2.2.3 Selection operation
The one-to-one greedy selection is employed by means of
comparing a parent and its corresponding offspring. And
this strategy enhances diversity in comparison to other
selection strategies such as tournament selection, rank
based selection and fitness proportional selection. The
selection operation at the K-th generation is described as
X
Kþ1
i
¼
U
K
i
if f ðU
K
i
Þf ðX
K
i
Þ
X
K
i
if f ðU
K
i
Þ[ f ðX
K
i
Þ
ð7Þ
where f(X) is the objective function value of each trial
vector.
2.3 Hybrid teaching–learning-based optimization
(TLBO–DE)
An efficient evolutionary algorithm should make use of
both the local information of solutions found so far and
the global information about the search space. The local
information of solutions found so far can be helpful for
exploitation, while the global information can guide the
search for exploring promising areas. The search in
TLBO is mainly based on the global information, and
TLBO has the advantage that learners will converge to a
single attractor Teacher. DE is mainly based on the dis-
tance and direction information which is a kind of local
information. DE has the advantage of not being biased
toward any prior defined guider which make DE can
maintain the diversity of population and explore local
search. The key reason for employing the hybridization is
that the hybrid algorithm can take advantage of the
strengths of each individual technique while simulta-
neously overcoming its main limitations. That is, instead
of employing a single modification learner in TLBO, we
use the integration of two modification learners in TLBO–
DE. The first is the classical modification learner of
TLBO, and the second is generated using the DE muta-
tion rules for learner. The detailed learning processes are
described below.
2.3.1 Teacher phase
To balance the global and local search ability, a modified
interactive learning strategy is proposed in teacher phase.
In this learning method, each learner is randomly assigned
to an interactive learning strategy (the learning strategy of
Teacher Phase in the standard TLBO or differential
learning based on DE).
In TLBO–DE, the updating formula of the learning for a
learner X
i
in teacher phase is proposed by the hybridization
of the learning strategy of Teacher Phase and the differ-
ential learning as follows
newX
i;j
¼ u V
1;j
ðtÞþð1 uÞV
2;j
ðtÞð8Þ
where u called the hybridization factor is a random number
in the range [0, 1] for the j-th dimension, V
1,j
is the learners
which is calculated according to Eq. (2) and V
2,j
is the
learners which is calculated according to Eq. (5).
2.3.2 Learner phase
At the same time, in the learner phase, learners also learn
from interaction between themselves. In this learning
method, one of learners randomly learns from the other
learner in the population. Let newX
i
represent the interac-
tive learning result of the learner X
i
and it can be expressed
as follows:
newX
i;j
¼ u V
1;j
ðtÞþð1 uÞV
2;j
ðtÞð9Þ
where u called the hybridization factor is a random number
in the range [0, 1] for the j-th dimension, V
1,j
is the learners
which is calculated according to Eq. (3) and V
2,j
is the
learners which is calculated according to Eq. (5).
As previously analyzed, the complete flowchart of the
TLBO–DE algorithm is shown in Fig. 1.
Begin
Initialize learners size(NP), dimension(D)
Modify each learner X
i
in the class
V
1j
= Learning strategy of Teacher Phase
V
2j
= DE Learning
newX
i j
= u*V
1j
+(1-u)*V
2j
newX
i
better X
i
Modify each learner X
i
in the class
V
1j
= Learning strategy of Learner Phase
V
2j
= DE Learning
newX
i j
= u*V
1j
+(1-u)*V
2j
X
i
= newX
i
X
i
= X
i
Yes No
newX
i
better X
i
X
i
= newX
i
Yes No
X
i
= X
i
termination
criteria satisfied
No
End
Yes
Calculate the Teacher and Mean
Learner
Phase
Teacher
Phase
Fig. 1 Flow chart showing the working of TLBO–DE algorithm
Neural Comput & Applic
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