IEEE Computational Intelligence Magazine - November 2021 - 88
This is expected due to the increase in
the dimensions of the fitness landscape.
It is also clear that genome growth
ceases earlier for low K. Figure 5 illustrates
the generation at which the additions
of the first three genes to the
genome are initially successful. It can be
seen that the first two genes are accepted
at roughly the same rate for all K
and N values, whereas the acceptance of
the third gene varies widely for N = 20.
The effects of increasing the number
of randomly added genes per growth
event are also explored. Figure 6 shows
results for G = 20, where with N = 20
and K > 4, the final fitness is significantly
enhanced compared to G = 1
(T-test, p < 0.05). This is attributed to
the fact that the complexity catastrophe
is more robustly avoided, as the final
genome lengths are notably greater than
with G = 1. In the case of N = 100, the
final fitness achieved is not significantly
different from the results with G = 1,
but the final lengths are also greater.
The generations when the final fitnesses
are reached and the corresponding
genome lengths are illustrated in
Fig. 7. It can be seen that for all K, the
evolution continues for a longer period
in comparison to no or limited genome
growth, particularly with N = 20 (as in
Fig. 4). The generation numbers when
new genes are acquired by the genome
are shown in Fig. 8. The addition of the
first sets of genes occurs in comparable
time steps as for the case of G = 1.
While the second sets are also added in
similar generation numbers for N = 100,
they take longer or are not even added
for N = 20. Consequently, adding longer
gene intervals may result in more
additions performed later during the
evolution. That is, a larger amount of
growth per addition can maintain the
conditions longer for more subsequent
growth. Here each increase in the size of
a fitness landscape supplies a number of
N = 20
N = 20
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
5
K
(a)
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
5
K
(c)
N = 100
0.5
0.55
0.6
0.65
0.7
0.75
10
15
(d)
FIGURE 2 (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) Example average fitness values through the initial steps of evolution.
10
15
0.5
0.55
0.6
0.65
0.7
0.75
K = 2
K = 6
K = 15
100 200 300 400 500
Generation
(b)
N = 100
K = 2
K = 6
K = 15
200 400 600 800 1,000
Generation
88 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2021
Fitness
Fitness
Fitness
Fitness
IEEE Computational Intelligence Magazine - November 2021
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