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combinatorial optimization problem. Such combination constitutes the optimum solu-
tion to the design problem under consideration. As mentioned in previous section,
harmony search method is found quite effective in obtaining the solution of such de-
sign problems. An optimum design algorithm that is based on harmony search method
has the following steps:
Step
1.
Initialization of Harmony Memory Matrix:
A harmony memory matrix
H
is generated and initialized first. This matrix incorporates a specified number of solu-
tions referred to as harmony size (
hms
). Each solution (harmony vector,
I
) consists
of
nv
integer number between 1 to
ns
selected randomly each of which corresponds
sequence number of design variables in the design pool, and is represented in a sepa-
rate row of the matrix; consequently the size of
H
is (
hms×nv
).
1
1
1
2
1
⎡
⎤
1
I
I
...
I
φ
(
I
)
nv
⎢
⎥
2
1
2
2
2
2
I
I
...
I
φ
(
I
)
⎢
⎢
⎥
⎥
nv
H
=
(1)
...
...
...
...
...
⎢
⎢
⎥
⎥
hms
hms
hms
nv
hms
I
I
...
I
φ
(
I
)
⎣
⎦
1
2
j
th
th
I
is the sequence number of the
i
design variable in the
j
randomly selected fea-
i
sible solution.
Step 2. Evaluation of Harmony Memory Matrix:
hms
solutions shown in Eq. 1 are
then analyzed, and their objective function values are calculated. The solutions evalu-
ated are sorted in the matrix in the increasing order of objective function values, that
is
I
2
hms
φ
(
)
≤
φ
(
I
)
≤
…≤
φ
(
I
)
.
Step 3. Improvizing a New Harmony:
A new
harmony
[
]
'
I
is impro-
vised (generated) by selecting each design variable from either harmony memory or
the entire discrete set. The probability that a design variable is selected from the har-
mony memory is controlled by a parameter called harmony memory considering rate
(
hmcr
). To execute this probability, a random number
r
is generated between 0 and
1 for each variable
I
. If
r
is smaller than or equal to
hmcr
, the variable is chosen
from harmony memory in which case it is assigned any value from the
i
-th column of
the
H
, representing the value set of variable in
hms
solutions of the matrix (Eq. 1).
Otherwise (if
=
I
′
,
I
′
,..,
I
′
1
2
nv
r
i
>
hmcr
), a random value is assigned to the variable from the entire
discrete set.
{
}
⎧
1
2
μ
′
if
r
≤
hmcr
⎪
⎨
I
∈
I
,
I
,...,
I
i
i
i
i
i
I
′
=
(2)
i
{
}
′
if
r
>
hmcr
⎪
⎩
I
∈
1
,..,
ns
i
i
If a design variable attains its value from harmony memory, it is checked whether
this value should be pitch-adjusted or not. Pith adjustment simply means sampling the
variable's one of the neighboring values, obtained by adding or subtracting one from
its current value. Similar to
hmcr
parameter, it is operated with a probability known
as pitch adjustment rate (
par
) in Eq. 3. If not activated by
par
, the value of the
variable does not change.
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