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applied query expansion techniques to address the first problem, they do not take multi-criteria into account to fit the
real-world situation (Jou & Liu, 2011; Shih, Tseng, & Yang, 2008).
Bearing this in mind, this study aims to develop a rapid prototyping approach by employing particle swarm
optimization (PSO) with multi-criteria to accelerate the development of drafts of teaching materials, as well as
utilizing wiki-based techniques to enhance the revision quality of the materials thus produced. The ultimate aim of
the study is to reduce the time, effort, and cost associated with the development of high-quality teaching materials.
Background and related work
Particle swarm optimization
PSO is a population-based optimization algorithm. Kennedy and Eberhart proposed the algorithm in 1995, inspired
by the social behaviors of fish schooling and bird flocking, because they thought swarm intelligence could increase
both the speed and the success rate for certain processes (Kennedy & Eberhart, 1995).
To carry out the PSO, each investigator has to formulate a fitness function according to the requirements of different
optimization problems. Following this, a swarm of particles is generated and then distributed over a problem space,
where each particle represents a potential solution to the optimization problem and is able to “remember” its own
past status. During the optimization process, the PSO algorithm quantifies the location of each particle through the
fitness function, and then utilizes the velocity function to produce the next generation until the process is terminated.
Simultaneously, each particle can keep track of its own coordinates in the N-dimensional problem space that are
related to the optimal solution it has achieved so far.
The velocity function consists of two models, cognition-only and social-only, which are both composed of two main
parameters, called personal best location (PBest) and global best location (GBest). The formulas of the velocity
function are described in the following paragraphs.
Cognition-only model
(1)
( )
V = V + C × rand() × P − X
id id 1
id id
Social-only model
( )
V = V + C × rand () × P − X
id id 2
gd id
Where Vid is the velocity vector of the ith particle in d dimension of the problem space, Pid is the personal best
position vector of the particle in d dimension, Pgd is the global best position vector of the particle in d dimension, Xid
is the current position vector of the ith particle in d dimension, C1 is the personal cognitive learning rate, C2 is the
social learning rate, and rand() is a random real number in [0,1].
As the velocity function relies on the social-only and cognition-only models, the following formula specifies the
complete velocity function, which combines Equation (1) with Equation (2).
( )
( t + ) = V ( t)
+ C × rand()
× ( P − X ( t)
) + C × rand()
× P − X ( t)
Vid 1 id 1 id id
2
gd id
(3)
Each particle’s velocity and direction are evaluated by Equation (3), and its current position is updated through
Equation (4).
(4)
( t + 1 ) = X ( t)
+ V ( t + 1)
X id
id id
In addition, Kennedy and Eberhart further presented a discrete binary version for the PSO algorithm in 1997
(Kennedy & Eberhart, 1997), and this is used for combinational optimization, where each particle is structured by a
binary vector of length d. Moreover, the velocity of a particle is represented by the probability that a decision
(2)
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