, the predicted value of the surrogate model will be more accurate. Furthermore, in the step S7, the knowledge transfer probability P k is 0.7. The knowledge transfer probability P k determines the probability of the loser particle to perform inter-task migration and intra-task migration. According to the experiment, when this value is used, the effect of the algorithm is better. Furthermore, in the step S8, the given threshold δ is 0.6, and the flip probability P f is 0.7. The value of the threshold δ is obtained based on the experience of existing research. Under this value, the obtained features are better. The flip probability P f . A higher flip probability will guide the algorithm to search in the direction of fewer feature numbers. Through experiments, it is known that when P f is 0.7, the effect is the best. Furthermore, in the step S9, in order to control the computational cost, the maximum number of fitness evaluations MaxFEs is 20,000 times. ​Compared with the prior art, the present invention has the following advantages and beneficial effects: 1. The present invention proposes a new task generation strategy, which uses two filtering methods, Pearson correlation coefficient and maximum information coefficient, to generate low-dimensional correlated tasks, taking into account both linear and non-linear correlations between features and labels, and helping to find a better feature combination. 2. The present invention proposes a proxy-assisted knowledge transfer strategy, which efficiently transfers positive knowledge by proxy-assisted evaluation of the offspring generated from aggregated knowledge and non-aggregated knowledge. Diversified knowledge can maintain the diversity of the population and prevent falling into local optima. Using a proxy model to assist in the transfer can more efficiently search for useful knowledge to better explore high-quality features. 3. The present invention proposes a bidirectional asymmetric flipping strategy, which flips the selected features to unselected features or flips the unselected features to selected features with a given asymmetric probability, guiding the population to search for a smaller feature subset with better classification performance to improve the accuracy. 4. Combining the advantages of the three new strategies, the present invention proposes an effective proxy-assisted evolutionary multi-task technical solution to solve the high-dimensional feature selection problem. In the classification task of a specific biological dataset with the characteristics of small samples and high dimensions, the solution proposed by the present invention can find a feature subset solution with higher classification accuracy. BRIEF DESCRIPTION OF THE DRAWINGS In order to more clearly illustrate the technical solutions in the embodiments of the present application, the following will briefly introduce the drawings required for the description of the embodiments. Obviously, the drawings in the following description are only some embodiments of the present application. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts. Figure 1 is a flowchart of the high-dimensional feature selection method of the proxy-assisted evolutionary multi-task optimization algorithm in the embodiments of the present invention; Figure 2 is a framework diagram of the high-dimensional feature selection method of the proxy-assisted evolutionary multi-task optimization algorithm in the embodiments of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS In order to enable those skilled in the art of the present technology to better understand the solution of the present application, the following will clearly and completely describe the technical solutions in the embodiments of the present application in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative efforts belong to the scope of protection of the present application. References to "embodiments" in this application mean that the specific features, structures, or characteristics described in connection with the embodiments can be included in at least one embodiment of this application. The phrase appears in various places in the specification and does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described in this application can be combined with other embodiments. Embodiment 1 See Figure 1 As shown, this embodiment discloses a high-dimensional feature selection method based on a proxy-assisted evolutionary multi-task optimization algorithm. The high-dimensional classification data is taken from feature data in the fields of leukemia, face images, text, genes, tumors, and lung cancer. Taking the cancer feature selection scenario as a specific implementation example, the high-dimensional feature selection method includes the following steps: S1. The 9_Tumor cancer feature dataset is a biological dataset with the characteristics of small samples and high dimensions for the high-dimensional cancer feature dataset. After obtaining this dataset, the dataset is divided into a training set and a test set using ten-fold cross-validation. At initialization, the population size of each task is set to 50, and the maximum number of evaluations is limited to 20,000. The overall framework diagram of the high-dimensional feature selection method based on the proxy-assisted evolutionary multi-task optimization algorithm is as Figure 2 shown, mainly including three stages: the task generation and population initialization stage, the population evolution stage, and the result output stage. Specifically, when a high-dimensional dataset is obtained, in the task generation and population initialization stage, 2 filtering methods are used to generate 4 low-dimensional feature selection tasks. Then, 4 populations are randomly initialized, and each population corresponds to the optimization of 1 low-dimensional feature selection task. In the population evolution stage, for each particle in each population, it is divided into a loser particle and a winner particle using a competition mechanism. For the loser particles, a proxy-assisted knowledge transfer strategy is used for update, and for the winner particles, a bidirectional asymmetric flip strategy