Construction and Application of Mathematical Model Based on Intelligent Test Paper Generation Algorithm

Transcription

1 Construction and Application of Mathematical Model Based on Intelligent Test Paper Generation Algorithm Jin Zhang * School of Science, Shandong University of Technology, Zibo 25500, China *Corresponding author( zhangjin16@163.com) Abstract Compared with the traditional examination forms, the computer aided test system can greatly improve the efficiency and quality of the examination by using the advantage of information. As the key part of the system, the intelligent test paper generation strategy has an important influence on the whole system performance. The traditional intelligent test paper generation strategy does not establish a suitable mathematical model. In addition, the commonly used algorithm of generating test paper, such as the random test paper generation algorithm and the backtracking algorithm, also have the defects of long running time and poor operation quality. In recent years, the resource of test bank is growing geometrically. It is of great significance in how to deal with the massive data effectively and at the same time to ensure the performance and quality of the test paper generation. According to the defects that the running time of intelligent test paper generation is long, unable to control the quality of test paper, and the test paper cannot find feasible solutions, the algorithm is further improved and optimized in three aspects of encoding scheme, gene modification and genetic operators and applied in the mathematical model put forward in the paper. A large number of simulation tests are carried out on the above intelligent test paper generation mathematical model and algorithm. The results showed that the running speed of the intelligent test paper generation strategy proposed in this paper is fast, the quality of test paper is controllable, and it avoids the phenomenon of unable to find feasible solutions. In conclusion, on the whole, the intelligent test paper generation model and algorithm proposed are feasible and effective. Keywords: Genetic algorithm; intelligent-generating test paper; multi-objective optimization; coding 1. INTRODUCTION With the explosive growth of test resources and continuous increase of test requirements, the artificial workload in traditional examination form will be heavier and heavier. As a result, the whole test period becomes longer, and unpredictable error is prone to occur in the manual operation process. With the entering of computer and Internet technology in the education industry, more and more schools began to structure their network education and network examination system, and thus computer aided examination (CAT) system occurred. As a new mode of examination, CAT is a kind of inheritance and innovation of traditional examination form. Inheritance is because it follows the process of traditional examination. Innovation is because it makes use of strong computing ability of computer and Internet transmission sharing capacity. It greatly reduces the cycle of the test preparation and statistical results, decreases artificial workload and avoids human error in the process of examination, so the examination safety, fairness and efficiency are fully guaranteed. This paper mainly studies and discusses the intelligent test paper generation based on genetic algorithm. Intelligent test paper generation is an important and central part of CAT system, and it is also the key factor that affects the quality of examination. A complete intelligent test paper generation strategy is finished by taking the national education resources construction technical specification and practical application demand as the starting point, the mathematical model and algorithm for the two lines, and through in-depth comparison, research and simulation. In addition, the development history of genetic algorithm is introduced and its characteristics to adapt to the intelligent task are analyzed. What s more, the standard genetic algorithm is improved, and the improved scheme is verified effective and scientific by simulation experiment in this paper. In the encoding scheme, genetic modification and control parameters of, genetic algorithm is improved to apply to the mathematical model in this paper, the performance of the mathematical model and intelligent test paper generation task application is analyzed through the simulation results. Finally, this paper summarizes the content of intelligent test paper that has been completed in this paper, and points out the parts needed for further improvement and perfection. 2. METHODS 2.1 Genetic algorithm The generation and study of genetic algorithm began in The professor J. Holland, inspired by biologists making use of computer for simulation of genetic systems, proposed the use of evolutionary thinking 230

