CN117131104B - Intelligent question-drawing and winding method and device, electronic equipment and storage medium - Google Patents
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Abstract
The application provides an intelligent question drawing and winding method, an intelligent question drawing and winding device, electronic equipment and a storage medium. The method comprises the following steps: acquiring test paper design parameters and a question quantification standard; the test paper design parameters comprise: the number of questions, the score of questions, the range of knowledge points, the course target and the repetition rate of test paper; the question quantization criteria include: knowledge point range ratio, course target ratio and test paper difficulty; and according to the test paper design parameters and the question quantification standard, taking a knowledge point range, a course target, a test paper repetition rate and difficulty as decision variables, and extracting the questions from the test paper database by utilizing a genetic algorithm based on a single-target elite retention strategy to complete the test paper. According to the method, the course targets, the knowledge points and the question attributes are organically combined together, the question standard of the test paper is quantized, the scoring standard of the target test paper is set, the intelligent question drawing and assembly paper is completed by utilizing the genetic algorithm based on the single-target elite retention strategy, the personalized requirements of test paper examination are met, and the examination quality is improved.
Description
Technical Field
The application relates to the technical field of educational systems, in particular to an intelligent question drawing and winding method, an intelligent question drawing and winding device, electronic equipment and a storage medium.
Background
The education industry is a field which is always paid attention to, and a great number of products surrounding education and teaching are in great contribution to education industry in the market at present. Particularly in recent years, the development of cloud computing and artificial intelligence has reached a new stage, and a solid foundation is laid for the stability, availability and usability of educational products, so that educational resources are extremely rich, and the learning and the working of students at all levels are greatly facilitated. In order to improve the working efficiency of teachers and detect the learning results of students through quantification standards, the standards when designing test papers are quantified by organically combining course targets, knowledge points and examination exercises of students, and finally, the examination papers are drawn by utilizing an algorithm
In the process, the traditional exercise questions and examination papers are often selected manually by teachers, so that the time consumption is long, and the control of the test question structure is not accurate enough. The related proposal provides an automatic proposal for composing the test paper, but has the problem of insufficient individuation of test paper examination, and influences the knowledge examination quality.
Disclosure of Invention
The embodiment of the application provides an intelligent question drawing and paper grouping method, device, electronic equipment and storage medium, which are used for solving the problem of insufficient individuation of examination paper examination in the related technology.
In a first aspect, an embodiment of the present application provides an intelligent question-drawing and winding method, including:
acquiring test paper design parameters and a question quantification standard; wherein, the test paper design parameters include: the number of questions, the score of questions, the range of knowledge points, the course target and the repetition rate of test paper; the question quantization criteria include: knowledge point range ratio, course target ratio and test paper difficulty;
and according to the test paper design parameters and the question quantification standard, taking the knowledge point range, the course target, the test paper repetition rate and the test paper difficulty as decision variables, and extracting questions from the test paper database by utilizing a genetic algorithm based on a single-target elite retention strategy to complete the test paper.
In one possible implementation manner, the method according to the test paper design parameter and the question quantization standard and using the knowledge point range, the course target, the test paper repetition rate and the test paper difficulty as decision variables includes:
according to the number of the questions and the number of the questions, using a sequencing coding mode, initializing N individual populations corresponding to N sets of test papers respectively according to a chromosome corresponding to each question, wherein the following matrix is expressed:
Wherein n is the number of questions in a question type, m is the number of the question type, and a is the question ID;
judging whether iteration of the current population meets an iteration stop condition or not; wherein the iteration stop condition includes: the total iteration times reach the upper limit, the score of the optimal individual has no obvious change, and the iterative evolution stagnation condition is reached;
if the iteration of the current population does not meet the iteration stopping condition, carrying out statistics and analysis on the current population according to a decision variable, and recording the optimal individual and average fitness;
selecting N-1 test papers from the currently extracted test paper set by using a competitive bidding competition algorithm as a test paper parent;
performing partial matching cross operation on N-1 test paper precursors according to a partial matching cross algorithm;
performing mutation operation on the N-1 test papers subjected to partial matching and crossing according to a reverse transformation algorithm;
calculating the optimal test paper of the current generation population, and inserting the optimal test paper into the first position of N-1 crossed test papers to obtain a new generation population;
and when the iteration of the current group meets the iteration stop condition, finding out an optimal test paper meeting the constraint condition.
In one possible implementation manner, the counting and analyzing the current population according to the decision variables, recording the optimal individual and average fitness, and the method includes:
Decoding the chromosomes, and splicing the chromosomes into a one-dimensional matrix according to the sequence to obtain a phenotype matrix Phen of the chromosomes:
Phen＝(a 1,1 a 1,2 a 1,3 … a m,n )
wherein n is the number of questions in a question type, m is the number of the question type, and a is the question ID;
setting a function Fk as a function of converting topics into knowledge points, inputting a topic ID, and outputting the number of knowledge points contained in the topic, wherein the function F k The method comprises the following steps:
F k (Phen)＝F k (a 1,1 ，a 1,2 ，a 1,3 ，...，a m,n )＝{k 1 ，k 2 ，...，k z }
wherein n is the number of topics in a topic, m is the number of topics, a is the topic ID, k is the knowledge point corresponding to the topic, z is the number of knowledge points corresponding to the topic, each topic corresponds to one or more course targets, and z is larger than or equal to m multiplied by n;
setting a function F o Inputting a topic ID as a function of the topic to the course target, and outputting the number of course targets contained in the topic, wherein the function F o The method comprises the following steps:
F o (Phen)＝F o (a 1，1 ，a 1，2 ，a 1，3 ，...，a m，n )＝{o 1 ，o 2 ，...，o s }
wherein o is s For course targets corresponding to the questions, s is the number of course targets, each question corresponds to one course target, and s=m×n;
calculating objective function values and a violation constraint matrix according to the population phenotype matrix;
and calculating the fitness of each individual by utilizing the linear scale transformation fitness according to the violation constraint matrix and the objective function matrix determined based on the objective function values, and recording the optimal individual and the average fitness.
