Information Technology Reference
In-Depth Information
Ta b l e 7 . 7 .
Distance matrix for Tour 1
Cities A
D
B
E
C
A
D
14
B
5
9
E
24
9
19
C
10
4
5
14
Ta b l e 7 . 8 .
Fitness for the population
Solution City 1 City 2 City 3 City 4 City 5
Fitness
1
1
4
2
5
3
66
2
4
2
1
3
5
48
3
3
1
5
2
4
48
4
5
3
4
1
2
62
5
5
2
3
4
1
72
6
2
4
1
5
3
66
7
1
4
3
5
2
62
8
5
3
1
4
2
66
9
2
5
3
1
4
66
10
1
3
5
2
4
66
7.5.3
Fitness Evaluation
The objective function for TSP is the cumulative distance between the cities, ending
and starting from the same city. Taking the example of the first solution in Table 7.6;
now termed Tour 1 =
{
A
,
D
,
B
,
E
,
C
}
, the equivalent representation is Tour 1 = =
{
1
,
4
,
2
,
5
,
3
. The distance matrix can now be represented as in Table 7.7.
Since the tour is cyclic, the tour can further be completely represented as Tour 1 =
}
{
. From distance matrix it is now the accumulation of the
tour distances Tour 1 = 14 + 9 + 19 + 14 + 10, which gives a total of 66.
Likewise, the total tour for all the solutions is calculated and is presented in
Tab le 7 . 8.
A
→
D
→
B
→
E
→
C
→
A
}
7.5.4
DE Application
The next step is the application of DE to each solution in the population. For this ex-
ample the DE
Rand1Bin
strategy is selected. At this point it is important to set the DE
scaling factor
F
. It can be given a value of 0.4.
DE application is simple. Starting from the first solution, each solution is evolved se-
quentially. Evolution in DE consists of a number of steps. The first step is to
randomly
select two other solutions from the population, which are unique from the solution cur-
rently under evolution. If we take the assumption that Solution 1 is currently under
evolution, then we can randomly select Solution 4 and Solution 7 for example. These
make the batch of
parent
solutions as given in Table 7.9.
Search WWH ::
Custom Search