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of weaker ones. Finally the weak conglomerates which could not to improve their per-
formance will collapse. These competitions among the conglomerates will cause all the
companies to converge to a state called monopoly where only one conglomerate exits
in the market and all the other companies become subsidiary companies of this holding
company.
To begin with, an initial population called perfect competition companies is created.
In a
D
-dimensional problem, the position of the
i
-th company is defined as
Company
i
=
[
x
i
,
1
,
x
i
,
2
,
,
N
c
,where
N
c
is total number of competition companies.
The cost function of the
i
-th company can be defined as:
···
,
x
i
,
D
],
i
= 1
,
2
,
···
f
i
=
cost
i
(
x
i
,
1
,
x
i
,
2
,
···
,
x
i
,
D
)
(14)
N
holding
of the most powerful competition companies are selected as the holding compa-
nies, which form different conglomerates. The remaining
N
sub
are the subsidiary com-
panies of these holding companies. Theoretically, the normalized cost of the
n
-th hold-
ing company can be defined as:
F
holding
f
holding
i
f
holding
= ma
i
{
}−
(15)
n
n
where
f
holding
n
is the cost of the
n
-th holding company.
The normalized power of each holding company is defined as:
N
holding
n
=1
P
holding
n
F
holding
n
F
holding
n
=
/
(16)
Then the initial number of subsidiary companies of a conglomerate becomes
N
su
n
=
round
P
holding
n
N
sub
,
0
{
×
}
(17)
where
N
su
n
is the initial number of subsidiary companies of the
n
-th conglomerate.
For each holding company,
N
su
n
of the subsidiary companies are randomly selected
and allocated. These subsidiary companies along with their holding company form the
conglomerate.
Then the subsidiary companies start to move toward their relevant holding compa-
nies. The positions of the subsidiary companies of the
n
-th conglomerate are updated.
SU B
n
,
i
=
sub
n
,
i
+[
rand
()
×
ω
(
holding
n
−
sub
n
,
i
)]
/
cos
θ
(18)
where
sub
n
,
i
is the position of the
i
-th subsidiary company of the
n
-th holding company,
rand
() is a random number between 0 and 1,
is a weight factor, and
holding
n
is the
position of the
n
-th holding company. To search different points around the holding
company, a random amount of deviation is added to the direction of movement. The
movement of a subsidiary company toward its relevant holding company at its new
direction
ω
θ
is a random angle between
−
ε
and
ε
,where
ε
>
0 is the parameter that
adjusts the deviation from the original direction.
However, a subsidiary company in a conglomerate may reach a position with lower
cost than its holding company. In such case, the positions of the holding company will
be replaced by the higher one. The rest will move toward the new holding company.
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