A multi-objective optimization-based topic selection method

Abstract

The application discloses a kind of based on multi-objective optimization's selecting subject method, comprising:1 obtains student and subject relevant data;2 training bottom cognitive diagnosis model;3 based on accuracy, diversity and security constructs multi-objective optimization problem;4 using heuristic multi-objective evolutionary algorithm to solve multi-objective optimization problem, obtain the student's selecting subject set.The application based on multi-objective evolutionary algorithm balances test accuracy, diversity and security, and by calculating and the answer prediction accuracy of the student similar to its ability level to the test accuracy of the student more intuitive and effective modeling, to ensure the prediction accuracy of student knowledge level ability.

Description

Technical Field

[0001] This invention relates to the fields of question selection strategies and multi-objective evolutionary algorithms in the field of computer adaptive testing. Background Technology

[0002] Computer-adaptive testing is a novel testing format that adopts the principles of "personalized testing" and "tailor-made testing," adaptively selecting the most suitable test for each student based on their ability level. Computer-adaptive testing has unique advantages, such as shorter test length, higher accuracy, and ease of satisfying various non-statistical constraints. With the rapid development of computer technology, computer-adaptive testing has been widely used in various large-scale tests, such as the GRE and CPA exams.

[0003] Research on computer-adaptive testing focuses on question selection strategies. In recent years, an increasing number of researchers have pointed out that question selection strategies need to consider not only statistical constraints—that is, whether the selected questions can accurately measure students' abilities—but also non-statistical constraints. Among these, question exposure control and knowledge point diversity are two very important non-statistical constraints, relating to test security, reliability, and validity, respectively. Researchers have conducted extensive studies on how to satisfy the three objectives of test accuracy, diversity, and security. A common method to improve test accuracy is to use information content indicators for question selection; however, the positive correlation between question information content and question discrimination can lead to overexposure of highly discriminative questions. Addressing test diversity typically involves narrowing the candidate question bank to a certain range of knowledge points, but this often comes at the cost of reduced accuracy. Addressing test security usually requires complex simulation experiments beforehand, which is overly cumbersome and complicated. These methods only address one objective, neglecting the importance of other objectives and often at the expense of others. Currently, there are some methods that simultaneously balance the three objectives, mainly mathematical programming and heuristic methods. Among them, mathematical programming relies on solvers and can lead to infeasible solutions when there are too many constraints; the idea of ​​heuristic methods is to simply combine the three objectives without considering the complex relationships between them, which often results in not obtaining the optimal solution. Summary of the Invention

[0004] To avoid the problems existing in the prior art, this invention proposes a topic selection method based on multi-objective optimization, which aims to balance the accuracy, diversity and safety of topic selection, and to improve the accuracy of topic selection by considering the approximate characteristics of students' ability levels, thereby accurately predicting students' knowledge level and ability.

[0005] The present invention adopts the following technical solution to solve the technical problem:

[0006] The characteristic of this invention's topic selection method based on multi-objective optimization is that it proceeds according to the following steps:

[0007] Step 1: Obtain relevant data on students and questions:

[0008] Obtain the student set S = {s1, s2, ..., s} u , ..., s |S|}, where |S| represents the number of students, s u Indicates student number u;

[0009] Obtain the candidate question bank Q = {q1, q2, ..., q} i , ..., q |Q|}, where |Q| represents the size of the candidate question bank, q i This represents the i-th question;

[0010] Obtain all knowledge points K = {k1, k2, ..., k j , ..., k |K|}, where |K| represents the total number of knowledge points, k j This represents the j-th knowledge point;

[0011] Obtain the relevant matrix G of the knowledge points in the question, and let G... ij Let q represent the i-th question. i With the j-th knowledge point k j Is it relevant, when G ij =1 indicates correlation, when G ij =0 indicates no correlation;

[0012] Obtain the student problem-solving dataset, and represent each student problem-solving record in the dataset as a triple (s u q i r ui ), where r ui ∈{0,1} represents student s with ID u. u For the i-th question q i Regarding the response, when r ui =0 indicates an incorrect answer, when r ui =1 indicates a correct answer;

[0013] Step 2: Input the student's question dataset into the model for training, and obtain the trained cognitive diagnostic model and its student and question-related parameters, including: student ability level, question difficulty, and question discrimination.

