Improved education competition optimization algorithm based on distribution estimation algorithm

Abstract

The invention belongs to the technical field of educational competition, and particularly relates to an improved educational competition optimization algorithm based on a distribution estimation algorithm, which adopts a contour comparison method to extract graphic key feature points, establishes feature point matching pairs through a K-nearest neighbor matching algorithm, and optimizes the educational competition. The contour similarity is calculated in combination with the number of matched pairs, the average distance of standard graphic feature points and the coordinate deviation value, accurate quantization of graphic similarity is achieved, modeling data abnormal value detection is conducted on modeling data through a box graph method, reasonable discrete data and unreasonable data are effectively distinguished in combination with the quartile distance characteristic of the data, and the accuracy of the data is improved. Different feature point extraction modes and different data models are adopted for comparison of different types of data, it can be guaranteed that the data models are more practical, and the extracted data have higher reliability.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of educational competition, and particularly relates to an improved educational competition optimization algorithm based on a distribution estimation algorithm. BACKGROUND

[0002] In the current mathematical competition, the judgment of geometric figures and function image type problems mainly depends on artificial comparison by experts. Experts need to judge the similarity of the competition solution figures and standard figures by subjective experience, such as the position deviation of the vertex of the geometric figure, the accuracy of the extreme point of the function image, and the like, and there is a lack of unified quantitative standard. On the one hand, different experts have different tolerances for figure deviation, which leads to different scoring results for the same solution, and the objectivity of the judgment is insufficient. On the other hand, when artificially extracting the feature points of the figure, it is easy to miss, and the coordinate deviation proportion between the feature points cannot be accurately calculated, so it is difficult to accurately quantify the similarity of the figures, and thus the judgment accuracy of the figure type problems is low, which cannot meet the requirement of the mathematical competition on the scoring accuracy. Therefore, an improved educational competition optimization algorithm based on a distribution estimation algorithm is improved and designed. SUMMARY

[0003] In view of the above problems in the prior art, the application provides an improved educational competition optimization algorithm based on a distribution estimation algorithm to solve the problems in the background art.

[0004] In order to solve the above technical problems, the application adopts the following technical scheme:

[0005] An improved educational competition optimization algorithm based on a distribution estimation algorithm, characterized in that it comprises the following steps:

[0006] S1: data preprocessing, which comprises mathematical competition figure data processing, mathematical competition modeling data processing and missing data sample processing;

[0007] S2: dynamic hybrid probability model construction, adopting a twin model architecture, processing the mathematical competition figure data and the mathematical competition modeling data through a Gaussian distribution sub-model and a Bayesian network sub-model respectively, and respectively outputting the probability distribution parameters of the continuous variables of the mathematical competition figure data and the dependent relationship and probability parameters of the discrete variables of the mathematical competition modeling data, which together constitute a complete dynamic hybrid probability model;

[0008] S3: multi-objective optimization, constructing a three-dimensional optimization system of quality and effect, optimizing the matching degree of the mathematical competition figure data, the accuracy of the mathematical competition modeling data and the algorithm processing efficiency, obtaining the optimized mathematical competition figure data and the optimized mathematical competition modeling data, and generating a scheme according to the obtained optimized mathematical competition figure data and the optimized mathematical competition modeling data in combination with the NSGA-II algorithm;

[0009] S4: Results verification and feedback. The independent samples t-test is used as the significance verification method to verify the optimization effect of the optimized mathematical competition graphic data and mathematical competition modeling data in S3. At the same time, the scheme and the optimized mathematical competition graphic data and mathematical competition modeling data are fed back.

[0010] S5: Experience database call, which takes over the solutions fed back in step S4 as well as the data of mathematical competition graphic data and mathematical competition modeling data, and realizes the reuse of model parameters and optimization strategies.

[0011] Preferably, the mathematical competition graphic data processing step in step S1 is as follows:

[0012] The contour comparison method is used to convert the standard graphics of the competition questions and the graphics of the contestant's solutions into vector graphics format, extract the contour feature points of the graphics, and form a set of feature points S of the standard graphics and a set of feature points T of the solution graphics.

[0013] The K-nearest neighbor matching algorithm is used to find the nearest neighbor feature point in the standard graphic feature point set S for each feature point in the solution graphic feature point set T and establish a matching pair. If a feature point in the solution graphic feature point set T has no matching point in the standard graphic feature point set S, it is marked as an isolated point.

[0014] Then, the coordinate deviation of the matching feature point pairs and the proportion of isolated points to the total number of feature points are calculated. The similarity of the outlines of the standard graphic of the competition question and the graphic of the contestant's solution is calculated using the obtained coordinate deviation and the number of matching pairs.

[0015] Preferably, the mathematical competition modeling data processing step in step S1 is as follows:

[0016] All data samples of the modeling variables are sorted in ascending order, the modeling data are divided using the quartile method, and outlier detection is performed on the divided modeling data by setting an outlier judgment range.

[0017] Preferably, the missing data sample processing step in step S1 is as follows:

[0018] Find k samples in the experience database that are highly similar to graphical data processed from mathematical competition graphical data or modeling data processed from mathematical competition modeling data.

[0019] The similarity weights between k samples and graphical or modeling data are calculated, i.e., the weights are normalized.

