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Table 7.12.
CR Application
Solution
City 1 City 2 City 3 City 4 City 5
Parent
1
4
2
5
3
Final
2.6
3.6
2.4
3.4
3
Random value
0.6
0.2
0.5
0.9
0.3
Table 7.13.
Child solution
Solution City 1 City 2 City 3 City 4 City 5
Parent
1
4
2
5
3
Child
2.6
4
2.4
3.4
3
Table 7.14.
Closest Integer Approach
Solution
City 1 City 2 City 3 City 4 City 5
Child
2.6
4
2.4
3.4
3
Closest integer
3
4
2
3
3
Table 7.15.
Hierarchical Approach
Solution
City 1 City 2 City 3 City 4 City 5
Child
2.6
4
2.4
3.4
3
Hierarchical Approach
2
5
1
4
3
Since
CR
has been set as 0.4, all indexes with random values greater than 0.4 are
selected into the child population. The rest of the indexes are filled by the variables
from the parent solution as given in Table 7.13.
Two different approaches now can be used in order to realize the
child
solution.
The first is to
closest integer approach
. In this approach the integer value closest to the
obtained real value is used. This is given as in Table 7.14.
The second approach is the
hierarchical approach
. In this approach, the solutions
are listed according to their placement in the solution itself. This is given in Table 7.15.
The advantage of the
hierarchical approach
is that no repairment is needed to the
final solution. However, it does not reflect the placements of DE values, and can be
misleading. Due to this factor, the first approach of
closest integer
approach is now
described.
The next step is to check if any solution exists outside of the bounds. According
to [18], all out of bound variables are randomly repaired. If the case of this example all
the values are within the bounds specified by the problem.
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