Evolutionary Algorithm Approach to Pupils' Pedantic Accomplishment

Evolutionary Algorithm Approach to Pupils’ Pedantic Accomplishment Devasenathipathi N. Mudaliar1,2 and Nilesh K. Modi3 1

2

MCA Department, SVIT Vasad, India R & D Centre, Bharathiar University, Coimbatore 3 MCA Department, SVICS, Kadi, India

Abstract. Group learning helps pupils in boosting their learning power by creating interactions among them. However, creating groups among pupils with appropriate coupling and cohesion is still a challenge. Pupils’ groups are formed with some constraints and group formation performed by a single individual is customarily prejudiced in one way or other. In this paper, an approach has been proposed using evolutionary algorithm to increase the pupils’ pedantic accomplishment. This approach helps in optimal pupil group formation on the basis on of their previous examination scores. To justify the proposal, a study was carried out among a class of pupils pursuing post graduation. The semester examination results of pupils before and after group learning were compared. More than 66.07% of pupils scored better than their previous semester examination which positively proved the proposed approach. Keywords: Group Formation, Genetic Algorithm, Group Optimization, Performance Prediction, Academic Improvement.

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Learning,

Introduction

Group learning is that approach of learning where pupils are collaborated into different groups and each group dawns in the direction of learning. In case of individual learning pupils learn on an individual basis having least interactions among their peers. However, many academicians feel that when pupils (in groups) interact and discuss about problems and their solutions of any given topic they grasp more understanding of it than learning individually (K. Shin-ike and H. Iima, 2009) [5]. Unfortunately, it is noted that not all groups perform better in group learning environment proving that there are some issues yet to be discovered in the creating of pupil groups. In addition to this very few literatures has focused on the approaches applied for forming groups among pupils. Group learning may not succeed because pupils may be randomly grouped together without any application of group formation technique. The authors suggest a broad group formation technique among pupils studying in a class in a regular college. A formula was devised to measure the increase in academic score of a given pupil among a group of pupils using their previous (latest) score. The main objective was to increase the sum of difference between the previous score and the predicted (calculated) score. Many approaches were available to solve this S.C. Satapathy et al. (Eds.): Proc. of Int. Conf. on Front. of Intell. Comput., AISC 199, pp. 415–423. DOI: 10.1007/978-3-642-35314-7_47 © Springer-Verlag Berlin Heidelberg 2013

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problem including exhaustive search. But exhaustive search option did not seem possible because of the dynamic group size and the size of the class. This created the need for using heuristic search techniques. Although these techniques do not assure of searching the best possible answer, they search an acceptable answer by requiring less computing power. Examples of heuristic search techniques include Ant colonization algorithms, particle swarm optimization, genetic algorithm, etc. Among all heuristic techniques, genetic algorithm was chosen for its simplistic and yet optimizing nature. Experimenting using other heuristic techniques mentioned above to create pupils groups was considered as part of future work. The remaining of paper is divided as follows: The second section presents an overview of the literatures published in connection to the pupils’ group formation using heuristics. Section three explains algorithm formation of creating pupils’ groups using genetic algorithm, while section four elucidates on the application of proposed algorithm in the specific case. The fifth section presents the attained results after the experimental work. Lastly sixth section concludes the paper in addition to providing a glimpse of the future possible experimental work in connection to the current work done.

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Background Work

There are many approaches followed by academic researchers for group formation among pupils. The parameters for group formation include pupil grasping level, characteristics of assignment, interaction level among pupils, etc (Yen-Ting Lin, Yueh-Min Huang, Shu-Chen Cheng, 2010) [12]. However, in context to group formation by pupils grasping level, the total number of pupils in the class and balanced grasping level among pupils of group can be considered as base. The below text gives a brief overview of the research work published in connection to group formation among pupils. The finding presented by (Julian, Demetrio & Rosa, 2012) [4] considers three characteristics for group formation among pupils viz. pupil knowledge levels, pupils’ communicative skills and pupil leadership skill. They proposed a generic method based on genetic algorithms for getting inter-homogenous and intra-homogenous groups. They measured all pupils’ outcomes and compared them with randomly formed groups and organized groups of pupils. To find if there was a notable difference in the learning processes among groups of pupils formed by the two methods, an analogous hypothetic test was performed. They found that there was a 0.11 difference in favor of the proposed method compared with the random method, while 0.15 differences compared with the self-organized method. Their research work proved that their proposed method succeeded in achieving inter-homogenous and intra-homogenous groups in addition to the characteristics envisaged affecting positively, the growth of actions among the group members. In the research article published by (Pedro P., Alvaro O. and Pilar R., 2010) [9], the authors have believed that learning styles provide proper ways to group pupils. Also they found that heterogeneous groups performed better than groups of pupils with similar characteristics. They defined pupils' attributes to compare the groups’ performance. Their method based on Far-so-close algorithm found different groups

