Generative adversarial network-based sparse large-scale multi-objective optimization method

Abstract

The invention discloses a sparse large-scale multi-objective optimization method based on a generative adversarial network, and relates to the technical field of large-scale multi-objective optimization, and the method comprises the following steps: carrying out the preprocessing of a large-scale high-dimensional sparse data set, so as to reduce the data dimension and noise, and guaranteeing that the solution space exploration of a sparse region is not ignored in the optimization process. Through sparse data preprocessing, a sparsity control mechanism and multiple rounds of adversarial learning circulation, the solution set diversity and coverage rate of the generative adversarial network in multi-objective optimization are improved, the mode collapse phenomenon is effectively avoided, and the optimization result is more comprehensive. When high-dimensional sparse data is processed, through feature extraction, dimensionality reduction and dynamic learning rate adjustment, calculation complexity is reduced, training efficiency and stability are improved, it is ensured that a generator can explore a sparse region and a high-density region of a solution space in a balanced mode, and efficient and reliable technical support is provided for a complex decision-making scene.

Description

Technical Field

[0001] The present invention relates to the technical field of large-scale multi-objective optimization, and in particular to a sparse large-scale multi-objective optimization method based on a generative adversarial network. Background Art

[0002] Sparse large-scale multi-objective optimization based on generative adversarial networks is a technical method that uses generative adversarial networks (GANs) to efficiently solve large-scale multi-objective optimization problems. Multi-objective optimization aims to optimize multiple conflicting objectives at the same time, but traditional methods are prone to high computational complexity and low search efficiency when dealing with large-scale data sets. To this end, this method introduces a generative adversarial network, which models and conducts adversarial learning on the optimization solution space through the generator and discriminator in GAN, and automatically generates high-quality candidate solutions. At the same time, sparse technology is used to reduce the number of solutions that need to be evaluated during the optimization process, reduce the computational burden, and improve the scalability and computational efficiency of the algorithm. This method can not only better approximate the Pareto optimal frontier, but also more effectively balance the trade-offs between multiple objectives when solving large-scale, multi-objective optimization tasks.

[0003] The prior art has the following deficiencies:

[0004] In the sparse large-scale multi-objective optimization process based on generative adversarial networks (GANs), the mode collapse phenomenon of the generator may lead to the loss of diversity in the optimization solution space, thus affecting the optimization effect. Mode collapse refers to the situation that the generator of GAN only generates a small number of candidate solutions with good performance during training, while ignoring other potential excellent solutions in the solution space. In multi-objective optimization, this phenomenon will lead to over-concentration of optimization results, covering only a small area of ​​the Pareto optimal frontier, and failing to provide a comprehensive solution set. Especially when dealing with high-dimensional sparse data sets, due to the imbalance and sparsity of data distribution, the GAN model tends to ignore the potential solutions in sparse areas, making it impossible to effectively optimize some objectives. This situation may lead to a lack of diversity in decision-making solutions in practical applications, which cannot meet the needs of different scenarios, and even biased decisions, resulting in resource waste and business risks. For example, in supply chain management, if the model only generates a few optimization solutions and ignores other solutions that may be more suitable for special scenarios, it may lead to the lack of response plans for enterprises when the market changes, resulting in serious economic losses.

[0005] The above information disclosed in this Background section is only for enhancement of understanding of the background of the present disclosure and therefore it may contain information that does not constitute the prior art that is already known to one of ordinary skill in the art. Summary of the invention

[0006] The purpose of the present invention is to provide a sparse large-scale multi-objective optimization method based on a generative adversarial network, which improves the diversity and coverage of solution sets of a generative adversarial network (GAN) in multi-objective optimization through sparse data preprocessing, sparsity control mechanism and multiple rounds of adversarial learning cycles, effectively avoids the phenomenon of mode collapse, and makes the optimization results more comprehensive. When processing high-dimensional sparse data, feature extraction, dimensionality reduction and dynamic learning rate adjustment are used to reduce computational complexity, improve training efficiency and stability, ensure that the generator can evenly explore sparse and high-density areas in the solution space, and provide efficient and reliable technical support for complex decision-making scenarios to solve the problems in the above-mentioned background technology.

[0007] In order to achieve the above object, the present invention provides the following technical solution: a sparse large-scale multi-objective optimization method based on a generative adversarial network, comprising the following steps:

[0008] Preprocess large-scale high-dimensional sparse data sets to reduce data dimensionality and noise, while ensuring that the exploration of the solution space in sparse areas is not ignored during the optimization process;

[0009] Initialize the generative adversarial network model and adjust the generator's loss function by introducing an adaptive regularization mechanism, so that the generator can explore the solution space more evenly during training and avoid a single distribution of generated solutions.

[0010] Using the adjusted generator model, multiple candidate solutions are generated in the sparse data space to cover the Pareto frontier in different regions, and the generated solutions are fed back to the discriminator for verification;

[0011] In the multi-objective optimization process, a dynamic objective weight adjustment algorithm is introduced to dynamically adjust the weight of the optimization objective according to the conflict degree between different objectives and the distribution of solutions, so as to ensure that the generated candidate solutions take all objectives into consideration in a balanced manner at different stages of optimization, thereby improving the diversity of the solution set and the optimization effect.

[0012] To address the mode collapse problem of the generator, a mode collapse suppression algorithm based on adversarial learning is introduced. By calculating the diversity index of the solutions in the generated solution set, the overly concentrated and lacking-diversity solution sets are penalized, thereby suppressing the mode collapse phenomenon and optimizing the comprehensive coverage of the solution space.

[0013] Preferably, the specific steps for preprocessing a large-scale high-dimensional sparse data set to reduce data dimension and noise, while ensuring that the solution space exploration of sparse areas is not ignored during the optimization process are as follows:

[0014] Clean up missing values, outliers, and noisy data to ensure the integrity and accuracy of the data set and reduce the interference of irrelevant data on optimization;

[0015] Extract core features through dimensionality reduction technology, remove redundant information, reduce data dimensions, and improve the efficiency and accuracy of optimization calculations;

[0016] Normalize the data features to eliminate dimensional differences so that each feature has the same weight and influence during the optimization process;

[0017] Filter and retain sparse features that have an important impact on target optimization, avoid information blind spots in sparse data, and improve the model's ability to explore the solution space.

[0018] Preferably, the generative adversarial network model is initialized, and the loss function of the generator is adjusted by introducing an adaptive regularization mechanism so that the generator explores the solution space more evenly during the training process and avoids the simplification of the generated solution distribution. The specific steps are as follows:

[0019] According to the characteristics of sparse data, we design adaptive generator and discriminator architectures, and improve the processing capability of sparse data through sparse activation functions and attention mechanisms;

[0020] Sparsity regularization and diversity penalty terms are introduced to optimize the loss function of the generator, ensuring that the generated solution set can cover the sparse data space and avoid mode collapse;

[0021] Through adversarial learning mechanism and learning rate adjustment strategy, the parameters of generator and discriminator are dynamically updated to maintain the balance and convergence stability of GAN model;

[0022] Combined with the core features of preprocessing, the generated solution set is verified and screened to ensure that the screened solutions can cover the key sparse areas and improve the diversity and effectiveness of the solution set.

[0023] Preferably, the specific steps of using the adjusted generator model to generate multiple candidate solutions in the sparse data space to cover the Pareto frontiers of different regions, and feeding the generated solutions back to the discriminator for verification are as follows:

[0024] Using the optimized generator model, multiple candidate solutions are generated according to the sparse data characteristics to ensure that the solution set covers the key areas in the sparse data space;

[0025] The distribution of candidate solutions is dynamically evaluated through the sparsity control mechanism to ensure that the solution set covers the Pareto frontier of different regions and avoid the solution set being concentrated in high-density areas;

[0026] Feed the generated solution set back to the discriminator for verification, evaluate the effectiveness and diversity of the solution, and provide adjustment signals to the generator to optimize the generation strategy;

[0027] Through the adversarial learning cycle of the generator and the discriminator, the quality of the solution set is continuously improved, ensuring that the model can continue to cover different areas of the sparse data space.

