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of the values in the solution:
x
=
{
8
,
4
,
3
,
1
,
3
,
5
,
6
,
8
,
10
,
9
}
. The values are exchanged
x
=
{
8
,
4
,
7
,
1
,
3
,
5
,
6
,
2
,
10
,
9
}
and the solution is evaluated for its fitness.
3.4.2.2 Insertion
Insertion is a more complicated form of mutation. However, insertion is seen as provid-
ing greater diversity to the solution than standard mutation.
As with standard mutation, two unique random numbers are selected
r
1
,
r
2
rand
[1
,
D
]. The value indexed by the lower random number
Solution
r
1
is removed and the
solution from that value to the value indexed by the other random number is shifted one
index down. The removed value is then inserted in the vacant slot of the higher indexed
value
Solution
r
2
∈
as given in Fig 3.7.
temp
=
Solution
r
1
;
for (int
i
=
r
1
;
i
<
r
2
;
i
++)
Solution
i
=
Solution
i
++
;
Solution
r
2
=
temp
;
Fig. 3.7.
Pseudocode for Insertion
Illustration
:
{
8
,
4
,
2
,
1
,
3
,
5
,
6
,
7
,
10
,
9
}
In this Insertion example, assume a solution given as:
x
=
.
Two random numbers are generated within the bounds:
Rnd
=
{
4
,
7
}
. These are the in-
8
,
4
,
7
,
dexes of the values in the solution:
x
=
{
4
,
3
,
5
,
7
,
2
,
10
,
9
}
. The lower indexed
8
,
4
,
7
,
4
,
3
,
5
,
7
value is removed from the solution
x
=
{
,
2
,
10
,
9
}
, and all values from
the upper index are moved one position down
x
=
{
8
,
4
,
7
,
|
3
,
5
,
6
,
|
,
2
,
10
,
9
}
.Thelower
indexed value is then slotted in the upper index:
x
=
{
8
,
4
,
7
,
3
,
5
,
6
,
1
,
2
,
10
,
9
}
.
3.4.3
Local Search
There is always a possibility of stagnation in Evolutionary Algorithms. DE is no ex-
emption to this phenomenon.
Stagnation is the state where there is no improvement in the populations over a period
of generations. The solution is unable to find new search space in order to find global
optimal solutions. The length of stagnation is not usually defined. Sometimes a period
of twenty generation does not constitute stagnation. Also care has to be taken as not
be confuse the local optimal solution with stagnation. Sometimes better search space
simply does not exist. In EDE, a period of five generations of non-improving optimal
solution is classified as stagnation. Five generations is taken in light of the fact that EDE
usually operates on an average of hundred generations. This yields to the maximum of
twenty stagnations within one run of the heuristic.
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