A method for screening effective substances of traditional Chinese medicine compound based on fruit growth optimization algorithm

Abstract

The application discloses a traditional Chinese medicine compound drug efficacy substance screening method based on a fruit growth optimization algorithm, and aims to solve the problem that existing methods and technologies are difficult to adapt to high-dimensional small sample, multiple collinearity, interaction and nonlinear traditional Chinese medicine compound dose-effect relationship data analysis problems. The application constructs and preprocesses the traditional Chinese medicine compound dose-effect relationship data set, initializes the fruit growth optimization algorithm population; through the stage type iteration and the stagnation escape strategy optimization of Sigmoid mapping, compound fitness calculation, nonlinear self-adaptive stratification, light decay regulation, the optimal feature subset is output, and the dose-effect analysis of the traditional Chinese medicine compound is realized by fitting the partial least squares method. The application has high precision, strong convergence and robustness, and provides quantitative support for traditional Chinese medicine efficacy substance research.

Description

Technical Field

[0001] This invention belongs to the field of traditional Chinese medicine formula efficacy mining technology, and relates to the field of computer technology, in particular to a method for screening active substances in traditional Chinese medicine compound formulas based on fruit growth optimization algorithm. Background Technology

[0002] The efficacy of traditional Chinese medicine (TCM) compound prescriptions is usually the result of multiple substances, multiple targets, multiple pathways, and multiple synergistic effects, exhibiting typical characteristics of complex substances and complex relationships. Accurately identifying the active ingredients that directly or indirectly contribute to the efficacy from dozens or even hundreds of compound substances, and eliminating redundant and irrelevant interfering substances, is one of the core tasks and challenges in analyzing the dose-effect relationship of TCM compound prescriptions.

[0003] Currently, the screening of active ingredients in traditional Chinese medicine (TCM) compound formulas largely relies on traditional statistical methods, such as correlation analysis, stepwise regression, and principal component analysis. These methods struggle to handle multicollinearity, interactions, and nonlinearity in TCM data, easily leading to the omission of key ingredients and the misselection of redundant ingredients. Furthermore, they are poorly suited for small datasets. In recent years, metaheuristic optimization algorithms have been gradually introduced into the field of feature selection. By simulating natural biological behavior, they achieve global optimization, possessing stronger nonlinear processing and global search capabilities compared to traditional statistical methods. However, existing mainstream metaheuristic algorithms, such as particle swarm optimization, gray wolf optimization, and whale optimization, generally suffer from an imbalance between global exploration and local exploitation capabilities when dealing with high-dimensional feature selection problems related to TCM dose-effect. They are prone to getting trapped in local optima in the later stages of iteration and have insufficient convergence accuracy, failing to achieve precise screening of key active ingredients in TCM compound formulas while ensuring the accuracy of efficacy prediction.

[0004] Therefore, there is an urgent need to develop a feature selection method that is adapted to the characteristics of traditional Chinese medicine compound data, can balance global search and local development, has high convergence accuracy, and is robust, in order to solve the problem of identifying key substances in the dose-effect relationship analysis of traditional Chinese medicine compound. Summary of the Invention

[0005] The purpose of this invention is to overcome the aforementioned problems in the prior art and provide a method for screening the active substances of traditional Chinese medicine compound prescriptions based on a fruit growth optimization algorithm. This method takes the fruit growth optimization algorithm (FGO) as its core, transforming the problem of screening the active substances of traditional Chinese medicine compound prescriptions into a global optimization process of the algorithm. By simulating the biological mechanisms of natural fruit tree growth, such as adaptive fruit thinning, light intensity attenuation regulation, and pollination renewal, it achieves a dynamic balance between the algorithm's global exploration and local development capabilities, accurately identifies key active substances in traditional Chinese medicine compound prescriptions, and effectively eliminates redundant and irrelevant features while ensuring the accuracy of efficacy prediction. Ultimately, it effectively achieves quantitative analysis of the dose-effect relationship of traditional Chinese medicine compound prescriptions.

[0006] The core of the method provided by this invention includes the following steps: Step S1 constructs a dose-effect relationship experimental dataset for traditional Chinese medicine compound prescriptions. The concentration of drug substances in the traditional Chinese medicine compound prescriptions is used as the input feature, and the corresponding pharmacological effect index is used as the output response variable. The dataset is standardized and preprocessed to obtain the feature set and label set. Step S2 generates N initial fruit individuals within a continuous search space that matches the input feature dimensions. Each fruit individual corresponds to a set of feature selection candidate solutions, and each dimension corresponds to a medicinal quality feature. The algorithm's maximum number of iterations, the proportion of retained fruits, the decay coefficient, and the iteration stagnation threshold are initialized. Step S3 maps the continuous values ​​of individual fruits to binary feature selection vectors using the Sigmoid function, filters feature subsets based on the binary feature selection vectors, constructs a partial least squares regression model, and constructs a composite fitness function by combining the prediction error of cross-validation with the proportion of feature subset size and calculating the fitness value of each individual fruit. In step S4, during each iteration, the number of retained results for the current iteration is calculated based on a nonlinear adaptive shrinkage strategy. With the number of fruits removed After sorting the population by fitness value, the remaining fruits are divided into retained fruits and thinned fruits; the light attenuation factor C is calculated, and according to the relationship between C and a set threshold, the pollination update operator in the exploration stage or the local development operator in the development stage is executed on the retained fruits respectively; the high-perturbation global search update strategy is executed on the thinned fruits to complete the population iterative update. During the S5 iteration process, the change of the global optimal fitness value is monitored in real time. When the stagnation judgment condition is met, a re-initialization operation is performed on the individuals that meet the condition to achieve population diversity update. Step S6: When the number of iterations reaches the maximum number of iterations T, the iteration is terminated. The optimal feature subset corresponding to the globally optimal fruit individual is output. Based on this optimal feature subset, the partial least squares regression model is refitted to obtain the quantitative analytical model of the dose-effect relationship of traditional Chinese medicine compound.

[0007] As a further aspect of the present invention, in step S1, the dose-effect relationship experimental dataset of traditional Chinese medicine compound is a dataset constructed based on the dose-effect relationship experiment of traditional Chinese medicine compound compatibility. The experiment has the core characteristics of multiple substances and multiple pharmacodynamics. The input features of the dataset are the concentration data of multiple active substances of traditional Chinese medicine in the compound compatibility system that can be qualitatively and quantitatively detected in the experiment, and the output response variables are multiple quantifiable pharmacological and pharmacodynamic evaluation indicators corresponding to the compound compatibility efficacy in the experiment.

[0008] As a further aspect of the present invention, in step S4, the calculation formula for the nonlinear adaptive contraction strategy is as follows: ; ; Where t is the current iteration number and T is the maximum iteration number. To determine the number of fruits to retain, To reduce the number of fruits, For the floor function, the retention ratio m is set to 0.2.

[0009] The formula for calculating the optical attenuation factor C is as follows: ;in, A uniformly random number within the interval (-1, 1). The attenuation coefficient is 0.002767; the set threshold is 0.5. When |C|≥0.5, the exploration phase begins, and when |C|<0.5, the development phase begins.

[0010] As a further aspect of the present invention, in step S4, the pollination update operator in the exploration phase includes a self-pollination operator and a cross-pollination operator. Two operators are randomly selected to perform individual updates. Simultaneously, a growth regulator with a Levy flight mechanism is introduced to control the update step size, specifically: Evolutionary component of the self-pollination operator Evolutionary components of cross-pollination operators .

[0011] The individual update rules are as follows: when hour, ; when hour, ; in, Let be the value of the globally optimal individual in the j-th dimension. Let be the value of the i-th fruit individual in the j-th dimension. Let be the value of the k-th random individual in the population in the j-th dimension. , , A uniformly random number within the interval (0,1). t represents the growth regulator, and t represents the current iteration number.