[0014] Step 3: Define the current iteration number as l, the maximum iteration number as L, and initialize l = 1;

[0015] Using binary method to analyze the l-th generation population Pu，l Each individual is encoded, and the dimension of each individual is |Q|; each individual represents a student's question selection pattern, and any i-th dimension gene of each individual represents the i-th question q. i Whether or not it was selected;

[0016] Let the m-th individual in the l-th generation represent student s with the number u. u The question selection pattern is denoted as x. u，l，m =(x u,l,m，1 x u，l，m，2 , ..., x u，l，m，i ..., x u，l，m，|Q| ); where, if x u，l，m，i =1 indicates that the m-th individual in the l-th generation population is represented by the u-th student s in the i-th dimension gene. u Choose the i-th question q i If x u，l，m，i =0 indicates that the m-th individual in the l-th generation population is represented by the student s in the i-th dimension gene. u Do not select question i q i ;

[0017] Using equation (1), construct the multi-objective optimization problem Maximize F(x) u，l，m ):

[0018] Maximize F(x u，l，m )=(acc(x u，l，m ),diver(x u，l，m ), secu(x) u，l，m )) T (1)

[0019] In equation (1), acc(x) u，l，m ) represents individual x u,l,m The accuracy of the test corresponding to the question selection pattern was assessed, and student s was obtained using a heuristic multi-objective evolutionary algorithm. u After compiling the selection of topics, then it will be combined with student number U. u A set of students with similar ability levels and their chosen questions are input into the trained cognitive diagnostic model to obtain a predicted set of answer results for the set of students with similar ability levels, which is then used to calculate the test accuracy, diver(x). u,l，m ) represents individual x u，l，m The knowledge points of the corresponding question selection mode are diverse, and can be obtained from equation (2), secu(x) u,l,m ) represents individual x u，l，m The security of the corresponding question selection mode is obtained from equation (3):

[0020]

[0021]

[0022] In equation (3), f i Let q represent the i-th question. i The actual exposure frequency, i.e., the i-th question q i The ratio of total exposures to total number of students, TL u Student s (number u) u The number of topics selected;

[0023] Step 4: Maximize F(x) for the multi-objective optimization problem using a heuristic multi-objective evolutionary algorithm. u，l，m The optimal question selection pattern is obtained by solving the problem.

[0024] Step 4.1: Set an exposure count value for each question in the candidate question bank Q, and initialize it to 0;

[0025] Calculate the expected model change value for each question to guide the evolutionary direction of the population;

[0026] Step 4.2: Initialize the current generation l population P u，l ;

[0027] Step 4.3: Generate the (l+1)th generation population P u，l+1 ;

[0028] Step 4.4: After assigning l+1 to l, determine whether l has reached L. If not, return to step 4.3.1 and execute sequentially; otherwise, it indicates that the Lth generation population P has been obtained. u，L ;

[0029] Step 4.5: Determine the optimal individual x u，L，fin :

[0030] Step 5: Obtain the optimal individual x u，L，fin The question number corresponding to the gene value of 1 is used to provide the question selection set corresponding to the question number to student s with the corresponding question number. u Answer the question.