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based on four factors viz. the collection of pupils, the number of pupils in each group, the pair threshold and group threshold. They developed a tool called TOGETHER (a visualization tool) which chose every time a different starting pupil and used a randomly chosen pupil ordering every time. The tool TOGETHER had pupil centered use and teacher centered use. In the pupil centered use of the proposed tool, 44% of pupils answered all 10 questions correctly and none of them failed in more than 6 questions. Similarly in teacher centered use, teachers entered the learning style of pupils previously collected. They found that most of the teachers found useful to use this tool. The authors (K. Shin-ike and H. Iima., 2009) [5] in their research paper proposed a method to improve the learning effect of collaborative learning. The authors used Synthetic Personality Inventory (SPI) test to measure the academic backgrounds and personalities of pupils. The personality test result was categorized into emotional aspect, an active aspect, a volitional aspect and a characteristic aspect. Linguistic ability and non-linguistic ability questions formed measuring factors of academic backgrounds. A neural network model was applied to predict the learning results of pairs of pupils in group learning using correctness rates. Further, genetic algorithm (as stochastic local search method) was applied with the predicted results to determine the optimal pairs of pupils. Thirty pupils (4 female and 26 male) participated in this experiment and the authors confirmed that their proposed method was effective. The authors (Hwang, G.J., Yin, P.Y., Hwang C.W., & Tsai C.C., 2008) [2] proposed an enhanced genetic algorithm in order to organize cooperative learning methods using multiple grouping factors. They expressed that teachers/instructors use various sets of grouping criteria according to situations/backgrounds in a group learning context. The authors formulated a Multi-Criteria Group Composition (MCGC) problem to meet their research objective. The evaluation of proposed algorithm was done by comparing the results of series of conducted experiments with already employed methods. They found 3 constraints in the process of group formation among pupils viz. each pupil should be assigned to exactly one group, difference of number of pupils among groups should not be more than one and there is at least one pupil in the group who has understood the concept well. The authors used Roulette-Wheel selection method for selecting chromosomes for crossover and mutation. In addition to this, a web-based interface was implemented and integrated with their distance learning system, for helping teachers. The limitations of their algorithm included no guarantee of confirming the solutions as best possible solution and the proposed method was slower than the greedy method. The authors (Isotani et al, 2009) [3] have tried to present an ontology (Reality based system) which would work as a framework for group formation in collaborative learning environment. The authors hypothesized that knowing pupils’ needs beforehand increases the benefits of collaboration learning and help in gaining individually and as a group. They used ontology to represent learning theories, in order to obtain the needs of the pupils. Using this approach, the authors were able to investigate the individual and group interactions to ascertain if pupils gained expected benefits or not, which in turn helped in better group formation. The authors focused on learning scenario designing concepts, which had higher impact on changes in pupils’ learning. Learning goal, role play and instructional-learning formed the main concepts of group formation. There were 2 pairs of quality instructors and 20

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participants (from 7 different countries). The experiment consisted of two phases. First phase was planning the collaborative learning session and second phase was actual implementation of it. Instructors dealt with the group problem and used their own methods in the first phase. Then they merged selected collaborative sessions. Instructors were asked to give content learned by participants, choice of forming groups, individual and group goals and creation of sequence activities. Then the same tasks were performed using the authors proposed ontology methods. After the experiment, instructors agreed that use of ontology helped very much in the planning phase. In addition to this, instructors were able to create and share collaborative learning sessions. In the second phase, the experimental group performed better than control groups in various dimensions, thereby positively proving the authors hypothesis. Thus, the proposed ontology helped in decision making when, how and why to use the learning theories in collaborative learning.

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Genetic Algorithm and Pupils’ Group Formation

A method which tries to copy the evolution process of nature and is a search algorithm and an optimization method is Genetic Algorithm (GA). A large number of real world problems have been solved using GA (P.J. Bentley, 1997) [8]. Every possible solution for a given problem in GA is formed as a chromosome, which in turn is again composed of genes. Operators like crossover and mutation are applied onto these chromosomes to produce better chromosomes (solutions which can solve the problem). Figure 1 represents typical functioning of a genetic algorithm.