[0012] As a further aspect of the present invention, growth regulators The calculation formula is: Where b is a constant with a value of 0.001. The attenuation coefficient is 0.002767. Let be the Levy flight step size, used to simulate random environmental perturbations; and when the lower bound of the input feature value lb≥0, Take the absolute value; when lb < 0, Keep the original value.

[0013] As a further aspect of the present invention, in step S4, the local development operator in the development stage first calculates the nutrient regulation component. Press again Perform individual updates; The high-perturbation global search update strategy for the thinned results selects two update modes using random numbers, with the specific rules as follows: when hour, ; when hour, ; in, Let be the value of the globally optimal individual in the j-th dimension. Let be the value of the i-th thinned fruit individual in the j-th dimension. , , A uniformly random number within the interval (0,1). As a growth regulator, Levy's flight stride length t is the decay coefficient, and t is the current iteration number.

[0014] As a further aspect of the present invention, in step S5, the stagnation determination condition is: the number of iterations. and continuous The global optimal fitness value did not improve, among which and The value of is 30; the individuals that meet the conditions are those whose current fitness value is equal to the historical best value, and the formula for performing the re-initialization operation on them is: ;in, For the value of the individual in the j-th dimension to be reinitialized, For the j-th dimension search interval Uniform random sampling within, Let j be the lower bound of the values ​​in the j-th dimension. Let be the upper bound of the values ​​for the j-th dimension.

[0015] As a further aspect of the present invention, in step S3, the Sigmoid function mapping mechanism specifically involves: firstly, through... Calculate the mapping probability, and then convert it into a binary variable based on a threshold. ,when hour When the j-th medicinal quality characteristic is selected, hour The corresponding material characteristics of the j-th Chinese medicine were eliminated.

[0016] As a further aspect of the present invention, in step S3, the calculation formula for the composite fitness function is: ;in, The root mean square error is calculated based on the partial least squares regression model and ten-fold cross-validation. The number of features selected for the current feature subset. The total number of input features is α, the prediction accuracy weight is 0.9, and the feature simplification weight is 0.1.

[0017] Explanation of beneficial effects: 1. This invention addresses the core characteristics of dose-effect data in traditional Chinese medicine (TCM) compound formulas, such as high dimensionality, small sample size, multicollinearity, interactions, and nonlinear relationships. It combines a fruit growth optimization algorithm with a partial least squares regression model to construct an end-to-end method for screening active substances in TCM compound formulas. Compared with traditional statistical methods, this method has stronger nonlinear feature optimization and high-dimensional feature screening capabilities, effectively handling the complex dose-effect relationships in TCM compound formulas and avoiding the omission of key active substances.

[0018] 2. This invention adapts and improves the fruit growth optimization algorithm to specific scenarios. It achieves dynamic stratification of the population through a nonlinear adaptive shrinkage strategy, dividing the tasks between dominant and inferior individuals. It achieves a smooth transition between the exploration and development stages through a light attenuation factor, solving the problem of imbalance between exploration and development in traditional metaheuristic algorithms. Through the Levy flight mechanism and stagnation escape strategy, it effectively avoids the algorithm from getting stuck in local optima in the later stages of iteration, significantly improving the convergence accuracy and result stability of feature selection.

[0019] 3. This invention constructs a composite fitness function that integrates prediction accuracy and feature simplification. By using weighting coefficients, it achieves a balance between the two optimization objectives. This ensures the prediction accuracy of the selected feature subset for drug efficacy while driving the algorithm to eliminate redundant features, reduce model complexity, and improve the generalization ability and interpretability of the dose-effect relationship model. This provides quantitative and objective technical support for the study of the pharmacodynamic material basis of traditional Chinese medicine compound prescriptions.

[0020] 4. The method of the present invention has wide applicability and can be adapted to different types of dose-effect experimental datasets of traditional Chinese medicine compound prescriptions, including multi-disease model pharmacodynamic datasets and single-disease multi-pharmacodynamic endpoint datasets. Whether it is the analysis of dose-effect relationship of classic prescriptions or the screening of pharmacodynamic substances in the research and development of new traditional Chinese medicine drugs, it has good application effects. Attached Figure Description

[0021] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used in conjunction with embodiments of the invention to explain the invention and do not constitute a limitation thereof. In the drawings: Figure 1 This is a flowchart of the steps of a method for screening active substances in traditional Chinese medicine compound prescriptions based on a fruit growth optimization algorithm, according to the present invention. Figure 2 This is a flowchart of the steps of the binary fruit growth optimization algorithm provided in the embodiments of the present invention; Figure 3 This is a comparison chart of the number of features selected by different algorithms provided in the embodiments of the present invention on various datasets; Figure 4 This is a schematic diagram showing the average ranking of the six algorithms provided in the embodiments of the present invention. Detailed Implementation

[0022] The preferred embodiments of the present invention will be described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are for illustration and explanation only and are not intended to limit the present invention.

[0023] Example 1 Please see Figure 1 The diagram shows a flowchart of the steps in a method for screening active substances in traditional Chinese medicine compound prescriptions based on a fruit growth optimization algorithm, according to the present invention. The specific steps are as follows: Step S1 involves constructing a dose-effect relationship experimental dataset of the target traditional Chinese medicine compound based on the dose-effect experimental data and performing preprocessing to obtain a feature set and a label set.

[0024] In the embodiments of this application, the target traditional Chinese medicine compound can be any traditional Chinese medicine compound whose dose-effect relationship needs to be analyzed, including classic prescriptions, hospital preparations, and prescriptions for new traditional Chinese medicine drug development. This application does not limit the number of medicinal ingredients or the composition of the compound. The experimental dataset of dose-effect relationship of traditional Chinese medicine compound refers to an experimental dataset containing the concentration of compound substances and corresponding efficacy indicators obtained through in vivo animal experiments, in vitro cell experiments, or clinical sample detection.

[0025] A dose-effect relationship experimental dataset of traditional Chinese medicine compound prescriptions was constructed. The concentration of drug substances in the traditional Chinese medicine compound prescriptions was used as the input feature, and the corresponding pharmacological effect index was used as the output response variable. The dataset was standardized and preprocessed to obtain the feature set and label set.

[0026] The aforementioned dataset of dose-effect relationship experiments on traditional Chinese medicine (TCM) compound prescriptions is a dataset constructed based on experiments on the dose-effect relationship of TCM compound prescriptions. These experiments possess the core characteristics of multiple substances and multiple pharmacodynamics, adapting to the synergistic effects of multiple herbal combinations and substances in TCM compound prescriptions. Specifically, the "multiple substances" characteristic refers to the experiment covering multiple sources of TCM active substances within the compound prescription system that can be qualitatively and quantitatively detected; the "multiple pharmacodynamics" characteristic refers to the experiment setting multi-dimensional and multi-level quantifiable pharmacological and pharmacodynamic evaluation endpoints around the clinical therapeutic efficacy of the compound prescription.

[0027] The input features of the dataset are the concentration data of various active substances of traditional Chinese medicine in the compound formulation system that can be qualitatively and quantitatively detected in the dose-response relationship experiment, including but not limited to the content of substances in the compound preparation, the content of substances entering the blood in biological samples after administration, and the content of substances distributed in target tissues; the output response variables of the dataset are multiple quantifiable pharmacological and pharmacodynamic evaluation indicators corresponding to the efficacy of the compound formulation in the experiment, including but not limited to the overall pathological evaluation indicators of the disease model, biochemical detection indicators at the tissue and organ level, and pharmacodynamic endpoint indicators at the cell and molecular level.

[0028] In some embodiments, for the two types of datasets mentioned above, at least three sets of parallel experimental samples are set for each dosing regimen. The average of the experimental results of all parallel samples under the same regimen is taken as a data sample, thereby eliminating random errors caused by individual biological differences in experimental animals and cell samples, and ensuring the stability and representativeness of each sample data.

