Forward Backward Transformation - Differential Evolution: A Topic for Global Permutation-Based Combinatorial Optimization - page 56

Table 3.19. Random Index

Solution Index

1 2 4

2 1 3

3 2 5

4 1 5

5 2 4

6 3 5

7 1 4

8 3 5

9 1 4

10 2 5

Table 3.20. Insertion process 1

Index 1 2 3 4 5

Solution 1 1 3 5 4

Table 3.21. Insertion process 2

Index 1 2 3 4 5

Solution 1 1 3 5 4

Step (6) describes the Standard Mutation schema. In standard mutation, a single
value swap occurs. Assume that a list of random indexes in Table 3.16 are generated
which show which values are to be swapped.
It can be seen from Table 3.16, that the values indexed by 4 and 2 are to be swapped
in Solution 1 and so forth for all the other solutions. The new possible solutions are
given in Table 3.17 with their calculated fitness values. The highlighted values are the
mutated values.
Only solution 7 improved in the mutation schema and replaces the old solution on
position 7 in the population. The final population is given in Table 3.18.
Step (7), Insertion also requires the generation of random indexes for cascading of
the solutions. A new set of random numbers can be visualized as in Table 3.19.
In Table 3.19 the values are presented in ascending order. Taking solution 1, the
first process is to remove the value indexed by the first lower index (2) as shown in
Tab le 3 . 2 0.
The second process is to move all the values from the upper index (4) to the lower
index as in Table 3.21.
The last part is to insert the first removed value from the lower index into the place
of the now vacant upper index aas shown in Table 3.22.