Information Technology Reference
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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