In one possible implementation, the calculating the objective function value and the violation constraint matrix according to the population phenotype matrix includes:
counting knowledge points contained in the test paper:
KC extract ＝F count (k 1 ，k 2 ，...，k z )＝{kc e1 ，kc e2 ，...，kc er }
wherein F is count As a statistical function, r isThe number of all knowledge point types in all test papers, kc e1 ，kc e2 ，...，kc er The number of times of occurrence of each knowledge point in the test paper;
counting the occurrence probability of knowledge points contained in the test paper:
wherein kp is e1， kp e2 ，...，kp er Kc is the probability of each knowledge point in the test paper after the test paper is assembled e1 ，kc e2 ，...，kc er For the occurrence times of each knowledge point in the test paper, z is the number of the knowledge points corresponding to the questions;
the scoring of the test paper knowledge points is as follows:
wherein kpi is the probability of setting the i knowledge point selected by the user, |kp ei Kpi is the difference between the probability of the ith knowledge point in the individual and the probability of the set knowledge point;
counting course targets of test paper:
OC extract ＝F count (o 1 ，o 2 ，...，o s )＝{oc e1 ，oc e2 ，...，oc et }
wherein F is count For statistical function, s is the number of targets for all courses in all papers, oc e1 ，oc e2 ，...，oc et The number of times of occurrence of each class of course targets in the test paper;
counting the probability of each course target in the test paper:
wherein op is e1 ，op e1 ，...，op e1 For the probability of each class of course targets after the group is rolled, oc e1 ，oc e2 ，...，oc et The number of times of each class of course targets in the test paper is s, which is the number of all class targets in all test paper;
The scoring of the test paper course targets is as follows:
wherein opi is the probability of setting the i-th course target selected by the user; op (op) ei Opi | is the difference between the probability of the i-th course goal and the probability of the set course goal;
calculating the overall difficulty score of the test paper:
wherein n is the number of questions in the set test paper, qi d Qi is the difficulty of the ith question s Score is the Score of the ith question, and Score is the total Score set for the test paper;
setting a fixed value of the test paper difficulty, wherein the score of the test paper difficulty is as follows:
D score ＝|D p -D avg |
wherein Dp is a fixed value for setting the difficulty of the test paper, D avg The difficulty of setting the test paper;
setting the test paper difficulty as a range value, and grading the test paper difficulty as follows:
wherein D is low And D high To set the upper limit and the lower limit of the difficulty range, D avg The difficulty of setting the test paper;
calculating a test paper repetition rate score:
wherein the test paper participating in comparison is P= { P 1 ，p 2 ，...，p j And j is the total number of test papers to be compared and PA i PB is the question set of the extracted test paper, and rate is the repetition rate between the two sets of test paper;
when the mode of calculating the difficulty is a fixed value, the calculation formula of the objective function value and the violation constraint matrix are as follows:
Objv＝K score +O score +D avg
CV＝[repetition]
when the difficulty is calculated in a range value, the calculation formula of the objective function value and the violation constraint matrix are as follows:
Objv＝K score +O score
CV＝[repetition，D avg ]
Wherein Objv is the objective function value, D avg To set the difficulty of test paper, O score Scoring the test paper course targets, K score Scoring the test paper knowledge points; repetition is the test paper repetition rate.
In one possible implementation, the objective function value is a score representing the goodness of the individual; the violation constraint matrix contains violation constraints corresponding to each individual.
In one possible implementation manner, before initializing the individual populations corresponding to the N sets of test papers respectively according to the question type number and the question number by using the ordering coding manner, the method further includes:
classifying and sorting the questions in the test question database according to the question types, and generating dictionary codes; wherein the dictionary is encoded as a topic ID.
In one possible implementation, the correspondence between the ordered IDs and the topic IDs is found according to the dictionary codes, and the topic IDs in the test paper are decoded.
In one possible implementation manner, before initializing the N individual populations corresponding to the N sets of test papers respectively according to the question type number and the question number by using the ordering and encoding manner, the method further includes:
and inquiring and acquiring topics conforming to the ordering coding rule from a test question database according to the course targets and the knowledge point range.
In a second aspect, an embodiment of the present application provides an intelligent question-drawing and winding device, including:
the acquisition module is used for acquiring the design parameters of the test paper; wherein, the test paper design parameters include: the number of questions, the score of questions, the range of knowledge points, the course goal, the repetition rate of test paper and the difficulty;
and the paper assembly module is used for taking the knowledge point range, the course target, the test paper repetition rate and the difficulty as decision variables, taking the question number, the question number and the question score as free variables, and extracting questions from the test question database according to a genetic algorithm to complete the paper assembly.
In a third aspect, embodiments of the present application provide an electronic device comprising a memory, a processor and a computer program stored in the memory and executable on the processor, the processor implementing the steps of the method according to the first aspect or any one of the possible implementations of the first aspect, when the computer program is executed by the processor.
In a fourth aspect, embodiments of the present application provide a computer readable storage medium storing a computer program which, when executed by a processor, implements the steps of the method as described above in the first aspect or any one of the possible implementations of the first aspect.
The embodiment of the application provides an intelligent question drawing and grouping method, an intelligent question drawing and grouping device, electronic equipment and a storage medium, which are organically combined together through course targets, knowledge points and question attributes, so that question drawing standards of test papers are quantized. And by setting the scoring standard of the target test paper, the genetic algorithm based on the single-target elite retention strategy is utilized to draw the question group paper, so that the knowledge coverage rate and difficulty degree of the group paper are scientific and reasonable.
Compared with other examination paper extracting methods, the method has more and more comprehensive considered factors, not only considers knowledge points and difficulty in extraction, but also considers factors such as actual course targets, past-year examination paper repetition rate, examination paper question scores and the like, can customize various questions, meets the personalized requirements of examination paper examination, and improves knowledge examination quality.
And the supporting matrix is formed by the association between the questions, the course targets and the knowledge points, and the study condition of students can be counted and analyzed conveniently before and after the examination.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present application, the drawings that are required for the embodiments or the description of the prior art will be briefly described below, it being obvious that the drawings in the following description are only some embodiments of the present application, and that other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flowchart of an implementation of an intelligent question-drawing and volume-grouping method according to an embodiment of the present application;
FIG. 2 is a schematic structural diagram of an intelligent question-drawing and winding device according to an embodiment of the present application;
fig. 3 is a schematic structural diagram of an electronic device according to an embodiment of the present application.
