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Ta b l e 7 . 9 .
Parent solutions
Solution City 1 City 2 City 3 City 4 City 5
Fitness
1
1
4
2
5
3
66
4
5
3
4
1
2
62
7
1
4
3
5
2
62
Table 7.10.
Parent solutions crossover
Solution City 1 City 2 City 3 City 4 City 5
1
1
4
2
5
3
4
5
3
4
1
2
7
1
4
3
5
2
Index
4
5
1
2
3
The second DE operating parameter crossover
CR
can now be set as 0.4. The starting
point of evolution in the solution is randomly selected. In this example, solution index
3 is selected as the first variable for crossover as given in Table 7.10.
The
mathematical
representation
of
DE
Rand1Bin
is
given
as:
x
current
+
x
random
2
.
x
random
1
in this instance refers to the first randomly selected
solution 4, and
x
random
2
is the second random solution 7. Since the starting index has
been randomly selected as 3, the linked values for the two solutions are subtracted as 4
−
•
x
random
1
−
F
3 = 1. This value is multiplied by
F
, which is 0.4 The result is (1 x 0.4 = 0.4). This
value is added to the current indexed solution 1: (0.4 + 2 = 2.4).
Likewise, applying the equation to the selected parent solutions yields the following
values given in Table 7.11:
Table 7.11.
Parent solutions final values
Solution City 1 City 2 City 3 City 4 City 5
1
1
4
2
5
3
4
5
3
4
1
2
7
1
4
3
5
2
Index
4
5
1
2
3
Final
2.6
3.6
2.4
3.4
3
The second part shown in Table 7.12 is to select which of the new variables in the
solutions will actually be accepted in the final child solution. The procedure of this is to
randomly generate random numbers between 0 and 1and if these random numbers are
greater than the user specified constant
CR
, then these values are accepted in the child
solution. Otherwise the current index values are retained.
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