[0020] After normalizing the weighted sum, the fill value is calculated according to the formula. ,in , For the first in the experience database The corresponding non-missing values ​​of the nearest neighbor samples.

[0021] Preferably, step S1 further comprises key feature variable screening, and the specific steps are as follows:

[0022] Set the core optimization result index: the accuracy rate of graphic data evaluation = the number of correct graphic matching questions / the total number of graphic questions; the accuracy rate of modeling data evaluation = the number of samples whose modeling scores are consistent with the artificial scores of experts / the total number of modeling samples;

[0023] The graphic data is layered according to the feature variables of geometric graphic data and function image data, and the modeling data is layered according to the modeling problem field. The within-group variance and between-group variance are calculated for each feature variable, and the influence weight is calculated through the within-group variance and the between-group variance. The feature variables with a weight reaching a threshold value are included in the candidate key feature set. Then, the correlation between the feature variables in the candidate key feature set is analyzed through the Pearson correlation coefficient, and the feature variables are further removed according to the weight. Then, the feature variables after further removal are input into a pre-validation model, and finally the key feature variable set is obtained.

[0024] Preferably, the three-dimensional optimization system in step S3 is specifically:

[0025] Graphic data matching degree: obtain the probability distribution parameters from the Gaussian distribution sub-model, calculate the absolute deviation of each feature variable value of the contestant's solution graphic from the standard graphic feature variable value, then perform weighted summation on each feature deviation to obtain the final quantitative value of the graphic data matching degree;

[0026] Modeling data accuracy: obtain the conditional probability table from the Bayesian network sub-model, calculate the deviation between the model prediction result and the standard result combined with the modeling data of the contestant team, and calculate the quantitative value according to the error type influence weight by comprehensively considering the modeling method selection error, variable constraint condition error and model solution result error;

[0027] Algorithm processing efficiency: standardize the total time from data preprocessing to output of the candidate scheme by multi-objective optimization to obtain the final quantitative value.

[0028] Preferably, step S3 further comprises three-dimensional optimization target weight coefficient distribution, and the specific steps are as follows:

[0029] Set the graphic data matching degree weight, the modeling data accuracy weight and the algorithm processing efficiency weight. The experts use the 1-9 scale method to compare and score the importance of any two optimization targets, calculate the average score of all expert scores, construct a 3x3 judgment matrix, then perform consistency check on the judgment matrix, calculate the characteristic vector of the judgment matrix by using the eigenvalue method after the consistency check is completed, and finally obtain the weight coefficients of the graphic data matching degree weight, the modeling data accuracy weight and the algorithm processing efficiency weight.

[0030] Preferably, the consistency check formula is: wherein , is 3, is the maximum eigenvalue of the judgment matrix, is the standard value found according to the authoritative standard index.

[0031] Preferably, the result verification and feedback specific steps in step S4 are:

[0032] Based on the small sample characteristics of education competition data, independent sample t test is used as the significance verification method, the verification objects include the matching accuracy of graphic data, the consistency of modeling data scores, and the actual processing time. The actual competition data is divided into experimental group and control group, the original hypothesis and alternative hypothesis are proposed for each verification index, the sample statistic is calculated, the t statistic is calculated by using the combined variance statistic formula, the one-sided critical value is obtained by t distribution table, and the hypothesis is judged by the p value output by independent sample t test. Finally, the verification results of the matching accuracy of graphic data, the consistency of modeling data scores and the actual processing time are obtained. The scheme that passes all three indexes is determined as the optimal scheme, and the scheme is fed back to the experience database.

[0033] Compared with the prior art, the present application has the following beneficial effects:

[0034] 1. The contour contrast method is used to extract the key feature points of the graph, the K nearest neighbor matching algorithm is used to establish the matching pairs of feature points, the contour similarity is calculated by combining the "number of matching pairs, average distance of standard graph feature points, coordinate deviation value", the accurate quantification of the graph similarity is realized, the scoring difference caused by the subjective experience of experts is avoided, and the explicit abnormal graph elimination threshold is set to automatically eliminate the abnormal graph, reduce the artificial screening workload, improve the judgment accuracy, the Gaussian distribution sub-model is constructed by grouping the geometric graphs and function images according to the graph type, the mean and variance of the continuous characteristic variables of each group are calculated, the parameter distortion caused by the mixing of cross-type data is avoided, and the accuracy of the probability distribution calculation of the graph characteristic variables is further improved; the box plot method is used for modeling data abnormal value detection, the reasonable discrete data and unreasonable data are effectively distinguished according to the quartile range characteristics of the data, the false deletion or omission is avoided, the missing values are filled by using the weighted adjacent algorithm, the samples with high similarity are given greater weight by using the distance reciprocal weighting method, the error is stabilized at 5% to 8%, and the missing data of different types can be adapted, then the feature variable weight is calculated by layering, the redundant variables are eliminated by combining Pearson correlation coefficient analysis, only the key features with a weight greater than or equal to 0.65 are reserved, the subjective experience bias of experts is avoided, and the influence weight of the feature variable on the modeling score is quantified by variance analysis, so that the modeling score is more consistent with the objective characteristics of the data, and the accuracy of the modeling question score is improved.

