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In-Depth Information
Modifications to the original algorithm may be classified into several categories,
which are placed in context by Figure 4:
•
Alternative initialisation procedures for HM, or an extended HM structure
-
Example:
Degertekin [48] generated
2
×
HMS
initial harmonies but placed
only the best
HMS
of these into the initial HM;
•
Variable, rather than fixed, parameters used when improvising a new harmony
-
Example:
Mahdavi et al [18] advocated parameters for pitch adjusting that
vary with the improvisation number
j
=
1
…
,
MaxImp
:
j
(
)
PAR
(
j
)
=
PAR
+
PAR
−
PAR
×
(6)
min
max
min
MaxImp
⎡
⎤
⎛
⎞
b
j
⎜
⎜
⎝
min
⎟
⎟
⎠
b
(
j
)
=
b
exp
ln
;
(7)
⎢
⎢
⎥
⎥
max
b
MaxImp
⎣
⎦
max
•
New or revised operations for new harmony improvisation
-
Example:
Li et al [64] introduced a non-uniform mutation operation from GA:
(
)
⎧
U
i
x
+
Δ
j
,
x
−
x
if
r
≤
0
5
⎪
⎨
new
,
i
new
,
i
1
x
′
=
(
)
(8)
new
,
i
L
i
x
−
Δ
j
,
x
−
x
if
r
>
0
.
5
⎪
⎩
new
,
i
new
,
i
1
b
⎛
j
⎞
-
where
Δ
(
j
,
y
)
=
y
×
r
×
⎜
⎜
⎝
1
−
⎟
⎟
⎠
and
r
,
r
∈
[
0
are random numbers;
2
1
2
MaxImp
•
Options for handling constraints during generation of new harmonies
-
Example:
After generating a new harmony, Erdal [47] used two methods to
handle constraints: if the new harmony was strongly infeasible, it was simply
discarded; if the error was small, it was considered for inclusion in HM, but
the acceptable error decreased as iterations progressed;
•
Different criteria for deciding when to include a new harmony in HM
-
Example:
Gao et al [57] included a new harmony only if it met three condi-
tions: (i) it is better than the worst harmony in HM, and (ii) there are less than
a critical number of similar harmonies already in HM, and (iii) its fitness is
better than the average fitness of the similar harmonies;
•
Revised termination criteria
-
Example:
Cheng et al [19] terminated iterations when the best objective func-
tion value changed less than a small amount after a given number of iterations;
•
Modifications to the algorithm's structure, that is, adding or removing blocks and
changing the processing sequence in the flowchart (Figure 4)
-
Structural changes may be relatively small, for example generating multiple
harmonies per improvisation [67], or they may be extreme, such as the HPSO
method [52], which is essentially PSO with occasional use of HM considering
to fix infeasible solutions.
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