Detailed Description
In the following description, for purposes of explanation and not limitation, specific details are set forth, such as particular system configurations, techniques, etc. in order to provide a thorough understanding of the embodiments of the present application. It will be apparent, however, to one skilled in the art that the present application may be practiced in other embodiments that depart from these specific details. In other instances, detailed descriptions of well-known systems, devices, circuits, and methods are omitted so as not to obscure the description of the present application with unnecessary detail.
The terms first, second and the like in the description and in the claims of the embodiments and in the above-described figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate in order to describe embodiments of the present application described herein. Furthermore, the terms "comprise" and "have," as well as any variations thereof, are intended to cover a non-exclusive inclusion.
The term "plurality" means two or more, unless otherwise indicated. The character "/" indicates that the front and rear objects are an "or" relationship. For example, A/B represents: a or B. The term "and/or" is an associative relationship that describes an object, meaning that there may be three relationships. For example, a and/or B, represent: a or B, or, A and B.
The words used in this application are merely for describing embodiments and are not intended to limit the claims. As used in the description of the embodiments and the claims, the singular forms "a," "an," and "the" (the) are intended to include the plural forms as well, unless the context clearly indicates otherwise. Similarly, the term "and/or" as used in this application is meant to encompass any and all possible combinations of one or more of the associated listed. Furthermore, when used in this application, the terms "comprises," "comprising," and/or "includes," and variations thereof, mean that the stated features, integers, steps, operations, elements, and/or components are present, but that the presence or addition of one or more other features, integers, steps, operations, elements, components, and/or groups thereof is not precluded. Without further limitation, an element defined by the phrase "comprising one …" does not exclude the presence of other like elements in a process, method or apparatus comprising such elements.
In this application, each embodiment focuses on the differences from other embodiments, and the same similar parts between the embodiments may be referred to each other. For the methods, products, etc. disclosed in the embodiments, if they correspond to the method sections disclosed in the embodiments, the description of the method sections may be referred to for relevance.
In the actual teaching process, in the same course, different professions can be given lessons, and the same profession has different courses. Each course has course targets and knowledge points of the course, but when different professions explain the same course, the specific course targets are different, and the range of the explained knowledge points is also different.
In the embodiment of the application, the same topic can be associated with a plurality of knowledge points or course targets under different professions, but under the same profession, one topic can be associated with only one course target.
The test question database types include single selection, multiple selection, judgment, gap filling, program questions, comprehensive questions and the like, and other types of questions such as simple answer questions, calculation questions and the like can be added in a self-defined mode.
Meanwhile, the difficulty of the test paper is determined by the difficulty and the fraction ratio of all the questions in the test paper. The test paper repetition rate is used for reducing the similarity with the past test paper and avoiding cheating, and belongs to constraint conditions in the process of composing the test paper.
When the examination paper is drawn, knowledge points, course targets, examination paper repetition rates, difficulty and the like of the questions are required to be comprehensively considered, the knowledge points, course targets, examination paper repetition rates, difficulty and the like can be used as decision variables to calculate the quality degree of the examination paper, meanwhile, the selection range of the knowledge points, the score of the questions and the like can influence and participate in the calculation process, so that after the examination paper is drawn by integrating multiple parameters, examination requirements of examination papers are met, different examination requirements of different professional classmates on the same department purpose are met, and knowledge examination quality is improved.
For the purpose of making the objects, technical solutions and advantages of the present application more apparent, the following description will be made with reference to the accompanying drawings by way of specific embodiments.
Fig. 1 is a flowchart of an implementation of an intelligent question-drawing and winding method according to an embodiment of the present application, as shown in fig. 1, where the method includes the following steps:
s101, acquiring test paper design parameters and a question quantization standard; the test paper design parameters comprise: the number of questions, the score of questions, the range of knowledge points, the course target and the repetition rate of test paper; the question quantization criteria include: knowledge point range ratio, course target ratio and test paper difficulty.
S102, according to the test paper design parameters and the question quantification standard, taking a knowledge point range, a course target, a test paper repetition rate and a test paper difficulty as decision variables, and extracting questions from a test paper database by utilizing a genetic algorithm based on a single target elite retention strategy to complete the test paper.
In this embodiment, the question standard of the test paper is quantified by organically combining the course target, the knowledge point and the question attribute. By setting the scoring standard of the target test paper, the test paper is drawn by using a genetic algorithm based on a single-target elite retention strategy, so that a relatively fair and fair examination state is achieved.
Compared with other examination paper extracting methods, the method has more and more comprehensive considered factors, not only considers knowledge points and difficulty in extraction, but also considers factors such as actual course targets, past-year examination paper repetition rate, examination paper question scores and the like, can customize various questions, meets the personalized requirements of examination paper examination, and improves knowledge examination quality.
And the supporting matrix is formed by the association between the questions, the course targets and the knowledge points, and the study condition of students can be counted and analyzed conveniently before and after the examination.
In a possible implementation manner, in step S102, according to the test paper design parameters and the question quantification standard, and using the knowledge point range, the course target, the test paper repetition rate and the test paper difficulty as decision variables, the test paper is completed by extracting the questions from the test paper database by using a genetic algorithm based on a single-target elite retention strategy, and the method comprises the following steps:
T1, initializing N individual populations corresponding to N sets of test papers respectively according to the number of the questions and the number of the questions by using a sequencing coding mode, wherein each question corresponds to one chromosome, and the following matrix is expressed:
wherein n is the number of questions in a question type, m is the number of the question type, and a is the question ID;
for example, assuming three types of questions in the set of rolls, three chromosomes are associated. The number of genotypes in each chromosome, i.e., the number of topics required for the winding. Assuming that 5 single choice questions, 4 judgment questions and 3 gap filling questions are required at present, the chromosome is 3 lines and can be represented by the following matrix:
wherein a is 1，1 ，a 1，2 ，a 1，3 ，a 1，4 ，a 1，5 The single choice question 5 questions are represented, the numbers 1 to 5 are coded in a sequencing mode, and the rest judgment questions and the gap filling questions are in a similar coding mode.
