A multi-objective synthetic oversampling method for unbalanced data
By using a multi-objective optimization framework based on genetic programming, high-quality synthetic samples are generated in batches, which solves the problems of insufficient capture of nonlinear data manifolds and noise propagation in existing technologies, and improves the classification performance and efficiency of imbalanced datasets.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SUZHOU UNIV
- Filing Date
- 2026-03-20
- Publication Date
- 2026-06-09
Smart Images
Figure CN122173928A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the fields of data mining and machine learning technology, specifically to a multi-objective synthetic oversampling method for imbalanced data. Background Technology
[0002] In machine learning, data mining, and other fields, data imbalance is a common problem, meaning that the number of samples in one class is far less than that of another. This imbalance can cause model training to favor the majority class, resulting in lower accuracy in identifying the minority class and consequently affecting the overall classification performance of the model. In real-world scenarios such as fault diagnosis, medical disease detection, network intrusion detection, and industrial quality inspection, minority class samples often carry crucial information; therefore, handling imbalanced data has significant practical implications.
[0003] Existing technologies similar to this invention can be categorized into two main types: data-level processing methods and evolutionary sampling methods. These two methods address the problem of imbalanced data resampling from the perspectives of data reconstruction logic and optimization mechanisms, respectively.
[0004] Data-level methods are the most widely used fundamental approach in imbalanced data processing. The core idea is to construct balanced data by directly adjusting the sample distribution without modifying the subsequent model structure. Undersampling achieves balance by removing redundant samples from the majority class, but it easily loses key feature information, leading to decreased model generalization ability. Hybrid sampling combines the advantages of oversampling and undersampling; for example, the SMOTE+ENN method first synthesizes minority class samples and then removes cross-class samples, but it still doesn't solve the problem of coordinating the quality and diversity of the synthesized samples. Oversampling is the mainstream direction of this approach, which can be further subdivided into random oversampling and synthetic oversampling: random oversampling achieves balance by repeatedly replicating minority class samples, which is simple to operate but easily leads to model overfitting; synthetic oversampling, based on SMOTE, generates new samples through interpolation, avoiding overfitting, but traditional SMOTE easily generates redundant, noisy, and cross-class samples. To optimize the synthesis effect, boundary optimization improvement methods have emerged, with Borderline-SMOTE being a typical example: interpolation is only performed on boundary samples close to the majority class, reducing redundant samples. However, these improved methods still have obvious shortcomings. They rely on a single distance threshold to judge samples, lack proactive optimization for diversity, and have no multi-objective collaborative mechanism. They also require manual setting of key parameters, have weak adaptive capabilities, and cannot dynamically adjust sample generation rules.
[0005] Evolutionary sampling methods are a novel sampling approach developed based on the optimization characteristics of evolutionary algorithms. Their core principle is the introduction of biological evolutionary thought, generating the optimal sample set through iterative search. Essentially, they transform the oversampling task into an optimization problem. These methods rely on the adaptive search capabilities of evolutionary algorithms (genetic algorithms, genetic programming, particle swarm optimization, etc.) to achieve dynamic optimization of the sampling process, making them more suitable for multiple objectives than traditional data-level methods. Among these, genetic algorithm-based sampling methods construct individuals by encoding sample features, optimizing the population with the goal of reasonable sample distribution. However, they often focus on a single optimization objective, and their encoding methods have poor adaptability, making them difficult to adapt to high-dimensional imbalanced datasets. Particle swarm optimization-based sampling methods search for the optimal synthetic sample through group collaboration, achieving fast convergence, but they are prone to getting trapped in local optima and have insufficient control over sample diversity.