[0031] The multi-objective optimization-based topic selection method described in this invention is also characterized in that step 4.2 includes:

[0032] Step 4.2.1: Initialize the l-th generation population P u，l Given N individuals, set the gene values ​​of each individual to 0 in all dimensions;

[0033] Step 4.2.2: Classify the questions in the candidate question bank Q according to knowledge points. Then, sort the questions under each knowledge point in descending order according to the expected model change value, and select the top-ranked questions as the first candidate question set (cands). u，l，emc Then, the questions under each knowledge point are sorted in ascending order according to their exposure count, and the top-ranked questions are selected as the second candidate question set (cands). u，l,exp ;

[0034] Step 4.2.3: Remove cands from the candidate question bank Q. u，l,emc and cands u，l,exp In the remaining question bank, for each individual x u，l，m Randomly select several questions as the third candidate question set (cands) u，l，m，rand Thus, we obtain the results from cands u，l，emc cands u，l，exp and cands u，l,m，rand The constituent individual x u，l，m The final candidate problem set is denoted as CANDS. u，l，m ;

[0035] Step 4.2.5: Calculate individual x using equation (4). u，l，m The probability p u，l，m :

[0036]

[0037] In equation (4), |CANDS u，l，m | represents an individual x u，l，m The final candidate problem set CANDS u，l，m The number of questions in the book;

[0038] According to individual x u，l，m The probability p u，l，m The candidate question set CANDS u，l，m The question number in the text corresponds to the individual x. u，l，m The gene value in dimension x is set to 1 to complete the individual x u，l,m The initialization is completed, thus completing the initialization of the l-th generation population P. u，l Initialization of N individuals.

[0039] Step 4.2 includes:

[0040] Step 4.3.1: Based on the multi-objective optimization problem shown in equation (1), calculate the population P of the l-th generation. u，l The fitness values ​​of all individuals are calculated, and a binary tournament selection method is used to select 2×N individuals with higher fitness to participate in evolution, resulting in the l-th generation evolutionary population P′. u，l ;

[0041] Step 4.3.2, from P′ u，l Two individuals are randomly selected and denoted as x′. u，l，m and x′ u，l，m′ Set the population P of generation l+1. u，l+1 One individual x u,l+1,m =x′ u，l，m ;

[0042] Step 4.3.3: Obtain individual x u，l+1，m The number of genes with a value of 1, num, if num > TL u Then proceed to step 4.3.4, if num < TL. u Then proceed to step 4.3.5;

[0043] Step 4.3.4, Select x′ u，l，m The gene value is 1 and x′ u，l，m The questions corresponding to gene values ​​of 0 in the set are used as the evolution problem set can1. A binary tournament selection method is used to select (num-TL) questions from the evolution problem set can1. u ) questions with larger exposure counts, thus reducing (num-TL) u The question number with the larger exposure count value corresponds to individual x u,l+1，m The gene values ​​in the dimension are set to 0 to generate an individual x. u,l+1,m ;

[0044] Step 4.3.5, Select x′ u，l，m The gene value is 0 and x′ u，l，m′ The questions corresponding to a gene value of 1 are set as evolutionary question set can0. A binary tournament selection method is used to select from can0 (TL). u -num) questions with large expected model changes, thus (TL) u -num) question numbers with large expected model changes correspond to individual x u，l+1，m The gene value in the dimension is set to 1 to generate an individual x. u，l+1，m ;

[0045] Step 4.3.6: Following the process from Step 4.3.2 to Step 4.3.5, generate N individuals and form the (l+1)th generation population P. u，l+1 .

[0046] Step 4.5 includes:

[0047] Step 4.5.1: Using (0, 0, 0) as the origin, establish a three-dimensional coordinate system with test accuracy as the x-axis, knowledge diversity as the y-axis, and security as the z-axis.

[0048] Step 4.5.2: Calculate the population P of generation L. u，L The accuracy, knowledge diversity, and security of each individual's test are assessed, and the calculated results are normalized to form a three-dimensional coordinate point that is then mapped onto a three-dimensional coordinate system.

[0049] Step 4.5.3: Select a three-dimensional coordinate point with the same three-dimensional coordinate values ​​from the three-dimensional coordinate system as a reference point, and connect the reference point to the origin to form a reference vector;

[0050] Step 4.5.4: Place the Lth generation population P in the three-dimensional coordinate system... u，L The three-dimensional coordinate points mapped to each individual are connected to the origin to form an individual vector, and the individual angle formed by each individual vector and the reference vector is obtained.