T2, judging whether iteration of the current population meets an iteration stop condition or not; wherein the iteration stop condition includes: the total iteration times reach the upper limit, the score of the optimal individual has no obvious change, and the iterative evolution stagnation condition is reached;
t3, if iteration of the current population does not meet the iteration stopping condition, carrying out statistics and analysis on the current population according to the decision variable, and recording the optimal individual and average fitness;
T4, selecting N-1 test papers from the currently extracted test paper set by using a competitive bidding competition algorithm as test paper precursors;
t5, performing partial matching cross operation on the N-1 test paper precursors according to a partial matching cross algorithm;
t6, carrying out mutation operation on the test paper after N-1 partial matching and crossing according to a reverse transformation algorithm;
t7, calculating the optimal test paper of the current generation population, and inserting the optimal test paper into the first position of N-1 crossed test papers to obtain a new generation population, namely a new test paper set; and repeatedly executing the iterative processing process in T2-T7 aiming at a new group (new test paper set);
and T8, when the iteration of the current group meets the iteration stop condition, finding out the optimal test paper meeting the constraint condition.
In one possible implementation manner, the statistics and analysis are performed on the current population according to the decision variables in the step T3, and the optimal individual and average fitness are recorded, including:
decoding the chromosomes, and splicing the chromosomes into a one-dimensional matrix according to the sequence to obtain a phenotype matrix Phen of the chromosomes:
Phen＝(a 1,1 a 1,2 a 1,3 … a m,n )
wherein n is the number of questions in a question type, m is the number of the question type, and a is the question ID;
setting a function Fk as a function of converting topics into knowledge points, inputting a topic ID, and outputting the number of knowledge points contained in the topic, wherein the function F k The method comprises the following steps:
F k (Phen)＝F k (a 1,1 ，a 1,2 ，a 1,3 ，...，a m,n )＝{k 1 ，k 2 ，...，k z }
wherein n is the number of topics in a topic, m is the number of topics, a is the topic ID, k is the knowledge point corresponding to the topic, z is the number of knowledge points corresponding to the topic, each topic corresponds to one or more course targets, and z is larger than or equal to m multiplied by n;
setting a function F o Inputting a topic ID as a function of the topic to the course target, and outputting the number of course targets contained in the topic, wherein the function F o The method comprises the following steps:
F o (Phen)＝F o (a 1，1 ，a 1，2 ，a 1，3 ，...，a m，n )＝{o 1 ，o 2 ，...，o s }
wherein o is s And s is the number of course targets, each question corresponds to one course target, and s=m×n.
T32, calculating objective function values and a violation constraint matrix according to the population phenotype matrix;
and T33, calculating the fitness of each individual by utilizing the linear scale transformation fitness according to the violation constraint matrix and the objective function matrix determined based on the objective function values, and recording the optimal individual and the average fitness.
The embodiments of the present application aim atAnd the passing questions are correlated with the knowledge points and the course targets and other question attributes, and intelligent question drawing and winding are performed. Such association, i.e., association of knowledge points, course objectives, topics, may be referred to as three-level linkage. The association relationship among knowledge points, course targets and topics of the subject is realized by the function F k Sum function F o The construction is convenient, and the intelligent question selection is finished conveniently.
In one possible implementation, calculating the objective function value and the violation constraint matrix according to the population phenotype matrix in step T32 includes:
t321, counting knowledge points contained in the test paper:
KC extract ＝F count (k 1 ，k 2 ，...，k z )＝{kc e1 ，kc e2 ，...，kc er }
wherein F is count R is the number of all knowledge point types in all test papers and kc is the statistical function e1 ，kc e2 ，...，kc er The number of times of occurrence of each knowledge point in the test paper;
counting the occurrence probability of knowledge points contained in the test paper:
wherein kp is e1 ，kp e2 ，...，kp er Kc is the probability of each knowledge point in the test paper after the test paper is assembled e1 ，kc e2 ，...，kc er For the occurrence times of each knowledge point in the test paper, z is the number of the knowledge points corresponding to the questions;
the scoring of the test paper knowledge points is as follows:
wherein kpi is the probability of setting the i knowledge point selected by the user, |kp ei Kpi is the probability and set knowledge point of the ith knowledge point in the individualThe difference between the probabilities of (2); after the summation, if K score The larger the score, the more inconsistent the knowledge points representing the questions in the test paper are with the set knowledge point targets, so K score The smaller the score, the better, if 0, the knowledge point fully accords with the setting;
t322, counting course targets of the test paper:
OC extract ＝F count (o 1 ，o 2 ，...，o s )＝{oc e1 ，oc e2 ，...，oc et }
wherein F is count For statistical function, s is the number of targets for all courses in all papers, oc e1 ，oc e2 ，...，oc et The number of times of occurrence of each class of course targets in the test paper;
counting the probability of each course target in the test paper:
wherein op is e1 ，op e1 ，…，op e1 For the probability of each class of course targets after the group is rolled, oc e1 ，oc e2 ，...，oc et And s is the number of the course targets in all the test papers for each class of course targets in the test papers.
The scoring of the test paper course targets is as follows:
wherein opi is the probability of setting the objective of the i-th course selected by the user. Op (op) ei Opi | is the difference between the probability of the i-th course goal and the probability of the set course goal; after summation, if O score The larger the score, the more inconsistent the course target for the subject in the test paper is with the set course target, so O score The smaller the score, the better, if 0, the better the score indicates that the set course goal is fully met.
T323, calculating the overall difficulty score of the test paper; optionally, the difficulty level of the test paper is set to be 5 levels, the simplest level is 1 level, and the most difficult level is 5 level; in other embodiments, the test paper difficulty level classification strategy can be adjusted according to specific requirements;
the calculation formula of the test paper difficulty is as follows:
wherein n is the number of questions in the set test paper, qi d Qi is the difficulty of the ith question s Score is the Score of the ith question, and Score is the total Score set for the test paper;
Setting a fixed value of the test paper difficulty, wherein the score of the test paper difficulty is as follows:
D score ＝|D p -D avg |
wherein Dp is a fixed value for setting the difficulty of the test paper, D avg The difficulty of setting the test paper; the absolute value of the difference between the two, i.e. the score of the difficulty, D score The smaller the fraction, the better, if 0, the full compliance with the set point.
Setting the test paper difficulty as a range value, and grading the test paper difficulty as follows:
wherein D is low And D high To set the upper limit and the lower limit of the difficulty range, D avg To set the difficulty of the test paper.
