Boosting GA Performance: A Fuzzy Approach to Uncertainty Issues

Involving Parameters in Genetic Algorithms

ao Victor Ribeiro Ferro

1 a

, Jos

e Rubens da Silva Brito

1 b

, Rob

erio Jos

e Rog

erio dos Santos

2 c

Roberta Vilhena Vieira Lopes

and Evandro de Barros Costa

Computing Institute, Federal University of Alagoas, Av. Lourival Melo Mota, Maceio, Brazil

Eixo das Tecnologias, Campus do Sert

ao, Federal University of Alagoas, Delmiro Gouveia, Brazil

Keywords:

Fuzzy Logic, Genetic Algorithms, Uncertainty, Optimization.

Abstract:

This article addresses issues involving two sources of uncertainty in the stochastic search problem based on

a genetic algorithm approach. We improve the mutation rate parameter by fuzzifying the population diver-

sity and the individual adaptation value. A relevant aspect of this investment is related to the fact that this

parameter, which presents uncertainty of the possibilistic type, directly interferes with the uncertainty of the

probabilistic type of the genetic algorithm and also in the convergence and quality of the solution found by

the genetic algorithm. Moreover, in parallel, we improve the understanding behavior of selection and replace-

ment methods. Experiments were carried out on the case study with the classic OneMax problem to evaluate

the performance of the proposed solution, analyzing aspects such as the convergence time, the quality of the

solution, and the diversity of the population. The results obtained through the treatment of uncertainty and

its impacts are presented in this article, showing relevant performance for the proposed algorithm, with the

respective treatment of uncertainties.

1 INTRODUCTION

One of the problems faced by stochastic optimiza-

tion models based on genetic algorithms (GA) is that

the speed of solution convergence is quite sensitive

to the choice of parameters such as mutation rate and

crossover rate. In addition, the process of deﬁning

these parameters is also associated with the uncertain-

ties of which values to choose to improve the perfor-

mance of the algorithmic solution. For this reason,

genetic algorithms, by deﬁnition, have two sources

of uncertainty: inherent uncertainty in the adopted

stochastic model and the uncertainty of choosing the

best parameters for a good quality of the stochastic

search performance process.

In this sense, uncertainty is present in the GA

through the genetic operators of crossover, selection

of individuals, mutation, and the deﬁnition of the

stop state since the choice of parameterization of each

method is a process done in a non-automatic way and

based only on the programmer’s experience levels,

https://orcid.org/0000-0001-5806-2798

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https://orcid.org/0000-0001-6304-0083

seen as a decision-making agent. In addition, we have

uncertainty linked to the very deﬁnition of the genetic

algorithm because it is a non-deterministic solution;

that is, each interaction can bring a different solution

but close to the optimal global solution.

In this way, we observe the need to reduce uncer-

tainty in the deﬁnition and selection of its key param-

eters because, on the one hand, the genetic mutation

operator conducts Exploration to identify yet unex-

plored solution subspaces i.e., those subspaces that

visit entirely new regions of a search space. On the

other hand, Exploitation is performed by crossover,

which operates on neighboring solution subspaces,

i.e., within the vicinity of previously visited points, to

ﬁnd optimal local solutions (

Crepin

sek et al., 2013).

When doing an Exploration, genetic algorithms

employ the mutation rate, responsible for determining

the number of new search subspaces to be considered

for construction in the next iteration of the algorithm.

However, determining the optimal value for the muta-

tion rate is a challenge, given that different problems

may require different values.

Programmers determine the mutation rate choice,

which can be used as a default value by trial and error.

However, these ways of choosing the mutation rate

750

Ferro, J., Brito, J., Santos, R., Lopes, R. and Costa, E.

Boosting GA Performance: A Fuzzy Approach to Uncertainty Issues Involving Parameters in Genetic Algorithms.

DOI: 10.5220/0012389200003636

Paper published under CC license (CC BY-NC-ND 4.0)

In Proceedings of the 16th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2024) - Volume 3, pages 750-757

ISBN: 978-989-758-680-4; ISSN: 2184-433X

may generate or not an efﬁcient Exploration search

due to all sources of uncertainty in the decision pro-

cess of selecting the proper parameters.

