EAs are used in creating pedagogical paths, based on the learners’ profile and their learning objectives. Azough, Bellafkih and Bouyakhf (2010) used genetic algorithms to resolve the problem of searching the most optimal path from a starting point, represented by learners’ profile, to a final point, represented by learning objectives, while passing through intermediate points, represented by courses. Huang, Huang and Chen (2007) use genetic algorithms for curriculum sequencing, but they don’t treat only the content problems, as Azough, Bellafkih and Bouyakhf (2010) do: they also search for the most optimal teaching operation (presentation, example, question or problem). Huang, Huang and Chen (2007) argue that learners’ ability should also be studied, when choosing the curriculum, besides considering learners’ interests and browsing behaviors.
Particle swarm optimization (PSO) is a very useful EA related technique, with a wide range of applications. Dheeban, Deepak, Dhamodharan and Elias (2010) show that PSO with inertia-coefficient is suitable for improving e-learning courses composition. They also underline that their PSO variant is better than the Basic particle swarm optimization algorithm (BPSO) and experimental results come to strengthen their hypothesis. Wong and Looi (2010) published a detailed study about the application of PSO in the content planning and e-assessment domain. They identified the work of Cheng, Lin and Huang (2009) to be the only known study about a PSO used in an adaptive dynamic question generation system for web-based testing: the key element of their work is the fitness function, which selects a different question on each step in the online test. The fitness function has three parameters: the difficulty level of the question (which has to be as closed as possible to the knowledge level of the user), the question item’s relevance (as close as possible to the course content that the instructor wishes to assess the learner on) and the number of times a question is chosen (as low as possible). Cheng, Ling and Huang (2009) compare the PSO search to the exhaustive search and conclude that the first one is more suitable for the large-scale item banks. Chen and Jiang (2007) apply PSO to an assessment paper generation system. According to Wong and Looi (2010), the main difference between an assessment paper generation system and an adaptive dynamic generation system for knowledge assessment is the step in which the PSO is applied: for the first system, the PSO is applied only once, at the beginning of the test, when all the questions are selected; for the second system, the PSO is applied at each test item selection. The PSO fitness function developed by Chen and Jiang (2007) has three sets of control variables: the learning points to cover, the ratios of the questions with different difficulty levels and the total marks of the paper. All these variables are pre-defined by the instructors. Yin, Chang, Hwang, Hwang and Chan (2006) use the same fitness function, but with different variables. Huang (2006) only uses the question difficulty as a function parameter. Wang and Chu (2008) combine a genetic algorithm with their PSO approach. Ho, Yin, Hwang, Shyn and Yean (2009) also use enhanced multi-objective PSO to improve the e-assessment services: they try to solve the problems of multiple assessment criteria and parallel test sheets’ composition from large item banks. Their proposed algorithm was compared to a competing genetic algorithm and they proved the superiority of PSO over classical genetic algorithm.
The current study shows another application of PSO to the e-assessment domain. The mainpurpose of the application is to enhance the formative features of e-assessment, which is not regarded only as a knowledge evaluation instrument, but a knowledge creation one. In order to illustrate the suitability of PSO for resolving the formative e-assessment problem, the applied PSO algorithm is further described. The variables used in the fitness function construction are suitable for a project management certification process. PSO algorithm is a robust stochastic optimization technique, which is inspired from the movement and intelligence of swarms. It uses a number of particles that constitute a group moving around in the search space looking for the best solution. It imitates the bird from a flock which is nearest to the food. All particles have fitness values, evaluated through the fitness function and velocities. The fitness function used for the PSO algorithm applied to project management e-assessment is the following one:
Where
q: the question id
A: ability level of the user, where, 0 ≤ A ≤1
D: desired difficulty of the e-test, where Dϵ{0, 25;0.50;0.75;1}, according to the four
certification levels awarded by the International Project Management Association (2006);
dq: difficulty of the question q, where, where 0 ≤ dq ≤1;
ExpMax: the maximum exposure number of a question from the questions pool;
Expq: the exposure number for question q, where where 0 ≤ Expq ≤ ExpMax;
CAq: the number of times in which question q has been correctly answered;
COq: number of concepts which are verified by the question q, contained by the competences established to be checked by the e-assessment session; the knowledge domain to be checked is divided in competences, which contain concepts;
The PSO algorithm is applied every time a new question is selected. The ability level of the user is updated after each given answer. The parameters from the third term of the fitness function from formula 1 are also changing each step on the way. The test difficulty and the number of concept are established by the trainee (if the session is part of one’s preparation process) or by the trainer (if the session is an official step from the certification process). The other elements besides the fitness function are the ones usually used in PSO approaches (Schutte & Groenwold, 2005).
In the PSO algorithm, the goal at each iteration is to find the question having the difficulty level closest to the trainee's ability level and closest to the targeted test difficulty level, being the least exposed so far and checking a large number of concepts from the established learning objectives. The initial ability level of the trainee is established via self-evaluation, a pre-test or uses a default value (taken from a database), as shown in Figure 8.5.
The prerequisites to access the PSO algorithm are:
- establish difficulty level of the test (for each level, a difficulty value is available: the values are taken by parameter D from formula 1);
- establish the ability level of the user; if the user chooses to self-evaluate himself (inserts his own level), the number is projected to the interval [0,1], to ensure compatibility with the values of the parameter A from formula 1;
- establish the knowledge to be checked by the test; whether the user chooses to step over this stage, all the concepts will be checked; the maximum exposure number of a question from the questions pool: this operation is made by calling the database and it is not visible to the user.
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