[0035] 2. By constructing the three-dimensional optimization system of "graph data matching degree, modeling data accuracy, algorithm processing efficiency", the quantification of the three optimization objectives is realized by weighted summation of feature deviation, comprehensive multi-type modeling error and standardized processing time; the weight of the optimization objective is determined by the 1-9 scale method combined with the analytic hierarchy process, the rationality of the weight is ensured through consistency test, the weight can be adjusted according to different competition scenes to meet the differentiated needs;

[0036] 3. According to the characteristics of small sample data of mathematical competition, the significance of the three optimization objectives of graph matching accuracy, modeling score consistency and processing time is verified by independent sample t test, only when the three indicators pass the verification, the strategy is determined to be effective, and the optimization effect is reliable, at the same time, a feedback mechanism is established, the cases of verification failure are fed back to the front-end module, triggering the model to iterate again, correcting the model deviation, improving the adaptation ability of the algorithm to complex scenes, and the robustness is significantly enhanced, and by constructing a three-level classification experience database, the reuse of the historical optimal parameters is realized, and the iteration time is greatly shortened. BRIEF DESCRIPTION OF DRAWINGS

[0037] Figure 1 The flowchart of the improved education competition optimization algorithm based on the distribution estimation algorithm. DETAILED DESCRIPTION

[0038] In order to enable those skilled in the art to better understand the present application, the technical solutions of the present application are further described below in conjunction with the drawings and examples.

[0039] Among them, the drawings are only used for illustrative explanation, and the representation is only a schematic diagram, not a physical diagram, and cannot be understood as a limitation on the patent; in order to better illustrate the embodiments of the present application, some components in the drawings will be omitted, enlarged or reduced, and do not represent the size of the actual product; for those skilled in the art, it is understandable that some known structures and their descriptions in the drawings can be omitted.

[0040] The same or similar reference numerals in the drawings of the embodiments of the present application correspond to the same or similar components; in the description of the present application, it should be understood that if the terms "upper", "lower", "left", "right", "inner", "outer" and the like indicate the orientation or positional relationship shown in the drawings, only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the devices or elements referred to must have a particular orientation, be constructed and operated in a particular orientation, therefore the terms describing the positional relationship in the drawings are only used for illustrative explanation, and cannot be understood as a limitation on the patent, for those skilled in the art, the specific meaning of the above terms can be understood according to the specific situation.

[0041] In the description of the present application, unless otherwise explicitly specified and limited, if the term "connection" and the like appear to indicate the connection relationship between components, the term should be understood broadly, for example, it can be fixedly connected, or detachably connected, or integrated; it can be mechanically connected, or electrically connected; it can be directly connected, or indirectly connected through an intermediate medium, or it can be the internal communication of two components or the interaction relationship between two components. For those skilled in the art, the specific meaning of the above-mentioned terms in the present application can be understood according to the specific circumstances.

[0042] Embodiment one:

[0043] As Figure 1 An improved education competition optimization algorithm based on distribution estimation algorithm, the present application comprises the following steps:

[0044] S1: data preprocessing, the data preprocessing includes mathematical competition graphic data processing, mathematical competition modeling data processing and missing data sample processing;

[0045] S2: dynamic hybrid probability model construction, adopting a twin model architecture, the Gaussian distribution sub-model and the Bayesian network sub-model are used to process the mathematical competition graphic data and the mathematical competition modeling data respectively, and the probability distribution parameters of the continuous variables of the mathematical competition graphic data and the dependent relationship and probability parameters of the discrete variables of the mathematical competition modeling data are output respectively, which together constitute a complete dynamic hybrid probability model;

[0046] S3: multi-objective optimization, a three-dimensional optimization system of quality and effect is constructed, the matching degree of the mathematical competition graphic data, the accuracy of the mathematical competition modeling data and the algorithm processing efficiency are optimized, and the optimized mathematical competition graphic data and mathematical competition modeling data are obtained, and a scheme is generated according to the obtained optimized mathematical competition graphic data and mathematical competition modeling data and in combination with the NSGA-II algorithm;

[0047] S4: result verification and feedback, independent sample t-test is used as a significance verification method to verify the optimization effect of the optimized mathematical competition graphic data and mathematical competition modeling data in S3, and the scheme is fed back to the optimized mathematical competition graphic data and mathematical competition modeling data;

[0048] S5: experience database calling, the scheme fed back in step S4 and the mathematical competition graphic data and mathematical competition modeling data are connected to realize the reuse of model parameters and optimization strategies.

[0049] The mathematical competition graphic data processing step in step S1 is:

[0050] The contour contrast method is used to convert the standard graph of the competition topic and the graph of the contestant's solution into a vector graph format, and the contour feature points of the graph are extracted to form a standard graph feature point set S and a solution graph feature point set T;

[0051] The K nearest neighbor matching algorithm is used to find the nearest feature point in the standard graph feature point set S for each feature point in the solution graph feature point set T, establish a matching pair, and mark a feature point in the solution graph feature point set T as an isolated point if there is no matching point in the standard graph feature point set S.

[0052] Then, the coordinate deviation of the matching feature point pair and the proportion of the number of isolated points to the total number of feature points are calculated, and the contour similarity of the standard graph of the competition topic and the graph of the contestant's solution is calculated through the obtained coordinate deviation and the number of matching pairs.

[0053] The mathematical competition modeling data processing step in step S1 is:

[0054] All data samples of the modeling variable are sorted in ascending order, the modeling data is divided by the quartile method, and the divided modeling data is subjected to outlier detection by setting an outlier judgment range.