Discussion of the cases: 1) As long as the calculated test paper difficulty value is in the range area, the value is 0, namely the condition is met. 2) And if the test paper difficulty value is lower than or higher than the upper limit and the lower limit of the set range, taking the difference value as a score.
If the first type is the first type, the difficulty of the test paper can be used as a decision variable in the objective function value, so that the closer the difficulty value of the test paper is to the set difficulty value, the better the difficulty value of the test paper is; if the second mode is adopted, the test paper difficulty is used as a median value of the violation constraint matrix, and the conditions are not met when the set difficulty range is exceeded.
T324, calculating the test paper repetition rate score:
wherein the test paper participating in comparison is P= { P 1 ，p 2 ，...，p j And j is the total number of test papers to be compared and PA i PB is the question set of the extracted test paper, the number of the question intersections is taken as the question set of the i-th set of the reference test paper, the number of the question intersections is divided by the number of the i-th set of the reference test paper, and then the repetition rate of the two sets of the test papers is obtained by multiplying 100, and the rate is the repetition rate between the two sets of the test papers;
When the mode of calculating the difficulty is a fixed value, the calculation formula of the objective function value and the violation constraint matrix are as follows:
Objv＝K score +O score +D avg
CV＝[repetition]
when the difficulty is calculated in a range value, the calculation formula of the objective function value and the violation constraint matrix are as follows:
Objv＝K score +O score
CV＝[repetition，D avg ]
wherein Objv is the objective function value, D avg To set the difficulty of test paper, O score Scoring the test paper course targets, K score Scoring the test paper knowledge points; repetition is the test paper repetition rate.
In one possible implementation, the objective function value is a score representing the goodness of the individual; the violation constraint matrix contains violation constraints corresponding to each individual. Each element is less than or equal to 0, indicating that the individual satisfies the constraint, and if greater than 0, indicating that the individual does not satisfy the constraint, the greater the value, the greater the degree of violation of the constraint.
In one possible implementation manner, before initializing the individual populations corresponding to the N sets of test papers respectively according to the number of questions and the number of questions in the step S102 by using the ordering and encoding manner, the method further includes:
classifying and sorting the questions in the test question database according to the question types, and generating dictionary codes; wherein the dictionary is encoded as a title ID. The corresponding relation between the topic ID and the ordered ID is kept, and the later-stage decoding of the winding result is also facilitated.
In one possible implementation, the correspondence between the ordered IDs and the topic IDs is found according to dictionary coding, and the topic IDs in the test paper are decoded.
In one possible implementation manner, before initializing the individual populations corresponding to the N sets of test papers respectively according to the number of questions and the number of questions in the step S102 by using the ordering and encoding manner, the method further includes:
and inquiring and acquiring the questions conforming to the ordering coding rule from the test question database according to the course targets and the knowledge point range.
In one possible implementation manner, before initializing the individual populations corresponding to the N sets of test papers respectively according to the number of questions and the number of questions in the step S102 by using the ordering and encoding manner, the method further includes:
classifying and sorting the questions in the test question database according to the question types, and generating dictionary codes; wherein the dictionary is encoded as a title ID;
and inquiring and acquiring the questions conforming to the ordering coding rule from the test question database according to the course targets and the knowledge point range.
It should be understood that the sequence number of each step in the foregoing embodiment does not mean that the execution sequence of each process should be determined by the function and the internal logic of each process, and should not limit the implementation process of the embodiment of the present application in any way.
The following are device embodiments of the present application, for details not described in detail therein, reference may be made to the corresponding method embodiments described above.
Fig. 2 is a schematic structural diagram of an intelligent question-drawing and winding device provided in an embodiment of the present application, as shown in fig. 2, for convenience of explanation, only a portion relevant to the embodiment of the present application is shown, as shown in fig. 2, where the device includes:
the acquisition module 201 is used for acquiring the test paper design parameters and the question quantization standard; the test paper design parameters comprise: the number of questions, the score of questions, the range of knowledge points, the course target and the repetition rate of test paper; the question quantization criteria include: knowledge point range ratio, course target ratio and test paper difficulty;
the assembly module 202 is configured to complete an assembly by extracting the questions from the question database using a genetic algorithm based on a single-objective elite retention policy according to the design parameters of the test paper and the quantization standard of questions, and using the knowledge point range, the course objective, the test paper repetition rate and the test paper difficulty as decision variables.
In this embodiment, the question standard of the test paper is quantified by organically combining the course target, the knowledge point and the question attribute. By setting the scoring standard of the target test paper, the test paper is drawn by using a genetic algorithm based on a single-target elite retention strategy, so that a relatively fair and fair examination state is achieved.
Compared with other examination paper extracting methods, the method has more and more comprehensive considered factors, not only considers knowledge points and difficulty in extraction, but also considers factors such as actual course targets, past-year examination paper repetition rate, examination paper question scores and the like, can customize various questions, meets the personalized requirements of examination paper examination, and improves knowledge examination quality.
And the supporting matrix is formed by the association between the questions, the course targets and the knowledge points, and the study condition of students can be counted and analyzed conveniently before and after the examination.
Fig. 3 is a schematic structural diagram of an electronic device according to an embodiment of the present application. As shown in fig. 3, the electronic apparatus 3 of this embodiment includes: a processor 30, a memory 31 and a computer program 32 stored in said memory 31 and executable on said processor 30. The processor 30, when executing the computer program 32, implements the steps of the various embodiments of the intelligent question-drawing and volume-grouping method described above, such as the steps shown in fig. 1. Alternatively, the processor 30 may perform the functions of the modules/units of the apparatus embodiments described above, such as the functions of the modules shown in fig. 2, when executing the computer program 32.
By way of example, the computer program 32 may be partitioned into one or more modules/units that are stored in the memory 31 and executed by the processor 30 to complete the present application. The one or more modules/units may be a series of computer program instruction segments capable of performing the specified functions for describing the execution of the computer program 32 in the electronic device 3. For example, the computer program 32 may be partitioned into the modules shown in FIG. 2.
The electronic device 3 may be a computing device such as a desktop computer, a notebook computer, a palm computer, a cloud server, etc. The electronic device 3 may include, but is not limited to, a processor 30, a memory 31. It will be appreciated by those skilled in the art that fig. 3 is merely an example of the electronic device 3 and does not constitute a limitation of the electronic device 3, and may include more or fewer components than shown, or may combine certain components, or different components, e.g., the electronic device may further include an input-output device, a network access device, a bus, etc.