[0051] Step 4.5.5: From the Lth generation population P u，L Among the individual angles formed by each individual, the individual corresponding to the smallest individual angle value is selected as the optimal individual x. u，L，fin .

[0052] The present invention provides an electronic device, including a memory and a processor, wherein the memory is used to store a program that supports the processor in executing any of the topic selection methods, and the processor is configured to execute the program stored in the memory.

[0053] The present invention provides a computer-readable storage medium on which a computer program is stored, wherein the computer program, when executed by a processor, performs any of the steps of the topic selection method.

[0054] Compared with existing technologies, the beneficial effects of this invention are reflected in:

[0055] 1. Based on a thorough review of relevant literature, this invention models the three objectives of test accuracy, diversity, and security, and designs a heuristic multi-objective evolutionary algorithm for topic selection, enabling the test to simultaneously meet multiple objectives and be easy to implement, which is beneficial for the practical application of computer adaptive testing.

[0056] 2. This invention uses the accuracy of predicting the answers of students with similar ability levels to the tested student to create a more intuitive and effective model of the student's test accuracy, thereby further improving the test accuracy.

[0057] 3. The present invention designs corresponding heuristic operators, including population initialization, generation of the next generation population, and determination of the optimal individual, which helps guide the population to evolve in the direction of better problem quality and accelerates the convergence speed of the evolutionary algorithm, thereby improving the accuracy of problem selection. Attached Figure Description

[0058] Figure 1 This is a flowchart of a topic selection method based on multi-objective optimization according to the present invention;

[0059] Figure 2 This is an example diagram of population initialization for the present invention;

[0060] Figure 3 This is an example diagram illustrating the generation of the next generation population according to the present invention. Detailed Implementation

[0061] In this embodiment, see Figure 1 A topic selection method based on multi-objective optimization is carried out in the following steps:

[0062] Step 1: Obtain relevant data on students and questions:

[0063] Obtain the student set S = {s1, s2, ..., s} u , ..., s |S|}, where |S| represents the number of students, s u Indicates student number u;

[0064] Obtain the candidate question bank Q = {q1, q2, ..., q} i , ..., q |Q|}, where |Q| represents the size of the candidate question bank, q i This represents the i-th question;

[0065] Obtain all knowledge points K = {k1, k2, ..., k j , ..., k |K|}, where |K| represents the total number of knowledge points, k j This represents the j-th knowledge point;

[0066] Obtain the relevant matrix G of the knowledge points in the question, and let G... ij Let q represent the i-th question. i With the j-th knowledge point k j Is it relevant, when G ij =1 indicates correlation, when G ij =0 indicates no correlation;

[0067] Obtain the student problem-solving dataset, and represent each student problem-solving record in the dataset as a triple (s u q i r ui ), where r ui ∈{0,1} represents student s with ID u. u For the i-th question q i Regarding the response, when r ui =0 indicates an incorrect answer, when r ui=1 indicates a correct answer;

[0068] Step 2: Input the student's question dataset into the model for training, and obtain the trained cognitive diagnostic model and its student and question-related parameters, including: student ability level, question difficulty, and question discrimination.

[0069] Step 3: Define the current iteration number as l, the maximum iteration number as L, and initialize l = 1. In this embodiment, L = 100.

[0070] Using binary method to analyze the l-th generation population P u，l Each individual is encoded, and the dimension of each individual is |Q|; each individual represents a student's question selection pattern, and any i-th dimension gene of each individual represents the i-th question q. i Whether or not it was selected;

[0071] Let the m-th individual in the l-th generation represent student s with the number u. u The question selection pattern is denoted as x. u，l，m =(x u，l,m,1 x u,l,m,2 , ..., x u,l,m,i ..., x u,l,m,|Q| ); where, if x u,l,m,i =1 represents student s, represented by the i-th gene of the m-th individual in the l-th generation population. u Choose the i-th question q i If x u，l，m，i =0 indicates that the m-th individual in the l-th generation population is represented by the student s in the i-th dimension gene. u Do not select question i q i ;