[0028] Preferably, in the multi-objective optimization process, a dynamic objective weight adjustment algorithm is introduced to dynamically adjust the weight of the optimization objective according to the conflict degree between different objectives and the distribution of solutions, thereby ensuring that the generated candidate solutions take all objectives into balanced consideration at different stages of optimization, thereby improving the diversity of the solution set and the optimization effect;

[0029] In the multi-objective optimization process, a dynamic objective weight adjustment algorithm is introduced to dynamically adjust the weight of the optimization objective according to the conflict degree between different objectives and the distribution of solutions, so as to ensure that the generated candidate solutions take all objectives into consideration in a balanced manner at different stages of optimization, thereby improving the diversity of the solution set and the optimization effect. The specific steps are as follows:

[0030] First, according to the performance of each target in the current candidate solution set, the target conflict matrix is ​​calculated. The calculation expression is as follows:

[0031] ,

[0032] In the formula, C ij is the degree of conflict between target i and target j, f i (k) is the function value of candidate solution k on target i, f j (k) is the function value of candidate solution k on target j, μ i is the average value of the target μ, μ j is the mean value of target j, σ i is the standard deviation of target i, σ j is the criterion for objective j, N is the number of candidate solutions;

[0033] According to the target conflict matrix C ij The importance weight of each target is dynamically adjusted according to the value of . The higher the weight, the more the target needs to be optimized at the current stage. The importance weight calculation expression is as follows:

[0034] ,

[0035] In the formula, w i is the importance weight of target i, M is the total number of targets, e is the natural base, and α is the conflict sensitivity adjustment factor, which is used to control the adjustment range of the weight;

[0036] In each round of optimization iteration, the dynamic weight of each target is dynamically updated based on the weight value of the previous round and the current distribution of candidate solutions. The calculation expression is as follows:

[0037] ,

[0038] In the formula, is the dynamic weight of target i in the tth iteration, is the dynamic weight of target i in the t-1th iteration, that is, the dynamic weight in the previous generation, and η is the learning rate;

[0039] Finally, according to the dynamic weight value of each target Calculate the final weight vector of the optimization target to guide the generator model to generate a new set of candidate solutions in the current iteration. The calculation expression is as follows:

[0040] ,

[0041] Where W (t) is the final weight vector of the optimization objective in the tth iteration.

[0042] Preferably, for the mode collapse problem of the generator, a mode collapse suppression algorithm of adversarial learning is introduced, and the diversity index of the solution in the generated solution set is calculated to punish the solution set that is too concentrated and lacks diversity, thereby suppressing the mode collapse phenomenon and optimizing the comprehensive coverage of the solution space. The specific steps are as follows:

[0043] In order to quantify the diversity of the generated solution set, the distribution entropy of each feature dimension in the solution set is first calculated to evaluate the coverage of the solution in the solution space. The distribution entropy calculation expression is as follows:

[0044] ,

[0045] In the formula, FDE h is the distribution entropy of the hth feature dimension, p yh is the probability distribution of the yth value in the hth feature dimension in the solution set, n h is the number of value types of the h-th feature dimension;

[0046] In order to ensure that the generated solution set can cover the key areas in the sparse data space, the sparse coverage index is further introduced, and the calculation expression is as follows:

[0047] ,

[0048] Where SCR is the sparse coverage rate, which indicates the coverage degree of sparse areas in the solution set, δ q is the indicator function of whether the qth sparse region is covered by the solution set, w q is the importance weight of the qth sparse region, and m is the total number of sparse regions;

[0049] In order to incorporate diversity into the generator's loss function, the diversity penalty term is calculated and the feature dimension distribution entropy FDE is h Considering the sparse coverage rate SCR comprehensively, the calculation expression is as follows:

[0050] ,

[0051] In the formula, DPT is the diversity penalty term, d is the total number of feature dimensions, α and β are weight coefficients, α controls the weight of feature distribution entropy in the penalty term, and β controls the weight of sparse coverage in the penalty term;

[0052] In the loss function of the generator, a diversity penalty term DPT is added to dynamically adjust the generation strategy of the generator. The loss function formula of the generator is as follows:

[0053] ,

[0054] In the formula, is the loss function of the generator, is the average evaluation value of the discriminator on the generated solution, that is, the "authenticity" score of the generated solution, is the expected value of the random variable z, z is the input random noise vector of the generator, p z (z) is the probability distribution of the input noise vector z, D(G(z)) is the judgment result of the discriminator D on the generated solution G(z), and λ is the weight coefficient of the diversity penalty term.

[0055] In the above technical solution, the technical effects and advantages provided by the present invention are:

[0056] The present invention can effectively improve the diversity of solution sets of generative adversarial networks (GANs) in multi-objective optimization through sparse data preprocessing, sparsity control mechanisms and multiple rounds of adversarial learning cycles, and ensure that the solution set covers the Pareto frontiers of different regions. When processing high-dimensional sparse data, traditional GAN ​​models are prone to mode collapse, that is, the generator only focuses on local areas in the solution space, resulting in over-concentration and lack of comprehensiveness in the optimization results. However, this solution uses a sparsity control mechanism to dynamically evaluate the coverage of candidate solution sets, identify sparse areas that have not been fully explored, and guide the generator to generate more solutions from these areas through the sparsity regularization term in the loss function, thereby improving the coverage of the solution set. This method ensures that the generator can generate high-quality solutions in different areas of the solution space, effectively avoids the phenomenon of mode collapse, makes the optimization results more diverse and comprehensive, and provides a more valuable reference solution for complex decision-making scenarios in practical applications.

[0057] When the present invention performs multi-objective optimization in a high-dimensional sparse data environment, the computational complexity of the model is often a key bottleneck, especially when the solution space is huge and the data distribution is sparse, it is difficult for traditional algorithms to converge efficiently. This solution significantly reduces the interference and computational burden of irrelevant features through feature extraction, dimensionality reduction and normalization processing in the data preprocessing stage, so that the GAN model can focus on the optimization of core features. At the same time, in the adversarial learning process, by dynamically adjusting the learning rate of the generator and the discriminator, the model can maintain a stable training effect at different training stages, avoiding oscillation and overfitting during the training process. In addition, the introduction of sparsity control mechanism and diversity penalty terms enables the generator to explore the solution space more efficiently during the optimization process, and no longer over-concentrate on high-density areas, thereby improving the exploration efficiency of sparse areas. These measures comprehensively improve the training stability and convergence speed of the GAN model when processing high-dimensional sparse data, and provide efficient and reliable technical support for the practical application of multi-objective optimization tasks. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments recorded in the present invention. For ordinary technicians in this field, other drawings can also be obtained based on these drawings.

[0059] Figure 1 This is a method flow chart of the sparse large-scale multi-objective optimization method based on the generative adversarial network of the present invention. DETAILED DESCRIPTION

[0060] Example embodiments will now be described more fully with reference to the accompanying drawings. However, example embodiments can be implemented in a variety of forms and should not be construed as limited to the examples set forth herein; rather, these example embodiments are provided so that the description of the present disclosure will be more comprehensive and complete, and the concept of the example embodiments will be fully conveyed to those skilled in the art.

[0061] The present invention provides Figure 1 The sparse large-scale multi-objective optimization method based on the generative adversarial network shown includes the following steps:

[0062] Preprocessing of large-scale high-dimensional sparse data sets, including feature extraction, normalization, and sparse feature screening to reduce data dimension and noise, while ensuring that the exploration of the solution space of sparse areas is not ignored during the optimization process;

[0063] The specific steps for preprocessing large-scale high-dimensional sparse data sets, including feature extraction, normalization, and sparse feature screening, to reduce data dimensions and noise, while ensuring that the exploration of the solution space of sparse areas is not ignored during the optimization process, are as follows:

[0064] Clean up missing values, outliers, and noisy data to ensure the integrity and accuracy of the data set and reduce the interference of irrelevant data on optimization;

[0065] Data cleaning is performed on large-scale sparse data sets to remove missing values, unreasonable values, and abnormal data points, and to filter out random noise in the data. First, missing value filling methods such as mean filling, nearest neighbor filling, or interpolation are used to ensure data integrity. Secondly, outliers that are obviously inconsistent with the rules in the data set are identified and removed. Statistical methods (such as the 3σ rule) or machine learning methods (such as the isolation forest algorithm) can be used to automatically detect abnormal data points. In addition, due to the characteristics of sparse data, special attention should be paid to low-frequency data points to avoid sparse features being incorrectly filtered. Noise filtering helps to reduce the impact of irrelevant or erroneous data on subsequent feature extraction and optimization, thereby improving the stability and accuracy of the model.

