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In-Depth Information
Procedure DE GT SP
Set CR
,
F
,
NP
,
TerCriterion
X
=
x
1
,
x
2
,..,
x
NP
f
π
x
i
i
:=1
,
2
,..,
NP
i
←
= 2
opt
π
i
←
x
i
i
=1
,
2
,..,
NP
0
i
←
x
i
0
π
=
LS
π
x
i
i
=1
,
2
,..,
NP
i
x
i
i
π
←
←
= arg min
f
π
i
←
x
i
i
=1
,
2
,..,
NP
g
←
x
i
0
π
g
←
x
i
π
B
:= π
k
:= 1
while
Not TerCriterion
do
V
ij
:=
x
ia
+
F
X
ib
+
X
ic
i
:=1
,
2
,..,
NP
,
j
=1
,
2
,..,
m
u
ij
=
v
ij
if r
ij
<
CR or j
=
D
j
x
k
−
1
ij
ot herwise
i
=1
,
2
,..,
NP
,
j
=1
,
2
,..,
m
f
π
i
←
U
i
i
:=1
,
2
,..,
NP
←
U
i
= 2
opt
π
i
←
U
i
i
=1
,
2
,..,
NP
i
π
=
LS
π
i
←
U
i
i
=1
,
2
,..,
NP
i
←
U
i
π
←
u
i
<
f
=
u
i
if f
π
k
−
1
←
X
k
−
1
i
i
π
X
i
i
x
k
−
1
i
ot herwise
i
=1
,
2
,..,
NP
g
←
X
g
= arg min
f
π
←
X
i
,
f
π
i
k
−
1
g
←
X
k
−
1
g
π
i
:=1
,
2
,..,
NP
π
B
←
X
B
= arg min
f
(π
B
←
X
B
)
,
f
π
g
←
X
g
k
:=
k
+ 1
endwhile
ret urn
π
B
←
X
B
Fig. 6.4.
The DDE Algorithm with Local Search Heuristics
where
H
i
,
OPT
and
R
are the objective function values generated by the DDE in each
run, the optimal objective function value, and the number of runs, respectively. For the
computational effort consideration,
t
avg
denotes average CPU time in seconds to reach
the best solution found so far during the run, i.e., the point of time that the best so
far solution does not improve thereafter.
F
avg
represents the average objective function
values out of five runs.
6.4.1
Solution Quality
Table 6.19 gives the computational results for each of the problem instances in detail.
As seen in Table 6.19, the DDE algorithm was able to obtain optimal solutions in at
least two of the five runs for 35 out of 36 problems tested (97%). For 32 (89%) out of
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