應用群聚智慧技術於數位學習輔助教材之產生機制

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Research Express@NCKU - Articles Digest

Research Express@NCKU Volume 14 Issue 4 - June 11, 2010

[ http://research.ncku.edu.tw/re/articles/e/20100611/2.html ]

Applying Swarm Intelligence to Generate e-Learning

Auxiliary Materials

Tien-Chi Huang

1

_{and Yueh-Min Huang}

2,*

1_{Department of Computer Science and Information Engineering, China University of Science and}

Technology

2_{Department of Engineering Science, National Cheng Kung University}

huang@mail.ncku.edu.tw

Expert Systems with Applications Volume 35, Issue 4, November 2008, Pages 2113-2122

T

he ultimate goal of an e-Learning system is not only to provide diversified and

standardized learning or educational materials with computer-assisted technologies, but also to offer efficient and effective learning for every kind of learner. In order to achieve this goal, a lot of researches have been done in this field. However, fixed content auxiliary materials were adopted in the studies; consequently, factors such as adaptation and interaction received less emphasis. Therefore, rather than looking for a one-size-fits-all model, adaptation and interaction of auxiliary materials need to be strengthened. An innovative approach that uses serial blog article composition with

PSO (SBACPSO) algorithm is proposed to optimize the selection of blog articles to compose serial auxiliary materials.

In order to compose blog articles for auxiliary materials, we consider a few criteria for selecting high-quality blog articles. The first criterion is the difficult of a blog article which is mapped to a degree given by the instructor. The association degree between blog articles and a specified topic is the second criterion which is also given by the instructor. In addition, the third and fourth criteria are two counts, the number of comments of blog articles and the number of trackbacks related to a blog article. These two criteria tested whether a blog article could raise the discussion within a certain issue and could be regarded as a useful learning resource.

Model Design

Firstly, we assume that K auxiliary materials would be produced in a specified course. To compose blog articles as the auxiliary material k, 1≤k≤K, the following variables are used in the proposed model:

● d_i, 1≤i≤N: the difficulty of ith blog article, where N is number of blog articles in the blog knowledge base. ● r_ij, 1≤i≤N, 1≤j≤M: the association degree between ith blog article and the topic j, where M is number of

topics in a course.

● c_i, 1≤i≤N: the number of comments of ith blog article. ● t_i, 1≤i≤N: the number of trackbacks of ith blog article.

● U: upper bound on the expected comments for each blog article. ● L: lower bound on the expected comments for each blog article.

● x_ik, 1≤i≤N and 1≤k≤K: the decision variable is set to 1 if blog b_i is in auxiliary material k; otherwise, it is set to 0.

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● h_j, 1≤j≤M: the lower bound on the expected relevance of the topic j.

● C(x): a membership function mapping the number of comments x into a degree. ● T(x): a function, which has a sigmoid form, maps trackback count x into a score.

Afterwards, the formal definitions of the proposed model are shown in the following equations and a constraint.

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Equation (1) calculates the difference between the average difficulty degree for each auxiliary material and the target difficulty degree D given by the lecturer. Herein, combinational blog articles should be selected such that the average difficulty degree of each auxiliary material is close to the target difficulty degree. In equation (2), the total relevance of the selected blog articles in each auxiliary material is firstly calculated (i.e. ), and then the expected relevance of each topic is used to calculate the relevance difference of each topic for each auxiliary material. The more relevance between blog articles and topics there is, the less the calculated relevance difference is. In equation (3), the trackback count of each blog article is used to calculate a score whose value increases with the trackback count. The inequality (4) stands for a constraint which indicates that the total comment count for each auxiliary material should be restricted in a specified range which is determined by the course designers. If the comment number does not meet the constraint, a penalty will be introduced to the objective function.