The processor 30 may be a central processing unit (Central Processing Unit, CPU), other general purpose processors, digital signal processors (Digital Signal Processor, DSP), application specific integrated circuits (Application Specific Integrated Circuit, ASIC), field-programmable gate arrays (Field-Programmable Gate Array, FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, or the like. A general purpose processor may be a microprocessor or the processor may be any conventional processor or the like.
The memory 31 may be an internal storage unit of the electronic device 3, such as a hard disk or a memory of the electronic device 3. The memory 31 may be an external storage device of the electronic device 3, such as a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card) or the like, which are provided on the electronic device 3. Further, the memory 31 may also include both an internal storage unit and an external storage device of the electronic device 3. The memory 31 is used for storing the computer program and other programs and data required by the electronic device. The memory 31 may also be used for temporarily storing data that has been output or is to be output.
It will be apparent to those skilled in the art that, for convenience and brevity of description, only the above-described division of the functional units and modules is illustrated, and in practical application, the above-described functional distribution may be performed by different functional units and modules according to needs, i.e. the internal structure of the apparatus is divided into different functional units or modules to perform all or part of the above-described functions. The functional units and modules in the embodiment may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit, where the integrated units may be implemented in a form of hardware or a form of a software functional unit. In addition, specific names of the functional units and modules are only for convenience of distinguishing from each other, and are not used for limiting the protection scope of the present application. The specific working process of the units and modules in the above system may refer to the corresponding process in the foregoing method embodiment, which is not described herein again.
In the foregoing embodiments, the descriptions of the embodiments are emphasized, and in part, not described or illustrated in any particular embodiment, reference is made to the related descriptions of other embodiments.
Those of ordinary skill in the art will appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, or combinations of computer software and electronic hardware. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the solution. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present application.
In the embodiments provided in the present application, it should be understood that the disclosed apparatus/electronic device and method may be implemented in other manners. For example, the apparatus/electronic device embodiments described above are merely illustrative, e.g., the division of the modules or units is merely a logical function division, and there may be additional divisions in actual implementation, e.g., multiple units or components may be combined or integrated into another system, or some features may be omitted, or not performed. Alternatively, the coupling or direct coupling or communication connection shown or discussed may be an indirect coupling or communication connection via interfaces, devices or units, which may be in electrical, mechanical or other forms.
The units described as separate units may or may not be physically separate, and units shown as units may or may not be physical units, may be located in one place, or may be distributed on a plurality of network units. Some or all of the units may be selected according to actual needs to achieve the purpose of the solution of this embodiment.
In addition, each functional unit in each embodiment of the present application may be integrated in one processing unit, or each unit may exist alone physically, or two or more units may be integrated in one unit. The integrated units may be implemented in hardware or in software functional units.
The integrated modules/units, if implemented in the form of software functional units and sold or used as stand-alone products, may be stored in a computer readable storage medium. Based on such understanding, the present application may implement all or part of the flow of the foregoing embodiment method, or may be implemented by implementing relevant hardware by using a computer program, where the computer program may be stored in a computer readable storage medium, and the computer program may implement the steps of each foregoing embodiment of the intelligent question-drawing and winding method when executed by a processor. Wherein the computer program comprises computer program code which may be in source code form, object code form, executable file or some intermediate form etc. The computer readable medium may include: any entity or device capable of carrying the computer program code, a recording medium, a U disk, a removable hard disk, a magnetic disk, an optical disk, a computer Memory, a Read-Only Memory (ROM), a random access Memory (Random Access Memory, RAM), an electrical carrier signal, a telecommunications signal, a software distribution medium, and so forth.
The above embodiments are only for illustrating the technical solution of the present application, and are not limiting; although the present application has been described in detail with reference to the foregoing embodiments, it should be understood by those of ordinary skill in the art that: the technical scheme described in the foregoing embodiments can be modified or some technical features thereof can be replaced by equivalents; such modifications and substitutions do not depart from the spirit and scope of the technical solutions of the embodiments of the present application, and are intended to be included in the scope of the present application.
Claims (7)
1. An intelligent question-drawing and winding method is characterized by comprising the following steps:
acquiring test paper design parameters and a question quantification standard; wherein, the test paper design parameters include: the number of questions, the score of questions, the range of knowledge points, the course target and the repetition rate of test paper; the question quantization criteria include: knowledge point range ratio, course target ratio and test paper difficulty;
according to the test paper design parameters and the question quantification standard, taking the knowledge point range, the course target, the test paper repetition rate and the test paper difficulty as decision variables, and extracting questions from a test paper database by utilizing a genetic algorithm based on a single-target elite retention strategy to complete a test paper;
The method takes the knowledge point range, the course target, the test paper repetition rate and the test paper difficulty as decision variables according to the test paper design parameters and the question quantization standard, and comprises the following steps:
according to the number of the questions and the number of the questions, using a sequencing coding mode, initializing N individual populations corresponding to N sets of test papers respectively according to a chromosome corresponding to each question, wherein the following matrix is expressed:
wherein n is the number of questions in a question type, m is the number of the question type, and a is the question ID;
judging whether iteration of the current population meets an iteration stop condition or not; wherein the iteration stop condition includes: the total iteration times reach the upper limit, the score of the optimal individual has no obvious change, and the iterative evolution stagnation condition is reached;
