IEEE Computational Intelligence Magazine - November 2021 - 97
same metric of the initial random
population c. 950 agents. When considering
the cumulative results of 10 runs,
outlined in Fig. 17(a), it is evident that a
further improvement of the average fitness
of the population occurs (average of
434 agents). Also, the final fitness of the
best individual produced during the
example run (approximately 415 agents)
compared with the randomly generated
initial one (c. 900 agents) is improved by
53.9%, as given in Fig. 16(b). In Fig. 17(b)
where all the results of 10 runs are considered,
it can be established that during
the rest of the runs the improvement is
similar and slightly better (average of
407 agents).
Here, in contrast
to adding one
type of NPs per mutation event, the
best solutions converge to the maximum
available composition (9 types),
as illustrated in Fig. 18. In some of the
runs the highest amount of NPs types
is reached by the 100th generation
(earlier than the previous case, i.e., the
120th generation), while in all runs the
composition of best solutions converges
to 9 by the 160th generation. As in
some cases in the NK model, whilst
fitness is not significantly improved by
the addition of more genes per growth
event, longer genomes emerge. This is
an indication of the bloat effect, but
one that is controllable due to the
parameter G.
We would like to emphasize that
our investigation of the NK model
(Section III) showed that possibility of
decreasing the genome length does not
Best Individual Composition.
1
2
3
4
5
6
7
8
9
10
020406080 100 120 140 160 180 200
Generations
FIGURE 15 Average and confidence levels (95%) results from 10 runs of EA with variable-length
genome for the composition of the best solution.
Average Fitness of Population.
Best Individual Fitness of a Population.
1,000
400
600
800
020406080 100 120 140 160 180 200
Generations
(a)
1
2
3
4
5
6
7
8
9
10
20
5
5
6
4
1
2
8
7
2
1
5
1
1
2
5
1
7
1
8
9
1,000
400
600
800
1
3
44 6
77 77 99 9
55 66 6
9 99
020406080 100 120 140 160 180 200
Generations
(b)
Evolution of Number of NPs
13 12 12 12 11 10
10 12 13
8
7
020406080 100 120 140 160 180 200
Generations
(c)
FIGURE 16 Results from example run of the EA with variable-length genome adding two types of NPs. (a) Evolution of average fitness of the population,
(b) evolution of the best individual in the population (where numbers indicate the number of types NPs) and (c) composition of population
in terms of types of NPs.
NOVEMBER 2021 | IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE 97
Average
Fitness of Population
Types of NPs
Number of NPs of Best Individual
Best
Fitness of Population
IEEE Computational Intelligence Magazine - November 2021
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