[0072] Using equation (1), construct the multi-objective optimization problem Maximize F(x) u，l，m ):

[0073] Maximize F(x u，l，m )=(acc(x u，l，m ),diver(x u，l，m ), secu(x) u，l，m )) T (1)

[0074] In equation (1), acc(x) u，l，m ) represents individual x u，l，m The accuracy of the test corresponding to the question selection pattern was assessed, and student s was obtained using a heuristic multi-objective evolutionary algorithm. u After compiling the selection of topics, then it will be combined with student number U. uA set of students with similar ability levels and their chosen questions are input into a trained cognitive diagnostic model to obtain a predicted set of answer results for the set of students with similar ability levels, which is then used to calculate test accuracy. Since student u's s u Since the answers to the selected questions cannot be obtained in advance, the accuracy of the test based on the selected questions cannot be directly calculated. Therefore, the accuracy is determined by calculating the results of the test with student number u. u By comparing the predicted responses of students with similar ability levels to a set of selected questions with their actual responses, test accuracy can be modeled and further improved. (diver(x)) u，l，m ) represents individual x u，l，m The diversity of knowledge points corresponding to the question selection patterns is determined by individual x u，l，m The ratio of the knowledge points covered by the corresponding question selection mode to the total number of knowledge points is used as a measure, and is obtained by equation (2). secu(x) u，l，m ) represents individual x u，l，m The security of the corresponding question selection pattern is measured by the reciprocal of the chi-square value, and is obtained from equation (3):

[0075]

[0076]

[0077] In equation (3), f i Let q represent the i-th question. i The actual exposure frequency, i.e., the i-th question q i The ratio of total exposures to total number of students, TL u Student s (number u) u In this embodiment, the number of topics to be selected is set to TL. u =15;

[0078] Step 4: Maximize F(x) for the multi-objective optimization problem using a heuristic multi-objective evolutionary algorithm. u，l，m The optimal question selection pattern is obtained by solving the problem.

[0079] Step 4.1: Set an exposure count value for each question in the candidate question bank Q, and initialize it to 0;

[0080] Calculate the expected model change value for each question to guide the evolutionary direction of the population;

[0081] Step 4.2: Initialize the current generation l population P u，l ;

[0082] Step 4.2.1: Initialize the l-th generation population P u，lThe system contains N individuals, and sets the gene values ​​of each individual to 0 in all dimensions. In this embodiment, N = 100.

[0083] Step 4.2.2: Classify the questions in the candidate question bank Q according to knowledge points. Then, sort the questions under each knowledge point in descending order according to the expected model change value, and select the top-ranked questions as the first candidate question set (cands). u，l，emc Then, the questions under each knowledge point are sorted in ascending order according to their exposure count, and the top-ranked questions are selected as the second candidate question set (cands). u，l,exp This is beneficial because the initial population is in a state where the expected model change value is high and the exposure count value is low. For example... Figure 2 Examples in, Figure 2 The left figure in the diagram represents the j-th knowledge point k. j The relevant questions are sorted in descending order of the expected model change value. The left slash indicates that the questions with the larger expected model change value are selected. The right figure shows that the j-th knowledge point k is selected. j The relevant questions are sorted in ascending order of exposure count, with the left slash indicating the question with lower exposure.

[0084] Step 4.2.3: Remove cands from the candidate question bank Q. u，l,emc and cands u，l,exp In the remaining question bank, for each individual x u，l，m Randomly select several questions as the third candidate question set (cands) u，l,m，rand This increases the diversity of the initial population, thereby obtaining individual x. u，l，m The final candidate problem set is denoted as CANDS. u,l,m =cands u，l，emc +cands u，l,exp +cands u，l,m,rand ;

[0085] Step 4.2.5: Calculate individual x using equation (4). u，l，m The probability p u，l，m :

[0086]

[0087] In equation (4), |CANDS u,l，m | represents an individual x u，l,m The final candidate problem set CANDS u,l，m The number of questions in the question.

