IEEE Systems, Man and Cybernetics Magazine - April 2023 - 13

Ci,, ,, ,,1
12 12 12
QQ Q
66 6@@@ 01
iT ij Ti ji im jn
)) ## ## #^h
(6)
where (3) is applied to guarantee that each leader is in a
correct learning team; (4) stipulates that every learner
can be assigned to only one team; (5) limits the number
of members for each team, and L[j] denotes how many
learners are required in learning team j; and (6) denotes
that there are no conflicts in any team.
Modeling LC-LTF for Project-Based Learning
For the problem of LC-LTF for project-based learning, the
specific modeling strategies are as follows:
1) Define the conflict matrix between learners and projects
as
C ,,! "
A 01 mn
, where
#
Ci , j 0
A
6 =@
A6 =@
The problem is modeled via E-CARGO, and the following
objective function is given:
max ,,Mi jT ij
n
m
t=|| @@ (11)
M
66
#
i =1 j =1
where 66!@@ denotes whether learner i is
6 =@
Ti ,,j 01
M
assigned to project j;
Ti , j 1
M
the following constraints:
M6 ^h@
| 6 ^h@Ti ,,M ji m11= ##
TH ,,
n
j =1
denotes that learner
i meets the requirements of project j, which means that
his or her capability values are not lower than the jth
team's expected intervals; otherwise, ,.Ci j 1
2) Obtain the comprehensive capability of each learner
corresponding to each project based on the evaluation
module.
3) Utilize E-CARGO to model this problem for projectbased
learning, based on learners' comprehensive capability
and conflict matrix
objective function:
C ,A
m
n
max ,,Ai jT ij
1
66
#
i =1 j =
where m and n represent the number of learners and
projects, respectively, and A[i, j] stands for the comprehensive
abilities of learner i in project j. Here,
Ti , jA
6 !@
A6 =@
as the leader of project j, and
Thus, Ti , jA
6
constraints:
n
| 6 ^h@Ti ,,A ji m11
j =1
## #
m
| 6 ^h@Ti ,,A jj n11= ##
i =1
Ci ,, ,,jT ij66) ## ## #^h@@
AA 01 im jn1
(9)
(10)
where (8) denotes that one learner can be assigned as
the leader to only one project, (9) specifies that there
is only one leader in every project, and (10) is set to
guarantee that all the selected leaders can satisfy the
expectation of projects.
4) Maximize the objective function to obtain the leaders
set
HH ,, ,,12 n
f
project j.
5) Similar to the problem of LC-LTF for course-based learning,
first, we calculate comprehensive compatibilities
between leaders and other learners to get the compatibility
matrix Q. Then, we define a conflict matrix CM
that reflects the conflict relationship among learners.
= " HH , where Hj
is the leader of
LC-LTF for Course-Based Learning
Suppose there are nine learners in a course learning environment
and that they are required to be divided into
three teams. Define that
= f 9
" 12
learners and that Gg ,, , is the set of teams. Based
= " gg
123
on our framework, we pick three learners with high comprehensive
ability as the leaders and assign the other six
learners to three teams for maximizing the overall learning
quality. We select five evaluation metrics, including u1
(i.e., skill proficiency), u2
munication skill), u4
(i.e., leadership), u3
(i.e., learning style), and u5
(i.e., com(i.e.,
personality),
and they are described in the form of interval
numbers. The assessment results of learners' abilities
are given in Table 3.
April 2023 IEEE SYSTEMS, MAN, & CYBERNETICS MAGAZINE 13
Case Study
(8)
601 , @ denotes whether learner i is assigned
6 =@
Ti , j 1
A
if learner i
is assigned as the leader of project j; otherwise,
Ti ,.j 0
@ satisfies the following
t=|| @@ (7)
A
Solving Module
After modeling the two types of LC-LTF problems via
E-CARGO, we can obtain the objective functions and constraints
in different application scenarios. By maximizing
the objective functions, we can get the final team formation
results. Existing research mainly solves the optimization
problem with a genetic algorithm [4], [14], [21] or clustering
algorithm [8], [40], [41]. In addition, the problem can also be
figured out with the IBM CPLEX optimization package,
Gurobi Optimizer, and other optimization methods. The following
section details an example of solving the LC-LTF
problem by using the CPLEX optimization package.
and get the following
i 1
m
=
Ci,, 11,0,
12 12
MM M
iT ij Ti j
12
,,
66 6@@ @)) ## ## #^h
ii mj n
Ci ,, ,,jT ij66) ## ## #^h@@
AM 01 im jn1
(15)
(16)
where (12) guarantees that the leader of each project
will not be assigned to other projects, (13) denotes that
each learner is assigned to only one project, (14) limits
the number of members of each project, and (15) and
(16) represent that there are no conflicts in any team.
| 6 ^h@Ti ,,M jL jn1
= ##
j
(14)
jjj n11= ##
(12)
(13)
to project j. Otherwise, ,.Ti j 0
M
6 =@
if learner i is assigned
Ti , jM
6
@ satisfies
Ss,, ,ss , is the set of
IEEE Systems, Man and Cybernetics Magazine - April 2023

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