[0006] Among existing evolutionary sampling methods, genetic programming has gradually become a research hotspot due to its flexible individual representation and multi-objective optimization potential. Research on applying genetic programming to data-level sampling is relatively limited, but it has already demonstrated potential. A representative work is DG-SMOTE, which uses genetic programming components to evolve rules for generating new samples. This framework automatically discovers sample generation strategies through evolutionary search, breaking through the limitations of fixed interpolation rules to some extent. However, it still uses a per-sample generation approach, requiring an evolutionary process for each synthesized sample, resulting in high computational costs and low efficiency. Most other methods based on genetic programming only use it as a general optimization tool, failing to design specific frameworks for synthesizing minority class oversampling scenarios. They lack customized objective systems for sampling quality, diversity, and boundary clarity; furthermore, they lack evolutionary constraint mechanisms that match oversampling requirements, making it impossible to accurately control the feature fit and class boundary distance of synthesized samples. This leads to problems such as insufficient synthesized sample effectiveness and slow convergence speed when directly applied to imbalanced data processing. Summary of the Invention
[0007] Purpose of the Invention: The main purpose of this invention is to address the following problems existing in current synthetic oversampling techniques: 1) Relying on linear interpolation within local neighborhoods, it fails to capture the widespread nonlinear data manifolds and complex decision boundaries in real data, leading to a systematic bias between synthetic samples and the real distribution; 2) Since the synthesis process relies entirely on the local neighborhood structure, when a sample or its nearest neighbor contains noise or outliers, linear interpolation will propagate the noise into the synthetic sample, and may even amplify it. This not only reduces the quality of the synthetic samples but also negatively impacts the training of subsequent classifiers; 3) Sample-by-sample synthesis only considers the local neighborhood information of each sample, lacking consideration for the overall quality of the synthetic sample set; 4) Lack of explicit evaluation and constraints on key attributes such as sample quality, boundary location, distribution consistency, and diversity. This invention provides a multi-objective synthetic oversampling method for imbalanced data. By introducing the symbolic representation capability of genetic programming, it automatically discovers sample combination paradigms that can capture nonlinear data relationships, so that the synthetic samples are no longer limited to the convex hull of existing sample points, thus more realistically approximating the complex data manifold of minority classes. We designed specialized multi-objective evaluation functions and constraints to ensure that each synthetic sample shows significant improvements in boundary location, local distribution, diversity, and sample quality. We employed batch sample generation and optimized the overall attributes of the synthetic sample set through multi-objective optimization to ensure that the generated sample set exhibits excellent classification performance overall.
[0008] Technical solution: The present invention provides a multi-objective synthetic oversampling method for imbalanced data, comprising the following steps:
[0009] Step 1: Obtain the original imbalanced data and extract features and class labels. Divide the original data into minority class and majority class sample sets according to the sample size of each class, and calculate their cluster centers: Minority class sample centers and majority class sample center ;
[0010] Step 2: Construct a multi-objective optimization framework based on genetic programming. Each individual uses a tree-based encoding method from genetic programming. This indicates that it corresponds to a rule for generating synthetic samples. The optimization objective and constraints are defined: the optimization objective includes a first objective that evaluates the classification boundary relationship between the synthetic samples and the majority and minority classes, denoted as... ; and a second objective, denoted as , to measure whether the synthesized samples conform to the inherent original distribution characteristics of the minority class samples. Constraints are used to constrain individuals from the perspectives of classification boundaries, sample quality, sample distribution, and diversity, ensuring their distribution consistency and representativeness, and constructing a higher-quality synthetic sample set of minority classes from all individuals that meet the constraints.
[0011] Step 3: Perform a multi-objective optimization process, including population initialization, individual crossover and mutation, tournament selection, and environment selection. In the environment selection phase, calculate the degree of constraint violation for each individual based on the constraints. Based on the optimization objective and the degree of constraint violation, prioritize feasible and non-dominated individuals to enter the next generation, and use feasible solutions or infeasible solutions with lower constraint violation degrees to generate a new generation of the population. Repeat the above process until the termination condition is met.
[0012] Step 4: After evolution terminates, extract all non-dominant individuals that satisfy the constraints from the final population to form a feasible solution set; use each individual in the feasible solution set as a sample generation rule to synthesize new minority class samples in batches, and merge all synthesized samples to form the final minority class sample set.
[0013] Step 5: Merge the final minority class sample set with the majority class sample set to obtain a balanced dataset. Use the balanced data as the training set to train the classifier and evaluate its classification performance on the test set.
[0014] Furthermore, in step 2, the first objective The second objective is the distance difference between the synthetic sample and the centers of the majority and minority classes. This represents the proportion of minority class samples among the k-nearest neighbors of the synthesized sample. Specifically, it is expressed as:
[0015]
[0016] in, For synthetic samples To the center Similarly, the Euclidean distance, For synthetic samples To the center Euclidean distance.
[0017]
[0018] in, For synthetic samples of A collection of neighbors, It is a minority class of sample sets.
[0019] Furthermore, in step 2, the constraints include: the minimum threshold of the first objective, the minimum distance between the synthetic sample and the minority class sample center, the maximum distance between the synthetic sample and the minority class sample center, and the angle constraint between the vectors formed by the synthetic sample and the majority and minority class sample centers. Specifically, this is expressed as:
[0020] First constraint: , indicating that the first target is greater than or equal to zero.