[0055] The missing data sample processing step in step S1 is:

[0056] In the experience database, find k samples with high similarity to the graph data processed by the mathematical competition graph data or the modeling data processed by the mathematical competition modeling data.

[0057] The similarity weight of the k samples and the graph data or the modeling data is calculated, i.e. the weight is normalized.

[0058] After normalization of the weight sum, the filling value is calculated according to the formula , wherein , is the corresponding non-missing value of the i-th nearest neighbor sample in the experience database.

[0059] The key feature variable screening step in step S1 is:

[0060] The core optimization result index is set: the graph data evaluation accuracy = the number of correctly matched topics / the total number of graph topics; the modeling data evaluation accuracy = the number of samples with consistent modeling scores and artificial expert scores / the total number of modeling samples.

[0061] ​The geometric data is layered according to characteristic variables of geometric data and function image data, the modeling data is layered according to modeling problem fields, the intra-group variance and the inter-group variance are calculated for each characteristic variable, the influence weight is calculated through the intra-group variance and the inter-group variance, the weight reaching a threshold is included in the candidate key feature set, then the correlation between the characteristic variables in the candidate key feature set is analyzed through the Pearson correlation coefficient, and the characteristic variables are further removed according to the weight, then the further removed characteristic variables are input into a pre-validation model, and finally the key characteristic variable set is obtained.

[0062] The three-dimensional optimization system in step S3 is specifically:

[0063] The geometric data matching degree: the probability distribution parameters are obtained from the Gaussian distribution sub-model, the absolute deviation of each characteristic variable value of the competition solution and the standard characteristic variable value is calculated, then the weighted sum of each characteristic deviation is obtained, and the final quantitative value of the geometric data matching degree is obtained;

[0064] The modeling data accuracy: the conditional probability table is obtained from the Bayesian network sub-model, the deviation between the model prediction result and the standard result is calculated combined with the modeling data of the competition team, the quantitative value is calculated according to the error type influence weight, the error of the modeling method selection, the error of the variable constraint condition and the error of the model solving result;

[0065] The algorithm processing efficiency: the total time from data preprocessing to multi-objective optimization output candidate scheme is counted, and the final quantitative value is obtained by standardizing the time.

[0066] Step S3 further includes three-dimensional optimization target weight coefficient distribution, and the specific steps are:

[0067] The geometric data matching degree weight, the modeling data accuracy weight and the algorithm processing efficiency weight are set, the importance of any two optimization targets is compared and scored by experts using the 1-9 scale method, the average score of all expert scores is calculated, a 3x3 judgment matrix is constructed, then the judgment matrix is subjected to consistency check, the eigenvalue method is used to calculate the eigenvector of the judgment matrix after the consistency check is completed, and finally the weight coefficients of the geometric data matching degree weight, the modeling data accuracy weight and the algorithm processing efficiency weight are obtained.

[0068] The consistency check formula is: , wherein , is 3, is the maximum eigenvalue of the judgment matrix, is the standard value found according to the authoritative standard index.

[0069] The specific steps of the result verification and feedback in step S4 are:

[0070] Based on the small sample characteristics of the education competition data, the independent sample t test is used as the significance verification method. The verification objects include the matching accuracy of the graphic data, the consistency of the modeling data score, and the actual processing time. The actual competition data is divided into experimental group and control group. The null hypothesis and alternative hypothesis are proposed for each verification index. The sample statistic is calculated. The t statistic is calculated using the combined variance statistic formula. The one-sided critical value is obtained through the t distribution table. The hypothesis is judged through the p value output by the independent sample t test. Finally, the verification results of the matching accuracy of the graphic data, the consistency of the modeling data score, and the actual processing time are obtained. The scheme that passes all three indexes is determined as the optimal scheme, and the scheme is fed back to the experience database.

[0071] Data preprocessing module:

[0072] Graphic data processing:

[0073] The contour contrast method is used to process the graphic data. The standard graphic of the competition topic and the contestant's answer graphic are converted into vector graphic format. The contour feature points of the graphic are extracted. For geometric figures, the key coordinate points such as vertices, footpoints, and circle centers are extracted. For function images, feature coordinate points such as intersection points with coordinate axes, extreme points, and inflection points are extracted to form a standard graphic feature point set and answer graphic Then, the K nearest neighbor matching algorithm is used to find the nearest feature point in the answer graphic for each feature point in the standard graphic feature point set to establish a matching pair , where , If a feature point in has no matching point in , it is marked as an isolated point. Then the coordinate deviation of the matching feature point pair is calculated. The proportion of the number of isolated points to the total number of feature points in the standard graphic feature point set is calculated . Finally, the final contour similarity is calculated by , where is the number of matching pairs, is the average distance between the feature points of the standard graphic, is the coordinate deviation value. Then, the abnormal graphic is removed by setting the graphic feature and topic graphic feature deviation ≥ 30% as , which is the abnormal graphic removal threshold;

[0074] Modeling data processing: Box plot method is used for modeling data outlier detection. Specifically, all data samples of a modeling variable are sorted in ascending order to obtain the first quartile , which is the value at the 25% position in the ascending data, and the third quartile , the value of the 75th position in ascending data, interquartile range , so as to reflect the dispersion degree of the middle 50% of the samples in the data, by setting the abnormal value determination range , The adjustment coefficient is 1.8, which ensures that reasonable dispersed data will not be mistakenly deleted, and detailed unreasonable data will not be missed;