2 to study adaptive systems, and introduced generation, fitness value and so on concepts in relevant researches. In 1975, he also published a highly influential book in the academic world, "Adaptation in Natural and Artificial systems", and since then genetic algorithm was known. In 1989, David Goldberg in the University of Illinois published "Genetic Algorithms in Search, Optimization, and Machine Learning", which became the monograph that had the greatest influence on genetic algorithms. Either in theory or in the practical application, it made rich analysis and examples for genetic algorithm. In 1992, Koza proposed the concept of genetic programming, which contributed greatly to the function learning problem with symbolic representation. It can be said that the participation and research of many scholars played a major role in promoting the theoretical research and practical application of genetic algorithms. Genetic algorithm is the searching algorithm generated in the process of simulating natural selection of Darwin's biological theory (the survival of the fittest) and biological evolution of Mendel's genetic mechanism. As a result, the algorithm draws a lot of genetics and molecular biology knowledge, so it is necessary to explain some terms in the genetic algorithm. Gene: A gene is used to express the characteristics of an individual. For example, the sequence S=0100, of which 0, 1, 0, and 0 are genes, and their values represent a characteristic of an individual. Chromosomes: chromosomes are also called individuals, which are made up of genes. A certain number of individuals constitute a population. Locus: The location of the gene in the algorithm indicates the location of a gene in the chromosome, sometimes referred to as locus. The locus is calculated from left to right. For example, in S=0100, the locus of 1 is 2. Fitness: The fitness degree of an individual in a population is called fitness. The larger the value (the larger the fitness), the better the solution represented by the corresponding chromosome. In order to reflect the adaptive ability of chromosomes, we introduce the fitness function that can measure the fitness degree of every chromosome. Population: A population is composed of a set of chromosomes, to describe the genetic space of the algorithm. Encoding: Encoding is to represent the problem parameters as the solution for genetic space, that is, in a certain way, to construct a chromosome, and its reverse operation is decoding. 2.2 Algorithm flow and characteristics Operation flow of standard genetic algorithm Because genetic algorithm is to simulate the evolution process of the nature, the operation process and the evolution process is very similar. First of all, the algorithm generates the initial population through the randomized mechanism, and makes the survival of the fittest of the population individuals by using the selection operation. In addition, it generates the next generation by using crossover and mutation operations, and improves the quality of the whole population. When the population reaches the desired termination condition, the algorithm ends. The whole operation flow is shown in Figure 1: Selection is to select the individuals that adapt to the environment from the population, and these selected individuals are used to reproduce the next generation, so it is also sometimes referred to as reproduction. The selection of individuals used for generating the next generation is to determine the amount of reproduction based on the individual's fitness to the environment, which is sometimes referred to as differential reproduction. The commonly seen selection methods in the genetic operators include the following kinds: sort selection, proportional selection, League selection and elite reservation. The crossover operation simulates the gene recombination process in nature, and exchanges the genes in the same position of different individuals, resulting in a new individual, and realizing the inheritance and continuity of father gene and children gene. At present, there are several common ways of crossover: single point crossover, multi-point crossover, uniform crossover and so on. The mutation operation simulates the mutation phenomenon of some genes in the evolution of the nature. The mutation operation is mainly acting on some genes in the individual, and the gene is replaced with other alleles, resulting in the generation of a new individual. At present, there are several common mutation ways, such as basic position mutation, uniform mutation and boundary mutation. 231

3 Figure 1. Basic flow of genetic algorithm Characteristics of genetic algorithm (1) Strong adaptability. The genetic algorithm is to operate the coding of algorithm, rather than the actual variable itself. It does not need to understand the internal nature of practical problems and the mathematical equation of clear problem. It only needs to design a suitable encoding scheme, and thus it can complete the algorithm calculation. Genetic algorithms can handle arbitrary forms of objective functions and constraints, including linear and nonlinear, continuous and discrete or even hybrid searching spaces. (2) Heuristic search. The search strategy of genetic algorithm is intelligent. It is not blind or exhaustive search, but self-learning intelligent search based on the internal scientific mechanism. The internal mechanism is the simulation of the evolution of natural process of selection, crossover, mutation and so on. It uses iterative population and continuously increasing fitness value to gradually approach the optimal solution, which is an iterative incremental optimization method. (3) Parallelism. Because the genetic algorithm uses the method of population for searching, it can involve and deal with the information of many different regions in the space at the same time, which has a high degree of implicit parallelism. In this way, we can ensure that the genetic algorithm can obtain a large return with a small computational cost. 232