[0029] After the dataset is constructed, the terminal performs preprocessing operations on the dataset. The core preprocessing process includes data cleaning and standardization, as detailed below: The first step is data cleaning, which removes outliers and missing values ​​from the dataset. Outliers are identified and removed using the Grubbs test. For indicators with a small number of missing values, the mean of parallel samples under the same dosing regimen is used to fill the missing values, ensuring the integrity of the dataset and avoiding the impact of missing values ​​on subsequent modeling. The second step is to perform data standardization. In this embodiment, the Z-score standardization method is used to standardize the input features and the output response variables respectively.

[0030] After preprocessing, the terminal splits the dataset into a feature set and a label set. The feature set consists of standardized concentration data of all active substances in traditional Chinese medicine, with each column corresponding to a substance feature and each row corresponding to an experimental sample. The label set consists of standardized data of all pharmacological effect indicators, with each column corresponding to a pharmacodynamic evaluation indicator and each row corresponding to an experimental sample. The feature set and label set are then passed into the subsequent algorithm initialization and modeling stages.

[0031] Step S2 initializes the population for the fruit growth optimization algorithm and configures the core operating parameters of the algorithm.

[0032] An initial candidate solution set is constructed for the algorithm, and the core parameters of the algorithm are initialized. The problem of screening the active substances of traditional Chinese medicine compound is first mapped to a continuous search space for global optimization, and then the final feature selection result is obtained through binarization mapping. Population initialization provides an initial candidate solution covering the entire search space for the entire optimization process, ensuring the population diversity in the initial stage of the algorithm.

[0033] First, the search space and population individuals are defined: the dimension of the search space is exactly the same as the total number of features D in the preprocessed feature set, that is, each dimension corresponds to a medicinal substance; each candidate solution in the search space is abstracted as a developing fruit individual, and each fruit individual is a D-dimensional continuous vector. The value of each dimension in the vector corresponds to the probability mapping basis of the selection of the medicinal substance in that dimension. All fruit individuals together form the initial population of the algorithm, that is, the initial candidate solution set for feature selection.

[0034] Subsequently, population initialization is performed. In this embodiment, a uniform distribution method is used to generate the initial population, ensuring that the initial individuals uniformly cover the entire search space. The initialization formula is: Formula 1 in, Let be the initial value of the i-th fruit individual in the j-th dimension feature; and These are the upper and lower bounds of the j-th dimension search space, respectively, set based on the range of standardized feature data values. In this embodiment, the standardized feature data follows a distribution with a mean of 0 and a standard deviation of 1, therefore, they are set... , This ensures that the search space completely covers the effective value range of the features. r is a uniform random number in the interval [0,1], used to introduce random distribution characteristics to the initial individuals and simulate the randomness of the initial growth resource distribution of the fruit.

[0035] After completing the population initialization, the terminal initializes and configures the core operating parameters of the algorithm. In this embodiment, all parameters are set with reasonable value ranges, and the optimal value of each parameter is determined based on the scenario characteristics of traditional Chinese medicine dose-effect characteristics selection, biological inspiration laws, and simulation experiments, as follows: 1. Total population size N: The value range is set to 20-100, with an optimal value of 30. For small-to-medium scale feature dimension scenarios in the selection of dose-effect characteristics of traditional Chinese medicine, a population size of 30 can ensure sufficient population diversity to fully cover the search space, while effectively controlling computational costs and balancing the optimization performance and running efficiency of the algorithm.

[0036] 2. Maximum number of iterations T: The value range is set to 50-500, with an optimal value of 100. For small- to medium-scale problems in the selection of dose-effect features of traditional Chinese medicine, 100 iterations ensure that the algorithm can fully complete the process from global exploration to local development, find the feature subset with the best overall performance, and control the overall running time, adapting to the efficiency requirements of actual scientific research and application scenarios.

[0037] 3. Retention rate m: The value range is set to 0.1-0.5, with the optimal value being 0.2. The optimal value of 0.2 not only conforms to the natural fruit set rate law of fruit tree growth, but also verifies through experiments on multiple sets of Chinese herbal medicine dose-effect datasets, enabling the algorithm to achieve the optimal balance between global exploration and local development.

[0038] 4. Attenuation coefficient The value range is set to 0.001-0.01, with the optimal value being 0.002767. The optimal value of 0.002767 can effectively balance the exploration and development of the metaheuristic optimization algorithm, and also achieve scale matching with the algorithm's iteration cycle. This allows the light attenuation factor to smoothly transition from strong exploration to strong development throughout the entire iteration cycle, avoiding abrupt changes in stage switching that could lead to a decrease in algorithm stability.

[0039] 5. Iteration Stagnation Threshold and The value range is set to 10-50, with the optimal value being 30. For scenarios with a maximum of 100 iterations, this ensures that the algorithm has enough time to complete global exploration in the early stages of iteration, while also being able to identify stalled states in a timely manner in the later stages of iteration and trigger the escape mechanism, thus balancing the algorithm's convergence and global optimization capabilities.

[0040] After completing the parameter configuration, the terminal will pass the initial population and algorithm parameters to the subsequent fitness calculation and iterative optimization stages.

[0041] Step S3 uses binarization mapping to convert continuous values ​​into discrete feature selection vectors, constructs a composite fitness function, and calculates the fitness value of each individual fruit.

[0042] First, a binary mapping from continuous values ​​to binary values ​​is performed. This embodiment uses a mapping mechanism based on the Sigmoid function. This mechanism can achieve a smooth conversion from continuous values ​​to discrete values, avoiding the problems of discontinuous optimization process and unstable algorithm convergence caused by hard threshold mapping. It is perfectly adapted to the iterative logic of continuous metaheuristic algorithms, and is specifically divided into two steps: The first step is to map the continuous values ​​of individual fruits to the probability of a feature being selected using the Sigmoid function. The formula for the Sigmoid function is: ;in, It represents the continuous value of the i-th fruit individual in the j-th dimension, which comes from the individual vector updated during the algorithm iteration process; This is the mapped probability value, whose range is strictly limited to the interval (0,1), representing the probability that the j-th medicinal quality feature is selected. The Sigmoid function has a smooth S-shaped curve, which can map any real number to the probability interval between 0 and 1, and its gradient is maximum near the value of 0. This allows the optimization process of the algorithm to maintain continuous differentiability, ensuring the stability of iterative updates.

[0043] The second step is to convert the mapped probability values ​​into binary feature selection vectors using a probability threshold. The conversion formula is as follows: ;in, This indicates that the j-th quality characteristic of a traditional Chinese medicine has been selected and included in the feature subset of the subsequent regression model. The j-th medicinal quality feature is excluded and not included in the regression model. In this embodiment, 0.5 is used as the probability threshold. This threshold is the optimal symmetric threshold without prior information, which can ensure the unbiasedness of the mapping process and will not tend to select too many or too few features in the initial stage of the algorithm. It ensures that the algorithm selects each feature based on an objective assessment of its efficacy contribution, rather than the bias of the initial mapping.

[0044] Furthermore, through the above two mapping steps, the D-dimensional continuous vector of each fruit individual will be converted into a D-dimensional 0-1 binary vector that matches the feature dimension. This vector directly corresponds to a feature subset, realizing the transformation from a continuous optimization space to a discrete feature selection problem.

[0045] Subsequently, the terminal constructs and calculates a composite fitness function. The selection of dose-effect features for traditional Chinese medicine (TCM) has two core optimization objectives: the first is to maximize the prediction accuracy of the feature subset for pharmacological effects, i.e., to minimize the model's prediction error, which is the core premise for dose-effect relationship analysis; the second is to minimize the number of selected features, eliminating redundant and irrelevant TCM substances, reducing model complexity, and improving the model's generalization ability and interpretability—this is the core purpose of feature selection. Traditional single-objective fitness functions only focus on prediction accuracy, leading the algorithm to tend to select all features, failing to realize the core value of feature selection. Therefore, this embodiment constructs a composite fitness function that integrates both optimization objectives, achieving a balanced optimization of the two goals.