[0088] According to individual x u，l，m The probability p u，l，m CANDS, the candidate problem set u,l,m The question number in the text corresponds to the individual x.u，l，m The gene value in dimension x is set to 1 to complete the individual x u,l,m The initialization is completed, thus completing the initialization of the l-th generation population P. u，l Initialization of N individuals;

[0089] Step 4.3: Generate the (l+1)th generation population P u，l+1 :

[0090] Step 4.3.1: Based on the multi-objective optimization problem shown in equation (1), calculate the population P of the l-th generation. u，l The fitness values ​​of all individuals are calculated, and a binary tournament selection method is used to select 2×N individuals with higher fitness to participate in evolution, resulting in the l-th generation evolutionary population P′. u，l ;

[0091] Step 4.3.2, from P′ u，l Two individuals are randomly selected and denoted as x′. u，l，m and x′ u，l，m′ Set the population P of generation l+1. u，l+1 One individual x u，l+1,m =x′ u，l，m ;

[0092] Step 4.3.3: Obtain individual x u，l+1，m The number of genes with a value of 1, num, if num > TL u Then proceed to step 4.3.4, if num < TL. u Then proceed to step 4.3.5;

[0093] Step 4.3.4, Select x′ u，l，m The gene value is 1 and x′ u，l，m′ The problems corresponding to a gene value of 0 are designated as the evolution problem set can1. A binary tournament selection method is used to select (num-TL) problems from the evolution problem set can1. u ) questions with larger exposure counts, thus reducing (num-TL) u The question number with the larger exposure count value corresponds to individual x u，l+1，m The gene values ​​in the dimension are set to 0 to generate an individual x. u，l+1，m ,like Figure 3 In the example, can1 is the left slash part, which selects the topic with the larger exposure count value and sets its corresponding gene value to 0;

[0094] Step 4.3.5, Select x′ u，l，m The gene value is 0 and x′ u，l，m′ The questions corresponding to a gene value of 1 are set as evolutionary question set can0. A binary tournament selection method is used to select from can0 (TL). u-num) questions with large expected model changes, thus (TL) u -num) question numbers with large expected model changes correspond to individual x u，l+1，m The gene value in the dimension is set to 1 to generate an individual x. u，l+1，m ,like Figure 3 In the example, can0 is the part with the right slash, from which the questions with larger expected model change values ​​are selected and their corresponding gene values ​​are set to 1;

[0095] Step 4.3.6: Following the process from Step 4.3.2 to Step 4.3.5, generate N individuals and form the (l+1)th generation population P. u，l+1 ;

[0096] Step 4.4: After assigning l+1 to l, determine whether l has reached L. If not, return to step 4.3.1 and execute sequentially; otherwise, it indicates that the Lth generation population P has been obtained. u，L ;

[0097] Step 4.5: Determine the optimal individual x u，L，fin :

[0098] Step 4.5.1: Using (0, 0, 0) as the origin, establish a three-dimensional coordinate system with test accuracy as the x-axis, knowledge diversity as the y-axis, and security as the z-axis.

[0099] Step 4.5.2: Calculate the population P of generation L. u，L The accuracy, knowledge diversity, and security of each individual's test are assessed, and the calculated results are normalized to form a three-dimensional coordinate point that is then mapped onto a three-dimensional coordinate system.

[0100] Step 4.5.3: Select a three-dimensional coordinate point with the same three-dimensional coordinate values ​​from the three-dimensional coordinate system as a reference point, and connect the reference point to the origin to form a reference vector;

[0101] Step 4.5.4: Place the Lth generation population P in the three-dimensional coordinate system... u，L The three-dimensional coordinate points mapped to each individual are connected to the origin to form an individual vector, and the individual angle formed by each individual vector and the reference vector is obtained.