4 (4) Genetic algorithm can produce a lot of potential feasible solutions to practical problems, and the calculation results of feasible solutions show that there is diversity. Genetic algorithm provides the high quality solutions for the users, and the final solution and selection can be determined by the users so that the algorithm has a greater flexibility. These characteristics of genetic algorithm are very suitable for intelligent test paper generation. In the first feature, the algorithm only needs to establish an objective function and the corresponding fitness function that can affect the search direction, no need for deeper extension and study of test paper generation model. The second feature, due to the inherent intelligence characteristics of genetic algorithm, it is very cheap for the researchers and users. In the third feature, since that the genetic algorithm uses the population and mutation to calculate, it involves the processing of information and data in various regions at the same time. The implicit parallelism in fact searches greater information at a lower cost [6]. The cost performance for running the algorithm is high, which has great advantages for the test questions library with rich amount of questions. For the fourth feature, it can produce enough feasible solutions, and generate enough high quality selection after running the algorithm, which makes the calculation efficiency of genetic algorithm reaching the maximum. Of course, there are still some areas for further research: (1) Through the simulation of evolution process, the algorithm makes continuous iteration to get the optimal solution of the problem. However, if the design is improper, it is particularly prone to the too long searching time and so on problems. Especially the premature convergence in some extreme points, it will increase the cost of time and reduce the optimization effect. (2) The coding scheme is not suitable for practical problems or the coding scheme is irregular. (3) Only through the genetic algorithm coding scheme, it may not be able to fully express the constraints of the optimization problem. 2.3 Improved optimization of operator control parameters Because of the problems of genetic algorithm, many methods have been put forward, and the most active field is the study of genetic operation. The genetic algorithm mainly makes iteration through genetic manipulation. The initial population of algorithm has a wide diversity. But when the group evolved into groups of individual difference, the role of genetic operator especially the crossover operator is not the main part, and the genetic operations rely on mutation operators to generate new individuals. However, since that the general algorithm needs to ensure the consistency of the evolution of population, the probability of mutation operator is generally very low, which leads to the occurrence of premature convergence. The crossover probability P c and mutation probability P m determine the convergence of genetic algorithm, which have a direct impact on the performance of genetic algorithms. Standard genetic algorithm directly defines the crossover probability and mutation probability. Schaffer, according to his own experience, proposed that P c ranges from , and P m ranges from The larger the value of P c, the stronger the ability of the algorithm to generate new individuals, and too great value will damage the structure of the better individuals. If P c is too small, it will reduce the diversity of population, making the premature convergence of the algorithm and trapped into a local optimum. The smaller the P m, the more difficult the population to produce new individuals, resulting in the slow process of overall evolution. If P m is too large, the algorithm becomes a random search problem, affecting the convergence rate. The current automatic test paper generation system uses a fixed probability of genetic operators, which cannot meet the different characteristics of the population. The probability of curing will lead to slow evolution or deviation of evolution direction. In this paper, the adaptive crossover probability and mutation probability are used in the design of the algorithm, which can be adjusted dynamically according to the fitness value difference in the evolution process. The definition of adaptive operator probability is shown in (1) and (2). 1 P (1) c 1 exp k1 * 1 P (2) m 1 exp k 2 * In the above formulas, f f, f avg refers to the average value of the population, and f max indicates avg max the fitness of the best individual of the population. k 1 and k 2 are flexible depending on the difference of problems. In the formula, is not greater than 0 from the beginning, the P c function value is in the range of (0.5,1), and the P m function value is in the range of (0,0.5). When the population tends to be discrete (i.e. becomes greater), P c increased and P m decreased, protecting the better individuals, to avoid the destruction of population structure [9]. When the population tends to converge (i.e. becomes smaller), P c decreased and P m increased. The capacity for the population to produce new individual is enhanced, avoiding being trapped into the premature convergence. 233