[0046] The formula for the composite fitness function is: Where F is the composite fitness value, which is the core objective of the algorithm optimization. The optimization direction of the algorithm is to minimize the F value. The smaller the F value, the better the comprehensive performance of the feature subset corresponding to the individual fruit. The weighting coefficients for prediction accuracy. The weight coefficients for feature simplification, and satisfying... This ensures the normalization of the two weights and avoids weight imbalance. The root mean square error of the partial least squares (PLS) regression model based on 10-fold cross-validation is used to quantify the predictive power of feature subsets on pharmacological effects. The smaller the value, the higher the prediction accuracy of the feature subset. Select the number of features to choose from the current binary feature vector, i.e., the number of 1s in the vector. This represents the total number of input features, i.e., the dimension of the feature set. The feature selection ratio, with a value between (0,1), is used to quantify the conciseness of the feature subset. The smaller the value, the fewer features are selected, and the simpler the model.

[0047] Regarding the weighting coefficients, this embodiment sets... The value range is 0.7-0.95. The value range is 0.05-0.3, and the optimal value is... =0.9, =0.1. The core premise of dose-effect relationship research in traditional Chinese medicine is to ensure the accuracy of efficacy prediction. The purpose of feature selection is to eliminate redundant features without sacrificing prediction accuracy; therefore, the weight of prediction accuracy must be higher than the weight of feature simplicity. If Too small If the number of features is too large, the algorithm will excessively pursue the reduction of the number of features, leading to the removal of key pharmacologically active substances, a significant drop in prediction accuracy, and the loss of the significance of dose-effect relationship analysis; if Too big If the weights are too small, the algorithm will focus excessively on prediction accuracy, failing to effectively drive the algorithm to remove redundant features and thus failing to achieve the core purpose of feature selection. The optimal weight combination of 0.9 and 0.1, verified through comparative experiments on multiple sets of traditional Chinese medicine dose-effect datasets, ensures that the algorithm prioritizes prediction accuracy while effectively driving the algorithm to remove redundant features, achieving the optimal balance between prediction accuracy and model simplicity.

[0048] In the fitness calculation process, this embodiment uses a partial least squares regression model as the basic prediction model and employs ten-fold cross-validation for calculation. The specific implementation steps are as follows: Traditional Chinese medicine (TCM) compound dose-effect data are characterized by small sample size, high feature dimensionality, and strong multicollinearity among features. Traditional multiple linear regression models often suffer from unstable model parameters and poor generalization ability when dealing with multicollinear data. However, partial least squares regression (PLR) is a multivariate statistical method that combines principal component analysis, canonical correlation analysis, and multiple linear regression. It can effectively handle small sample size, high dimensionality, and multicollinearity data, perfectly adapting to the unique characteristics of TCM dose-effect relationship data and ensuring the stability and prediction accuracy of the model.

[0049] For the number of latent variables in the partial least squares regression model, this embodiment sets it to the smaller value between the number of selected features and 5, with a minimum value of 1. Latent variables are orthogonal composite variables extracted from the original features in the partial least squares regression model. Too many latent variables can lead to overfitting of the training data and a significant decrease in generalization ability; too few latent variables can prevent the model from fully extracting the efficacy information from the features, resulting in insufficient prediction accuracy. The sample size of traditional Chinese medicine dose-effect data is usually small, and the model is prone to overfitting if the number of latent variables exceeds 5. Therefore, the upper limit for the number of latent variables is set to 5. At the same time, the number of latent variables cannot exceed the number of selected features, otherwise a singular matrix problem will occur. Therefore, it is ultimately set to the smaller value between the number of selected features and 5 to fundamentally avoid overfitting and matrix singularity problems, ensuring the stability and generalization ability of the model.

[0050] Furthermore, regarding 10-fold cross-validation, the implementation process in this embodiment is as follows: The preprocessed dataset is randomly divided into 10 non-overlapping subsets with balanced sample sizes. Nine subsets are selected as the training set each time, and the remaining subset is used as the test set. Based on the current feature subset, a partial least squares regression model is fitted on the training set, and the root mean square error (RMSE) between the predicted and actual values ​​is calculated on the test set. This process is repeated 10 times, with each subset used as a test set once. Finally, the average of the 10 MMS errors is taken as the result. The sample size of dose-effect data for traditional Chinese medicine is relatively small, and the results of a single split between the training and test sets are highly random. Ten-fold cross-validation can fully utilize the limited sample data to comprehensively evaluate the model's generalization ability. It can more objectively reflect the true predictive ability of feature subsets, avoid the algorithm from being guided by accidental good results to make incorrect evolution, and ensure the stability and reliability of the optimization process.

[0051] Furthermore, after calculating the fitness values ​​of all individual fruits, the terminal transmits the fitness values ​​to the subsequent population sorting and iterative optimization stages, and records the individual with the smallest fitness value in the current population as the globally optimal individual, and updates the globally optimal fitness value.

[0052] Step S4: Based on the adaptive hierarchical iterative optimization strategy, complete the iterative update of the population.

[0053] At the start of each iteration, the number of retained fruits and the number of thinned fruits are first calculated based on a nonlinear adaptive shrinkage strategy. Then, based on the fitness values ​​calculated in the previous step, all individuals in the population are sorted in ascending order to divide the population into a retained fruit group and a thinned fruit group. Next, the light attenuation factor of the current iteration is calculated to determine the optimization stage of the current iteration. Then, the update operator corresponding to the stage is executed on the retained fruit group, and a high-perturbation global search update strategy is executed on the thinned fruit group. Finally, the two updated groups are merged to obtain a new generation of fruit population, completing one iteration update.

[0054] First, a nonlinear adaptive shrinkage strategy is implemented, inspired by the natural fruit thinning mechanism in fruit tree growth: in the early stages of growth, fruit trees retain a large number of young fruits, and as the growth cycle progresses, they gradually remove weaker fruits, concentrating limited nutrients on the dominant fruits to ultimately ensure fruit quality and yield. This strategy maps this biological mechanism into the algorithm, achieving adaptive dynamic shrinkage of the population size. In the early iterations, the population size is large to ensure sufficient global exploration; in the later iterations, the population size shrinks, concentrating computational resources on finely developing the neighborhood of the dominant solution, improving convergence accuracy and computational efficiency.

[0055] The formula for calculating population shrinkage is: Formula 2 Formula 3 in, This represents the number of retained results in the current iteration. t is the number of results removed in the current iteration; t is the current iteration number; T is the maximum iteration number; m is the lower limit of the proportion of results retained, with an optimal value of 0.2. The floor symbol ensures that the number of retained and removed fruits are positive integers, which conforms to the counting logic of the population.

[0056] Furthermore, this advantage can be clearly demonstrated through extreme case analysis of the formula: in the initial stage of iteration, t=0, at this time... ,therefore In other words, all individuals are treated as retained fruits in the initial iteration and participate in the global exploration, ensuring that the search range is maximized in the initial stage, which perfectly matches the biological principle of retaining all young fruits in the early stage of fruit tree growth.

[0057] At the end of the iteration, t=T, at this time ,therefore This means that at the end of the iteration, only a fixed proportion of dominant individuals are retained as surviving fruits, and concentrated local intensive development is carried out, which matches the biological law that only a small number of dominant fruits are retained for ripening at the end of the fruit tree's growth.