In this article, we investigate the impact of uncer-

tainty sources of a genetic algorithm in the combi-

nation of selection and substitution methods on the

GA convergence time and population diversity, eval-

uating the behavior of two types of uncertainty: the

uncertainty inherent to the stochasticity of the algo-

rithm itself (probabilistic uncertainty) and the possi-

bilistic uncertainty present in the deﬁnition of popu-

lation diversity, as well as in the deﬁnition of chro-

mosomal ﬁtness as the main parameters, due to the

inherent vagueness of these concepts, in the view of

the decision-making agent (the programmer of the ge-

netic algorithm).

Thus, our proposal focused on the development

of a self-adaptive genetic algorithm, investing in the

mutation rate with variation in the combination of se-

lection and substitution methods, but also in the use

of fuzzy logic to deal with the conceptual vagueness

present in the deﬁnition’s parameters of population di-

versity and chromosomal ﬁtness.

In summary, the main contribution of this article

is to expose how uncertainty affects the genetic al-

gorithm due to its stochastic nature, but also how to

take advantage of the correct choice of evolutionary

methods responsible for the search for the optimal in-

dividual and the convergence time of the genetic al-

gorithm, dealing directly with conceptual vagueness,

with fuzzy sets, associated with population variability

and chromosomal aptitude of the best-adapted indi-

viduals.

2 SOURCES OF UNCERTAINTY

IN THE GENETIC

ALGORITHM

In the evaluation of a genetic algorithm, we ﬁnd two

sources of uncertainty:

1) uncertainty inherent to the stochastic GA model

2) uncertainty inherent in random choices of param-

eterization by the programmer

In GA, uncertainty is based on these two points.

On the one hand, we have to model through the

genetic operators of mutation, crossover, algorithm

stopping point, and method of choosing the most

adapted individuals from one generation to another;

on the other hand, we have the programmer (decision-

making agent) with his prior knowledge on how to

properly deﬁne these parameters, which often need

to be modiﬁed and tested during application develop-

ment, being adjusted empirically and often based on

vague deﬁnitions about quality of the parameters to

choose.

The GA itself uses the uncertainty of the prob-

abilistic type in the process of search and self-

adaptation of individuals better adapted to the solu-

tion environment, being carried out through distribu-

tions of random variables that underlie the process of

stochastic search and directly inﬂuence the conver-

gence itself, still being related to GA parameteriza-

tion.

On the other hand, the possibilistic uncertainty is

due to the vagueness in the precision of the informa-

tion regarding the choice of parameters that best ﬁt

a stochastic search problem and is associated with the

programmer’s decision (and his degree of knowledge)

about the most appropriate values for the parameters

from GA.

These two types of uncertainty signiﬁcantly im-

pact the results and performance of a genetic algo-

rithm, as some of the uncertainty factors can affect the

quality of the result, leading to inaccurate results or a

longer computation time than necessary (Majumder

et al., 2018). In addition, uncertainty can make it dif-

ﬁcult to compare results between different cycles of

executions of the genetic algorithm.

Therefore, it is essential to consider the types of

uncertainty and their impacts when developing and

evaluating genetic algorithms and ﬁnding strategies to

mitigate such expected impacts.

3 RELATED WORK

In this section, we presented current studies consid-

ering these types of uncertainty and their impacts on

GA’s overall performance.

Some studies evaluate the behavior of genetic al-

gorithms by varying the crossover and mutation rate

as pointed out by (Hassanat et al., 2019), (Sun and Lu,

2019). In addition to these studies, some use Fuzzy

Logic such as (Fadel et al., 2021), which shows its

use in reducing GA convergence time. However, in

most of these works, there is no comparison between

the developed algorithm, the impact of selection and

substitution methods, and the characterization of un-

certainty in the genetic algorithm.

The work of (Hassanat et al., 2019) shows the im-

portance of varying the mutation rate and crossover

population size to solve various problems, demon-

strating each method’s impact in ﬁnding the optimal

solution. However, selection and substitution meth-

ods also show how they can help or hinder the search

Boosting GA Performance: A Fuzzy Approach to Uncertainty Issues Involving Parameters in Genetic Algorithms

751

for the optimal individual.

The work of (Sun and Lu, 2019) depicts that the

premature convergence of GA unexpectedly affects

the algorithm’s performance. The main reason is that

the evolution of exceptional individuals, which mul-

tiply rapidly, will lead to premature loss of popula-

tion diversity. To solve the problem, we constructed a

method to qualify the diversity of the population and

the similarity between adjacent generations.