[0021] The second constraint: ,in, The average distance between minority class samples indicates that the Euclidean distance from the composite sample to the minority class center is greater than or equal to the average distance between minority class samples.
[0022] The third constraint: ,in The maximum distance between minority class samples indicates that the Euclidean distance from the composite sample to the minority class center is less than or equal to the maximum distance between minority class samples.
[0023] The fourth constraint: ,in For spatial vectors and space vectors The included angle between them indicates that the included angle between them is less than or equal to .
[0024] Furthermore, in step 2, the genetically programmed individuals are represented as a tree structure, with non-terminal nodes containing arithmetic operators and leaf nodes representing minority class samples.
[0025] Furthermore, in step 3, the environment selection is as follows: For each individual, the degree of violation of multiple constraints is normalized and merged to obtain a constraint violation degree of a uniform scale. Based on the degree of constraint violation, the population is divided into feasible and infeasible solutions. During the selection process, if the number of feasible solutions is greater than the population size, a non-dominated sorting is performed according to the optimization objective; if the number of feasible solutions is less than the population size, all feasible solutions are retained, and the remaining population is selected from the infeasible solutions in ascending order of constraint violation degree to fill the gaps until the population size is reached. The degree of constraint violation is specifically represented as follows:
[0026]
[0027] in For the initial population, The number of constraints. Represented as: Merge constraints and use the initial population The individual with the largest value is used as the standard, and it is normalized.
[0028] Furthermore, in step 4, at the end of each evolutionary search process, all feasible solutions in the final population are used to synthesize a new sample, and the evolutionary search process is repeated multiple times until the total number of synthesized minority class samples reaches the preset balance number.
[0029] Furthermore, in step 4, each time a new batch of minority class samples is synthesized, it is merged with the current minority class sample set to ensure the diversity of the synthesized samples.
[0030] The present invention provides a multi-objective synthetic oversampling system for imbalanced data, comprising:
[0031] Preprocessing module: used to acquire raw imbalanced data and preprocess it, dividing the preprocessed dataset into minority class sample sets and majority class sample sets;
[0032] Multi-objective optimization module: A multi-objective optimization framework is constructed based on genetic programming. Each individual adopts a tree-like encoding from genetic programming and corresponds to a rule for generating synthetic samples. Optimization objectives and constraints are set: the first objective is to evaluate the classification boundary relationship between the synthetic sample and the majority and minority classes; the second objective is to measure whether the synthetic sample conforms to the inherent distribution characteristics of the minority class samples. Constraints are used to constrain individuals from the perspectives of classification boundary, sample quality, sample distribution, and diversity, ensuring their distribution consistency and representativeness. A higher-quality set of minority class synthetic samples is then constructed from all individuals that meet the constraints.
[0033] The constraint processing module: For each individual, the degree of violation of multiple constraints is normalized and merged to obtain a uniform constraint violation degree. Based on this constraint violation degree, the population is divided into feasible and infeasible solutions. During the selection process, if the number of feasible solutions is greater than the population size, non-dominated sorting is performed according to the optimization objective; if the number of feasible solutions is less than the population size, all feasible solutions are retained, and the remaining population is selected from infeasible solutions in ascending order of constraint violation degree to fill the gaps until the population size is reached.
[0034] Sample synthesis module: At the end of each evolutionary search process, a new sample is synthesized from all feasible solutions in the final population and merged with the original minority class sample to form a new minority class sample set.
[0035] An electronic device according to the present invention includes a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein the computer program, when loaded onto the processor, implements any of the methods described herein.
[0036] The present invention provides a storage medium storing a computer program, characterized in that the computer program, when executed by a processor, implements any one of the methods described above.
[0037] Beneficial effects: Compared with the prior art, the present invention has the following significant advantages:
[0038] (1) This invention combines genetic programming with multi-objective evolutionary optimization, and simultaneously optimizes the classification boundary distance and the quality of the synthesized samples. It solves the performance shortcomings caused by the single-objective optimization of existing methods, and achieves multi-objective synergistic improvement. The synthesized samples not only fit the characteristics of the original minority class samples, but also have good diversity and are not easy to cross the class boundary, effectively mitigating the adverse effects of class imbalance on the classification model.
[0039] (2) This invention can adapt to imbalanced datasets with different feature distributions without requiring manual adjustment of too many parameters. It can automatically select high-quality samples and dynamically optimize sample generation rules during the iteration process. The individual representation based on genetic programming can adaptively capture the complex feature distribution of imbalanced datasets, breaking through the limitations of traditional oversampling methods that rely on fixed interpolation logic and have poor adaptability. It is especially suitable for high-dimensional minority class sample synthesis scenarios with nonlinear feature associations.