[0066] The dataset is a dataset for portfolio investment optimization, which usually contains a large amount of historical data of different asset classes, such as stocks, bonds, real estate investment trusts (REITs), commodities, and cryptocurrencies. These data have high dimensionality, non-uniform distribution, and significant sparsity. In order to improve the optimization effect, such datasets must be preprocessed, including feature extraction, normalization, and screening of sparse features to reduce data dimensions and noise, while ensuring that the solution space of sparse areas is not ignored during the optimization process. First, feature extraction is a key step. It is necessary to extract indicators that are crucial to investment decisions from the original data, such as the historical returns, volatility, market liquidity, industry classification, macroeconomic factors (such as interest rates, inflation rates), etc. of assets, and reduce data redundancy through principal component analysis (PCA) or dimensionality reduction techniques. Secondly, normalization is a necessary measure to ensure that different asset features are optimized on the same scale, such as standardizing the return rate, trading volume, and other features of various assets to the range of [0,1] to avoid model bias caused by inconsistent scales between features. Finally, sparse feature screening mainly targets assets with low transaction frequency and more missing data in the market. It uses missing value filling, data interpolation and intelligent clustering methods to screen out representative features to ensure that these sparse areas are covered during the optimization process, and potential high-quality investment opportunities are not ignored due to data sparsity. Through this series of preprocessing steps, the data set for portfolio investment optimization is more complete and standardized, and provides high-quality input for the subsequent optimization model based on the generative adversarial network (GAN), thereby ensuring the comprehensiveness and reliability of the final investment portfolio solution.

[0067] Extract core features through dimensionality reduction technology, remove redundant information, reduce data dimensions, and improve the efficiency and accuracy of optimization calculations;

[0068] The high-dimensional features in the data set are extracted and reduced in dimension, and the core features of the data are extracted using methods such as principal component analysis (PCA), linear discriminant analysis (LDA) or autoencoders. Since sparse data usually contains a large number of irrelevant or redundant features, the dimensionality reduction process aims to retain the main information of the data while reducing the data dimension and improving computational efficiency. In the feature extraction process, the actual application scenarios of the data need to be considered, and the features that are of practical significance to multi-objective optimization should be retained, while those redundant features that are irrelevant to the optimization objectives should be removed. This step helps to transform high-dimensional sparse data into a more compact and information-intensive representation, thereby reducing the computational complexity of subsequent algorithms.

[0069] Normalize the data features to eliminate dimensional differences so that each feature has the same weight and influence during the optimization process;

[0070] Normalization is performed on different feature dimensions of the data to ensure that different features have the same scale during the optimization process. Normalization methods can be selected such as minimum-maximum normalization, Z-score normalization, or quantile normalization to eliminate the dimensional differences between different features and avoid some feature values ​​from dominating the optimization process due to their large range. For example, for a feature set that includes user age, income, and product click-through rate, if the data is not normalized, the income feature may mask the influence of other features due to its large value range. Normalized data can keep the optimization algorithm balanced on each feature and improve the algorithm's ability to explore the solution space.

[0071] Filter and retain sparse features that have an important impact on target optimization, avoid information blind spots in sparse data, and improve the model's ability to explore the solution space;

[0072] Through the sparse feature screening algorithm, sparse features that have an important impact on the optimization target are identified and retained. Sparse features can be quantitatively evaluated by methods such as L1 regularization, sparse coding, or feature importance evaluation. L1 regularization automatically resets the weights of unimportant features to zero during model training, thereby retaining only key features; sparse coding finds the association between sparse features and targets by representing data as sparse matrices; feature importance evaluation can identify features that have a greater impact on target variables through algorithms such as random forests or XGBoost. The core goal of this step is to avoid the "information blind spots" in sparse data, ensure that the GAN model can fully explore potential solutions in the sparse data space, and avoid ignoring innovative solutions that may be brought about by sparse areas. By screening sparse features, unnecessary computational burdens can be reduced, while ensuring that the optimization algorithm pays attention to sparse areas, thereby improving the comprehensiveness and accuracy of multi-objective optimization.

[0073] Initialize the generative adversarial network model, including the architecture design of the generator and the discriminator, and adjust the loss function of the generator by introducing an adaptive regularization mechanism, so that the generator can explore the solution space more evenly during the training process and avoid the distribution of generated solutions being too uniform;

[0074] Initialize the generative adversarial network model, including the architecture design of the generator and the discriminator, and adjust the loss function of the generator by introducing an adaptive regularization mechanism, so that the generator can explore the solution space more evenly during the training process and avoid the simplification of the distribution of generated solutions. The specific steps are as follows:

[0075] According to the characteristics of sparse data, we design adaptive generator and discriminator architectures, and improve the processing capability of sparse data through sparse activation functions and attention mechanisms;

[0076] First, according to the preprocessed sparse data features, the adaptive generator and discriminator architectures are designed. The input layer of the generator needs to match the core feature dimensions after preprocessing, and generate candidate solutions in the solution space through a multi-layer fully connected network or a convolutional network. For the discriminator, it is necessary to consider the uneven distribution of sparse data characteristics, and introduce a discriminant network with an attention mechanism so that the discriminator can more accurately identify the distribution of generated solutions. In order to adapt to high-dimensional sparse data, sparse activation functions (such as ReLU, Leaky ReLU) can be introduced to effectively process sparse features. In addition, the number of layers and neurons of the generator and discriminator should be adjusted according to the data scale and the complexity of the target optimization problem to avoid overfitting or underfitting problems. This architectural design can provide a powerful representation capability for the GAN model, enabling it to better explore the sparse data space.

[0077] Sparsity regularization and diversity penalty terms are introduced to optimize the loss function of the generator, ensuring that the generated solution set can cover the sparse data space and avoid mode collapse;

[0078] In order to avoid the phenomenon of mode collapse in the generator during training, it is necessary to adjust its loss function and introduce an adaptive regularization mechanism. In traditional GAN, the goal of the generator is to maximize the error rate of the discriminator, but in the sparse data optimization scenario, simply pursuing error maximization can easily cause the generator to focus on local solutions. Therefore, this step incorporates the diversity and sparsity of the solution into the loss function by introducing sparsity regularization terms and diversity penalty terms. For example, a diversity indicator is added to the generator loss, the sparse coverage of the generated solution set is calculated, and a penalty is imposed on low coverage solutions. This adaptive regularization mechanism can dynamically adjust the generator's attention to sparse areas, ensuring that the generator does not ignore potential solutions in sparse areas during training, thereby achieving a comprehensive exploration of the solution space.

[0079] Through adversarial learning mechanism and learning rate adjustment strategy, the parameters of generator and discriminator are dynamically updated to maintain the balance and convergence stability of GAN model;

[0080] After initializing the model, an adversarial learning mechanism is required to dynamically update its parameters through the mutual game between the generator and the discriminator. After the generator generates a candidate set of solutions, the solution set is input into the discriminator for judgment. The discriminator feeds back the quality and diversity of the generated solutions and adjusts the parameters of the generator based on the feedback results. In this process, special attention should be paid to the discriminator's ability to recognize sparse features to prevent the discriminator from converging to certain specific patterns too early, thereby ignoring the solutions in sparse areas. In addition, during the dynamic update process, a learning rate adjustment strategy can be introduced to dynamically adjust the learning rates of the generator and the discriminator according to the performance of the generated solutions to prevent the GAN model from experiencing unstable convergence or oscillation in the early stages of training. The introduction of this mechanism helps to maintain the dynamic balance of the GAN model, thereby improving the diversity and coverage of the optimized solution set.

[0081] Combined with the core features of preprocessing, the generated solution set is verified and screened to ensure that the screened solutions can cover the key sparse areas and improve the diversity and effectiveness of the solution set;

[0082] In the solution set generated by the generator, the solution set needs to be verified and screened in combination with the core features extracted in the preprocessing process and the sparse feature screening results. Specifically, the discriminator compares the generated solution with the actual data set to evaluate the effectiveness of the solution and the coverage of the sparse features. If some solutions fail to cover the key areas of the sparse data space, the feedback mechanism guides the generator to readjust the generation strategy. During the verification process, the weight adjustment algorithm of the sparse features can be used to evaluate the feature importance of different solutions to ensure that the screened solution set has a higher optimization value. This process can effectively prevent sparse features from being ignored, thereby improving the diversity of the optimized solution set and solving the common mode collapse problem in the generative adversarial network model.