[0075] For data samples with missing values, find similar samples with high similarity to the target sample in graphical data or modeling data , The sample value is 4-6, which ensures that the filling error is stable between 5% and 8%, and can adapt to different types of missing data, and through weighted Nearest neighbor algorithm, the contribution of the nearest neighbor sample with higher similarity to the filling value is greater, which improves the filling accuracy;

[0076] The weight calculation method adopts the distance reciprocal weighting method, which normalizes the weight by calculating the similarity weight, and the similarity weight , wherein is the Euclidean distance between the target sample and the th nearest neighbor sample, is the minimum value, which avoids =0 when the weight is infinite, and after normalization of the weight sum, the filling value , wherein , is the corresponding non-missing value of the th nearest neighbor sample in the experience database.

[0077] To ensure data integrity, the integrity of the filled data needs to be ensured to be more than 96%.

[0078] Then the competition judge accuracy rate is used as the core optimization result index, for graphical data, the judge accuracy rate = the number of correct graphical matching questions / the total number of graphical questions, for modeling data, the judge accuracy rate = the number of samples with consistent modeling scores and expert manual scores / the total number of modeling samples, then the feature variables are grouped, and the within-group variance reflects the random error of the samples in the same group, then the between-group variance is calculated, and the influence weight , The closer a value is to 1, the greater its impact on the optimization result. Then, the weights of the feature variables are calculated hierarchically. Graphical data is divided into two categories: geometric data and function graph data. For geometric data, the weights of the features such as side length, angle, vertex coordinates, perimeter, and area are calculated separately for their impact on the "accuracy of graphic evaluation." For function graph data, the weights of the features such as domain, range, extreme point coordinates, inflection point coordinates, and monotonicity interval are calculated separately. The modeling data is stratified according to the modeling problem domain and by graphic / modeling data. The weight calculation logic is adjusted to better reflect the structured characteristics of mathematical competition data, taking into account the characteristics of the competition domain. Then, the feature variables with a weight greater than or equal to 0.65 in each layer are included... The candidate key feature set is entered, and the correlation between candidate feature variables is analyzed using Pearson correlation coefficient. The higher the correlation coefficient after analysis, the stronger the association between the two variables. Variables with higher weights are retained, while variables with lower weights are removed. The remaining key feature variables are input into a pre-validation model to test their ability to support the competition optimization results. If the evaluation accuracy of the pre-validation model is ≥90% and the iteration time is ≤8 minutes, the screening results are valid. If the accuracy is <90%, the screening threshold needs to be lowered and influencing variables need to be re-included. If the iteration time is >8 minutes, the threshold needs to be raised to further remove redundant variables. After successful validation, the final set of key feature variables is determined, and the influence weights are quantified by analysis of variance to avoid bias from expert subjective experience.

[0079] Dynamic mixture probability model building module:

[0080] A twin model architecture is adopted, which uses a Gaussian distribution sub-model and a Bayesian network sub-model to process the graphical data variables and the modeling data variables respectively. The Gaussian distribution sub-model outputs the probability distribution parameters of the continuous variables of the graphical data, while the Bayesian network sub-model outputs the dependencies and probability parameters of the discrete variables of the modeling data. Together, they constitute a complete dynamic mixed probability model.

[0081] Gaussian distribution sub-model: Key feature variables of the graphic data after anomaly removal thresholding are input into the model. The core parameters of the model are mean and variance. The mean reflects the central tendency of the variable values, and the variance reflects the dispersion of the variable values. The model parameters are calculated using the maximum likelihood estimation method. By finding a set of parameters in the Gaussian distribution sub-model, the probability of the occurrence of the key feature variable samples of the currently observed graphic data is maximized. The specific calculation is as follows:

[0082] Assume the sample set of continuous deformation variables in the graphical data is ,in For the first Key feature variable values ​​of each participating sample Let be the sample size, and assume the samples follow a normal distribution. , the probability density function of a single sample is: , the likelihood function of all samples is: , then take the logarithm of the likelihood function to get the log-likelihood function, , take the partial derivative of and respectively, and set the partial derivative to 0 to get the mean estimate and variance estimate. For different types of graphical data, because of the differences in the distribution characteristics of continuous variables, the graphical data is grouped by type, and a Gaussian distribution sub-model is constructed for each group to calculate the mean and variance of different graphical data groups to prevent parameter distortion caused by mixing of cross-type data.

[0083] For modeling data, the Bayesian network sub-model is used to analyze the discrete key feature variables of the modeling data after elimination. The core structure of the Bayesian network sub-model is composed of nodes and directed edges. The node represents the discrete key feature variable, and the directed edge represents the dependency relationship between variables. By calculating the mutual information value between variables, it is determined whether there is a dependency relationship between variables. If the mutual information value of two variables is greater than 0 and passes the significance test, it is considered that there is a dependency relationship between them, and a directed edge is added, indicating that the choice of modeling method will affect the setting of variable constraint conditions. Then the conditional probability table of each node is calculated, that is, the probability of each value of the current node given the value of the parent node.