[0040] (3) The constraint processing mechanism designed in this invention uniformly screens and retains synthetic samples from the perspectives of classification boundary, sample quality, sample distribution, and diversity, thereby reducing the negative impact of noise samples and inter-class overlap on classification performance and accelerating the convergence process.
[0041] (4) Based on the population evolution method, multiple feasible solutions that meet the constraints are obtained at the same time, and the feasible solutions are directly used as synthetic samples. Compared with the oversampling method of generating samples one by one or searching single solutions, the sample generation efficiency is significantly improved, which is beneficial for application in large-scale or highly imbalanced data scenarios. Attached Figure Description
[0042] Figure 1 This is a schematic diagram of the present invention.
[0043] Figure 2 This is a flowchart of the multi-objective optimization process of the present invention. Detailed Implementation
[0044] The technical solution of the present invention will be further described below with reference to the accompanying drawings.
[0045] like Figure 1 As shown, this embodiment of the invention provides a multi-objective synthetic oversampling method for imbalanced data, comprising the following steps:
[0046] Step S1: Obtain the original imbalanced data, normalize the continuous features, and encode the discrete features; based on the sample class labels, divide the preprocessed dataset into minority class sample sets and majority class sample sets, extract the feature vectors and class information of the samples, calculate the ratio of minority class samples to majority class samples, and determine the number of samples to be synthesized.
[0047] Step S2: Construct a multi-objective optimization framework based on genetic programming, setting two optimization objectives: Objective 1 is the difference between the distances of the synthesized sample and the majority and minority class centers; Objective 2 is the difference between the distances of the synthesized sample and the majority and minority class centers. The proportion of the minority class among the nearest neighbors. Simultaneously, constraints are set, including: a minimum threshold for objective one; the minimum distance between the synthesized sample and the minority class center; the maximum distance between the synthesized sample and the minority class center; and the angle between the synthesized sample and the majority and minority class centers.
[0048] Step S3: Execute the multi-objective optimization process, including population initialization, individual crossover and mutation, tournament selection, and environment selection. In the environment selection phase, calculate the constraint violation degree for each individual based on the constraints. Based on the optimization objective and constraint violation degree, prioritize feasible and non-dominated solutions to enter the next generation, and use feasible solutions or infeasible solutions with lower constraint violation degrees to generate a new generation of the population. In this process, if the number of feasible solutions is greater than the population size, non-dominated sorting is performed; if the number of feasible solutions is less than the population size, feasible solutions directly enter the next generation, and then infeasible solutions are sorted according to their constraint violation degree. The values are sorted by size, and individuals with lower default rates are selected to fill the population until the population size is reached.
[0049] Step S4: After evolution terminates, extract all non-dominant individuals that meet the constraints from the final population to form a feasible solution set; use each individual in the feasible solution set as a sample generation rule to synthesize new minority class samples in batches until the number of samples reaches balance, and merge all synthesized samples to form the final minority class sample set.
[0050] Step S5: Merge the final minority class sample set with the majority class sample set to obtain a balanced dataset. Use the balanced data as the training set to train the classifier and evaluate its classification performance on the test set.
[0051] like Figure 2 As shown, this embodiment of the invention provides a multi-objective synthetic oversampling method for imbalanced data. The multi-objective optimization process includes the following steps:
[0052] First, the imbalanced data is preprocessed, dividing it into minority and majority class sample sets based on class labels. Then, the population is randomly initialized, with minority class samples as terminal nodes and "+", "-", and "×" as non-terminal nodes. A constrained multi-objective optimization process is then executed. In the environment selection phase, parent and child populations are merged, duplicate individuals are removed, and the constraint violation degree for each individual is calculated. Individuals are then sorted according to their values. If a feasible solution is larger than the population size, a non-dominated sort is performed, prioritizing feasible and non-dominated solutions for the next generation. If a feasible solution is smaller than or equal to the population size, infeasible solutions with less constraint violation are added to the new generation. This process is repeated until the termination condition is met. Feasible solutions are then separated from the final population, and new minority class samples are synthesized in batches. The objective optimization process is executed multiple times until the sample is balanced.