[0083] Using the adjusted generator model, multiple candidate solutions are generated in the sparse data space. The candidate solution set ensures the distribution of solutions is diversified through the sparsity control mechanism to cover the Pareto frontiers in different regions, and the generated solutions are fed back to the discriminator for verification.

[0084] Using the adjusted generator model, multiple candidate solutions are generated in the sparse data space. The candidate solution set ensures the distribution of solutions is diversified through the sparsity control mechanism to cover the Pareto frontier in different regions, and the generated solutions are fed back to the discriminator for verification. The specific steps are as follows:

[0085] Using the optimized generator model, multiple candidate solutions are generated according to the sparse data characteristics to ensure that the solution set covers the key areas in the sparse data space;

[0086] The optimized generator model uses random noise or prior features as input to generate multiple candidate solutions in a high-dimensional sparse data space. The input dimension of the generator model is consistent with the core feature dimension after preprocessing to ensure that the solution set generation conforms to the distribution characteristics of sparse data. During the generation process, the generator dynamically adjusts the feature distribution of the solution set according to the adaptive regularization loss function so that it covers the key areas in the sparse data space. The generated candidate solutions include not only solutions in high-density areas, but also focus on exploring potential solutions in sparse areas, thereby improving the comprehensiveness of the solution set. This step inherits the adjustment of the generator in the initialization stage, making the solutions generated by the model more balanced and avoiding excessive concentration of the solution space in local areas.

[0087] The distribution of candidate solutions is dynamically evaluated through the sparsity control mechanism to ensure that the solution set covers the Pareto frontier of different regions and avoid the solution set being concentrated in high-density areas;

[0088] In the process of generating candidate solutions, the sparsity control mechanism is used to constrain the distribution of the solution set to ensure that the generated solution set can cover the Pareto front of different regions. The sparsity control mechanism dynamically evaluates the feature coverage of candidate solutions and identifies possible "blind spots" or sparse areas in the current solution set, thereby guiding the generator to generate more solutions to these areas. Specific implementation methods include introducing sparsity penalty terms, rewarding areas with insufficient coverage, or using coverage optimization algorithms to ensure the breadth and balance of the solution set distribution. This mechanism can effectively prevent the solution set from being concentrated in certain high-density areas, enhance the optimization algorithm's ability to explore sparse data, and make the coverage of the Pareto front more comprehensive.

[0089] Feed the generated solution set back to the discriminator for verification, evaluate the effectiveness and diversity of the solution, and provide adjustment signals to the generator to optimize the generation strategy;

[0090] The solution set generated by the generator needs to be verified by the discriminator to ensure the validity and diversity of the solution. In the feedback process, the discriminator evaluates the solution set based on the feature distribution, target optimization value and sparse coverage of the solution, and feeds the evaluation results back to the generator. The discriminator calculates the diversity score and sparse coverage of the solution to identify whether the solution set has problems such as mode collapse and uneven distribution. If the solution set lacks diversity or ignores sparse areas, the discriminator will send an adjustment signal to the generator so that the generator pays more attention to the distribution breadth and diversity of the solution in the next round of generation. This feedback link can dynamically optimize the generation strategy of the generator to ensure that the generated solution set can effectively meet the requirements of multi-objective optimization.

[0091] Through the adversarial learning cycle of the generator and the discriminator, the quality of the solution set is continuously improved to ensure that the model can continue to cover different areas of the sparse data space;

[0092] Through the adversarial learning mechanism of the generator and the discriminator, a cyclic process of solution set generation-verification-feedback-regeneration is formed to continuously optimize the quality of the candidate solution set. In each round of feedback loop, the generator adjusts its generation strategy through the feedback results of the discriminator, and the discriminator dynamically updates its evaluation criteria based on the new solution set. This cyclic process can adopt multiple rounds of dynamic adjustment strategies to gradually improve the sparse coverage and optimization performance of the solution set in each iteration. In addition, combined with the core features and sparse features extracted in the preprocessing stage, the discriminator can more accurately identify the deficiencies in the solution set, thereby more effectively guiding the generator to generate a diversified solution set covering the Pareto frontier. Through this continuously optimized feedback loop, the model can gradually improve the quality of multi-objective optimization tasks and ensure comprehensive exploration of the sparse data space.

[0093] In the multi-objective optimization process, a dynamic objective weight adjustment algorithm is introduced to dynamically adjust the weight of the optimization objective according to the conflict degree between different objectives and the distribution of solutions, so as to ensure that the generated candidate solutions take all objectives into consideration in a balanced manner at different stages of optimization, thereby improving the diversity of the solution set and the optimization effect.

[0094] In the multi-objective optimization process, a dynamic objective weight adjustment algorithm is introduced to dynamically adjust the weight of the optimization objective according to the conflict degree between different objectives and the distribution of solutions, so as to ensure that the generated candidate solutions take all objectives into consideration in a balanced manner at different stages of optimization, thereby improving the diversity of the solution set and the optimization effect. The specific steps are as follows:

[0095] First, the target conflict matrix is ​​calculated based on the performance of each target in the current candidate solution set. The higher the value of the target conflict matrix, the greater the contradiction between the optimization of the two targets. The calculation expression is as follows:

[0096] ,

[0097] In the formula, C ij is the degree of conflict between target i and target j, f i (k) is the function value of candidate solution k on target i, f j (k) is the function value of candidate solution k on target j, μ i is the average value of the target μ, μ j is the mean value of target j, σ i is the standard deviation of target i, σ j is the criterion for objective j, N is the number of candidate solutions;

[0098] The calculated conflict matrix C ij It is used to calculate dynamic weights in subsequent steps to ensure that the weights can reflect the actual conflict situation between targets.

[0099] According to the target conflict matrix C ij The importance weight of each target is dynamically adjusted according to the value of . The higher the weight, the more the target needs to be optimized at the current stage. The importance weight calculation expression is as follows:

[0100] ,

[0101] In the formula, w i is the importance weight of target i, M is the total number of targets, e is the natural base, and α is the conflict sensitivity adjustment factor, which is used to control the adjustment range of the weight;

[0102] The weight calculation takes into account the conflict between each goal and all other goals, and introduces nonlinear adjustment through exponential function to make the change of weight more flexible. i Will be used for weight updates in subsequent steps.

[0103] In each round of optimization iteration, the dynamic weight of each target is dynamically updated based on the weight value of the previous round and the current distribution of candidate solutions. The weight update introduces conflict weight accumulation terms and solution distribution balance terms to ensure balanced weight distribution in solution sets at different stages. The calculation expression is as follows:

[0104] ,

[0105] In the formula, is the dynamic weight of target i in the tth iteration, is the dynamic weight of target i in the t-1th iteration, that is, the dynamic weight in the previous iteration, and η is the learning rate, which is used to control the speed of weight update;

[0106] The dynamic update of weights takes into account the distribution of candidate solution sets, ensuring that the optimization process will not over-focus on a certain goal while maintaining the smoothness of weight updates.

[0107] Finally, according to the dynamic weight value of each target Calculate the final weight vector of the optimization target to guide the generator model to generate a new set of candidate solutions in the current iteration. The calculation expression is as follows:

[0108] ,

[0109] Where W (t) is the final weight vector of the optimization objective in the tth iteration.

[0110] The final weight vector W (t) The normalization of each target weight is ensured, so that the generator model can generate a more balanced set of candidate solutions in the solution space according to the current weight distribution, thereby improving the diversity and coverage of the solution set.

[0111] To address the mode collapse problem of the generator, an adversarial learning mode collapse suppression algorithm is introduced. By calculating the diversity index of the solution in the generated solution set and taking it as part of the generator loss function, the overly concentrated and lacking-diversity solution set is penalized, thereby suppressing the mode collapse phenomenon and optimizing the comprehensive coverage of the solution space.