if the iteration of the current population does not meet the iteration stopping condition, carrying out statistics and analysis on the current population according to a decision variable, and recording the optimal individual and average fitness;
selecting N-1 test papers from the currently extracted test paper set by using a competitive bidding competition algorithm as a test paper parent;
performing partial matching cross operation on N-1 test paper precursors according to a partial matching cross algorithm;
performing mutation operation on the N-1 test papers subjected to partial matching and crossing according to a reverse transformation algorithm;
Calculating the optimal test paper of the current generation population, and inserting the optimal test paper into the first position of N-1 crossed test papers to obtain a new generation population;
when the iteration of the current group meets the iteration stop condition, finding out an optimal test paper meeting the constraint condition;
the statistics and analysis are carried out on the current population according to the decision variables, and the optimal individual and average fitness are recorded, including:
firstly, decoding the chromosomes, and splicing the chromosomes into a one-dimensional matrix according to the sequence to obtain a phenotype matrix Phen of the chromosomes:
Phen＝(a 1，1 a 1，2 a 1，3 … a m，n )
wherein n is the number of questions in a question type, m is the number of the question type, and a is the question ID;
setting a function F k To turn the questions into knownA function of identifying points, inputting a topic ID, outputting the number of knowledge points contained in the topic, wherein the function F k The method comprises the following steps:
F k (Phen)＝F k (a 1，1 ，a 1，2 ，a 1，3 ，...，a m，n )＝{k 1 ，k 2 ，...，k z }
wherein n is the number of topics in a topic, m is the number of topics, a is the topic ID, k is the knowledge point corresponding to the topic, z is the number of knowledge points corresponding to the topic, each topic corresponds to one or more course targets, and z is larger than or equal to m multiplied by n;
setting a function F o Inputting a topic ID as a function of the topic to the course target, and outputting the number of course targets contained in the topic, wherein the function F o The method comprises the following steps:
F o (Phen)＝F o (a 1，1 ，a 1，2 ，a 1，3 ，...，a m，n )＝{o 1 ，o 2 ，...，o s }
wherein o is s For course targets corresponding to the questions, s is the number of course targets, each question corresponds to one course target, and s=m×n;
calculating objective function values and a violation constraint matrix according to the population phenotype matrix;
calculating the fitness of each individual by utilizing the linear scale transformation fitness according to the violation constraint matrix and the objective function matrix determined based on the objective function value, and recording the optimal individual and the average fitness;
the calculating the objective function value and the violation constraint matrix according to the population phenotype matrix comprises the following steps:
counting knowledge points contained in the test paper:
KC extract ＝F count (k 1 ，k 2 ，...，k z )＝{kc e1 ，kc e2 ，...，kc er }
wherein F is count R is the number of all knowledge point types in all test papers and kc is the statistical function e1 ，kc e2 ，...，kc er For each test paperThe number of times the knowledge point species appears;
counting the occurrence probability of knowledge points contained in the test paper:
wherein kp is e1 ，kp e2 ，...，kp er Kc is the probability of each knowledge point in the test paper after the test paper is assembled e1 ，kc e2 ，...，kc er For the occurrence times of each knowledge point in the test paper, z is the number of the knowledge points corresponding to the questions;
the scoring of the test paper knowledge points is as follows:
wherein kpi is the probability of setting the i knowledge point selected by the user, |kp ei Kpi is the difference between the probability of the ith knowledge point in the individual and the probability of the set knowledge point;
Counting course targets of test paper:
OC extract ＝F count (o 1 ，o 2 ，...，o s )＝{oc e1 ，oc e2 ，...，oc et }
wherein F is count For statistical function, s is the number of targets for all courses in all papers, oc e1 ，oc e2 ，...，oc et The number of times of occurrence of each class of course targets in the test paper;
counting the probability of each course target in the test paper:
wherein op is e1 ，op e1 ，...，op e1 For the probability of each class of course targets after the group is rolled, oc e1 ，oc e2 ，...，oc et The number of times of each class of course targets in the test paper is s, which is the number of all class targets in all test paper;
the scoring of the test paper course targets is as follows:
wherein opi is the probability of setting the i-th course target selected by the user; op (op) ei Opi | is the difference between the probability of the i-th course goal and the probability of the set course goal;
calculating the overall difficulty score of the test paper:
wherein n is the number of questions in the set test paper, qi d Qi is the difficulty of the ith question s Score is the Score of the ith question, and Score is the total Score set for the test paper;
setting a fixed value of the test paper difficulty, wherein the score of the test paper difficulty is as follows:
D score ＝|D p -D avg |
wherein Dp is a fixed value for setting the difficulty of the test paper, D avg The difficulty of setting the test paper;
setting the test paper difficulty as a range value, and grading the test paper difficulty as follows:
wherein D is low And D high To set the upper limit and the lower limit of the difficulty range, D avg The difficulty of setting the test paper;
calculating a test paper repetition rate score:
Wherein the test paper participating in comparison is P= { P 1 ，p 2 ，...，p j And j is the total number of test papers to be compared and PA i PB is the question set of the extracted test paper, and rate is the repetition rate between the two sets of test paper;
when the mode of calculating the difficulty is a fixed value, the calculation formula of the objective function value and the violation constraint matrix are as follows:
Objv＝K score +O score +D avg
CV＝[repetition]
when the difficulty is calculated in a range value, the calculation formula of the objective function value and the violation constraint matrix are as follows:
Objv＝K score +O score
CV＝[repetition，D avg ]
wherein Objv is the objective function value, D avg To set the difficulty of test paper, O score Scoring the test paper course targets, K score Scoring the test paper knowledge points; repetition is the test paper repetition rate.
2. The intelligent question-drawing and winding method according to claim 1, wherein the objective function value is a score indicating the degree of merit of an individual; the violation constraint matrix contains violation constraints corresponding to each individual.
3. The method for intelligent question drawing and grouping according to claim 1, wherein before initializing the individual population of N sets of test papers respectively corresponding to N sets of test papers by using the ordering and encoding method according to the number of questions and the number of questions, the method further comprises:
classifying and sorting the questions in the test question database according to the question types, and generating dictionary codes; wherein the dictionary is encoded as a topic ID.
4. The method for intelligent question drawing and paper assembly according to claim 1, wherein before initializing the individual populations of N sets of test papers respectively corresponding to N sets of test papers by using a sequencing coding method according to the number of questions and the number of questions, the method further comprises:
and inquiring and acquiring topics conforming to the ordering coding rule from a test question database according to the course targets and the knowledge point range.