[0102] Step 4.5.5: From the Lth generation population P u，L Among the individual angles formed by each individual, the individual corresponding to the smallest individual angle value is selected as the optimal individual x. u,L,fin ;

[0103] Step 5: Obtain the optimal individual x u，L，fin The question number corresponding to the gene value of 1 is used to provide the question selection set corresponding to the question number to student s with the corresponding question number. uAnswer the question.

[0104] In this embodiment, an electronic device includes a memory and a processor. The memory stores a program that supports the processor in executing the above-described method, and the processor is configured to execute the program stored in the memory.

[0105] In this embodiment, a computer-readable storage medium stores a computer program, which is executed by a processor to perform the steps of the above method.

Claims

1. A topic selection method based on multi-objective optimization, characterized in that, The procedure is as follows: Step 1: Obtain relevant data on students and questions: Get student collection ,in, Indicates the number of students. express Student No. 1; Obtaining the candidate question bank ,in, Indicates the size of the candidate question bank. This represents the i-th question; Get all knowledge points ,in, This represents the total number of knowledge points. This represents the j-th knowledge point; Obtain the relevance matrix of the knowledge points in the question and order This represents the i-th question. With the j-th knowledge point Whether it is relevant, when =1 indicates correlation, when =0 indicates no correlation; Obtain the student problem-solving dataset, and represent each student problem-solving record in the dataset as a triple. ,in, Indicates student number u For the i-th question The response situation, when =0 indicates an incorrect answer. = 1 indicates a correct answer; Step 2: Input the student's question dataset into the model for training, and obtain the trained cognitive diagnostic model and its student and question-related parameters, including: student ability level, question difficulty, and question discrimination. Step 3: Define the current iteration number as... The maximum number of iterations is L, and it is initialized. ; Using binary mode for the first Generation population Each individual is encoded, and the dimension of each individual is... Each individual represents a student's question selection pattern, and any number of questions selected by each individual... Dimension Gene indicates the first Question Whether or not it was selected; Order No. The first generation of the population The characteristics of each individual Student No. The question selection mode is denoted as Among them, if Indicates the first The first generation of the population The individual in the first The characteristics of the gene Student No. Select the Question ,like Indicates the first The first generation of the population The individual in the first The characteristics of the gene Student No. Do not select the first Question ; Construct a multi-objective optimization problem using equation (1) : (1) In equation (1), Represents an individual The test accuracy of the corresponding question selection pattern was obtained through a heuristic multi-objective evolutionary algorithm. Student No. After compiling the selection of topics, then... Student No. A set of students with similar ability levels and their chosen questions are input into the trained cognitive diagnostic model to obtain a set of predicted answer results for the set of students with similar ability levels, which is then used to calculate the accuracy of the test. Represents an individual The diversity of knowledge points corresponding to the question selection patterns is obtained from equation (2). Represents an individual The security of the corresponding question selection mode is obtained from equation (3): (2) (3) In equation (3), This represents the i-th question. The actual exposure frequency of the i-th question. The ratio of total exposures to the total number of students. express Student No. The number of topics selected; Step 4: Apply a heuristic multi-objective evolutionary algorithm to the multi-objective optimization problem. The optimal question selection pattern is obtained by solving the problem. Step 4.1: Prepare a candidate question bank. Each question in the program is assigned an exposure count value and initialized to 0. Calculate the expected model change value for each question to guide the evolutionary direction of the population; Step 4.2: Initialize the current... Generation population ; Step 4.3, generate the first Generation population ; Step 4.4, Assign to Then, make a judgment Has it been achieved? If the condition is not met, return to step 4.3.1 and execute sequentially; otherwise, it indicates that the first step has been reached. Generation population ; Step 4.5: Determine the optimal individual : Step 5: Obtain the optimal individual The question number corresponding to the gene value of 1 is used to provide the selection set of questions with the corresponding question number. Student No. Answer the question.