[0112] In order to solve the mode collapse problem of the generator, a mode collapse suppression algorithm based on adversarial learning is introduced. By calculating the diversity index of the solution in the generated solution set and taking it as part of the generator loss function, the over-concentrated and lack-of-diversity solution set is penalized to suppress the mode collapse phenomenon and optimize the comprehensive coverage of the solution space. The specific steps are as follows:

[0113] In order to quantify the diversity of the generated solution set, the distribution entropy of each feature dimension in the solution set is first calculated to evaluate the coverage of the solution in the solution space. The higher the distribution entropy, the more uniform the distribution of the generated solutions in this dimension and the wider the coverage. On the contrary, the lower the distribution entropy, the more concentrated the generated solutions are in certain specific areas and there is a risk of mode collapse. The distribution entropy calculation expression is as follows:

[0114] ,

[0115] In the formula, FDE h is the distribution entropy of the hth feature dimension, p yh is the probability distribution of the yth value in the hth feature dimension in the solution set, n h is the number of value types of the h-th feature dimension;

[0116] First, perform feature analysis on the solution set, divide each feature dimension into multiple intervals (such as high, medium, and low intervals), calculate the proportion of solutions in each interval, and obtain the probability distribution p of each interval. yh Then the entropy value of each feature dimension is calculated using the distribution entropy formula. The higher the entropy value, the more balanced the feature distribution and the higher the diversity of the solution set. This step outputs the entropy value FDE of each feature dimension h , for use in subsequent steps.

[0117] In order to ensure that the generated solution set can cover the key areas in the sparse data space, the sparse coverage rate indicator is further introduced. The sparse coverage rate refers to the coverage degree of the generated solution set in the sparse area. The calculation expression is as follows:

[0118] ,

[0119] Where SCR is the sparse coverage rate, which indicates the coverage degree of sparse areas in the solution set, δ q is the indicator function of whether the qth sparse region is covered by the solution set, w q is the importance weight of the qth sparse region, which is obtained by business scenario or feature importance analysis, and m is the total number of sparse regions;

[0120] By analyzing the distribution of sparse features, it is marked whether each sparse region is covered by the generated solution and assigned different weight values ​​w q To indicate the importance of each sparse region. The higher the SCR value, the more fully the solution set covers the sparse region, which helps to solve the problem of ignoring sparse regions caused by mode collapse.

[0121] In order to incorporate diversity into the generator's loss function, the diversity penalty term is calculated and the feature dimension distribution entropy FDE is hConsidering the sparse coverage rate SCR comprehensively, this penalty term is used to dynamically adjust the exploration direction of the generator in the process of solution set generation to suppress the mode collapse phenomenon. The calculation expression is as follows:

[0122] ,

[0123] In the formula, DPT is the diversity penalty term, which is part of the generator loss function, d is the total number of feature dimensions, α and β are weight coefficients, α controls the weight of the feature distribution entropy in the penalty term, indicating the importance of the distribution balance of each feature in the generated solution set in the overall diversity evaluation, β controls the weight of the sparse coverage rate in the penalty term, indicating the importance of the coverage of the generated solution set to the sparse area in the overall diversity evaluation;

[0124] This step considers the feature distribution entropy and sparse coverage comprehensively and converts them into a penalty value DPT. If the feature distribution of the solution set is balanced and the sparse coverage is high, the penalty value DPT will be close to 0; otherwise, the penalty value will become larger, forcing the generator to pay more attention to the diversity of the solution set and the coverage of the sparse area in the next round of generation.

[0125] In the loss function of the generator, a diversity penalty term DPT is added to dynamically adjust the generation strategy of the generator to prevent the generated solution set from concentrating on a specific pattern, while improving the coverage and diversity of the solution. The loss function formula of the generator is as follows:

[0126] ,

[0127] In the formula, is the loss function of the generator, is the average evaluation value of the discriminator on the generated solution, that is, the "authenticity" score of the generated solution, is the expected value of the random variable z, z is the input random noise vector of the generator, usually sampled from a standard normal distribution or uniform distribution, p z (z) is the probability distribution of the input noise vector z, which is generally a Gaussian distribution or a uniform distribution, and is used to generate different candidate solutions. D(G(z)) is the judgment result of the discriminator D on the generated solution G(z), and outputs a value between 0 and 1, where 1 means closer to the real data and 0 means more like the generated data. λ is the weight coefficient of the diversity penalty term, which controls the influence of the diversity penalty term DPT in the generator loss function.

[0128] The loss function of the traditional generator only considers the discriminator feedback score of the generated solution, while the diversity penalty term DPT introduced in this step takes into account the distribution diversity and sparse coverage of the generated solution. By adjusting the weight coefficient λ, the quality of the solution and the diversity of the solution can be balanced to effectively suppress the mode collapse phenomenon and optimize the comprehensive coverage of the solution space.

[0129] Implementation method 1: In multi-objective optimization tasks, the processing of sparse data is an important challenge faced by optimization algorithms, because the high dimensionality, high noise and uneven distribution of data will cause the key areas in the solution space to be ignored. In order to effectively solve this problem, large-scale high-dimensional sparse data sets are first systematically preprocessed. The preprocessing process includes data cleaning, feature extraction, dimensionality reduction, normalization and sparse feature screening. These five links complement each other to ensure that the data set is more compact and accurate, and provide high-quality input for the subsequent generative adversarial network (GAN) model.

[0130] Data cleaning and noise filtering: Sparse data sets often contain a large number of missing values, unreasonable values, and outliers, which can cause the optimization model to deviate from the true solution space. Therefore, the data set is first cleaned to fill in missing values, remove unreasonable values ​​and abnormal data points, and reduce the interference of irrelevant noise on the optimization process. At the same time, according to the distribution of the data, a suitable anomaly detection algorithm, such as the isolation forest algorithm, is used to automatically identify and remove outliers.

[0131] Since high-dimensional features in sparse data sets usually contain a lot of redundant information, which easily leads to high computational complexity, feature extraction and dimensionality reduction techniques are used to extract the core features of the data. Dimensionality reduction can be achieved by using algorithms such as principal component analysis (PCA) and linear discriminant analysis (LDA), ensuring that while the data dimension is reduced, information that is critical to the optimization goal is retained. Through dimensionality reduction, the data set becomes more compact and the efficiency of the optimization algorithm is greatly improved.

[0132] The dimensional differences of different features will cause some features to have too large weights during the optimization process, affecting the distribution of the solution set. To avoid this problem, the data features are normalized so that all features can be compared on the same scale. Commonly used methods include min-max normalization and Z-score normalization, and the specific choice depends on the distribution of the data. The normalized data is input into the GAN model to ensure that the optimization process of the model in each feature dimension is more balanced.

[0133] In order to avoid the problem of information blind spots in sparse data, sparse features that have an important impact on the optimization target are screened out through methods such as L1 regularization, sparse coding or feature importance evaluation. The screened sparse features will be the focus of subsequent generative adversarial networks, thereby improving the GAN model's ability to explore sparse areas.

[0134] After completing the data preprocessing, the generative adversarial network model is initialized, including the architecture design of the generator and the discriminator. The task of the generator is to generate candidate solutions in the solution space, while the discriminator is responsible for evaluating the effectiveness and diversity of these solutions. By introducing an adaptive regularization mechanism, the loss function of the generator is optimized to ensure that the generator can explore the solution space in a balanced manner rather than focusing on certain local solutions. The combination of sparse data preprocessing and the GAN model not only improves the quality of the solution set, but also avoids the occurrence of the mode collapse problem, providing a more comprehensive and diverse solution set for the optimization task.

[0135] Implementation method 2: In the process of sparse data optimization, the diversity and balanced distribution of candidate solutions are crucial. In order to ensure that the generated candidate solution set can effectively cover different areas in the solution space, a sparsity control mechanism is introduced to dynamically evaluate the distribution of the solution set and guide the generator to generate more solutions to uncovered areas when necessary. In addition, the solution set is verified and fed back by the discriminator to form a dynamically adjusted feedback loop, thereby continuously improving the diversity of the solution set and the optimization effect.

[0136] When using the generator to generate candidate solutions, the generator will generate multiple candidate solutions based on the input random noise or preprocessed core features. In order to evaluate the distribution of these solutions, a sparsity control mechanism is introduced to identify sparse areas that have not been fully explored by calculating the coverage of candidate solutions in the solution space. This evaluation result can dynamically guide the generator to focus on generating insufficiently covered areas in the next round of generation to ensure a more balanced distribution of the solution set.

[0137] The sparsity control mechanism can be implemented through sparsity penalty terms and coverage optimization algorithms. Specifically, a sparsity penalty term is added to the generator's loss function to give higher weights to uncovered areas in the solution set, encouraging the generator to generate more solutions from these areas. At the same time, the coverage optimization algorithm dynamically adjusts the solution set generation strategy so that the solution set can cover different areas in the solution space, rather than just focusing on high-density areas. This sparsity control mechanism effectively avoids the occurrence of mode collapse.