5. An intelligent question drawing and winding device is characterized by comprising:
the acquisition module is used for acquiring the test paper design parameters and the problem-setting quantization standard; wherein, the test paper design parameters include: the number of questions, the score of questions, the range of knowledge points, the course target and the repetition rate of test paper; the question quantization criteria include: knowledge point range ratio, course target ratio and test paper difficulty;
the test paper assembly module is used for extracting questions from the test paper database by using a genetic algorithm based on a single-target elite retention strategy to complete the test paper according to the test paper design parameters and the question quantification standard and by taking the knowledge point range, the course target, the test paper repetition rate and the test paper difficulty as decision variables;
the paper grouping module is specifically configured to initialize N individual populations corresponding to N sets of test papers respectively according to the number of questions and the number of questions by using a manner of ordering and encoding, where each question corresponds to one chromosome, and the following matrix is represented:
Wherein n is the number of questions in a question type, m is the number of the question type, and a is the question ID;
judging whether iteration of the current population meets an iteration stop condition or not; wherein the iteration stop condition includes: the total iteration times reach the upper limit, the score of the optimal individual has no obvious change, and the iterative evolution stagnation condition is reached;
if the iteration of the current population does not meet the iteration stopping condition, carrying out statistics and analysis on the current population according to a decision variable, and recording the optimal individual and average fitness;
selecting N-1 test papers from the currently extracted test paper set by using a competitive bidding competition algorithm as a test paper parent;
performing partial matching cross operation on N-1 test paper precursors according to a partial matching cross algorithm;
performing mutation operation on the N-1 test papers subjected to partial matching and crossing according to a reverse transformation algorithm;
calculating the optimal test paper of the current generation population, and inserting the optimal test paper into the first position of N-1 crossed test papers to obtain a new generation population;
when the iteration of the current group meets the iteration stop condition, finding out an optimal test paper meeting the constraint condition;
the winding module is further specifically configured to decode the chromosomes first, splice the chromosomes into a one-dimensional matrix according to the sequence, and obtain a phenotype matrix Phen of the chromosomes:
Phen＝(a 1，1 a 1，2 a 1，3 … a m，n )
Wherein n is the number of questions in a question type, m is the number of the question type, and a is the question ID;
setting a function F k Inputting a question ID for a function of converting a question into knowledge points, and outputting the number of knowledge points contained in the question, wherein the function F k The method comprises the following steps:
F k (Phen)＝F k (a 1，1 ，a 1，2 ，a 1，3 ，...，a m，k )＝{k 1 ，k 2 ，...，k z }
wherein n is the number of topics in a topic, m is the number of topics, a is the topic ID, k is the knowledge point corresponding to the topic, z is the number of knowledge points corresponding to the topic, each topic corresponds to one or more course targets, and z is larger than or equal to m multiplied by n;
setting a function F o Inputting a topic ID as a function of the topic to the course target, and outputting the number of course targets contained in the topic, wherein the function F o The method comprises the following steps:
F o (Phen)＝F o (a 1，1 ，a 1，2 ，a 1，3 ，...，a m，n )＝{o 1 ，o 2 ，...，o s }
wherein o is s For course targets corresponding to the questions, s is the number of course targets, each question corresponds to one course target, and s=m×n;
calculating objective function values and a violation constraint matrix according to the population phenotype matrix;
calculating the fitness of each individual by utilizing the linear scale transformation fitness according to the violation constraint matrix and the objective function matrix determined based on the objective function value, and recording the optimal individual and the average fitness;
the group paper module is also specifically used for counting knowledge points contained in the test paper:
KC extract ＝F count (k 1 ，k 2 ，...，k z )＝{kc e1 ，kc e2 ，...，kc er }
Wherein F is count R is the number of all knowledge point types in all test papers and kc is the statistical function e1 ，kc e2 ，...，kc er The number of times of occurrence of each knowledge point in the test paper;
counting the occurrence probability of knowledge points contained in the test paper:
wherein kp is e1 ，kp e2 ，...，kp er Kc is the probability of each knowledge point in the test paper after the test paper is assembled e1 ，kc e2 ，...，kc er For the occurrence times of each knowledge point in the test paper, z is the number of the knowledge points corresponding to the questions;
the scoring of the test paper knowledge points is as follows:
wherein kpi is the probability of setting the i knowledge point selected by the user, |kp ei Kpi is the difference between the probability of the ith knowledge point in the individual and the probability of the set knowledge point;
counting course targets of test paper:
OC extract ＝F count (o 1 ，o 2 ，...，o s )＝{oc e1 ，oc e2 ，...，oc et }
wherein F is count For statistical function, s is the number of targets for all courses in all papers, oc e1 ，oc e2 ，...，oc et The number of times of occurrence of each class of course targets in the test paper;
counting the probability of each course target in the test paper:
wherein op is e1 ，op e1 ，...，op e1 For the probability of each class of course targets after the group is rolled, oc e1 ，oc e2 ，...，oc et The number of times of each class of course targets in the test paper is s, which is the number of all class targets in all test paper;
the scoring of the test paper course targets is as follows:
wherein opi is the probability of setting the i-th course target selected by the user; op (op) ei Opi | is the difference between the probability of the i-th course goal and the probability of the set course goal;
Calculating the overall difficulty score of the test paper:
wherein the method comprises the steps ofN is the number of questions in the set test paper, qi d Qi is the difficulty of the ith question s Score is the Score of the ith question, and Score is the total Score set for the test paper;
setting a fixed value of the test paper difficulty, wherein the score of the test paper difficulty is as follows:
D score ＝|D p -D avg |
wherein Dp is a fixed value for setting the difficulty of the test paper, D avg The difficulty of setting the test paper;
setting the test paper difficulty as a range value, and grading the test paper difficulty as follows:
wherein D is low And D high To set the upper limit and the lower limit of the difficulty range, D avg The difficulty of setting the test paper;
calculating a test paper repetition rate score:
wherein the test paper participating in comparison is P= { P 1 ，p 2 ，...，p j And j is the total number of test papers to be compared and PA i PB is the question set of the extracted test paper, and rate is the repetition rate between the two sets of test paper;
when the mode of calculating the difficulty is a fixed value, the calculation formula of the objective function value and the violation constraint matrix are as follows:
Objv＝K score +O score +D avg
CV＝[repetition]
when the difficulty is calculated in a range value, the calculation formula of the objective function value and the violation constraint matrix are as follows:
Objv＝K score +O score
CV＝[repetition，D avg ]
wherein Objv is the objective function value, D avg To set the difficulty of test paper, O score Scoring the test paper course targets, K score Scoring the test paper knowledge points; repetition is the test paper repetition rate.
6. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that the processor implements the steps of the method according to any of the preceding claims 1-4 when the computer program is executed.
7. A computer readable storage medium storing a computer program, characterized in that the computer program when executed by a processor implements the steps of the method according to any of the preceding claims 1 to 4.
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