[0084] In the mutual information value calculation process, a weight coefficient is introduced to strengthen the recognition ability of the core variable dependency relationship and suppress the interference of secondary variables. Specifically, if the variable is a core variable, that is, the influence weight is greater than or equal to 0.65, then the weight coefficient is taken as 1.2~1.3, and if the variable is a secondary variable, that is, the influence weight is less than 0.65, then the weight coefficient is taken as 1.1~1.2. The improved mutual information value formula is , where is the traditional mutual information value, and the calculation formula is , , are the weight coefficients of variables X and Y, respectively, and pass the significance test to determine whether it is caused by random factors.

[0085] Multi-objective optimization module:

[0086] Since the optimization core of mathematical competition data is to ensure the quality of evaluation and improve the processing data, a three-dimensional optimization system of quality and effect is needed to optimize the matching degree of graphical data, the accuracy of modeling data, and the processing efficiency of algorithm;

[0087] For the matching degree of graphic data: the probability distribution parameters of the key characteristic variables of the continuity of the graphic data are obtained from the Gaussian distribution sub-model, namely the mean estimate and variance estimate. The absolute deviation between the characteristic variable values ​​of each participating solution graphic and the characteristic variable values ​​of the standard graphic is calculated. ,in For the first Characteristic variable values ​​of the graphs in the submitted solutions. The mean is used as the basis for weighted summation of the individual feature deviations to obtain the final quantified value of the graphic data matching degree: ,in The number of key feature variables for continuous graphical data; For the first The influence weights of each feature variable For the first The relative deviation of each characteristic variable; the smaller the deviation value, the higher the degree of matching between the graphic and the standard graphic.

[0088] Regarding the accuracy of modeling data: Conditional probability tables of discrete key feature variables in the modeling data are obtained from the Bayesian network sub-model. Combined with the modeling data from the participating teams, the deviation between the model prediction results and the standard results is calculated. This includes considering the errors in modeling method selection, variable constraint conditions, and model solution results. Finally, the final quantitative value of the modeling data accuracy is calculated based on the influence weight of each error type. ,in To determine the number of error types in the modeling, For the first The weight of the impact of class error, For the first Standardized values ​​of class errors, The smaller the value, the smaller the error rate and the higher the accuracy.

[0089] Regarding algorithm processing efficiency: the total time from the start of the data preprocessing module to the output of candidate solutions by the multi-objective optimization module is statistically analyzed, including the time spent on all stages such as data cleaning, feature extraction, model building, and solution selection, excluding manual intervention time. Then, the collected time is standardized to obtain a quantitative value of algorithm processing efficiency. ,in This represents the actual time spent. The smaller the standardized quantization value obtained as the baseline processing time, the higher the algorithm's processing performance.

[0090] Three weighting coefficients are set: graphic data matching degree weighting. Modeling data accuracy weights And algorithm processing efficiency weights The three weight coefficients are used to balance the importance of the three optimization objectives and meet the differentiated needs of different mathematical competition scenarios. The determination of the three weight coefficient values ​​should follow two principles: 1. Expert experience-led; 2. Scientific method support.

[0091] Experts were asked to compare the importance of any two optimization objectives pairwise using a 1-9 scale. Based on the pairwise comparison scores from all experts, the average score was calculated, and a 3x3 judgment matrix was constructed. The judgment matrix was then subjected to a consistency test, and the largest eigenvalue was calculated. Calculate the consistency index ,in It is 3, according to Find the corresponding table in the standard table Value, calculate the consistency ratio ,like If the value is less than 0.1, then the consistency requirement is met. If the score is greater than or equal to 0.1, it needs to be re-scored. Then, the eigenvector of the judgment matrix is ​​calculated using the eigenvalue method. After normalizing the eigenvector, three weight coefficients are obtained, and the sum of the three weight coefficients is 1. Since the experts are different in different environments and the mathematical competition scenarios are different, the optimization target scores given by the experts for pairwise comparisons are different in each scenario. Therefore, it can be adapted to different scenarios, and the rationality of each weight coefficient is ensured through optimization.

[0092] Obtaining the optimal solution based on the NSGA-II algorithm:

[0093] The dynamic mixed probability model is constructed from the output of the module, and the parameters are optimized by combining graphical data and modeling data to generate candidate solutions. Then, the superior solutions are selected in a hierarchical manner through fast non-dominated sorting.

[0094] Result verification and feedback module:

[0095] Since math competition data typically consists of small samples, the independent samples t-test is used as a significance verification method. Based on three optimization objectives, quantifiable practical performance indicators are used as the verification objects:

[0096] Image data matching accuracy: After adopting the optimization strategy, the proportion of samples whose image judgment results are consistent with the expert manual judgment results out of the total number of samples is: ;

[0097] Consistency of Modeling Data Scores: After adopting the optimization strategy, the correlation coefficient between the automatic modeling scores and the expert human scores is denoted as... The closer the correlation coefficient is to 1, the higher the consistency.