5 3. SIMULATION EXPERIMENT VERIFICATION In the previous chapters, the methods of mathematical modelling and the improvement strategy of the genetic algorithm have been introduced. However, because of the particularity of the intelligent test paper generation tasks, it must be improved in many aspects before the combination of the model and algorithm. At the same time, in order to verify the feasibility of the strategy, it is necessary to use simulation experiments to test the performance of the model and algorithm. In this paper, the standard genetic algorithm and the improved genetic algorithm are carried out with simulation verification by the simulation of standard questions library. The test database includes three sub-test questions libraries, namely, the selection test questions, the judgment test questions and the subjective test questions, and each question library consists of questions. All the test questions in the library are randomly generated by the computer, and the attributes of the questions include the difficulty, the degree of differentiation, the number of times, the time of completion and the final exposure time. In this paper, the test paper consists of three question types, including 25 selection questions, 14 judgment questions, and 8 subjective questions. The experimental environment for the algorithm: processor: Intel core i3 2.27GHz; memory: Samsung DDR3 1067MHz 2GB; hard disk: WDC WD3200BEVT-08A23T1 320GB; operating system: Microsoft Windows Server 2003; and compiler: Microsoft Visual C By comparison of two algorithms based on multi-objective mathematical model put forward, for the standard genetic algorithm, the crossover probability and mutation probability were 0.5 and 0.01, respectively. In the probability formula of operator, k 1 and k 2 are 0.5 and 20, respectively. The number of individuals in the population is 50, and the evolutionary algebra is 150. The degree of difficulty, degree of differentiation, number of times, time of completion and final exposure time were selected as 0.3, 0.3, 0.2, and 0.1, respectively. The target difficulty value, the discrimination value, the number of times, the completion time and the final exposure time were 0.7, 0.5, 3, 100, and 20, respectively. Among them, the last exposure time is converted to real number. The confidentiality of all questions are open types, and the scores of all test questions are added manually by the test paper organizers after the operation of the algorithm. 4. RESULTS AND DISCUSSION Through the contrast between the standard genetic algorithm and improved genetic algorithm proposed in this paper, the maximum population fitness is shown in Figure 2, and the population average fitness situation is shown in Figure 3. Figure 2. Comparison of maximum fitness value of the population 234

6 Figure 3. Comparison of mean fitness values of the population According to the simulation results and parts of the data, we compare the quality and efficiency of the test paper using different models and algorithms, as shown in table 1. Random extraction algorithm (general model) Backtracking heuristics (general model) Standard genetic algorithm (model) Improved genetic algorithm (model) Table 1. Operational results of different teat paper generation models and algorithms Maximum fitness value Maximum mean fitness value Algorithm running time /ms Probability for finding feasible solutions Beyond description > % Beyond description > % % % From Figure 2, Figure 3 and table 1, we can see that the quality of the test paper cannot be described quantitatively by using the random extraction algorithm and the backtracking test method, and the running is too long, having the problem of unable to find feasible solutions. Using this model, the application of standard genetic algorithm avoids the problem that the test paper cannot find feasible solutions, and it can evaluate the quality of test paper. Whereas, the algorithm is easily trapped into the local optimal solution and then enters premature convergence trap. In addition, the average fitness value rises slowly, and the improvement of population quality is not obvious, resulting in slow overall evolution. The improved algorithm in this paper can effectively eliminate the defects of standard genetic algorithm in the application of the test paper, which greatly improved the execution efficiency of intelligent test paper generation task, and evaluated and controlled the quality of test paper quantificationally. What s more, there is no big difference between the improved algorithm and the standard genetic algorithm in the running time. After the operation of the algorithm, it produces five sets of optimal solutions for the test paper organizer to select, as shown in table 2. Properties Alternative solution Table 2. The final test paper generation results Difficulty Discrimination Usage Completion Last frequency time time exposure Overall quality