[0058] Furthermore, after calculating the number of retained and removed fruits, the terminal performs population stratification: all fruits from the previous generation are sorted in ascending order of fitness value from smallest to largest, and the sorted individuals are ranked... Individuals with lower fitness values ​​and better overall performance in their corresponding feature subsets are classified as the retained fruit group; the remaining individuals... Each individual is divided into a thinning fruit group.

[0059] Subsequently, the terminal divides the calculation and optimization phases of the light attenuation factor. The light attenuation factor is the core regulatory factor in the algorithm that controls the switching between the exploration and development phases. It comes from the Beer-Lambert law in forest ecology, which states that light intensity decreases exponentially with the increase of plant canopy thickness. Correspondingly, in the fruit tree growth process, as the growth cycle progresses, the available light and nutrient resources gradually decrease, and the fruit growth gradually shifts from the initial rapid expansion (corresponding to the exploration phase of the algorithm) to the later nutrient accumulation (corresponding to the development phase of the algorithm).

[0060] The formula for calculating the optical attenuation factor is: Formula 4 in, The function is to introduce random perturbations into the light attenuation factor within the interval (-1, 1), preventing the algorithm from having a fixed search direction, enhancing the diversity of the population, and allowing the value of C to vary. Dynamic changes within the interval; t is the decay coefficient, with an optimal value of 0.002767; t is the current iteration number.

[0061] As the number of iterations t increases, The value of C decreases exponentially, therefore the expected value of C also decreases exponentially. In the early stages of iteration, the value of C is relatively large, indicating the algorithm is in the exploration phase; in the later stages of iteration, the value of C is relatively small, indicating the algorithm is in the development phase. In this embodiment, 0.5 is set as the threshold for phase division. That is, when |C|≥0.5, the algorithm enters the exploration phase; when |C|<0.5, the algorithm enters the development phase.

[0062] Next, update operators are executed for the surviving fruit population at the corresponding stages. First is the pollination update operator for the exploration stage, executed when |C|≥0.5. Based on the self-pollination and cross-pollination mechanisms of fruit trees, self-pollination ensures the stable inheritance of dominant traits, corresponding to the algorithm's local search near the current optimal solution; cross-pollination enables gene recombination between different individuals, introducing new traits, corresponding to the algorithm's global search. By randomly switching between the two pollination methods, the exploration stage is ensured to maintain effective information about dominant solutions while also fully expanding the search range.

[0063] In the pollination update operator, growth regulators This is the core parameter controlling the individual update step size. Its function is to simulate the disturbance of environmental factors on fruit growth during the fruit tree growth process. Simultaneously, the Levy flight mechanism is introduced to enhance the algorithm's ability to escape local optima. The formula for calculating the growth regulation factor is: Formula 5 in, The value is the disturbance amplitude control constant, ranging from 0.0005 to 0.005, with an optimal value of 0.001. This is the attenuation term, which follows the same attenuation law as the light attenuation factor. Its function is to gradually reduce the perturbation amplitude as the iteration progresses. The perturbation is large in the early stage of the iteration, which enhances the global exploration capability, and the perturbation is small in the later stage of the iteration, which ensures the stability of convergence. This is completely consistent with the stage switching logic of the algorithm. This is the Levy flight stride, used to simulate sudden environmental disturbances during fruit growth.

[0064] The formula for calculating Levy's flight stride is: Formula Six Wherein, 0.005 is the step size scaling factor, which is used to scale the step size of Levy flight to a scale that matches the search space, so as to avoid the individual jumping out of the effective search space due to excessively large step size; and Let be a random variable that follows a uniform distribution on the interval [0,1]. The scale parameter controls the tail thickness of the Levy distribution. The smaller the value, the thicker the tail of the distribution, and the higher the probability of large step sizes appearing. The larger the step size, the thinner the tail of the distribution, the lower the probability of large step sizes appearing, and the more concentrated the step size is within a small range. For based on The distribution scale parameter is calculated using the following formula: Formula 7 in, is the gamma function, a standard function in statistics used to describe the Levy distribution and to achieve a continuous extension of the factorial.

[0065] In this embodiment, the scale parameter The setting is dynamically changed with the number of iterations, and the dynamic change formula is: Formula 8 In the early stages of the iteration Approaching 0, At this point, the tail of the Levy distribution is relatively thick, the probability of large strides is high, the algorithm has strong global exploration ability, and can fully cover the entire search space; at the end of the iteration, Approaching 1, At this point, the Levy distribution degenerates into a Gaussian distribution, the step size is concentrated in a small range, the algorithm has strong local exploitation ability, and can perform fine search in the neighborhood of the optimal solution.

[0066] Meanwhile, this embodiment sets a sign correction rule for the Levy flight step size: when the lower bound of the input feature value is... hour, ;when hour, Keep the original value.

[0067] Furthermore, after calculating the growth regulators, the terminal performs updates for self-pollination and cross-pollination. First, the self-pollination operator corresponds to the stable inheritance of individual traits, while simultaneously introducing guidance from the globally optimal individual to ensure the search direction moves towards the optimal solution region. The formula for calculating the evolutionary components of the self-pollination operator is: Formula Nine in, The value of the currently globally optimal individual in the j-th dimension corresponds to the feature subset with the best overall performance found by the algorithm, which serves as the search guide for the entire population. A uniformly distributed random number within the interval (0,1), used to control the scaling ratio of individual characteristics. During the update process, individuals introduce mutations, enhancing their ability to withstand local perturbations; Let be the value of the i-th retained result in the j-th dimension; The absolute value sign ensures the amplitude of the evolutionary components is positive, preventing directional cancellation; C is the light attenuation factor, controlling the amplitude of the evolutionary components. C is larger in the early stages of iteration. It has a large range, strong global search capability, and small C value in the later stages of iteration. It has a small amplitude, strong local search capability, and perfectly matches the stage logic of the algorithm.

[0068] Following this is the cross-pollination operator, which corresponds to gene recombination between different individuals, introducing diversity information within the population and enhancing global search capabilities. The formula for calculating the evolutionary components of the cross-pollination operator is: Formula 10 in, A uniformly random number within the interval (0,1) is used to adjust the guidance strength of the globally optimal individual. The random fluctuations correspond to the uncertainty of pollen source during cross-pollination, thus enhancing population diversity; Let be the value of the k-th randomly selected individual in the population in the j-th dimension, and This ensures that information from other individuals is introduced, enabling gene recombination between different individuals; the definitions of the remaining parameters are consistent with those of the self-pollination operator.

[0069] The two pollination methods are selected using random numbers, and the individual update rule is as follows: Formula Eleven in, The uniform random number in the interval (0,1) is used to randomly select two pollination methods with a selection probability of 50% for each method. This ensures that the execution probabilities of the two operators are balanced, which not only guarantees the stable inheritance of the dominant traits but also fully introduces population diversity. It is the value of the j-th dimension of the i-th individual in the current iteration. It is the value of the next iteration; the first term The first term is the individual's current baseline value, corresponding to the individual's existing trait baseline; the second term is the growth regulation term, corresponding to the impact of environmental disturbances on individual growth, introducing the random step size of Levy flight; the third term is the pollination evolution term, corresponding to the trait changes brought about by the pollination process, guiding the individual to move closer to the global optimal solution.

[0070] When C < 0.5, the algorithm enters the development phase, and the surviving fruit population executes the local development operator. At this point, the surviving fruit population no longer conducts a large-scale global exploration, but instead performs local fine-tuning around the globally optimal individual. This operator is inspired by the source-sink theory in plant physiology, which states that well-developed dominant fruits have higher sink strength, attract more assimilates, and concentrate nutrients for expansion and ripening. Correspondingly, in the algorithm, dominant individuals perform fine-tuning searches around the globally optimal solution, improving convergence accuracy.