is used for update. Finally, each population searches for an optimal feature subset, and among the four feature subsets, the one with the highest classification accuracy is selected as the result. If the classification accuracies are the same, the feature subset with the smallest number of features is selected as the result, and this feature subset will be tested on the test set and output as the result. S2. First, in task generation, the task generation strategy is executed. The Pearson correlation coefficient and the maximum information coefficient are used as two filtering methods to calculate the feature weights. The inflection point selection strategy is used to distinguish high-correlation features and low-correlation features, and features in the low-correlation feature subset are selected with a probability of 0.1 and combined with all features in the high-correlation feature subset to construct 4 low-dimensional feature selection tasks. S3. Initialize 4 populations with a size of 50 randomly according to the 4 tasks, and each population corresponds to the optimization of 1 low-dimensional feature selection task. S4. For each population, evaluate the fitness values of all particles using the objective function. Among them, the classification accuracy rate in the objective function is calculated using the balanced accuracy algorithm, that is, the classification accuracy rate is calculated by using the k-NN classifier with a nearest neighbor size of 5 through five-fold cross-validation for the training set. S5. Use the binary representation of all population particles in the current generation and their corresponding true fitness values to train the surrogate model, and establish a k-NN linear regression surrogate model with a nearest neighbor size of 3. For each dimension of the particle, if its value is greater than the given threshold of 0.6, the corresponding dimension in the binary representation of the particle is set to 1; otherwise, the corresponding dimension is set to 0. S6. For each particle swarm population, randomly pair the particles two by two, and these two particles will be compared through a competition mechanism, that is, by comparing the fitness values of the particles, the particle with the larger fitness value is called the loser particle, and the particle with the smaller fitness value is called the winner particle; S7. If the particle is a loser, adopt a surrogate-assisted knowledge transfer strategy to update the particle. For each loser particle, if the random number drawn from [0, 1] is less than the knowledge transfer probability P k = 0.7, then perform knowledge transfer between tasks, otherwise, perform knowledge transfer within the task. S701. Knowledge transfer between tasks generates aggregated knowledge and non-aggregated knowledge. Non-aggregated knowledge is to select one corresponding winner particle from each of the other 3 populations as the source knowledge, that is, for each of the other tasks, one non-aggregated knowledge can be obtained. Aggregated knowledge is to select three corresponding winner particles from each of the other 3 populations as the source knowledge, and then aggregate the knowledge according to the inverse ratio of the fitness values of the winner particles. S702. The loser particle i that performs knowledge transfer between tasks learns the aggregated knowledge and non-aggregated knowledge, and for each knowledge, two possible candidate offspring are generated respectively. S703. For the two possible candidate offspring generated by the aggregated knowledge and the six possible candidate offspring generated by the non-aggregated knowledge, use the established k-NN linear regression surrogate model with a nearest neighbor size of 3 to assist in the evaluation, and select the candidate offspring with the smallest predicted fitness value obtained by the evaluation as the new loser particle. S704. Knowledge transfer within the task adopts the update method of the original competitive particle swarm algorithm, that is, learn the particles in the current population. S8. If the particle is a winner, adopt a two-way asymmetric flip strategy to update the particle. S801. For the i-th winner particle in the current population First, calculate the i-th winner particle Binary representation For For each dimension in, if its value is greater than the given threshold of 0.6, then the corresponding dimension in is set to 1; otherwise, the corresponding dimension is set to 0. S802. According to the flipping probability P f , randomly flip one dimension in to obtain a new solution x new . If the random number drawn from [0, 1] is less than P f = 0.7, then the bit with a random 1-bit dimension value of 1 in is flipped to 0; otherwise, the bit with a random 1-bit dimension value of 0 in is flipped to 1; S803. Calculate the fitness of x new . If its fitness is improved, then change the corresponding dimension of the winner particle new according to the dimension flipped in x . S9. Steps S4 - S8 are the evolutionary stage of the population. Each time the particles are evaluated using the objective function, the number of fitness evaluations will increase by one. When the total number of fitness evaluations for the 4 low-dimensional tasks reaches the maximum number of fitness evaluations MaxFEs, each task will generate a feature subset with the highest fitness. Among the four feature subsets, select the one with the highest classification accuracy as the result. If the classification accuracies are the same, select the feature subset with the smallest number of features as the result, and test this feature subset on the test set and output it as the result. Otherwise, continue to execute steps S4 - S8 until the number of fitness evaluations meets the pre-set maximum number of fitness evaluations MaxFEs. To verify that the high-dimensional feature selection method of the agent-assisted evolutionary multi-task optimization algorithm proposed in this application can find a higher classification accuracy and a lower number of feature subsets for a specific small-sample high-dimensional biological dataset, the following verification experiments are carried out:

