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this step as follows: randomly choose a value m
[1 ,n [ , and split the n sequences
into two groups: 1 st group from 1 to m sequences, and 2 nd group from ( m +1)
to n ; randomly choose two integer values x and y, in such way that k adjacent
gaps are insterted beginning from column x for the first group, and from column
y for the second group; randomly choose a subsequence shift direction D, either
left or right; finally, to insert the k adjacent gaps in the relative positions for
each sequence, and shift the subsequence to the D direction. During the shifting
phase, it is possible to miss n
0 bits with value 1; in this case, InsGap will
select n bits with value 0, different from the k gaps inserted, and they will be
flipped to 1, rebuilding the correct sequence. Figure 1, plot (a), shows an example
of how the InsGap procedure works, with k =3 ,m = 2 and right shift direction.
Fig. 1. GAP operator has the purpose to insert, by InsGap procedure (a), or remove,
by RemGap procedure (b), adjacent gaps into the proposed alignment
RemGap procedure,simply,remove k adjacent gaps, and move the sub-
sequences towards a randomly chosen direction, either left or right. Plot (b) of
figure 1 shows an example of such an operator.
C
BlockShuing Operator
The second perturbation operator is the BlockShuffling operator,which
is based on the block definition. This operator moves aligned blocks left or right:
a block is selected in each alignment starting from a random point in a se-
quence.Three different approaches where developed: BlockMove moves whole
blocks either to the left or to the right; BlockSplitHor divides the blocks in
two levels, upper and lower, and shifting only one level, randomly chosen; and
BlockSplitVer, which randomly choose a column in the block which divides
it into two sides (left and right), and shifting only one side, randomly chosen as
well. Figure 2 summarizes the three operators.
Finally, the function Strip Gaps( P ( ) ) moves matched gap columns to the
right end side of the matrix. This function is always applied before the fitness
function is evaluated.
 
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