[0071] The local development operator first calculates the nutrient regulation component, using the following formula: ;Formula 12 The core of the nutrient regulation component is calculating the residual between the current individual and the globally optimal individual, and controlling the correction magnitude of the residual through the light attenuation factor C. After entering the development phase... And it continues to decay, therefore The amplitude will gradually decrease as the iteration progresses, and the corresponding algorithm will gradually shift from coarse tuning to fine tuning to ensure that the individual can converge smoothly to the global optimal solution, and avoid oscillations around the optimal solution due to excessive step size, which would prevent stable convergence.

[0072] Then, an individual update is performed, using the following formula: Formula Thirteen During the development phase, individual updates are no longer based on the individual's current position, but instead directly on the globally optimal individual. With this as the core, we ensure that all remaining individual results perform local searches around the globally optimal solution, concentrating computational resources to improve convergence accuracy. The first term... The first term is the value of the globally optimal individual, which serves as the core benchmark for updates; the second term... The first term is the environmental regulation term, which introduces a small random perturbation to the optimal solution through growth regulation factors to prevent all individuals from converging to the same point, thus avoiding the loss of population diversity and getting trapped in a local optimum; the third term... It is a residual correction term, used to correct the gap between the current individual and the optimal solution, guiding the individual to converge toward the optimal solution.

[0073] Furthermore, while updating the remaining fruit population, the terminal executes a high-perturbation global search update strategy on the thinned fruit population. The thinned fruit population consists of disadvantaged individuals within the population, whose corresponding feature subsets exhibit poor overall performance and are far from the current global optimum. Therefore, they do not participate in local development but instead execute a high-perturbation global search strategy. This strategy originates from risk-sensitive foraging theory, which states that when individuals are in a resource-deficient disadvantageous state, they tend to engage in high-risk, high-reward search behaviors to find better resource areas. In the corresponding algorithm, the thinned fruit population explores new optimal solution regions throughout the search space through significant random perturbation, supplementing the population's diversity and preventing the algorithm from getting trapped in local optima.

[0074] The update settings for thinning fruit have two modes, selected by random number generation, with the update rules as follows: Formula Fourteen in, The number is a uniformly random number in the interval (0,1), used to randomly select two update modes, each with a selection probability of 50%, to ensure the balanced execution of the two search modes; As the attenuation term, it follows the same attenuation law as the light attenuation factor, allowing the search step size of the sparse result to gradually decrease as the iteration progresses. The step size is large in the early stage of the iteration, resulting in strong global exploration capability, while the step size decreases in the later stage of the iteration, gradually moving closer to the optimal solution region and avoiding invalid searches in the later stage of the iteration. It is the Levy flight step size, which introduces strong random perturbations to the update of thinning results, thereby enhancing the global search capability; , The search uses uniformly random numbers within the interval (0,1) and introduces random scaling to enhance the diversity of the search. This is the value of the currently thinned fruit individual. It represents the value of the globally optimal individual.

[0075] The first mode uses the current position of the thinned-out individual as the center for perturbation search. This individual explores a large area around its current solution region to determine if any undiscovered optimal solutions exist, avoiding overlooking potential optimal solution regions. The second mode uses the position of the globally optimal individual as the center for perturbation search. This individual moves closer to the current optimal solution region while introducing a significant perturbation, exploring a large area around the optimal solution region to find solutions better than the current global optimum, supplementing the search range of the remaining individuals. By randomly switching between these two modes, the thinned-out individuals can both conduct a large-scale global exploration throughout the search space and move closer to optimal solution regions, avoiding ineffective computations caused by completely random searches. Simultaneously, it continuously introduces new diversity into the population, effectively preventing the algorithm from getting trapped in local optima.

[0076] Furthermore, after completing the update of all individuals of the retained and thinned fruits, the terminal merges the two updated populations to obtain a new generation of fruit populations. The new generation of populations is then introduced into the next round of fitness calculation, completing one iteration cycle.

[0077] Step S5 monitors the change in the global optimal fitness value. When the stagnation judgment condition is met, the individual regeneration operation is performed to achieve stagnation escape.

[0078] First, the stall state is determined. In this embodiment, the stall determination condition is set as follows: when the iteration number reaches a certain threshold... and continuous When the historical best value has not improved, the algorithm is considered to have entered a stagnant state. and The optimal value for all of them is 30.

[0079] When the stagnation condition is met, the terminal executes an individual regeneration strategy. In this embodiment, the individual regeneration strategy does not reset the entire population, as doing so would affect convergence efficiency and waste resources. To enable the algorithm to efficiently escape local convergence, this method only reinitializes individuals whose current fitness value equals their historical best value.

[0080] The formula for individual reinitialization is: Formula Fifteen in, For the value of the individual in the j-th dimension to be reinitialized, For the search interval in the j-th dimension Uniform random sampling is performed within the population, which is completely consistent with the sampling method in the initialization phase. This allows the selected individuals to generate a completely new candidate solution that is uniformly distributed in the search space, introducing new diversity into the population and driving the algorithm to break out of local optima and continue the global search.

[0081] After each individual regeneration operation is completed, the terminal will pass the updated population to the fitness calculation stage of the next iteration; if the stagnation judgment condition is not met, it will directly enter the next iteration.

[0082] Step S6 determines whether the iteration should terminate. If the termination condition is met, the optimal feature subset and the analytical model of the quantity-efficiency relationship are output.

[0083] First, the iteration termination judgment is executed. In this embodiment, the iteration termination condition is set as follows: when the number of iterations t reaches the preset maximum number of iterations T, the iteration loop of the algorithm is terminated.

[0084] After the iteration terminates, post-processing operations are performed. The specific process is as follows: The first step is to extract the globally optimal fruit individual: from the final population, extract the globally optimal individual with the smallest fitness value. This individual corresponds to the candidate solution with the best overall performance found by the algorithm throughout the entire iteration process. The second step is to obtain the optimal feature subset through binarization mapping: the continuous vector of the global optimal individual is mapped to a binary feature selection vector through the Sigmoid function in step S3 and the probability threshold of 0.5. The medicinal substances corresponding to the dimensions with a value of 1 are the key pharmacodynamic substances selected. These substances together form the optimal feature subset. The third step is to refit the partial least squares regression model: Based on the selected optimal feature subset, the partial least squares regression model is refitted using all the dose-effect datasets of traditional Chinese medicine compound prescriptions to obtain the final quantitative analytical model of the dose-effect relationship of traditional Chinese medicine compound prescriptions. This model can accurately characterize the quantitative relationship between key active substances and pharmacological effects, and achieve accurate analysis of the dose-effect relationship of traditional Chinese medicine compound prescriptions.

[0085] The final output consists of two parts: first, the optimal feature subset, which is the list of key pharmacodynamic substances selected, providing data support for the pharmacodynamic material basis research of traditional Chinese medicine compound prescriptions; second, the final partial least squares regression model, including the model's regression coefficients, prediction accuracy indicators, latent variable information, etc., providing a quantitative analysis model for dosage optimization, efficacy prediction, and compatibility mechanism analysis of traditional Chinese medicine compound prescriptions.

[0086] Example 2 Using the dose-response relationship experimental data of Da Chengqi Decoction in the treatment of acute simple intestinal obstruction as the core validation carrier, this study systematically verified the effectiveness and superiority of the Binary Fruit Growth Optimization (BFGO) algorithm in the identification of key active substances in traditional Chinese medicine compound prescriptions and the quantitative analysis of dose-response relationship through multi-algorithm horizontal comparison, multi-dimensional index evaluation and non-parametric statistical significance test. The study also clarified the application value of this algorithm in the selection of dose-response characteristics of traditional Chinese medicine.