[0077] In the verification experiment, the high-dimensional feature selection method of the agent-assisted evolutionary multi-task optimization algorithm proposed in the present invention is applied to the 9_Tumor biological dataset classification task. The 9_Tumor biological dataset has the characteristics of small samples and high dimensions. This dataset contains 60 samples, each sample has 5726 features, and there are 9 categories. The parameter settings in this experiment are as shown in Table 1 below: Table 1. Parameter settings in the experiment Variable Value or value range Number of nearest neighbors of k-NN classifier k＝5 Knowledge transfer probability <![CDATA[P k = 0.7]]> Flip probability <![CDATA[P f = 0.7]]> End condition of particle swarm optimization algorithm MaxFEs = 20000 Total number of particles in all particle swarms N＝200 To illustrate the advantages of the method of this application over the prior art, in this experiment, three advanced high-dimensional feature selection algorithms based on evolutionary multi-task optimization algorithms (i.e., MTPSO, MFCSO, and MBDPSO) were simultaneously used to perform classification on the 9_Tumor biological dataset. In this experiment, ten-fold cross-validation was used to obtain the training set and the test set. To reduce experimental errors, each algorithm was independently executed 30 times to obtain the results. The final experimental results are shown in Table 2: Table 2. Experimental comparison result table Feature selection method Classification accuracy Number of features MTPSO 39.44％ 285.17 MFCSO 44.67％ 125.08 MBDPSO 38.00％ 703.53 SAMCSO 45.22％ 365.75 As can be seen from Table 2, when using MTPSO for feature selection in the classification task of the 9_Tumor biological dataset, only a classification accuracy of 39.44% was obtained, and the number of selected feature subsets was 285.17; when using MFCSO for feature selection in the classification task of the 9_Tumor biological dataset, only a classification accuracy of 44.67% was obtained, and the number of selected feature subsets was 125.08; when using MBDPSO for feature selection in the classification task of the 9_Tumor biological dataset, only a classification accuracy of 38.00% was obtained, and the number of selected feature subsets was 703.53; while using the feature selection method proposed by the present invention, a classification accuracy of 45.22% was obtained on the 9_Tumor biological dataset, and the number of selected feature subsets was 365.75. The experimental results show that in the classification task of a specific biological dataset with the characteristics of small samples and high dimensions, the SAMCSO method proposed by the present invention can find a feature subset solution with higher classification accuracy. The feature subset solution found by this method has a higher classification accuracy and a relatively lower number of feature subsets compared to the feature subset solutions found by the three advanced high-dimensional feature selection algorithms MTPSO, MFCSO, and MBDPSO based on evolutionary multi-task optimization algorithms. The technical features of the above embodiments can be combined arbitrarily. For the sake of brevity of description, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, it should be considered as the scope recorded in this specification. The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any other changes, modifications, substitutions, combinations, and simplifications made without departing from the spirit and principle of the present invention shall be equivalent replacement methods and are all included in the protection scope of the present invention.

