748 D. Chen et al.
4 Teaching–learning-based optimization based
on PS model (PSTLBO)
4.1 The main motivation of PSTLBO
As previously reviewed, the main idea of TLBO is to imitate
the teaching–learning process in a classroom. The teacher
tries to disseminate his or her knowledge among the learners
to increase the average grades of the whole class, and the
learners also study knowledge from the others to improve
their grades. The operations of TLBO are simple, and there
are no parameters that should be predefined in updating equa-
tions except that there are some training parameters as well
as used in other EAs.
The process of choosing new individuals of TLBO in
teacher or learner phases shows that all new individuals
should be evaluated for comparing with their old solutions in
a generation, the computation cost of the algorithm is heavy.
In large parts of EAs, all the individuals are often evalu-
ated only once in an iteration. How to decrease computation
cost and take full advantage of TLBO is very important for
improving the performance of it. In PS model, the producer
exploits new position according to its ability with a random
angle and a maximal radius, the scroungers update their posi-
tions only with the area-copying operator, and can quickly
track the best position of the producer. All the producers and
scroungers are only evaluated once in each iteration. Com-
bining TLBO and PS model, a new algorithm called PSTLBO
is proposed in the paper. In the given method, some individ-
uals adopt operators of the TLBO algorithm and some of
them update their position with the area-copying operator.
In each iteration, the individuals of the swarm are adopted
hybrid updating methods, which can decrease fitness evalua-
tions of the algorithm. Moreover, in PS model, the producer
can exploit new positions according to a random angle and
a maximal radius even when the diversity of the swarm is
worse, which can increase the ability of the algorithm escap-
ing from local optima. Based on this analysis, the goal of
our work is to improve the global performance of TLBO by
combining the operators of PS model and the advantages of
TLBO algorithm.
4.2 The main operations of PSTLBO
In PSTLBO, the swarm consists of three types of individuals:
producers, scroungers and the remainders. The behaviors of
producers and scroungers are based on the PS model and the
behaviors of the remainders are based on TLBO.
(1) The behavior of producer
For convenience of computation, assuming that there is
only one producer at each generation. The individual with
the best fitness is chosen as the producer, and it renews its
position as follow.
X
new_producer
(P, k) = X
old_producer
(P, k)
+r
3
l
max
cos(2πr
4
) (12)
where, X
new_producer
(P, k) and X
old_producer
(P, k) are the
new and old positions of the kth dimension variable of pro-
ducer P, respectively. r
3
and r
4
are the random numbers in
the range [0,1], l
max
∈ R
1
is the maximum pursuit distance
of the producer.
Equation (12) indicates that the producer updates its posi-
tion around the old position within the maximum pursuit
radius. If the producer finds a better resource (fitness value)
than its current position, it will fly to the new position imme-
diately. Otherwise, it will stay in its current position. The
appropriate radius will benefit for the swarm getting away
from local optima.
(2) The behavior of scroungers
To take advantage of PS model, some individuals are ran-
domly selected as scroungers according to the predefined
probability P
s
. The scroungers will keep searching for oppor-
tunities to join the resources found by the producer. In PS
model (Barnard and Sibly 1981), Barnard and Sibly observed
the following basic scrounging strategies in house sparrows
(Passer domesticus). (1) Area copying: moving across to
search in the immediate area around the producer; (2) Fol-
lowing: following another animal around without exhibit-
ing any searching behavior; and (3) Snatching: taking a
resource directly from the producer (He et al. 2009). There
is no searching behavior in following and snatching in the
PSTLBO algorithm, only area-copying, which is the com-
monest scrounging behavior in sparrows, is adopted. At the
kth iteration, the area-copying behavior of the ith scrounger
can be modeled as a random walk toward the producer.
X
k+1
i
= X
k
i
+r
5
(X
k
p
− X
k
i
) (13)
where r
5
∈ R
n
is an uniform random sequence in the range
[0,1]. X
k+1
i
and X
k
i
are the positions of ith individual in the
(k + 1)th and kth iteration, respectively. X
k
p
is the position
of the producer in the kth iteration.
(3) The behavior of the remainders
The rest of the individuals of the current swarm update
their positions according to the method in the TLBO algo-
rithm except that there is no operator of removing duplicate
individuals. In teacher phase, the producer is chosen as the
teacher for individuals with TLBO operators.
4.3 The steps of PSTLBO
The steps of PSTLBO algorithm are shown as follow.
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