[0098] Actual processing time: The actual time to process all competition data using the optimized strategy is denoted as . ;

[0099] The actual competition data is divided into experimental and control groups. The experimental group uses the optimal strategy output by the multi-objective optimization module to process the data, with a sample size of The control group uses the traditional method to process the data, with a sample size of ,

[0100] In the graphical data matching accuracy index verification, the original hypothesis is proposed There is no significant difference in the graphical data matching accuracy between the experimental and control groups, that is , The experimental group's overall mean is The control group's overall mean is The graphical data matching accuracy of the experimental group is significantly higher than that of the control group, that is Then calculate the sample statistics: the experimental group's sample mean The control group's sample mean is The experimental group's sample standard deviation is The control group's sample standard deviation is Since the sample sizes of the two groups are not equal, the combined variance is used The statistical formula is Where is the combined variance, According to the degrees of freedom , the one-sided critical value is obtained from the t distribution table If the calculated t statistic , and the corresponding p value is less than 0.05, the original hypothesis is rejected , and it is considered that the graphical data matching accuracy of the experimental group is significantly higher than that of the control group. If Or the p value is greater than or equal to 0.05, the original hypothesis is accepted, and it is considered that the optimization effect is not significant. At the same time, the modeling data scoring consistency and actual processing time indicators are tested by t-test, and the verification structure of the three indicators is finally integrated. If all three indicators pass the verification, it is determined that the optimal strategy is effective overall. If two indicators pass and one does not, it is determined based on the competition scene requirements. If only one or no indicator passes the verification, it is determined that the strategy is not effective.

[0101] The feedback module, on the one hand, stores the effective strategies and parameters verified, forming a mathematical competition experience database. In subsequent processing of the same type of competition data, historical parameters can be directly called, greatly shortening the optimization time. On the other hand, the cases that fail the verification are fed back to the front-end module, triggering the model to iterate again, correcting the model bias, and improving the algorithm's ability to adapt to complex scenarios.

[0102] Mathematical competition experience database calling module:

[0103] The historical effective data deposited by the verified and feedback module is used to receive, through database calling, the reuse of the historical optimal model parameters and optimization strategies, and the iteration time of new competition data optimization is greatly shortened.

[0104] The database content is classified into three levels, the first level is classified according to the competition level, the second level is classified according to the data type, and the third level is classified according to the question characteristics, and the calling mechanism follows the search matching, difference analysis, parameter fine-tuning and verification adaptation process.

[0105] The search matching includes accurate matching search according to the competition level, data type and question characteristic label, fuzzy matching search by relaxing the matching conditions of the question characteristic label, and effect priority search by searching from the candidate entries according to the optimization effect index.

[0106] Difference analysis: extract the competition characteristics corresponding to the reused historical data and the current competition characteristics, and compare and analyze the differences between the two.

[0107] Parameter fine-tuning: according to the difference analysis result, fine-tune the historical parameters within 10% according to the same level subtle difference fine-tuning, cross-level and cross-domain moderate adjustment principle, to ensure that the parameters can adapt to the current competition scene.

[0108] Verification adaptation: for graphic data verification, randomly extract 10% to 15% of the graphic data samples of the current competition, calculate the matching degree using the fine-tuned parameters, and the matching accuracy is greater than or equal to 85% to pass the verification; for modeling data verification, randomly extract 10% to 15% of the modeling data samples of the current competition, calculate the accuracy using the fine-tuned parameters, and if the scoring consistency is greater than or equal to 0.85, the verification is passed.

[0109] The above is only an embodiment of the present application, and the circuit, electronic components and modules involved are all prior art, and those skilled in the art can realize them without further description. The content protected by the present application does not involve the improvement of software and methods. The specific structure and characteristics of the scheme known in the art are not described in detail here. Those skilled in the art know all the ordinary technical knowledge in the field of the application as of the filing date or priority date, can know all the prior art in the field, and have the ability to apply conventional experimental means before the date. Those skilled in the art can improve and implement the present scheme based on their own ability under the guidance of the present application. Some typical known structures or known methods should not be an obstacle for those skilled in the art to implement the present application. It should be noted that for those skilled in the art, without departing from the structure of the present application, a number of modifications and improvements can be made, which should be considered as the protection scope of the present application, and these will not affect the effect and practicality of the patent.

Claims

1. An improved education competition optimization algorithm based on distribution estimation algorithm, characterized in that, Comprise the following steps: S1: data preprocessing, the data preprocessing includes mathematical competition graphics data processing, mathematical competition modeling data processing and missing data sample processing; S2: dynamic hybrid probability model construction, adopt twin model architecture, through Gaussian distribution sub model and Bayesian network sub model respectively process mathematical competition graphics data and mathematical competition modeling data, and respectively output probability distribution parameters of mathematical competition graphics data continuous variable and dependent relationship and probability parameters of mathematical competition modeling data discrete variable, both constitute complete dynamic hybrid probability model; S3: multi-objective optimization, construct three-dimensional optimization system of quality and effect, optimize mathematical competition graphics data matching degree, mathematical competition modeling data accuracy and algorithm processing efficiency, obtain optimized mathematical competition graphics data and mathematical competition modeling data, generate scheme according to obtained optimized mathematical competition graphics data and mathematical competition modeling data and combine NSGA-Ⅱ algorithm; S4: result verification and feedback, adopt independent sample t test as significance verification method, verify the optimization effect of optimized mathematical competition graphics data and mathematical competition modeling data in S3, and feedback scheme and optimized mathematical competition graphics data and mathematical competition modeling data; S5: experience database calling, undertake scheme and mathematical competition graphics data and mathematical competition modeling data data fed back in step S4, realize reuse of model parameters and optimization strategy.

