IEEE Computational Intelligence Magazine - November 2021 - 89

sub-optimal gene values, thereby maintaining
an overall low fitness level,
which in turn may aid the acceptance of
a new random sequence.
In [24] the NK model was used to
show that the evolutionary optimization
is more robust when additions to a genome
are smaller (for N = 16 and K = 2).
This effect happens because the gradual
increase of dimensionality leads to continuous
fitness landscape changes, without
abrupt shifts. That is, a point in the
landscape where the fitness is high
under smaller dimensions should lead to
an appropriate new, higher fitness score
when dimensions increase. A similar
idea was outlined in [20] under the
static genome sizes of the standard NK
model when altering the size of mutation
steps. When the mutation operator
can generate genomes greater than the
correlation length in the fitness landscape,
the period needed to reach an optima increases
considerably.
In our work, the results demonstrate
that the first instance of the
lengthy gene additions
is achieved
within the range of K values studied,
namely without limitations based on
the correlation of the fitness landscape.
However, as depicted in Fig. 8, for N
= 20 a second addition instance is not
acquired for 4 < K < 10 and a possible
third one does not typically happen for
all K values. This is in contrast to the case
with small addition intervals (G = 1)
as depicted in Fig. 5. This could be
caused by the level of correlation
between the two landscapes, despite the
fact that additions are successful for low
values of K.
In nature, the most frequent end
result of new gene additions is their dismissal.
This may happen through different
mechanisms such as fractionation
N = 20
N = 20
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
35
30
25
20
5
K
(a)
N = 100
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
120
115
110
105
100
5
K
(c)
10
15
5
K
(d)
FIGURE 3 (a, c) Average fitness values at 20000 generation steps for different K and N values (maximum and minimum values are indicated by
vertical bars). (b, d) Average genome length values (maximum and minimum values are indicated by vertical bars) for increasing functionality by
one gene (G = 1).
10
15
10
15
5
K
(b)
N = 100
10
15
NOVEMBER 2021 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 89
Fitness
Fitness
Length N′
Length N′

IEEE Computational Intelligence Magazine - November 2021

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