Fig. 1. Representation of (Genetic Algorithm) Process


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From the figure it is clear that an initial set of chromosome called initial population is formed as the first step of GA process. Each chromosome is a valid solution for the given problem. Next these initial set of chromosomes is evaluated for goodness of fit (called as fitness value) using some fitness function and they (chromosomes) can be arranged according to the fitness value. Some chromosomes from the initial population are selected using techniques like Roulette Wheel selection, Tournament selection, Rank selection, etc. The selected chromosomes are then cloned and sent for crossover and mutation and the next generation of population is evolved, which replaces the initial population. The process iterates till some fixed number of generations evolutions or till some fitter chromosomes are not obtained. GA can be helpful in solving the Traveling Salesman Problem (TSP). In TSP, a salesman needs to travel to every city and only once to every city with least traveling cost. In terms of GA, all valid paths are considered as chromosomes and using crossover operators (for TSP like Partially Mapped Crossover, Order Crossover, Edge Recombination Crossover, etc.) and mutation operators (like displacement mutation, insertion mutation, exchange mutation, etc.) onto the initial selected chromosomes, through various generations yield better paths with respect to the fitness function. In TSP, normally the fitness value is the total distance/cost of the given path (chromosome), which is obtained through a fitness function. The lesser the total distance of a path, the more fit is the chromosome. In TSP, the ordering of cities (genes) is important with respect to the fitness value. Pupils’ group formation problem is similar to Traveling Salesman Problem. It has been proved that group members affect the performance of individual pupils (in that group) in a group learning environment (Yen-Ting Lin, Yueh-Min Huang, Shu-Chen Cheng, 2010) [10]. A formula was formulated to compute the increase in a given pupil’s academic performance (in terms of percentage) among a given group of pupils (Devasenathipathi N., Nilesh K. Modi, 2011) [1]. To achieve this task, the previous performance (in terms of Cumulative Performance Index) of all the pupils was taken into consideration. Chromosomes represented the order of pupils’ future (calculated) performance (in terms of percentage). Each pupils future score acted as genes of chromosomes. The summation of the positive difference between the previous scores and the future scores was the fitness value. Higher this value more fit was the chromosome. It seemed difficult to use traditional crossover operators as a pupil cannot be put in more than one group. As this problem resembles ordering problem (like TSP where the order of cities is important), applying only crossover operators suited for it would be feasible. Similar was the case with mutation operator. Only mutation operators suited for ordering problems (like TSP) would be beneficial.

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Methodology

Any pupils’ performance working in group depends on two factors (Wilkinson, I. A. G., & Fung, I. Y. Y., 2001, Kyparisia Papanikolaou, Evangelia Gouli, 2010, Kuisma, R., 1998) [11] [7] [6], the grasping level of the individual pupil and the contribution level of other pupils of the group. Using these two factors, the authors have

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formulated a formula that could help in predicting the examination score of any given pupil among other group members. It was constrained that each group should consist of exactly 5 members. However, there were 56 pupils in that particular class. So 10 groups with 5 pupils in each group and one group (11th group) with six pupils was planned. Figure 2 shows the chromosomal representation of Travelling Salesman Problem and chromosomal representation of Pupils’ group formation problem (for 56 pupils).

Fig. 2. Representing Chromosomes of (Pupils Group Formation Problem)

The formula for calculating the future score among other group members is as follows (for any given group): ((((∑xi – xi)/4) * xi)/100)/5 + xi

(1)

where xi is the previously obtained score of the pupils among that particular group of pupils. The fitness function evaluated the total difference between the previous score and the predicted score of all the pupils. Higher positive difference represented more fit chromosomes. We used Partially Mapped Crossover technique for crossing over among chromosomes and Displacement Mutation technique for mutation. The functions coded (in C language) for achieving these tasks are as follows: 1. 2. 3. 4. 5.

Initialization of Population (1000 random chromosomes) Fitness value calculation through fitness function Selection of top 500 chromosomes Crossover Performing (PMX) Mutation Performing (Displacement Mutation)


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Results

The results of the experiment presented in this section can be viewed from three different angles. First angle is the number of pupils matching the predicted score, while second is the number of pupils scoring higher than their previous scores and final angle is the measure representing similarity among the predicted score and the actual score of the pupils. The graph in Figure 3 represents closeness between the actual score of pupils after the experiment and the predicted score of pupils before the experiment.

Fig. 3. (Representing closeness between Predicted Score and Actual Score)

Number of Pupils Matching the Prediction: The total number of pupils matching the prediction is 25 out of 56 pupils (with an error level of 5%). The below table shows the error level (in percentage) and the number of pupils matching the prediction. Table 1. (Error level in Predicting Scores of Students)

Error Level (in Percentage) 0–1 1–2 2–3 3–4 4–5

Number of Pupils 3 3 5 3 11

Number of Pupils Scoring Higher than Previous Examinations: 37 pupils out of 56 pupils (66.07%) scored higher than their previous examinations. The below graph in Figure 4 shows the increase in score of pupils after the experiment compared to the previous examinations result.

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Fig. 4. (Representing Increase in Pupils’ Scores after the Experiment)

Similarity Measure among Predicted Score and Actual Score of Pupils: Karl Pearson’s Linear Correlation method was used to calculate similarity measure among pupils’ predicted score and the actual score in 4th semester. The result was 0.6371 which means the method adopted is 63.71% reliable about in the pupils score using the given methodology

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Conclusion and Future Work

We have tried to present a work in relation to the pupils’ group formation method using an evolutionary algorithmic approach (more specifically genetic algorithm). Since a formula to predict the score of a pupil among other group members was already proved, it was easy to form the fitness function. The array of pupils’ scores (predicted future score) formed a chromosome. Crossover and Mutation operators were applied onto these formed chromosomes and a better chromosome was chosen, which formed the solution. In this paper we formed groups only on the basis of previous scores of pupils. Although only the score of 25 pupils (out of 56 pupils) matched the prediction (with 5% error level), it may be noted that 37 pupils (out of 56 pupils) scored better than previous semester, which positively proved our stated hypothesis. As part of future work, we would like to form groups of pupils based on many other relevant factors responsible for group formation as well try to use other heuristics based approach. In addition to this, the same kind of experiment can also be performed among people of other industries which may result in better services and production.


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