基于IRT的量子遗传算法选题策略

Item Selection Strategy with Quantum Genetic Algorithm and Item Response Theory

选题的本质是一个优化问题,虽然已有多种算法,但是大部分算法收敛速度慢、易陷入早熟、需要建立复杂的数学模型等。量子遗传算法在普通遗传算法中引入了量子计算的概念,能够使算法在种群规模很小的情况下呈现种群的多样性,而且能在很广的范围内寻优,不易陷入早熟,量子计算的并行性使算法能比普通遗传算法更快地解决寻优问题。本研究采用基于项目反应理论的量子遗传算法的选题策略。将两者的实验结果作比较,结果显示,量子遗传算法在各评价指标下的效果都优于经典遗传算法,体现出量子遗传算法搜索效率高,适应性强,收敛性速度快的特点。

The essence of the item selection is optimization. Although there are many kinds of algorithms, most of them are easy to fall into the premature status and need to establish the complex mathematical model. Furthermore, their rates of convergence are relatively slow. Quantum genetic algorithm introduces the concept of quantum computation in general genetic algorithm, which will allow the algorithm to show the diversity of the population in the case of a small population size. In addition, it can carry out optimization within a wide range, not falling into the premature status. The parallelism of quantum computation allows the algorithm to solve the optimization problem, which is faster than ordinary genetic algorithm. Research objective： （1） Selecting the items suitable for the requirements from the virtual question bank. The questions in each test paper were automatically selected according to constraint conditions, which included question type, quantity, score, and the number of words should be less than 7000. The total score of each paper was 100, and 100 questions were included. （2） Various sets of parallel test papers were selected to maintain the security of the questions. （3） Exploring the performance of the genetic algorithm and quantum genetic algorithm on question selection. Firstly, this research used matlab2012 software programming to establish the virtual question bank, which included question type, number of words, difficulty degree, distinction degree and guessing parameter. Hereinto, difficulty degree, distinction degree and guessing parameter were imitated on the basis of Item Response Theory. Secondly, this paper explored the actual test information function expression of the lowest criterion of examination. The specific method was to assign the value of HSK lowest criterion 7t as 0.6, and then adopted the three parameters Logistic model of Item Response Theory. Thus the test information function expression at the lowest criterion of examination of 0.6 was obtained, which was to be taken as the objective function of the two algorithms. Thirdly, the general genetic algorithm and quantum genetic algorithm were used to carry out the question selection test, during which the parameters of the algorithm were conducted with experimental design. The population size and the iterations of the algorithm worked as the experimental variable, and carried out the experimental design with 3×3 two elements at random. Thus 9 kinds of experimental conditions were formed. It could be called optimal algorithm only when it was optimal in all or most corresponding parameters combination. We took the maximum score test information content at the lowest criterion of examination, and the test information flatness, the question selection time, the robustness of the algorithm near the lowest criterion served as the indexes to determine whether the question selection algorithm was good or bad. We carried out double factors analysis of variance on the results and compared the advantages and the disadvantages of the two algorithms on question selection indexes. The main research conclusions included： （1） The item selection experiment result of this study with genetic algorithm showed that although there were relatively enormous test information contents at the lowest criterion of examination, the robustness of the algorithm would be deceased with the standard deviation of multiple question selection. （2） We analyzed the maximum test information content at the lowest criterion of examination and information content flatness near the lowest criterion of general genetic algorithm and quantum genetic algorithm with t-test. The result showed that under the identical population size and iteration, although the maximum test information function of general genetic algorithm was larger than quantum genetic algorithm in most cases, information content flatness near the lowest criterion of examination of question selection with general algorithm was obviously worse than quantum genetic algorithm. In addition, the question selection time of quantum genetic algorithm was shorter than general genetic algorithm, whereas its robustness was much better than general genetic algorithm. Therefore, the comprehensive performance on question selection of quantum genetic algorithm was better than general genetic algorithm.