The experiment results show that it can search for

the optimal solution for almost all reference functions

and effectively maintain the diversity of the popula-

tion. Where (Fadel et al., 2021) uses the integrated

Fuzzy Logic and GA method and uses the growth rate

function to calculate the change of maximum ﬁtness

and average ﬁtness between two successive genera-

tions to adapt the crossover and mutation parameters

of GA dynamically, the results showed that the pro-

posed technique gives a high and more accurate per-

formance in terms of maximum ﬁtness and average

ﬁtness. Despite this, no investigation shows the im-

pact of choosing the combination of selection and re-

placement methods on the algorithm’s performance

and also observes how the algorithm would behave if

we chose diversity population as a parameter in fuzzy

Logic.

In (Bajaj and Sangwan, 2019), work investigates

the effectiveness of test case prioritization based on

genetic algorithms. The work aims to ﬁnd the best pa-

rameter settings and operator roles to increase the ef-

fectiveness of test case prioritization, which can save

time and resources. A strength of this work is the in-

vestigation of how parameter conﬁguration and oper-

ator roles affect the effectiveness of test case prioriti-

zation, providing a basis for improving the effective-

ness of test case prioritization. However, a weakness

is that the work is speciﬁc to genetic algorithm-based

test case prioritization, which means that its ﬁndings

do not necessarily apply to other optimization prob-

lems. Nevertheless, fuzzy Logic considerably im-

proves the convergence time of the genetic algorithm

compared to simple GA.

In addition, it shows how easy it is to implement

and how it helps programmers who will use this tech-

nique to solve problems. However, one question re-

mained: How can the choice of types of combination

of selection and substitution methods impact the con-

vergence time and uncertainty reduction using the al-

gorithm optimized by Fuzzy Logic? We pointed out

the ease of implementing these procedures of self-

adaptation of mutation rate within the pseudo-code of

a Genetic Algorithm (see algorithm 1) and the help

that adopting these methods delivers to novice pro-

grammers in evolutionary computing.

4 METHODOLOGY

This section was divided into steps to show the treat-

ment of uncertainties presented in GA. The ﬁrst

shows the environment in which we ran the algo-

rithm, the second describes a chosen use case, the

third presents the selected evaluation metrics to com-

pare the algorithms to design and measure how good

they were, and ﬁnally, it shows how a simple GA, in

operation and a GA that used the treatment of uncer-

tainty with fuzzy vagueness that was implemented in

the GA, as well as the combination of selection and

substitution parameters chosen in this work.

4.1 Test Environment

The test environment used to make the comparisons

was Google Colab (Google Computer Engine) which

has the following settings:

• RAM: 12GB

• HD: 108GB

We used Python version 3.7.13, and some libraries

were also used, such as:

• ipython-autotime version 0.3.1 to determine the

execution time

• matplotlib version 3.2.2 to display the graphs

• scikit fuzzy version 0.4.2 to build the fuzzy sys-

tem

4.2 Case Study

The case study chosen in this work was OneMax,

which consists of counting the one (1) bit each chro-

mosome has and also represents the individual’s ﬁt-

ness. Thus, the optimal binary is the individual who

has all bits in one (1). Although the solution space

or domain of the OneMax problem depends on the

length of the chromosome, an essential feature of the

OneMax domain is that all bits are unrelated (Giguere

and Goldberg, 1998). The simplicity of the OneMax

problem makes it an excellent candidate for studying

uncertainty reduction by evaluating the performance

of the simple genetic algorithm and the self-adaptive

algorithm on mutation rate and verifying selection

and replacement methods.

4.3 Evaluation Metrics

The metrics chosen in this work to perform the com-

parison of the Simple GA and the GA with the ap-

plication of Fuzzy Logic were the number of genera-

tions to ﬁnd the solution to the problem, the diversity

ICAART 2024 - 16th International Conference on Agents and Artiﬁcial Intelligence

752

of the population, the execution time in seconds re-

quired for the genetic algorithm to ﬁnd the optimal so-

lution. Thus, shows, in a broad way, the performance

obtained in the choice of each mutation method, se-

lection, and replacement method.

In addition, We adopted the Kruskal-Wallis hy-

pothesis test, the non-parametric test used when com-

paring three or more independent samples. It tells

us if there is a difference between the GAs that

used the combinations with substitution and selection.

For comparison between the GAs, the Dwass-Steel-

Crichtlow-Fligner (DSCF test) was used.