Claims

1. A high-dimensional feature selection method based on a proxy-assisted evolutionary multi-task optimization algorithm, where the high-dimensional features are taken from the feature data in the fields of leukemia, face images, text, genes, tumors, and lung cancer. It is characterized in that The high-dimensional feature selection method includes the following steps: S1. Divide the high-dimensional data set into a training set and a test set using ten-fold cross-validation; S2. For the training set, use a task generation strategy to generate 4 low-dimensional related tasks. The process of the task generation strategy is as follows: S201. Calculate the feature weights using two filtering methods, namely the Pearson correlation coefficient and the maximum information coefficient; S202. Use the inflection point selection strategy to distinguish high-correlation features and low-correlation features, and select features in the low-correlation feature subset with probability p, and combine them with all features in the high-correlation feature subset to construct tasks; S3. Initialize 4 particle swarm populations with a population size of M according to the 4 tasks. Each population corresponds to the optimization of a low-dimensional feature selection task; S4. For each particle swarm population, use k-NN as a classifier to evaluate the fitness of the particles according to the training set. The objective function of the fitness is as follows: Where AC(x) represents the classification accuracy of the classifier based on the features selected by x, NS(x) and NT respectively represent the number of features selected by x and the number of features in the original feature set, and α represents the weight of the classification error rate; S5. Establish a surrogate model based on the k-NN linear regression model, and train the surrogate model using the binary representation of all population particles in the current generation and their corresponding true fitness values; S6. For each particle swarm population, randomly pair the particles, and these two particles will be compared through a competition mechanism, that is, by comparing the fitness values of the particles, the particle with the larger fitness value is called the loser particle, and the particle with the smaller fitness value is called the winner particle; S7. Update the loser particles using a proxy-assisted knowledge transfer strategy, which consists of two update rules: inter-task knowledge transfer and intra-task knowledge transfer. For the i-th loser particle If the random number drawn from [0, 1] is less than the knowledge transfer probability P k , then inter-task knowledge transfer is performed; otherwise, intra-task knowledge transfer is performed. S8. Update the winner particles using the bidirectional asymmetric flip strategy; S9. Each time the particles are evaluated using the objective function, the fitness evaluation times will increase by one. When the total fitness evaluation times of the 4 low-dimensional tasks reach the maximum fitness evaluation times MaxFEs, each of the 4 low-dimensional tasks will generate a feature subset with the highest fitness. Among the 4 feature subsets, select the one with the highest classification accuracy as the result. If the classification accuracies are the same, select the feature subset with the smallest number of features as the result. Otherwise, continue to execute steps S4 to S8 until the fitness evaluation times meet the pre-set maximum fitness evaluation times MaxFEs; 2. The high-dimensional feature selection method of the agent-assisted evolutionary multi-task optimization algorithm according to claim 1, wherein The process of step S7 is as follows: S701. Use aggregated knowledge and non-aggregated knowledge as the knowledge to be transferred for knowledge transfer between tasks. The non-aggregated knowledge is to select a corresponding winner particle from each of the other three populations as the source knowledge, that is, for each of the other tasks, a non-aggregated knowledge can be obtained; the aggregated knowledge is to select three corresponding winner particles from each of the other three populations as the source knowledge, and then aggregate the knowledge according to the inverse of the fitness size of the winner particles. The formula for aggregating knowledge from winner particles of different tasks is defined as follows: Among them, μ k represents the aggregation weight of the k-th winner particle selected from three tasks, A i represents the aggregated knowledge used to update the i-th loser particle , f(·) represents the objective function, represents the k-th winner particle; S702. The loser particle i undergoing knowledge transfer between tasks learns the aggregated knowledge and the non-aggregated knowledge. For each piece of knowledge, two possible candidate offspring are generated respectively. The update formula for generating candidate offspring is as follows: where r1, r2, and r3 are three random numbers drawn from [0, 1], denotes the loser particle the j-th dimension of the velocity, denotes the j-th dimension of the aggregated or non-aggregated knowledge obtained by the loser particle i; S703. For the two possible candidate offspring generated from aggregated knowledge and the six possible candidate offspring generated from non-aggregated knowledge, use the established k-NN linear regression surrogate to assist in the evaluation, and select the candidate offspring with the smallest predicted fitness value obtained from the evaluation as the new loser particle; S704. The in-task knowledge transfer adopts the update method of the original competitive particle swarm algorithm, that is, learn the winner particle in the current population.

3. The high-dimensional feature selection method based on the agent-assisted evolutionary multi-task optimization algorithm according to claim 1, characterized in that The process of the two-way asymmetric flipping strategy in step S8 is as follows: S801. For the i-th winning particle in the current population First, calculate the i-th winning particle Binary representation For each dimension in, if its value is greater than the given threshold δ, then the corresponding dimension in is set to 1; otherwise, the corresponding dimension is set to 0; S802. According to the flip probability P f , randomly flip one dimension among them to obtain a new solution x new . If the random number drawn from [0, 1] is less than P f , then the bit with a random 1-bit dimension value of 1 among them is flipped to 0; otherwise the bit with a random 1-bit dimension value of 0 among them is flipped to 1; S803. Calculate x new The fitness of new If the fitness of x is smaller than the fitness of the winner particle , then change the corresponding dimension of the winner particle according to the flipped dimension in x new . ​ 4. The high-dimensional feature selection method of the proxy-assisted evolutionary multi-task optimization algorithm according to claim 1, characterized in that In step S2, the probability p is 0.1; in step S3, the population size M is 50.

5. The high-dimensional feature selection method of the proxy-assisted evolutionary multi-task optimization algorithm according to claim 1, wherein In step S4, k of the k-NN classifier is 5, and the weight α of the classification error rate is 0.

9.

6. The high-dimensional feature selection method based on the agent-assisted evolutionary multi-task optimization algorithm according to claim 1, characterized in that In step S5, k of the k-NN linear regression model is 3.

7. The high-dimensional feature selection method based on the proxy-assisted evolutionary multi-task optimization algorithm according to claim 2, characterized in that In the step S7, the knowledge transfer probability P k is 0.

7.

8. The high-dimensional feature selection method based on the agent-assisted evolutionary multi-task optimization algorithm according to claim 3, characterized in that In the step S8, the given threshold δ is 0.6, and the flipping probability P f is 0.

7.

9. The high-dimensional feature selection method based on the agent-assisted evolutionary multi-task optimization algorithm according to claim 1, wherein In step S9, the maximum number of fitness evaluations MaxFEs is 20,000 times.

10. The high-dimensional feature selection method of the proxy-assisted evolutionary multi-task optimization algorithm according to claim 1, characterized in that In step S9, after obtaining the target feature subset, test it on the test set.

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