The membership function C(x) maps a comment count x into a degree which is defined in the close interval [0,1]. x₁ and x₂ are two control values which respectively indicate the lower and upper bounds of the comment count. If the comment count of a blog article is less than x₁, students may not get interested in the article and it might not get commented

enthusiastically. On the other hand, if the comment count of a blog article is larger than x₂, the article can attract numerous discussions and it should get

a higher degree. In addition, is designed to evaluate the trackback count of a blog article. When the trackback count x of a blog article is small, a slight score is given to this blog entry. The score of a blog article with a higher trackback count should be larger than one with a lower trackback count. The purpose of using a sigmoid form function is to make a curve such that the score can significantly increase as the trackback count

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increases.

SBACPSO Algorithm

Input: N blog articles b₁,b₂,...,b_N, M topics c₁,c₂,...,c_M, the expected relevance of topic j, h_j, the target article difficulty D, the number of required auxiliary materials, K, and the lower and upper bounds, L and U, of the comment count.

Output: gbest is the best solution which is a optimum combination set of blog entries.

● Step 1. Initial swarm generation

The particle is a candidate solution of evaluating the combination of blog entries, which is represented by an NK-dimensional vector, [x₁₁x₂₁...x

N1x12x22...x1Kx2K...xNK]. As mentioned above, xik is a binary value; if

the blog entry b_i is contained in the auxiliary material k, x_ik is set to 1; otherwise, it is set to 0.

● Step 2. Fitness function design

In the proposed model, O₁, O₂, and O₃ are three objective functions that need to be minimized. Additionally, the selected particles should meet constrain (4). Therefore, if constrain (4) is violated, a penalty needs to be considered in the design of fitness function. The penalty term is shown below:

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If the comment count does not fall into the specified range, which is less than the lower bound or larger than the upper bound, the penalty term will be summed in the fitness function. Ultimately, the fitness function can be represented as equation (6),

(6) where w₁ and w₂ are weights for equation (2) and the penalty term for falling into the interval (0,1).

● Step 3. Combination of social and cognition models for velocity updating

Since a PSO-based algorithm possesses characteristics that are similar to the coordination and behavior consistence of a biological colony in a realistic environment, each particle needs to own the best experience itself and the best global solution. Two models are utilized to describe these two solutions; the cognition model and the social model. In the cognition model, the ith particle moves with a velocity v_i, which is a function of the best solution found by the particle itself (i.e. called pbest_i). Each particle is able to cognizes selfhood at every iteration. Moreover, the best solution (i.e. called gbest) found among all particles should be delivered to each particle, which means each particle can socially communicate in a colony. The PSO-based algorithm combines these two models to present the velocity modification of each particle in the whole swarm. The velocity of the ith particle at iteration t is represented by the following:

(7) where φ₁ and φ₂ are acceleration constants, and μ₁ and μ₂ are uniformly distributed random numbers which fall into an open interval (0,1). y_i(t-1) indicates the position of the ith_{particle at the t-1 iteration.}

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● Step 4. Update of positions

In this step, the position of each particle needs to be updated to find a better solution. The update of positions simply depends on the velocity of each particle, which is shown as equation (8).

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● Step 5. Reinforcement of the auxiliary materials

In order to enrich the content in auxiliary materials for a specific course, a periodic reinforcement process needs to execute. The reinforcement strategy adopted is that existing blog articles in an auxiliary material are kept permanently, and the proposed algorithm executes as long as the amount of new blog articles in the blog knowledge base achieves a certain number defined by the course designer. Clearly, the existing blog entries should not be considered in the subsequent execution and new blog entries reinforce the auxiliary materials.

Despite this body of research has the undeniable merit of offering valuable insights into the generation of auxiliary materials, there are a few limitations should be noted in this study. The blog entries analyzed are all from the knowledge base. If we can collect lots of blog entries via blog search engines, it must be able to enrich the contents of auxiliary materials. Additionally, personalized learning cannot be achieved in this study. In the future, it needs to put lots of efforts into this issue through information retrieval techniques.