IEEE Computational Intelligence Magazine - November 2021 - 98

1,000
Average Fitness of Population.
300
400
500
600
700
800
900
020406080 100 120 140 160 180 200
Generations
(a)
300
400
500
600
700
800
900
1000
Best Individual Fitness of a Population.
020406080 100 120 140 160 180 200
Generations
(b)
FIGURE 17 Average and confidence levels (95%) results from 10 runs 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.
lead to marked difference in the evolved
genome lengths and the final fitness.
Therefore, this option is not tested
in the computationally expensive cancer
simulator.
VI Discussion
The best solution found in this study has
a fitness of approximately 405 cancer
agents remaining after the three days of
simulated treatment. Note that the fittest
individual of the initial random population
was evaluated at 900 agents, translating
to an improvement of 55%. To
further comprehend the fitness level of
this solution, a comparison is drawn with
previous studies utilizing the same simulator
and similar fitness functions, but
1
2
3
4
5
6
7
8
9
10
020406080 100 120 140 160 180 200
Generations
FIGURE 18 Average and confidence levels (95%) results from 10 runs of the EA with variablelength
genome adding two types of NPs for the composition of the best solution.
with different approaches. In [28] the
best solution found indicated a 4.8% fitness
improvement (best fitness of the initial
random population was 420 agents,
while the final best fitness was approximately
400 agents), in [29] an improvement
of 13.3% (c. 450-390) and in [30]
an improvement of 16.9% (c. 415-345).
As it can be seen, the best fitness (in
terms of percentage reduction of tumor
size) in this study largely outperforms all
previous ones. However, if the fitness is
expressed as the absolute number of
remaining cells, the results are somewhat
weaker. This can be attributed to the following
side factors: the initial population
in the aforementioned studies is different
than this one (i.e., the initial best fitness
Best Individual Composition.
in [30] is c. 450, whereas it is c. 900 here)
and the method in this study operates on
a continuously altering fitness landscape.
Furthermore, using only a simple mutation
operator undoubtedly limits the
pace of the evolutionary search. Nevertheless,
note that this is the first attempt
of a simulated multi-NP treatment using
the physics-based tumor simulator.
Given that the real-world problem
described here needs to be under a metameric
representation, the specialized crossover
operators required are omitted.
Instead, the simplest variation of evolution,
mutation operator, is implemented. As a
result, the genome length is controlled to a
greater degree compared with a case of
utilizing specialized metameric crossover
operators. Moreover, as no significant difference
arises from having both addition
and deletion in the genome length while
testing the abstract NK model, this is not
tested on the computationally expensive
simulator. As an aspect of future work, different
growth and deletion schemes will
be explored, such as those which selfadapt
over time (after [34]), along with
recombination and crossover operators.
Despite the fact that the amount of
types of NPs in the evolution with addition
of one type of NPs (Fig. 15) does
not reach the maximum available (i.e.,
10), in the case of adding two types of
NPs per step (Fig. 18) the composition
reaches
the highest possible (i.e., 9-
because the initial composition is 1 and
there are 2 added per step). Nonetheless,
98 IEEE COMPUTATIONAL INTELLIGENCE MAGAZINE | NOVEMBER 2021
Average Fitness of Population
Number of NPs of Best Individual
Best Fitness of Population

IEEE Computational Intelligence Magazine - November 2021

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