4.4 Algorithm Speciﬁcation

This section is divided into each procedure presented

in implementing the Genetic Algorithms adopted

that are AGEE, AGETV, AGRE, AGRTV, AGFEE,

AGFETV, AGFRE, AGFRTV. To show in detail, the

choices adopted were divided into three topics, the

ﬁrst showed the basis of the algorithms, that is, what

they have in common, in second showed the types of

simple GA and the nomenclature used and in the third

the types of proposed GA, the nomenclature used and

the application of fuzzy Logic.

4.4.1 Basis of Both Algorithms

It shows how the basis of the two algorithms is de-

ﬁned, being:

• The representation deﬁned was binary.

• Adopted chromosome size was twelve (12).

• Population size was one hundred (100) individu-

als.

• The crossover, the rate was 90%, so as not to in-

terfere with the ﬁnal result.

• Crossover was chosen with a cutoff point.

The algorithm has the following format, as seen in

(Jong, 2009):

4.4.2 Simple Genetic Algorithm, Without

Uncertainty Treatment

In the Simple Genetic Algorithm, variations are found

with the selection and substitution method, but the

mutation rate is ﬁxed.

• Adopted mutation rate 50

The nomenclature shown in Table 1 combines the

selection and substitution methods.

Input: Typical Parameters

Output: Final Solution Population

1: INITIALIZES population with random

candidate solutions

2: EVALUATE each candidate

3: while condition do

4: SELECT parents

5: RECOMBINE pairs of parents

6: MUTATION the resulting descendants

7: EVALUATES new candidates

8: REPLACES the individuals for the new

generation

9: end while

Algorithm 1: Pseudocode of a Typical GA.

Table 1: Nomenclature of Simple GA Types.

Substitution

Selection Elitist Life Time

Elitist AGEE AGETV

Roulette Method AGRE AGRTV

4.4.3 Genetic Algorithm with Fuzzy Logic

Approach

The GA combined with fuzzy Logic implies modiﬁ-

cations in the methods of selection and substitution,

in addition to the deﬁnition of the implementation of

Fuzzy Logic.

Table 2 shows the terminology used in the algo-

rithms implemented with combinations of selection

and substitution methods:

Table 2: Nomeclature of the Proposed GA Types.

Substitution

Selection Elitist Life Time

Elitist AGFEE AGFETV

Roulette Method AGFRE AGFETV

4.4.4 Application of Fuzzy Logic

The population diversity is assessed by calculating the

percentage of unique individuals within the current

population, i.e., those with non-repeating genetic ma-

terial, as depicted in Equation 1. This computation re-

ﬂects the diversity within the current population. This

calculation is performed globally at each algorithm

generation to determine the population diversity rate.

Additionally, the individual’s score within the popu-

lation is computed to be used as input in Fuzzy rules,

thereby determining the mutation percentage (MP).

PD =

UniqueIndividuals

Population

x100 (1)

Boosting GA Performance: A Fuzzy Approach to Uncertainty Issues Involving Parameters in Genetic Algorithms

753

Twenty-ﬁve rules for the OneMax prob-

lem were considered in the application using

the triangular membership function representa-

tion. The rules have the following antecedent

values of individual’s adaptation and popula-

tion diversity (PD), both with the fuzzy set

verybad

bad

medium

good

, and

verygood

as represented in Figure 1 and as a consequence the

individual’s MP, which is represented by the fuzzy set

verylow

low

medium

high

veryhigh

which is

depicted in Figure 2 [ 0,100].

Figure 1: Population Quality and Diversity.

Figure 2: Mutation Percentage Graph.

The rules chosen in the fuzzy system were ex-

pressed as follows:

5 RESULTS AND DISCUSSION

To compare uncertainty issues and their treatment

performance, we executed each algorithm a hundred

(100) times; that is, each execution means that the al-

gorithm was started and just stopped when it found

the solution to the problem. When found, the data is

stored, and the system is restarted. This looping hap-

pens until the 100 runs are completed, and then, the

extraction of the results is performed. Another critical

factor was the division into two sections, one with the

Table 3: Fuzzy Rules.

results of the Simple GA and another with the results

of the Proposed GA.

5.1 Results Obtained in Simple GA,

Without Uncertainty Treatment

First, simple genetic algorithms’ convergence time

and their variations were analyzed.

Figure 3 shows the time for each of the 100 runs

that each algorithm obtained, that is, the time each run

took to ﬁnd the best solution to the OneMax problem.

Given the above, it is remarkable the difference that

exists in the execution time of the algorithms.

The AGRE algorithm, on average, obtained the

worst performance, about 22.80 seconds (s), com-

pared to the other simple genetic algorithms, which

obtained AGEE 21.60 s, AGETV 0.30 s, and AGRTV

0.28 s.