[0138] After the candidate solutions are generated, the solution set is verified by the discriminator. The discriminator scores the solution set based on the feature distribution, diversity, and sparse coverage of the solution. If the discriminator detects that there is a problem of mode collapse or uneven distribution in the solution set, it will feed back the adjustment signal to the generator, so that the generator will pay more attention to the exploration and diversity of sparse areas in the next round of generation. This feedback process can dynamically optimize the quality of the solution set and ensure the comprehensiveness and effectiveness of the multi-objective optimization task.

[0139] Implementation method three: In order to continuously improve the quality of the solution set generated by the GAN model, a multi-round adversarial learning cycle mechanism is adopted to continuously improve the optimization effect through the game between the generator and the discriminator. In each round of the cycle, the generator generates a solution set, the discriminator verifies the solution set and feeds back the results, and the generator adjusts the generation strategy based on the feedback, thereby generating a better solution set in the subsequent cycle.

[0140] The core of the multi-round adversarial learning cycle lies in the dynamic game between the generator and the discriminator. At the beginning of each round, the generator generates a set of candidate solutions based on the preprocessed feature data, which will serve as the input of the discriminator. The discriminator analyzes the solution set, evaluates its distribution and sparse coverage, and feeds back adjustment signals to the generator based on the evaluation results.

[0141] In the cyclic process, the adjustment of learning rate is the key to ensure the stable convergence of the model. In the early stage of training, the learning rate is high to promote the generator and discriminator to quickly learn the characteristics of the solution space. In the later stage of training, the learning rate is gradually reduced to prevent model oscillation or overfitting. By dynamically adjusting the learning rate, the model can maintain good training results at different stages, thereby continuously generating high-quality candidate solutions.

[0142] After each cycle, the generated solution set will be screened and verified by the discriminator to ensure the effectiveness and diversity of the solution set. If it is found that some solutions fail to cover key sparse areas, the generator will focus on optimizing the solutions in these areas in the next round of generation. This continuous optimization mechanism can ensure that the generator continues to explore different areas of the solution space and gradually improve the overall effect of multi-objective optimization.

[0143] The present invention discloses a sparse large-scale multi-objective optimization method for solving the portfolio investment optimization problem based on a generative adversarial network (GAN). The portfolio investment optimization problem involves a reasonable allocation among multiple investment assets to maximize the return under the premise of controllable risks. This type of problem usually has a multi-objective attribute, involving multiple conflicting objectives such as return, risk, liquidity, etc., and there is data sparsity in large-scale investment portfolios. Some assets may lack sufficient historical data or have a low transaction frequency, which makes it difficult for traditional optimization methods to effectively handle them. In this context, the present invention introduces a generative adversarial network (GAN), which can learn the deep-level features of data in a complex portfolio optimization process through adversarial training of generators and discriminators, and generate optimal investment plans that conform to market laws. In addition, in order to solve the high-dimensional sparsity problem of large-scale portfolio investment data, the present invention adopts a sparse feature screening and preprocessing mechanism to ensure that GAN can identify and focus on potential effective features in sparse data during the optimization process, so as to avoid affecting the comprehensiveness and accuracy of the optimization results due to missing or unevenly distributed data.

[0144] In the application process, the present invention first preprocesses the downloaded data set of the portfolio investment optimization problem. These data sets usually contain high-dimensional features such as historical prices, volatility, yields, and market correlation of multiple assets, and some of the data may be missing or sparse due to market fluctuations, data acquisition cycles, or abnormal events. In order to improve the effectiveness of optimization, the present invention adopts processing steps such as feature normalization, missing value filling, and data dimensionality reduction to ensure the quality and consistency of the input data. Specifically, the normalization process makes the characteristics of different assets comparable, avoiding the bias of the optimization model caused by excessive differences in the range of feature values; missing value filling uses an intelligent completion algorithm based on time series regression and market correlation to infer the reasonable value of missing data, and prevents optimization errors caused by data sparsity; dimensionality reduction processing removes redundant features through methods such as principal component analysis (PCA), improves the efficiency of data processing, and reduces computational complexity. Finally, the preprocessed data set can provide a stable and reliable basis for the training of the GAN model, so that the generator can fully consider the dynamic correlation between assets when learning the portfolio investment model, and generate investment plans that adapt to market changes.

[0145] At the technical implementation level, the present invention fully considers the characteristics of portfolio investment optimization in the design of the GAN architecture. The input features of the generator include historical return data of different assets, market trend indicators, industry classification information, etc., and combined with sparse data processing technology, it ensures that important investment opportunities will not be missed in the multi-objective optimization process. In order to prevent the generator from being overly biased towards assets with good historical performance, the present invention introduces a diversity loss function in the discriminator, so that the discriminator not only considers the profitability of the investment portfolio, but also evaluates its robustness under different market conditions. In addition, the optimization process of the present invention adopts a dynamic target weight adjustment algorithm, which adaptively adjusts the weights of the return, risk and liquidity targets according to the preferences of investors, changes in the market environment and real-time updates of asset performance, ensuring that the optimized solution is both in line with the current market conditions and can provide stable returns for long-term investments. In this way, the present invention not only improves the applicability of GAN in portfolio investment optimization problems, but also significantly reduces the risk of excessive portfolio concentration caused by data sparsity and mode collapse.

[0146] In solving the potential mode collapse problem in the GAN optimization process, the present invention proposes a mode collapse suppression algorithm based on adversarial learning. For portfolio investment optimization scenarios, mode collapse may cause the generated investment portfolio to be overly concentrated in certain specific assets or industries, ignoring other asset categories that may have potential returns, thereby affecting the diversification characteristics of the overall investment portfolio. To this end, the present invention introduces a diversity evaluation indicator based on Pareto frontier coverage. The discriminator will perform a diversity analysis on the investment portfolio output by the generator, and impose diversity constraints on the generator during the training process, encouraging the generator to generate a more balanced and comprehensive investment plan. Through this mechanism, the present invention avoids the situation where the investment portfolio generated by GAN is concentrated on a single asset or strategy during the optimization process, ensuring that the optimization results not only meet the diversified needs of investors, but also can cope with the risk challenges under different market conditions.

[0147] In practical applications, the present invention can be widely used in financial fields such as asset management, fund portfolio optimization, pension allocation, etc. In particular, in large-scale portfolio management, the present invention can effectively integrate a large amount of market data, automatically generate the optimal investment portfolio, and continuously adjust it according to the dynamic changes of the market. Compared with traditional portfolio optimization methods, such as mean-variance models or Monte Carlo simulations, the GAN optimization method of the present invention can still maintain high computational efficiency under sparse high-dimensional data, and provide more adaptive investment strategies under complex market conditions. Finally, the sparse large-scale multi-objective optimization method of the present invention provides a new and intelligent solution to the problems of data sparsity, high computational complexity, and dynamic changes in the market environment in current portfolio investment optimization.

[0148] In order to more intuitively illustrate the application of the present invention in the portfolio investment optimization problem, it is assumed that a fund company wants to optimize its investment portfolio through a sparse large-scale multi-objective optimization method based on a generative adversarial network (GAN) to achieve the following three main goals:

[0149] Maximize investment returns: Ensure that the investment portfolio achieves higher returns amid market fluctuations.

[0150] Minimize investment risks: control asset fluctuations and reduce possible losses.

[0151] Improve liquidity: Ensure that the portfolio can be quickly liquidated to meet funding needs when needed.

[0152] In traditional portfolio optimization methods, such as the mean-variance model (Markowitz model), the mean and variance of historical data are mainly relied on to determine the optimal portfolio. However, in practical applications, due to market uncertainty and data incompleteness, traditional methods often face problems such as sparse data, high computational complexity, and insufficient adaptability. For example, some assets in emerging markets may be ignored in traditional optimization methods due to less historical data, while these assets may actually have higher growth potential.

[0153] In order to solve the above problems, the present invention first preprocesses the downloaded portfolio investment optimization problem dataset. Assume that a fund company has a set of investment data containing 500 different assets, which include stocks, bonds, real estate investment trusts (REITs), cryptocurrencies, etc. The data sources include financial trading platforms, government statistics, third-party financial institutions reports, etc. However, due to differences in the transaction frequency, market maturity and data collection methods of different assets, the dataset has the following sparsity problems:

[0154] There may be missing trading records for some assets. For example, the monthly trading data for some small-cap stocks may not be sufficient to support accurate modeling.