[0087] Preferably, this embodiment employs a smoothing mapping mechanism based on the Sigmoid function to convert the continuous fruit growth factor components generated by the FGO algorithm iterations into binary variables representing the "selection / removal" of corresponding features. This retains the global search advantage of the FGO algorithm in continuous space while effectively transforming the search process into a discrete feature combination optimization problem. The specific mapping formula is as follows: Formula Sixteen Formula 17 in, For the first The first fruit individual The continuous growth factor components of the dimension are derived from the iterative update results of the FGO algorithm; The selected probability of the mapped feature is strictly limited to the range of (0,1); Indicates the first The specific characteristics of the drugs were selected and incorporated into the subsequent regression model. This indicates that the substance has been removed.

[0088] In this embodiment, the core objectives of selecting dose-effect features for traditional Chinese medicine compound prescriptions include two dimensions: first, maximizing the predictive accuracy of the feature subset for pharmacological effects to ensure the accuracy of dose-effect relationship analysis; and second, minimizing the number of selected features to eliminate redundant and irrelevant substances and improve the interpretability of the model. Based on this, this embodiment constructs a composite fitness function that integrates both objectives. The core basis for the BFGO algorithm's optimization is as follows: Formula 18 in, The root mean square error is calculated based on partial least squares (PLS) regression combined with ten-fold cross-validation. The smaller this value, the stronger the explanatory power of the current feature subset for the pharmacological effect index, and the better the model prediction effect. The number of features selected for the current feature subset. The total number of input features is represented by this term, which serves as a penalty to suppress the introduction of redundant features and drive the algorithm to select a more compact subset of features.

[0089] This embodiment, based on the core framework of the FGO algorithm and combining the aforementioned binarization mapping mechanism and composite fitness function, establishes a BFGO algorithm for selecting dose-effect characteristics of traditional Chinese medicine. The complete execution flow of the BFGO algorithm can be found in [reference needed]. Figure 2 The flowchart shown is for the BFGO algorithm.

[0090] To systematically verify the performance of the BFGO algorithm, this embodiment uses the dose-effect relationship experimental data of Da Chengqi Decoction as the verification carrier, sets up multiple sets of comparison algorithms, unified evaluation indicators and standardized parameter configurations to ensure the fairness, repeatability and reliability of the experimental results.

[0091] This embodiment uses seven sets of dose-response relationship experimental data of Da Chengqi Decoction in the treatment of acute simple intestinal obstruction, which are divided into 12 standardized dose-response relationship subsets. These subsets cover multiple pharmacodynamic endpoints during the treatment of acute intestinal obstruction with Da Chengqi Decoction, including small intestinal pathological changes, inflammatory factor levels, gastrointestinal motility indicators, tissue damage scores, mortality, and food intake and defecation. The input features of the datasets are the concentrations of 20 quantitatively detectable active substances of traditional Chinese medicine, such as rhein, rhein, sennoside, gallic acid, magnolol, and chlorogenic acid, in the decoction of Da Chengqi Decoction. The output response variables are the corresponding pharmacodynamic evaluation indicators, fully covering the typical scenarios of dose-response relationship research of traditional Chinese medicine compound prescriptions.

[0092] Furthermore, to verify the superiority of the BFGO algorithm, this embodiment selects five mainstream binary heuristic feature selection algorithms as horizontal comparison objects, namely the Binary Groundhog Optimization Algorithm (BTHRO), the Binary Harris Eagle Optimization Algorithm (BHHO), the Binary Particle Swarm Optimization Algorithm (BPSO), the Binary Gray Wolf Optimization Algorithm (BGWO), and the Binary Whale Optimization Algorithm (BWOA). The above algorithms are all classic algorithms with wide application and excellent performance in the field of feature selection, and the comparison results have sufficient industry representativeness.

[0093] Furthermore, to ensure the fairness of the experimental results, all algorithms in this embodiment use the same basic parameter settings: the population size is fixed at [value missing]. The maximum number of iterations is fixed. The random seed was fixed at 42, and all algorithms employed the same binarization mapping mechanism, composite fitness function, and cross-validation partitioning strategy. During the regression modeling phase, the number of latent variables in the PLS model for all algorithms was set to the smaller of the number of selected features and a preset upper limit value. The preset upper limit value was set to 5 to balance modeling capability and numerical stability, while avoiding the risk of overfitting.

[0094] The experimental results of six binary meta-heuristic optimization algorithms on the dose-effect relationship dataset of traditional Chinese medicine are shown in the table below:

[0095] Overall, the prediction performance of the six algorithms differed significantly across the 12 quantity-effect relationship datasets. The BFGO algorithm proposed in this invention demonstrated the best prediction ability on most datasets and maintained high stability in both RMSE and MAE metrics.

[0096] On the CG, GD(y2), FI, and TW(y4) datasets, BFGO achieved the best results among all algorithms in both RMSE and MAE, demonstrating a particularly significant advantage. Taking the CG dataset as an example, BFGO's RMSE was only 0.0610, far lower than the best-performing algorithm of 0.1264, resulting in a 51.7% improvement in prediction accuracy. On the FI dataset, BFGO's RMSE was 0.6426, a 12.6% improvement compared to the second-best performing BPSO algorithm, fully validating BFGO's core advantages in identifying key pharmacodynamic substances.

[0097] On the GD(y1), TW(y1), and TW(y2) datasets, BFGO achieved completely consistent prediction results with the best-performing BTHRO algorithm, reaching the optimal prediction level on these datasets. This indicates that BFGO has stable performance comparable to the mainstream best algorithm in this type of scenario.

[0098] On the CW, GD(y3), MR, and TW(y3) datasets, although BFGO did not achieve the best results, it was still significantly better than most of the comparison algorithms such as BHHO and BWOA, and was in the second tier overall. It did not show large fluctuations in prediction performance and demonstrated strong robustness.

[0099] Based on the results of 12 datasets, BFGO achieved the best or tied best prediction results on 8 datasets and maintained a good prediction level on the remaining 4 datasets without any obvious performance shortcomings. This indicates that BFGO can achieve the best balance between global exploration and local development in the feature search process, effectively identify the Chinese medicinal substances that play a key role in drug efficacy prediction, and significantly improve the prediction accuracy of the dose-effect relationship model.

[0100] While ensuring prediction accuracy, this embodiment further compares the size of the feature subsets selected by different algorithms to evaluate the algorithm's feature compression capability and model simplification. Please refer to [link to relevant documentation]. Figure 3 As shown, the number of features selected by different algorithms on various datasets is compared. The statistical results show that the BFGO algorithm can achieve the best prediction performance with fewer or moderate numbers of features on most datasets, demonstrating a strong ability to remove redundant features.

[0101] On core datasets such as CW, CG, GD(y1), and FI, the number of features selected by BFGO is at a relatively low level among all algorithms, while the corresponding RMSE and MAE indices remain in the optimal range. This indicates that BFGO can effectively remove redundant and irrelevant substances in traditional Chinese medicine compound prescriptions and obtain a more compact subset of key pharmacodynamic substances while ensuring prediction accuracy.

[0102] Among the comparative algorithms, BHHO selects the fewest features on some datasets, but its prediction error is much higher than BFGO and other algorithms. This shows that simply reducing the number of features does not improve model performance. On the contrary, the removal of key elements will lead to a significant drop in prediction accuracy. BPSO and BGWO tend to select more features on most datasets, but their prediction performance is not better than BFGO. This shows that the introduction of redundant features not only fails to improve model performance, but also increases model complexity and reduces interpretability.

[0103] BFGO achieves a balance between "reasonable number of features and optimal prediction accuracy" on all datasets. It avoids losing key efficacy information due to excessive pursuit of feature simplification, and also avoids affecting model performance by introducing too many redundant features, perfectly meeting the core requirements for the selection of dose-effect features in traditional Chinese medicine compound prescriptions.