[0053] To verify the effectiveness of this invention, an imbalanced dataset publicly available in the KEEL database was used for analysis. The parameters used in the experiment were set as follows: population size: 30; number of iterations: 100; tournament selection: size set to 3; crossover rate: 0.8; mutation rate: 0.2. The imbalanced dataset and its basic parameters are shown in Table 1. Using KNN as the classifier, comparisons were made with mainstream sampling methods: Random Oversampling (ROS), Borderline-1 Synthetic Minority Oversampling (SMOTE), and the latest genetic programming-based oversampling method (DG-SMOTE). The experimental results on F1-Score and AUC are shown in Tables 2 and 3.
[0054] Table 1 Imbalanced Datasets
[0055] Table 2 Comparison results of the oversampling method with the F1-Score (×100) index
[0056] Table 3. Comparison of AUC (×100) results with oversampling methods.
[0057] F1-Score and AUC were selected as evaluation metrics for classification performance. F1-Score comprehensively reflects the precision and recall of the classification model, effectively measuring its performance on imbalanced data. AUC characterizes the model's ability to distinguish between positive and negative samples; a higher AUC value indicates better generalization performance. Tables 2 and 3 compare this invention with mainstream oversampling methods and the latest genetic programming-based oversampling methods. To reduce the interference of random factors on the experimental results, the four methods (ROS, SMOTE, Borderline-1, and DG-SMOTE) were each run independently 30 times on 10 datasets. The average of the 30 experimental results was taken as the final statistical data to ensure the reliability and stability of the experimental results.
[0058] As shown in Table 2, in the F1-Score comparison of the 10 datasets, the F1-Score of the present invention is higher than that of ROS, SMOTE, Borderline-1, and DG-SMOTE. This indicates that the method of the present invention can effectively improve the balance between precision and recall of the classification model, solve the overfitting or underfitting problems that are prone to occur in traditional oversampling methods, and has significant advantages in imbalanced data classification tasks. As shown in Table 3, the AUC of the present invention is also better than that of the four control methods. This proves that the minority class samples generated by the present invention are more representative, which can effectively improve the classification model's ability to distinguish between positive and negative samples, thereby improving the model's generalization performance.
[0059] As can be seen from the experimental results in Tables 2 and 3, in most cases, the present invention outperforms other methods, exhibiting higher F1-Score and AUC values, and achieving the best classification results. This demonstrates that the present invention has significant advantages in improving minority class recognition ability and overall classification robustness. The objectives and constraints designed in this invention can improve the effectiveness of synthetic samples from multiple perspectives, including classification boundary, distribution consistency, diversity, and sample quality, thereby significantly improving the classification performance of the classifier.
Claims
1. A multi-objective synthetic oversampling method for imbalanced data, characterized in that, Includes the following steps: Step 1: Obtain the original imbalanced data and extract features and class labels. Divide the original data into minority class and majority class sample sets based on the number of samples in each class, and calculate their cluster centers: Minority class sample centers and majority class sample center ; Step 2: Construct a multi-objective optimization framework based on genetic programming. Each individual uses tree-based encoding from genetic programming. This indicates that it corresponds to a rule for generating synthetic samples, setting optimization objectives and constraints: the optimization objective includes a first objective of evaluating the classification boundary relationship between the synthetic sample and the majority and minority classes, denoted as... ; and a second objective, denoted as , to measure whether the synthesized samples conform to the inherent original distribution characteristics of the minority class samples. Constraints are used to constrain individuals from the perspectives of classification boundaries, distribution consistency, diversity, and sample quality, ensuring their distribution consistency and representativeness, and constructing a higher-quality synthetic sample set of minority classes from all individuals that meet the constraints. Step 3: Perform the multi-objective optimization process, including population initialization, individual crossover and mutation, tournament selection, and environment selection; in the environment selection phase, calculate the degree of constraint violation for each individual based on the constraints; based on the optimization objective and the degree of constraint violation, prioritize the selection of feasible and non-dominated individuals to enter the next generation, and use feasible solutions or infeasible solutions with a small degree of constraint violation to generate a new generation of population; repeat the above process until the termination condition is met. Step 4: After evolution terminates, extract all non-dominant individuals that satisfy the constraints from the final population to form a feasible solution set; use each individual in the feasible solution set as a sample generation rule to synthesize new minority class samples in batches, and merge all synthesized samples to form the final minority class sample set; Step 5: Merge the final minority class sample set with the majority class sample set to obtain a balanced dataset; use the balanced data as the training set to train the classifier, and evaluate the classification performance on the test set.