[0155] Different assets have different time horizons. For example, cryptocurrency trading data is usually more abundant, while REITs have more limited historical data.

[0156] There is unstructured data such as news sentiment, social media influence, etc. which is not evenly distributed across asset classes.

[0157] In this case, the present invention adopts the following preprocessing steps to improve data quality:

[0158] Feature normalization: For example, normalizing indicators such as stock returns and bond returns to fall into the same range (e.g. [0, 1]) so that GAN can more effectively learn the relationship between different assets.

[0159] Missing value filling: For missing asset return data, the present invention introduces a time series regression model to intelligently fill in the missing data based on historical trends. For example, if the return data of a small-cap stock in a certain month is missing, it can be estimated by the performance of its industry-related index or similar assets.

[0160] Data dimensionality reduction: Use principal component analysis (PCA) to reduce the dimensionality of high-dimensional feature data to reduce redundant information. For example, 50 different macroeconomic indicators can be reduced to 5 main influencing factors, such as inflation rate, interest rate level, etc., to reduce computational complexity.

[0161] After the above data preprocessing steps, the fund company can obtain a more complete and uniform investment data set, which provides reliable input for the subsequent GAN optimization process.

[0162] In the model training stage of GAN, the architecture design of the generator and the discriminator is particularly critical. Assuming that the input of the generator is the historical data of various assets, including price fluctuations, trading volume, industry categories, etc., the role of the discriminator is to evaluate whether the investment portfolio generated by the generator has high returns, low risks and good liquidity. The present invention adjusts the loss function of the generator during the training process through an adaptive regularization mechanism to avoid excessive concentration of the generated investment portfolio on certain specific assets. For example, if the generator is overly inclined to a certain type of high-yield but high-risk technology stocks during the training process, the discriminator will guide the generator to diversify its investment through feedback signals, so that the investment plan covers more low-risk traditional industries, such as utilities or consumer goods industries.

[0163] In practical applications, the present invention generates diversified investment portfolios through multi-objective solution generation in sparse data space. For example, a fund manager wants to generate 10 different investment portfolios, each with different risk preferences in asset allocation. During the training process, GAN will generate the following exemplary investment plans based on the sparsity characteristics of the data:

[0164] Option 1 (conservative): 50% bonds, 30% blue chip stocks, 10% cash, 10% commodities;

[0165] Option 2 (Growth): 40% technology stocks, 30% consumer goods, 20% global stocks, 10% cryptocurrencies;

[0166] Option 3 (aggressive): 50% cryptocurrencies, 20% growth stocks, 20% emerging market stocks, and 10% commodities.

[0167] In the process of generating these optimization schemes, the present invention introduces a dynamic target weight adjustment algorithm to ensure the balance between return, risk and liquidity targets under different market conditions. For example, when market volatility intensifies, GAN will automatically adjust the optimization target, reduce the weight of high-risk assets, and increase the allocation ratio of stable assets such as bonds to ensure the risk resistance of the investment portfolio.

[0168] In addition, in order to avoid mode collapse during the training process of GAN, that is, the generated investment portfolio is overly concentrated in a few assets or a single strategy, the present invention introduces a mode collapse suppression algorithm based on adversarial learning. For example, in a certain training cycle, GAN may tend to generate an investment portfolio dominated by technology stocks, while ignoring investment opportunities in other industries. At this time, the discriminator will feedback the generator based on the diversity index and impose penalties to encourage it to generate more diversified investment plans, ensuring that the final investment portfolio can be evenly distributed across different industries and asset categories.

[0169] Finally, the present invention provides fund companies with a complete portfolio investment optimization solution that can adapt to changes in the market environment. Compared with traditional portfolio optimization methods, the GAN optimization method of the present invention has the following advantages when facing high-dimensional and sparse data:

[0170] More comprehensive coverage of investment options: Ability to explore data-sparse areas and discover investment opportunities overlooked by traditional methods.

[0171] More efficient computing power: Through the parallel computing power of GAN, a variety of investment portfolios can be quickly generated to meet the needs of different investors.

[0172] Better adaptability: The investment portfolio can be adjusted dynamically according to changes in the market environment to improve investment flexibility and robustness.

[0173] In summary, the present invention can not only help fund companies optimize their investment portfolios in a sparse large-scale data environment, but also significantly improve the flexibility and competitiveness of investment strategies, providing strong support for intelligent investment decisions in the financial market.

[0174] The present invention can effectively improve the diversity of solution sets of generative adversarial networks (GANs) in multi-objective optimization through sparse data preprocessing, sparsity control mechanisms and multiple rounds of adversarial learning cycles, and ensure that the solution set covers the Pareto frontiers of different regions. When processing high-dimensional sparse data, traditional GAN ​​models are prone to mode collapse, that is, the generator only focuses on local areas in the solution space, resulting in over-concentration and lack of comprehensiveness in the optimization results. However, this solution uses a sparsity control mechanism to dynamically evaluate the coverage of candidate solution sets, identify sparse areas that have not been fully explored, and guide the generator to generate more solutions from these areas through the sparsity regularization term in the loss function, thereby improving the coverage of the solution set. This method ensures that the generator can generate high-quality solutions in different areas of the solution space, effectively avoids the phenomenon of mode collapse, makes the optimization results more diverse and comprehensive, and provides a more valuable reference solution for complex decision-making scenarios in practical applications.

[0175] When the present invention performs multi-objective optimization in a high-dimensional sparse data environment, the computational complexity of the model is often a key bottleneck, especially when the solution space is huge and the data distribution is sparse, it is difficult for traditional algorithms to converge efficiently. This solution significantly reduces the interference and computational burden of irrelevant features through feature extraction, dimensionality reduction and normalization processing in the data preprocessing stage, so that the GAN model can focus on the optimization of core features. At the same time, in the adversarial learning process, by dynamically adjusting the learning rate of the generator and the discriminator, the model can maintain a stable training effect at different training stages, avoiding oscillation and overfitting during the training process. In addition, the introduction of sparsity control mechanism and diversity penalty terms enables the generator to explore the solution space more efficiently during the optimization process, and no longer over-concentrate on high-density areas, thereby improving the exploration efficiency of sparse areas. These measures comprehensively improve the training stability and convergence speed of the GAN model when processing high-dimensional sparse data, and provide efficient and reliable technical support for the practical application of multi-objective optimization tasks.

[0176] The above formulas are all dimensionless and numerical calculations. The formula is a formula for the most recent real situation obtained by collecting a large amount of data and performing software simulation. The preset parameters in the formula are set by technicians in this field according to actual conditions.

[0177] The above description is only by way of illustration of certain exemplary embodiments of the present invention. It is undoubted that those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the above drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

[0178] It should be noted that, in this article, if there are relational terms such as first and second, etc., they are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0179] It should be understood that in the various embodiments of the present application, the size of the serial numbers of the above-mentioned processes does not mean the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present application.

[0180] Those of ordinary skill in the art will appreciate that the units and algorithm steps of each example described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional and technical personnel can use different methods to implement the described functions for each specific application, but such implementation should not be considered to be beyond the scope of this application.

[0181] Those skilled in the art can clearly understand that, for the convenience and brevity of description, the specific working processes of the systems, devices and units described above can refer to the corresponding processes in the aforementioned method embodiments and will not be repeated here.

[0182] The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place or distributed on multiple network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0183] In addition, each functional unit in each embodiment of the present application may be integrated into one processing unit, or each unit may exist physically separately, or two or more units may be integrated into one unit.

[0184] The above is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art who is familiar with the present technical field can easily think of changes or substitutions within the technical scope disclosed in the present application, which should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

[0185] The above description is only by way of illustration of certain exemplary embodiments of the present invention. It is undoubted that those skilled in the art can modify the described embodiments in various ways without departing from the spirit and scope of the present invention. Therefore, the above drawings and descriptions are illustrative in nature and should not be construed as limiting the scope of protection of the claims of the present invention.