[0104] Preferably, statistical significance testing was performed. To verify whether the performance differences of different algorithms on the dose-response relationship dataset were statistically significant, this embodiment conducted Friedman's nonparametric test on six algorithms based on the RMSE index results of 12 datasets. The test results showed that the Friedman statistic was 31.5250, with a corresponding p-value of 7.38 × 10⁻⁶. -6 The p-value is much smaller than the significance level of 0.05, so the null hypothesis that "there is no difference in the performance of the algorithms" can be rejected, proving that the performance differences of the six feature selection algorithms on the RMSE index are statistically significant, and the performance improvement of BFGO is not caused by random fluctuations.

[0105] Based on the statistical significance test, this embodiment further calculated the average rank of each algorithm on 12 datasets. The smaller the average rank value, the better the overall performance of the algorithm. The specific results are as follows: Figure 4 As shown in the figure, the average ranking results show that BFGO has an average ranking of 2.125, ranking first among all six algorithms. This indicates that the method achieves better or near-optimal prediction performance on most datasets and has the most stable overall performance. BTHRO and BPSO follow, both with an average ranking of 2.792, placing them in the second tier. BGWO, BWOA, and BHHO have lower average rankings, indicating weaker overall performance than the first three algorithms. This result is completely consistent with the prediction error experimental results of the aforementioned datasets, further statistically verifying the overall superiority of BFGO in the selection of dose-effect characteristics for traditional Chinese medicine compound prescriptions.

[0106] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for screening the active ingredients of traditional Chinese medicine compound prescriptions based on a fruit growth optimization algorithm, characterized in that, Includes the following steps: Step S1 constructs a dose-effect relationship experimental dataset for traditional Chinese medicine compound prescriptions. The concentration of drug substances in the traditional Chinese medicine compound prescriptions is used as the input feature, and the corresponding pharmacological effect index is used as the output response variable. The dataset is standardized and preprocessed to obtain the feature set and label set. Step S2 generates N initial fruit individuals within a continuous search space that matches the input feature dimensions. Each fruit individual corresponds to a set of feature selection candidate solutions, and each dimension corresponds to a medicinal quality feature. The algorithm's maximum number of iterations, the proportion of retained fruits, the decay coefficient, and the iteration stagnation threshold are initialized. Step S3 maps the continuous values ​​of individual fruits to binary feature selection vectors using the Sigmoid function, filters feature subsets based on the binary feature selection vectors, constructs a partial least squares regression model, and constructs a composite fitness function by combining the prediction error of cross-validation with the proportion of feature subset size and calculating the fitness value of each individual fruit. In step S4, during each iteration, the number of retained results for the current iteration is calculated based on a nonlinear adaptive shrinkage strategy. With the number of fruits removed After sorting the population by fitness value, the remaining fruits are divided into retained fruits and thinned fruits; the light attenuation factor C is calculated, and according to the relationship between C and a set threshold, the pollination update operator in the exploration stage or the local development operator in the development stage is executed on the retained fruits respectively; the high-perturbation global search update strategy is executed on the thinned fruits to complete the population iterative update. During the S5 iteration process, the change of the global optimal fitness value is monitored in real time. When the stagnation judgment condition is met, a re-initialization operation is performed on the individuals that meet the condition to achieve population diversity update. Step S6: When the number of iterations reaches the maximum number of iterations T, the iteration is terminated. The optimal feature subset corresponding to the globally optimal fruit individual is output. Based on this optimal feature subset, the partial least squares regression model is refitted to obtain the quantitative analytical model of the dose-effect relationship of traditional Chinese medicine compound.

2. The method for screening active substances in traditional Chinese medicine compound prescriptions based on fruit growth optimization algorithm according to claim 1, characterized in that, In step S1, the dataset for the dose-effect relationship experiment of traditional Chinese medicine compound is a dataset constructed based on the dose-effect relationship experiment of traditional Chinese medicine compound compatibility. The experiment covers multiple active substances of traditional Chinese medicine that can be qualitatively and quantitatively detected in the compound compatibility system, as well as multiple quantifiable pharmacological and efficacy evaluation indicators corresponding to the efficacy of the compound compatibility. The input features of the dataset are the concentration data of multiple active substances of traditional Chinese medicine that can be qualitatively and quantitatively detected in the compound compatibility system in the experiment, and the output response variables are multiple quantifiable pharmacological and efficacy evaluation indicators corresponding to the efficacy of the compound compatibility in the experiment.

3. The method for screening active substances in traditional Chinese medicine compound prescriptions based on fruit growth optimization algorithm according to claim 1, characterized in that, In step S4, the calculation formula for the nonlinear adaptive contraction strategy is as follows: ； ； Where t is the current iteration number and T is the maximum iteration number. To determine the number of fruits to retain, To reduce the number of fruits, For floor operations, m is the lower limit of the percentage of results to be retained; The formula for calculating the optical attenuation factor C is as follows: ;in, A uniformly random number within the interval (-1, 1). The attenuation coefficient is set to 0.

5. When |C|≥0.5, the exploration phase begins, and when |C|<0.5, the development phase begins.

4. The method for screening active substances in traditional Chinese medicine compound prescriptions based on fruit growth optimization algorithm according to claim 1, characterized in that, In step S4, the pollination update operators in the exploration phase include self-pollination and cross-pollination operators. Two operators are randomly selected to perform individual updates. Simultaneously, a growth regulator with a Levy flight mechanism is introduced to control the update step size, specifically: Evolutionary component of the self-pollination operator Evolutionary components of cross-pollination operators ; The individual update rules are as follows: when hour, ; when hour, ; in, Let be the value of the globally optimal individual in the j-th dimension. Let be the value of the i-th fruit individual in the j-th dimension. Let be the value of the k-th random individual in the population in the j-th dimension. , , A uniformly random number within the interval (0,1). t represents the growth regulator, and t represents the current iteration number.

5. The method for screening active substances in traditional Chinese medicine compound prescriptions based on a fruit growth optimization algorithm according to claim 4, characterized in that, The growth regulator The calculation formula is: Where b is a constant. The attenuation coefficient is... This is the Levy flight step size, used to simulate random environmental disturbances.

6. The method for screening active substances in traditional Chinese medicine compound prescriptions based on fruit growth optimization algorithm according to claim 1, characterized in that, In step S4, the local development operator in the development phase first calculates the nutrient regulation component. Press again Perform individual updates; The high-perturbation global search update strategy for the thinned results selects two update modes using random numbers, with the specific rules as follows: when hour, ; when hour, ; in, Let be the value of the globally optimal individual in the j-th dimension. Let be the value of the i-th thinned fruit individual in the j-th dimension. , , A uniformly random number within the interval (0,1). As a growth regulator, Levy's flight stride length t is the decay coefficient, and t is the current iteration number.

7. The method for screening active substances in traditional Chinese medicine compound prescriptions based on fruit growth optimization algorithm according to claim 1, characterized in that, In step S5, the stagnation determination condition is: the number of iterations. and continuous The historical best value has not improved, among which and The value of is 30; the individuals that meet the conditions are those whose current fitness value is equal to the historical best value, and the formula for performing the re-initialization operation on them is: ;in, For the value of the individual in the j-th dimension to be reinitialized, For the j-th dimension search interval Uniform random sampling within, Let j be the lower bound of the values ​​in the j-th dimension. Let be the upper bound of the values ​​for the j-th dimension.

8. The method for screening active substances in traditional Chinese medicine compound prescriptions based on fruit growth optimization algorithm according to claim 1, characterized in that, In step S3, the formula for calculating the composite fitness function is: ;in, The root mean square error is calculated based on the partial least squares regression model and ten-fold cross-validation. The number of features selected for the current feature subset. The total number of input features is α, the prediction accuracy weight is α, and the feature descalability weight is β. The Sigmoid function mapping mechanism is specifically as follows: firstly, through... Calculate the mapping probability, and then convert it into a binary variable based on a threshold. ,when hour When the j-th medicinal quality characteristic is selected, hour The corresponding material characteristics of the j-th Chinese medicine were eliminated.

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