2. The multi-objective synthesis oversampling method for imbalanced data according to claim 1, characterized in that, In step 2, the first target The second objective is the distance difference between the synthetic sample and the centers of the majority and minority classes. This represents the proportion of minority class samples among the k-nearest neighbors of the synthesized sample; specifically expressed as: ； in, For synthetic samples To the center Similarly, the Euclidean distance, For synthetic samples To the center Euclidean distance; ； in, For synthetic samples of A collection of neighbors, It is a minority class of sample sets.
3. The multi-objective synthesis oversampling method for imbalanced data according to claim 1, characterized in that, In step 2, the constraints include: the minimum threshold of the first objective, the minimum distance between the synthetic sample and the minority class sample center, the maximum distance between the synthetic sample and the minority class sample center, and the angle constraint between the vectors formed by the synthetic sample and the majority and minority class sample centers; specifically expressed as: First constraint: , indicating that the first target is greater than or equal to zero; The second constraint: ,in, The average distance between minority class samples indicates that the Euclidean distance from the composite sample to the minority class center is greater than or equal to the average distance between minority class samples. The third constraint: ,in The maximum distance between minority class samples indicates that the Euclidean distance from the composite sample to the minority class center is less than or equal to the maximum distance between minority class samples. The fourth constraint: ,in For spatial vectors and space vectors The included angle between them indicates that the included angle between them is less than or equal to .
4. The multi-objective synthesis oversampling method for imbalanced data according to claim 1, characterized in that, In step 2, the genetically programmed individuals are represented as a tree structure, with non-terminal nodes containing arithmetic operators and leaf nodes representing minority class samples.
5. A multi-objective synthesis oversampling method for imbalanced data according to claim 1, characterized in that, In step 3, the environment selection is as follows: For each individual, the degree of violation of multiple constraints is normalized and merged to obtain a constraint violation degree of a uniform scale. Based on the degree of constraint violation, the population is divided into feasible and infeasible solutions. During the selection process, if the number of feasible solutions is greater than the population size, a non-dominated sorting is performed according to the optimization objective. If the number of feasible solutions is less than the population size, all feasible solutions are retained, and the remaining population is selected from the infeasible solutions in ascending order of constraint violation degree to fill the gaps until the population size is reached. The degree of constraint violation is specifically expressed as follows: ； in For the initial population, The number of constraints. Represented as: Merge constraints and use the initial population The individual with the largest value is used as the standard, and it is normalized.
6. A multi-objective synthesis oversampling method for imbalanced data according to claim 1, characterized in that, In step 4, at the end of each evolutionary search process, all feasible solutions in the final population are combined to form a new sample. This evolutionary search process is repeated multiple times until the total number of synthesized minority class samples reaches the preset equilibrium number.
7. A multi-objective synthesis oversampling method for imbalanced data according to claim 1, characterized in that, In step 4, each time a new batch of minority class samples is synthesized, it is merged with the current minority class sample set to ensure the diversity of the synthesized samples.
8. A multi-objective synthesis oversampling framework for imbalanced data, characterized in that, include: Preprocessing module: used to acquire raw imbalanced data and preprocess it, dividing the preprocessed dataset into minority class sample sets and majority class sample sets; Multi-objective optimization module: Constructs a multi-objective optimization framework based on genetic programming; Each individual uses a tree-like encoding from genetic programming and corresponds to a rule for generating synthetic samples. Optimization objectives and constraints are set: the first objective is to evaluate the classification boundary relationship between the synthetic sample and the majority and minority classes, and the second objective is to measure whether the synthetic sample conforms to the inherent distribution characteristics of the minority class samples. Constraints are used to constrain individuals from the perspectives of classification boundary, distribution consistency, diversity, and sample quality to ensure their distribution consistency and representativeness. A higher-quality set of minority class synthetic samples is constructed from all individuals that meet the constraints. Constraint processing module: For each individual, the degree of violation of multiple constraints is normalized and merged to obtain a uniform constraint violation degree; based on this constraint violation degree, the population is divided into feasible solutions and infeasible solutions; During the selection process, if the number of feasible solutions is greater than the population size, non-dominated sorting is performed according to the optimization objective; if the number of feasible solutions is less than the population size, all feasible solutions are retained, and the remaining population is selected from infeasible solutions in order of increasing constraint violation until the population size is reached. Sample synthesis module: At the end of each evolutionary search process, a new sample is synthesized from all feasible solutions in the final population and merged with the original minority class sample to form a new minority class sample set.
9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the computer program is loaded into the processor, it implements the method as described in any one of claims 1-8.
10. A storage medium storing a computer program, characterized in that, When the computer program is executed by a processor, it implements the method as described in any one of claims 1-8.