One of the reasons analyzed for this difference in

time of the simple GA that chose the Elitist substitu-

tion about the simple GA with the lifetime substitu-

tion was the delay of convergence of the population

as seen in (Kim and Han, 2000) due to the size of the

population that directly impacts on its convergence

time, that is, the substitution by Life Time maintains

ICAART 2024 - 16th International Conference on Agents and Artiﬁcial Intelligence

754

Figure 3: Execution Time Simple GA.

a more signiﬁcant amount of living individuals per

time interval, unlike the Elitist that in each iteration

eliminates the individuals with a lower score, impair-

ing the emergence of the optimal solution. Another

critical point is that the roulette wheel method allows

the crossover to individuals with different conﬁgura-

tions of their chromosomes, bringing them good or

bad, which provides a larger sweep in the Exploita-

tion search. At the same time, the Electoral selection

can be stuck at the local optimum.

Figure 4: Population Diversity by Generation Simple GA.

In addition, the diversity of the population present

in a run was veriﬁed, as shown in Figure 4. It was

observed that the Simple Genetic Algorithms with

Elitism in the present replacement diversity, in the be-

ginning, were equal to the simple GA with replace-

ment by lifetime, but over the generations, this di-

versity changes because the algorithms AGETV and

AGRTV have a larger population, but the lifetime set

in each generation is different, thus implying a more

signiﬁcant amount of living individuals, but when the

maximum lifetime is reached this generation is de-

stroyed, which helps in the high diversity. On the

other hand, the AGEE and AGRE algorithms have a

reduced population, but the amount of different indi-

viduals within it is not large by keeping optimal indi-

viduals, which sometimes have the same genetic ma-

terial.

Figure 5: Result of the Generation by Run.

Finally, Figure 5 shows the number of genera-

tions needed to ﬁnd the optimal individual in each

run, which averaged AGRTV 41.48, AGRE 5253.03,

AGEE 4798.50 and AGETV 41.42. Being high-

lighted, the Simple GA is implemented with the life-

time, which can ﬁnd the optimal individual ﬁrst and

with a small number of iterations.

5.2 Results Obtained in the Proposed

GA with Fuzzy Approach

The tests performed on the Simple Genetic Algorithm

were also performed on the Genetic algorithm com-

bined with Fuzzy Logic with its variations on the

substitution and selection method to be able to make

comparisons between them.

Figure 6: Proposed GA Runtime.

The AGFRE algorithm had the worst perfor-

mance, averaging about 6.52 s compared to the

other genetic algorithms combined with Fuzzy Logic,

which had AGFETV 0.16s, AGFRTV 0.30s, and

AGFEE 0.23s.

The self-adaptive genetic algorithms that used the

method of Lifetime Replacement have an increased

population, which impacts reducing the convergence

time of the GA. In addition, the self-adaptive GA

maintains a high search in the Exploration approach,

Boosting GA Performance: A Fuzzy Approach to Uncertainty Issues Involving Parameters in Genetic Algorithms

755

i.e., effectively sweeps a more signiﬁcant number of

search spaces; this occurs because it can infer an ap-

propriate mutation rate for each chromosome in the

population, taking into account the diversity of the

population and the quality of the chromosome, which

interferes with faster convergence.

Figure 7: Population Diversity by Generation Proposed GA.

There was a check on the diversity of the popu-

lation present in a run, as shown in Figure 7. It was

observed that the Self-Adaptive Genetic Algorithms

with Electism in the substitution present diversity, in

the beginning, equal to that of the Self-Adaptive GA

with replacement by Life Time, but during the gener-

ations, this diversity diverges because the algorithms

AGFETV and AGFRTV have a larger population and

their diversity as well. On the other hand, the algo-

rithms AGFEE and AGFRE have a reduced popula-

tion, which impacts an increasing diversity through-

out the generations; that is, there is a greater chance

of having individuals with the same genetic material.

Figure 8: Generation of Each Proposed GA Run.

Figure 8 illustrates the number of generations

needed to ﬁnd the best-ﬁt chromosome, which had an

average of AGFRTV 7.92, AGFRE 356.84, AGFEE

3.76, AGFETV 3.40 generations. The algorithms that

stood out were AGFEE and AGFETV, which had the

Elitist selection method. It shows the importance of

correctly deﬁning the mutation rate and the choice of

selection and substitution methods.

