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colony is constituted of
three groups: employed bees, onlookers and scouts. Employed bees search the
destination where food is available, translated by the amount of their nectar. They
collect the food and return back to their origin, where they perform waggle dance
depending on the amount of nectar
In this formalism, the population of the arti
cial bees
'
s food available at the destination. The onlooker
bee watches the dance and follows the employed bee depending on the probability
of the available food.
In ABC algorithm, the population of bees is divided into two parts consisting of
employed bees and onlooker bees. The sizes of each part are usually taken equal to.
Employed bee, representing a potential solution in the search space with dimension,
updates its new position by using the movement Eq. (
22
) and follows greedy
selection to
'
find the best solution. The objective function associated with the
solution is measured by the amount of food.
Let us consider a population with N
2 individuals in the search space. The
position of the ith employer at iteration time k is de
=
ned as:
x
i
;
1
k
x
i
;
2
k
x
i
;
d
k
x
i
;
D
k
X
k
¼
;
; ...;
; ...;
ð
22
Þ
where D is the number of decision variables, i is the index on N
2 employers.
In the dth dimension of search space, the new position of the ith employer, as
well as of the ith onlooker, is updated by means of the movement equation given as
follows:
=
x
i
;
d
k
þ
x
i
;
k
þ
r
k
x
i
;
k
x
m
;
d
k
¼
ð
23
Þ
1
where r
k
1, 1]. It can be
also chosen as a normally distributed random number with mean equal to zero and
variance equal to one as given in Karaboga (
2005
). The employer
is a uniformly distributed random number in the interval [
−
'
is index m
6¼
i is a
randomly number in the interval [1, N/2].
Besides, an onlooker bee chooses a food source depending on the probability
value of each solution associated with that food source, calculated as follows:
f
i
;
d
k
P
N
=
2
n
p
i
;
d
k
¼
ð
24
Þ
f
n
;
d
k
where f
i
;
d
k
fitness value of the ith solution at iteration k.
When the food source of an employed bee cannot be improved for some pre-
determined number of cycles, called
is the
and denoted by L,
the source food becomes abandoned and the employer behaves as a scout bee and it
searches for the new food source using the following equation:
“
Limit for abandonment
”
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