2. The improved education competition optimization algorithm based on distribution estimation algorithm according to claim 1, characterized in that, The mathematical competition graphics data processing step in step S1 is: Contour contrast method is used to convert the standard graphics of the competition topic and the solution graphics into vector graphics format, the contour feature points of the graphics are extracted, and the standard graphic feature point set S and the solution graphic feature point set T are formed; K nearest neighbor matching algorithm is used to find the nearest feature point in the standard graphic feature point set S for each feature point in the solution graphic feature point set T, and a matching pair is established, if there is no matching point in the standard graphic feature point set S for a feature point in the solution graphic feature point set T, it is marked as an isolated point; Then the coordinate deviation of the matching feature point pair is calculated, and the proportion of the number of isolated points to the total number of feature points is calculated, and the contour similarity of the competition topic standard graphics and the solution graphics is calculated through the obtained coordinate deviation and the number of matching pairs.

3. The improved educational competition optimization algorithm based on distribution estimation algorithm according to claim 2, characterized in that, The mathematical competition modeling data processing step in step S1 is: All data samples of the modeling variable are sorted in ascending order, the modeling data is divided by quartile method, and the divided modeling data is detected for outliers by setting outlier judgment range.

4. The improved education competition optimization algorithm based on distribution estimation algorithm according to claim 3, characterized in that, The missing data sample processing step in step S1 is: Find k samples with high similarity to the graphics data processed by mathematical competition graphics data or the modeling data processed by mathematical competition modeling data in the experience database; The similarity weight of the k samples and the graphics data or the modeling data is calculated, that is, the weight is normalized; After normalizing the weighted sum, the fill value is calculated according to the formula. ,in , For the first in the experience database The corresponding non-missing values ​​of the nearest neighbor samples.

5. The improved educational competition optimization algorithm based on distribution estimation algorithm according to claim 1, characterized in that, In step S1, it also includes key feature variable screening, and the specific steps are: Set the core optimization result index: the accuracy rate of graphic data evaluation = the number of correct graphic matching questions / the total number of graphic questions; the accuracy rate of modeling data evaluation = the number of samples whose modeling scores are consistent with the artificial scores of experts / the total number of modeling samples; The graphic data is layered according to the feature variables of geometric graphic data and function image data, and the modeling data is layered according to the modeling problem field. For each feature variable, the within-group variance and the between-group variance are calculated, and the influence weight is calculated through the within-group variance and the between-group variance. The weight reaching the threshold is included in the candidate key feature set. Then the correlation between the feature variables in the candidate key feature set is analyzed through the Pearson correlation coefficient, and the feature variables are further removed according to the weight. Then the further removed feature variables are input into the pre-validation model, and finally the key feature variable set is obtained.

6. The improved educational competition optimization algorithm based on distribution estimation algorithm according to claim 1, characterized in that, The three-dimensional optimization system in step S3 is specifically: Graphic data matching degree: obtain the probability distribution parameters from the Gaussian distribution sub-model, calculate the absolute deviation of each feature variable value of the competition solution graphic and the standard graphic feature variable value, then weighted sum each feature deviation to get the final quantitative value of the graphic data matching degree; Modeling data accuracy: obtain the conditional probability table from the Bayesian network sub-model, combine the modeling data of the participating team to calculate the deviation between the model prediction result and the standard result, and comprehensively calculate the quantitative value according to the error type influence weight, including modeling method selection error, variable constraint condition error and model solution result error; Algorithm processing efficiency: the total time from data preprocessing to multi-objective optimization output candidate scheme is calculated, and the final quantitative value is obtained by standardizing the time.

7. The improved educational competition optimization algorithm based on distribution estimation algorithm according to claim 1, characterized in that, Step S3 also includes three-dimensional optimization target weight coefficient distribution, and the specific steps are: Set the graphic data matching degree weight, the modeling data accuracy weight and the algorithm processing efficiency weight. The experts use the 1-9 scale method to compare and score the importance of any two optimization targets, calculate the average score of all expert scores, build a 3x3 judgment matrix, then perform consistency test on the judgment matrix, calculate the characteristic vector of the judgment matrix by eigenvalue method, and finally obtain the weight coefficients of the graphic data matching degree weight, the modeling data accuracy weight and the algorithm processing efficiency weight.

8. The improved educational competition optimization algorithm based on distribution estimation algorithm according to claim 7, characterized in that, The consistency checking formula is: wherein , is 3, is the maximum eigenvalue of the judgment matrix, is the standard value found according to the authoritative standard index.

9. The improved educational competition optimization algorithm based on distribution estimation algorithm according to claim 1, characterized in that, The specific steps of the result verification and feedback in step S4 are: Based on the small sample characteristics of education competition data, independent sample t test is used as the significance verification method. The verification objects include graphic data matching accuracy, modeling data score consistency and actual processing time. The actual competition data is divided into experimental group and control group. The null hypothesis and alternative hypothesis are proposed for each verification index. The sample statistic is calculated, the t statistic is calculated by using the combined variance statistic formula, the one-sided critical value is obtained through the t distribution table, and the hypothesis is judged through the p value output by the independent sample t test. Finally, the verification results of the graphic data matching accuracy, the modeling data score consistency and the actual processing time are obtained. The scheme that passes all three indexes is determined as the optimal scheme, and the scheme is fed back to the experience database.

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