5.3 Hypothesis Testing

The Kruskal-Wallis test is a non-parametric test used

when comparing three or more independent samples.

It indicates if there is a difference between at least two

of them (Rumsey, 2015).

Therefore, the number of generations needed to

ﬁnd the optimal individual per run was selected for

analysis. First, the following hypotheses were raised

to check if there is a difference in the choice between

the selection and replacement methods:

• H

: There is no statistically signiﬁcant difference

between the group means.

• H

: There is a difference between group means.

A signiﬁcance level of 5% was chosen. The test

result was less than 0.001 s; that is, the result is lower

than the signiﬁcance level, and there is a statistical

difference. Table 4 shows the comparison between

each of the Simple GA types.

Table 4: Kruskal-Wallis Test Simple GA.

W p

AGEE AGETV -17.261 0.001

AGEE AGRE 0.734 0.955

AGEE AGRTV -17.257 0.001

AGETV AGRE 17.225 0.001

AGETV AGRTV 1.294 0.797

AGRE AGRTV -17.240 0.001

Table 4 shows no difference between the AGEE

and AGRE methods, and the same is true for AGETV

and AGRTV. However, the Life Time Replacement

method causes a statistically relevant difference in the

cases.

The same test was performed with the GAs that

used Fuzzy Logic, adopting a signiﬁcance level of

5%. Again, the result was less than 0.001 s; that is,

there is a statistical difference between the groups.

Table 5 shows the comparison between the groups.

Table 5: Kruskal-Wallis Test GA with Fuzzy Logic.

W p

AGFEE AGFETV -0.142 0.987

AGFEE AGFRE 17.317 0.001

AGFEE AGFRTV 6.721 0.001

AGFETV AGFRE 17.308 0.001

AGFETV AGFRTV 6.9787 0.001

AGFRE AGFRTV -17.283 0.001

In Table 5, there is no difference between the

AGFEE and the AGFETV methods, whereas there is

ICAART 2024 - 16th International Conference on Agents and Artiﬁcial Intelligence

756

a statistically signiﬁcant difference between the other

methods.

6 CONCLUSION AND FUTURE

WORK

In this article, we present an approach that addresses

types of uncertainty inherent in the development and

execution of genetic algorithms. Experimentally, we

applied the proposed method with the fuzzy approach

and different selection and substitution methods. We

showed that the genetic algorithm combined with

the conceptual vagueness treatment, using the elitist

selection and the lifetime substitution method, pre-

sented the best results compared to the other combi-

nations. In this sense, this work highlights the rel-

evance of this approach to improve the performance

of genetic algorithms and also shows the reduction of

uncertainty found in genetic algorithms through im-

plementing a self-adaptive algorithm that helps and

facilitates the search for the global optimum. This

contribution is a signiﬁcant step towards improving

performance and knowledge representation in GA.

In our approach, Fuzzy Logic was used in the pro-

posed algorithm in a simple way to implement, which

conﬁrms the adoption of these modiﬁcations in its

implementation, showing the importance of modiﬁ-

cation in the current population-sensitive interactive

mutation rate.

In addition, it was also shown the importance of

testing with different methods of substitution and se-

lection because the reduction in convergence time is

signiﬁcant in the OneMax problem, this difference in

most cases tested being greater than 90%, i.e., the

methods that used Time of Life substitution had an

advantage. On the other hand, the methods that used

Elitism had an increasing diversity along the genera-

tions and a long time of convergence.

Using Fuzzy has a downside linked to the algo-

rithm’s convergence time; a larger population results

in longer computational times. This study is lim-

ited by analyzing only a single test case, the Onemax

problem, diminishing the generalization of diversity

understanding for uncertainty reduction in the GA.

In future work, we intend to apply the proposed

GA to other classes of problems and analyze how this

algorithm behaves. In this way, it facilitates the devel-

oper in deciding which problems the adoption of the

self-adaptive genetic algorithm is recommended. For

example, in the Traveling Salesman Problem (TSP)

function Optimization, the methodology adopted in

this work focuses on the variation of the mutation

rate and variation of the substitution and selection

method to corroborate the results obtained in this

work. Linked to this, analyze in more detail in Fuzzy

Logic the consequences of changing the mutation rate

in different functions of representation of knowledge

as the Trapezoidal, Gaussian.

Another thread for future work is to verify if the

methodology applied here can be extended to all rates,

such as crossover and population size variation. Thus,

the importance of changing the parameters during the

execution of the genetic algorithm iterative can be

seen.

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