7 According to the type and form of the test paper, the test paper organizer can select the group of the test paper so that the whole task of the test paper can satisfy the needs of the test paper organizer to the maximum. In this chapter, the combination of the model and the algorithm is improved, and the working flow of the test paper generation algorithm is introduced. Through multiple test simulation experiments, we tested the performance of the model and algorithm. The results showed that the algorithm ran faster, the evolutionary process was steady and improved, and it can generate the optimal solution sets, providing enough quality test paper selections for test paper organizers. 5. CONCLUSION According to the defects of some intelligent test paper generation that the running time is long, unable to control the quality of test paper, and unable to find a feasible solution, the test paper generation algorithm is improved in three aspects of encoding scheme, gene modification and genetic operators and applied in the mathematical model in the paper. Test paper simulation experiment is carried out for the mathematical model and algorithm of above intelligent test paper generation. The results showed that the proposed intelligent test paper generation model and algorithm run faster, the test paper quality is controllable, and it avoids the occurrence of test paper unable to find the feasible solutions. On the whole, the intelligent test paper generation model and algorithm are feasible and effective. The method can be applied to all kinds of standardized CAT tests. In addition, the improved genetic algorithm proposed in this paper can also be used as a reference for other multi-objective optimization problems. References Hu, Z., & Xing, C. (2016). An Intelligent Test Paper Generation Method Based on Genetic Particle Swarm Optimization. In Web Information Systems and Applications Conference, th, Gao, S. M. (2016). Research on high quality intelligent test paper generation based on a genetic algorithm. In Information Science and Electronic Engineering: Proceedings of the 3rd International Conference of Electronic Engineering and Information Science (ICEEIS 2016), 4-5 January, 2016, Harbin, China, CRC Press. Zamli, K. Z., Din, F., Kendall, G., & Ahmed, B. S. (2017). Supplementary Material for the Information Sciences Paper: An Experimental Study of Hyper-Heuristic Selection and Acceptance Mechanism for Combinatorial t- way Test Suite Generation. arxiv preprint arxiv: Nalawade, G., & Ramesh, R. (2016). Automatic Generation of Question Paper from User Entered Specifications Using a Semantically Tagged Question Repository. In Technology for Education (T4E), 2016 IEEE Eighth International Conference, Zitnick, C. L., Agrawal, A., Antol, S., Mitchell, M., Batra, D., & Parikh, D. (2016). Measuring machine intelligence through visual question answering. arxiv preprint arxiv: Hernández-Orallo, J., Martínez-Plumed, F., Schmid, U., Siebers, M., & Dowe, D. L. (2016). Computer models solving intelligence test problems: progress and implications. Artificial Intelligence, 230, Ibrahim Teo, N. H., & Joy, M. (2017). Validation of Course Ontology Elements for Automatic Question Generation. In E-Learning, E-Education, and Online Training: Third International Conference, eleot 2016, Dublin, Ireland, August 31 September 2, 2016, Revised Selected Papers, Kimura, H., Noda, H., Watanabe, H., Higuchi, T., Kobayashi, R. (2017). 3.5 A 40nm flash microcontroller with 0.80 µs field-oriented-control intelligent motor timer and functional safety system for next-generation EV/HEV. In Solid-State Circuits Conference (ISSCC), 2017 IEEE International, Mazidi, K., & Tarau, P. (2016). Infusing NLU into Automatic Question Generation. In The 9th International Natural Language Generation conference,43. Jouault, C., Seta, K., & Hayashi, Y. (2016). Content-Dependent Question Generation using LOD for History Learning in Open Learning Space. New Generation Computing, 34(4), Zhou, Y., Huang, X., Liu, C., Zhang, R., Gu, X., Guan, G. (2016). Color-Multiplexing-Based Fluorescent Test Paper: Dosage-Sensitive Visualization of Arsenic (III) with Discernable Scale as Low as 5 ppb. Analytical chemistry, 88(12), Binh, N. T., & Tung, K. T. (2016). A Novel Fitness function of metaheuristic algorithms for test data generation for simulink models based on mutation analysis. Journal of Systems and Software, 120, García-Floriano, A., Ferreira-Santiago, Á., Yáñez-Márquez, C. (2017). Social Web Content Enhancement in a Distance Learning Environment: Intelligent Metadata Generation for Resources. The International Review of Research in Open and Distributed Learning, 18(1). Kim, Y., Hyeon, J., Oh, K. J., & Choi, H. J. (2016). Medical Prognosis Generation from General Blood Test Results Using Knowledge-Based and Machine-Learning-Based Approaches. In Australasian Joint Conference on Artificial Intelligence,