Claims

1. A sparse large-scale multi-objective optimization method based on generative adversarial networks, characterized in that: The following steps are involved: Preprocess large-scale high-dimensional sparse data sets to reduce data dimensionality and noise, while ensuring that the exploration of the solution space in sparse areas is not ignored during the optimization process; Initialize the generative adversarial network model and adjust the generator's loss function by introducing an adaptive regularization mechanism, so that the generator can explore the solution space more evenly during training and avoid a single distribution of generated solutions. Using the adjusted generator model, multiple candidate solutions are generated in the sparse data space to cover the Pareto frontier in different regions, and the generated solutions are fed back to the discriminator for verification; In the multi-objective optimization process, a dynamic objective weight adjustment algorithm is introduced to dynamically adjust the weight of the optimization objective according to the conflict degree between different objectives and the distribution of solutions, so as to ensure that the generated candidate solutions take all objectives into consideration in a balanced manner at different stages of optimization, thereby improving the diversity of the solution set and the optimization effect. To address the mode collapse problem of the generator, a mode collapse suppression algorithm based on adversarial learning is introduced. By calculating the diversity index of the solutions in the generated solution set, the overly concentrated and lacking-diversity solution sets are penalized, thereby suppressing the mode collapse phenomenon and optimizing the comprehensive coverage of the solution space.

2. The sparse large-scale multi-objective optimization method based on generative adversarial network according to claim 1 is characterized in that: The specific steps for preprocessing large-scale high-dimensional sparse data sets to reduce data dimensionality and noise while ensuring that the exploration of the solution space in sparse areas is not ignored during the optimization process are as follows: Clean up missing values, outliers, and noisy data to ensure the integrity and accuracy of the data set and reduce the interference of irrelevant data on optimization; Extract core features through dimensionality reduction technology, remove redundant information, reduce data dimensions, and improve the efficiency and accuracy of optimization calculations; Normalize the data features to eliminate dimensional differences so that each feature has the same weight and influence during the optimization process; Filter and retain sparse features that have an important impact on target optimization, avoid information blind spots in sparse data, and improve the model's ability to explore the solution space.

3. The sparse large-scale multi-objective optimization method based on generative adversarial network according to claim 1 is characterized in that: The specific steps to initialize the generative adversarial network model and adjust the generator's loss function by introducing an adaptive regularization mechanism so that the generator can explore the solution space more evenly during training and avoid the simplification of the generated solution distribution are as follows: According to the characteristics of sparse data, we design adaptive generator and discriminator architectures, and improve the processing capability of sparse data through sparse activation functions and attention mechanisms; Sparsity regularization and diversity penalty terms are introduced to optimize the loss function of the generator, ensuring that the generated solution set can cover the sparse data space and avoid mode collapse; Through adversarial learning mechanism and learning rate adjustment strategy, the parameters of generator and discriminator are dynamically updated to maintain the balance and convergence stability of GAN model; Combined with the core features of preprocessing, the generated solution set is verified and screened to ensure that the screened solutions can cover the key sparse areas and improve the diversity and effectiveness of the solution set.

4. The sparse large-scale multi-objective optimization method based on generative adversarial network according to claim 1 is characterized in that: The specific steps of using the adjusted generator model to generate multiple candidate solutions in the sparse data space to cover the Pareto frontiers in different regions and feeding the generated solutions back to the discriminator for verification are as follows: Using the optimized generator model, multiple candidate solutions are generated according to the sparse data characteristics to ensure that the solution set covers the key areas in the sparse data space; The distribution of candidate solutions is dynamically evaluated through the sparsity control mechanism to ensure that the solution set covers the Pareto frontier of different regions and avoid the solution set being concentrated in high-density areas; Feed the generated solution set back to the discriminator for verification, evaluate the effectiveness and diversity of the solution, and provide adjustment signals to the generator to optimize the generation strategy; Through the adversarial learning cycle of the generator and the discriminator, the quality of the solution set is continuously improved, ensuring that the model can continue to cover different areas of the sparse data space.

5. The sparse large-scale multi-objective optimization method based on generative adversarial network according to claim 1, characterized in that: In the multi-objective optimization process, a dynamic objective weight adjustment algorithm is introduced to dynamically adjust the weight of the optimization objective according to the conflict degree between different objectives and the distribution of solutions, so as to ensure that the generated candidate solutions take all objectives into consideration in a balanced manner at different stages of optimization, thereby improving the diversity of the solution set and the optimization effect. In the multi-objective optimization process, a dynamic objective weight adjustment algorithm is introduced to dynamically adjust the weight of the optimization objective according to the conflict degree between different objectives and the distribution of solutions, so as to ensure that the generated candidate solutions take all objectives into consideration in a balanced manner at different stages of optimization, thereby improving the diversity of the solution set and the optimization effect. The specific steps are as follows: First, according to the performance of each target in the current candidate solution set, the target conflict matrix is ​​calculated. The calculation expression is as follows: ， In the formula, C ij is the degree of conflict between target i and target j, f i (k) is the function value of candidate solution k on target i, f j (k) is the function value of candidate solution k on target j, μ i is the average value of the target μ, μ j is the mean value of target j, σ i is the standard deviation of target i, σ j is the criterion for objective j, N is the number of candidate solutions; According to the target conflict matrix C ij The importance weight of each target is dynamically adjusted according to the value of . The higher the weight, the more the target needs to be optimized at the current stage. The importance weight calculation expression is as follows: ， In the formula, w i is the importance weight of target i, M is the total number of targets, e is the natural base, and α is the conflict sensitivity adjustment factor, which is used to control the adjustment range of the weight; In each round of optimization iteration, the dynamic weight of each target is dynamically updated based on the weight value of the previous round and the current distribution of candidate solutions. The calculation expression is as follows: ， In the formula, is the dynamic weight of target i in the tth iteration, is the dynamic weight of target i in the t-1th iteration, that is, the dynamic weight in the previous generation, and η is the learning rate; Finally, according to the dynamic weight value of each target Calculate the final weight vector of the optimization target to guide the generator model to generate a new set of candidate solutions in the current iteration. The calculation expression is as follows: ， Where W (t) is the final weight vector of the optimization objective in the tth iteration.

6. The sparse large-scale multi-objective optimization method based on generative adversarial network according to claim 1, characterized in that: In order to solve the mode collapse problem of the generator, the adversarial learning mode collapse suppression algorithm is introduced. By calculating the diversity index of the solution in the generated solution set, the over-concentrated and lack-of-diversity solution set is punished, thereby suppressing the mode collapse phenomenon and optimizing the comprehensive coverage of the solution space. The specific steps are as follows: In order to quantify the diversity of the generated solution set, the distribution entropy of each feature dimension in the solution set is first calculated to evaluate the coverage of the solution in the solution space. The distribution entropy calculation expression is as follows: ， In the formula, FDE h is the distribution entropy of the hth feature dimension, p yh is the probability distribution of the yth value in the hth feature dimension in the solution set, n h is the number of possible values ​​of the h-th feature dimension.

7. The sparse large-scale multi-objective optimization method based on generative adversarial network according to claim 6 is characterized in that: In order to ensure that the generated solution set can cover the key areas in the sparse data space, the sparse coverage index is further introduced, and the calculation expression is as follows: ， Where SCR is the sparse coverage rate, which indicates the coverage degree of sparse areas in the solution set, δ q is the indicator function of whether the qth sparse region is covered by the solution set, w q is the importance weight of the qth sparse region, and m is the total number of sparse regions; In order to incorporate diversity into the generator's loss function, the diversity penalty term is calculated and the feature dimension distribution entropy FDE is h Considering the sparse coverage rate SCR comprehensively, the calculation expression is as follows: ， Where DPT is the diversity penalty term, d is the total number of feature dimensions, α and β are weight coefficients, α controls the weight of feature distribution entropy in the penalty term, and β controls the weight of sparse coverage in the penalty term.

8. The sparse large-scale multi-objective optimization method based on generative adversarial network according to claim 7, characterized in that: In the loss function of the generator, a diversity penalty term DPT is added to dynamically adjust the generation strategy of the generator. The loss function formula of the generator is as follows: ， In the formula, is the loss function of the generator, is the average evaluation value of the discriminator on the generated solution, that is, the "authenticity" score of the generated solution, is the expected value of the random variable z, z is the input random noise vector of the generator, p z (z) is the probability distribution of the input noise vector z, D(G(z)) is the judgment result of the discriminator D on the generated solution G(z), and λ is the weight coefficient of the diversity penalty term.

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