2. The topic selection method based on multi-objective optimization according to claim 1, characterized in that, Step 4.2 includes: Step 4.2.1, Initialize the first Generation population Given N individuals, set the gene values ​​of each individual to 0 in all dimensions; Step 4.2.2: Select the candidate question bank. The questions are categorized according to knowledge points. Then, the questions under each knowledge point are sorted in descending order based on the expected model change value. The top-ranked questions are then selected as the first candidate question set. Then, the questions under each knowledge point are sorted in ascending order according to their exposure count, and the top-ranked questions are selected as the second candidate question set. ; Step 4.2.3: In the candidate question bank Except and In the remaining question bank, for each individual Several questions were randomly selected as the third candidate question set. Thus, we obtain from , ,and The constituent individuals The final candidate problem set is denoted as ; Step 4.2.5: Calculate the individual using formula (4). probability : (4) In equation (4), Represents an individual Final candidate problem set The number of questions in the book; According to individuals probability The candidate question set The question number in the text corresponds to the individual. The gene value in the dimension is set to 1 to complete the individual. The initialization is completed, thus fulfilling the initialization of the first... Generation population Initialization of N individuals.

3. The topic selection method based on multi-objective optimization according to claim 2, characterized in that, Step 4.2 includes: Step 4.3.1: Based on the multi-objective optimization problem shown in equation (1), calculate the first... Generation population The fitness values ​​of all individuals are calculated, and a binary tournament selection method is used to select the individual with the highest fitness. Each individual participates in evolution, resulting in the [number]th [evolutionary stage]. Generational Evolutionary Population ; Step 4.3.2, from Two individuals are randomly selected and denoted as follows: and , set the Generation population One of the individuals ; Step 4.3.3: Obtain the individual The number of genes with a value of 1 ,like Then proceed to step 4.3.4, if Then proceed to step 4.3.5; Step 4.3.4, Select The gene value is 1 and The questions corresponding to a gene value of 0 are used as an evolutionary question set. Using a binary tournament selection method to evolve problem sets Choose from 1 The question with the highest exposure count, thus... The question number with the highest exposure count corresponds to the individual The gene value in the dimension is set to 0 to generate an individual. ; Step 4.3.5, Select The gene value is 0 and The questions corresponding to a gene value of 1 are used as an evolutionary question set. Using a binary tournament selection method from Select The question with the largest expected model change value, thus... The question number with the largest change in the expected model corresponds to the individual. The gene value in the dimension is set to 1 to generate an individual. ; Step 4.3.6: Generate N individuals according to the process from Step 4.3.2 to Step 4.3.5 and form the first... Generation population .

4. The topic selection method based on multi-objective optimization according to claim 3, characterized in that, Step 4.5 includes: Step 4.5.1, with Using test accuracy as the origin, the x-axis as the knowledge diversity, and security as the z-axis, a three-dimensional coordinate system is established. Step 4.5.2, calculate the first... Generation population The accuracy, knowledge diversity, and security of each individual's test are assessed, and the calculated results are normalized to form a three-dimensional coordinate point that is then mapped onto a three-dimensional coordinate system. Step 4.5.3: Select a three-dimensional coordinate point with the same three-dimensional coordinate values ​​from the three-dimensional coordinate system as a reference point, and connect the reference point to the origin to form a reference vector; Step 4.5.4: In the three-dimensional coordinate system, the first... Generation population The three-dimensional coordinate points mapped to each individual are connected to the origin to form an individual vector, and the individual angle formed by each individual vector and the reference vector is obtained. Step 4.5.5, from the first Generation population Among the individual angles formed by each individual, the individual corresponding to the smallest individual angle value is selected as the optimal individual. .

5. An electronic device, comprising a memory and a processor, characterized in that, The memory is used to store a program that supports the processor in executing any of the topic selection methods of claims 1-4, and the processor is configured to execute the program stored in the memory.

6. A computer-readable storage medium storing a computer program thereon, characterized in that, The computer program, when run by a processor, performs the steps of any of the topic selection methods described in claims 1-4.

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