Diversifying Techniques & Neutrality in Genetic Algorithms
Seamus Hill and Colm O’Riordan
College of Engineering & Informatics, National University of Ireland, Galway, Ireland
Keywords:
Neutral Theory, Genetic Drift, Neutrality, Genotype, Phenotype, Genetic Algorithms.
Abstract:
This paper examines the implicit maintenance of diversity within a population through the inclusion of a
layered genotype-phenotype map (GP-map) in a Genetic Algorithm (GA), based on the principal of Neutral
theory (Kimura, 1968). The paper compares a simple GA (SGA), incorporating a variety of diversifying tech-
niques, to the multi-layered GA (MGA) as proposed by the authors. The MGA creates a neutral representation
by including a layered GP-map based on the biological concepts of Transcription and Translation. In standard
GAs, each phenotype is represented by a distinct genotype. However by allowing a higher number of alleles to
encode phenotypic information on the genotype, one can create a situation where a number of genotypes may
represent the same phenotype. Through this process one can introduce the idea of redundancy or neutrality
into the representation. This representation allows for adaptive mutation (hot spots) and silent mutation (cold
spots). This combination enables the level of diversity to dynamically adjust during the search, and directs the
search towards closely related neutral sets. Previous work has shown that introducing this type of representa-
tion can be beneficial; in this paper we show how this representation is useful at introducing and maintaining
diversity. Here we compare the performance of the MGA against traditional diversifying techniques used in
conjunction with a SGA over a fully deceptive changing landscape.
1 INTRODUCTION
Genetic algorithms are search mechanisms based on
Darwinian principals. However, simple genetic algo-
rithms (SGA), through the representation used, im-
plement a process of evolution without including the
concept of neutral mutations. That is, representations
in SGA do not adopt the notion of Neutral theory.
Neutral theory can be described as a situation where
the size of the search space is increased, without an
equivalent increase in the solution space. This al-
lows silent mutations to occur, where a mutated in-
dividual, at the genotypic level, can still represent the
same phenotype. Kimura’s work indicated that the
vast majority of mutations are caused by genetic drift
rather than selection (Kimura, 1968). With this in
mind, while natural selection is an important feature
in the evolutionary process, only a fraction of DNA
changes result in adaptation. This means that the ma-
jority of mutations taking place are phenotypically
silent (Kimura, 1983). The motivation is to develop
a tunable, synonymous, non-trivial GA representation
which incorporates neutrality and to compare the im-
plicit diversity created by the representation with that
of a SGA, using a variety of diversifying techniques.
The contribution is to examine the use of a GA which
is designed to implicitly maintain diversity within the
population through its representation and to analyse
the impact of the representation on population evolu-
tion. The paper is laid out as follows: Section 2 gives
a brief background to Neutral theory and the use of
neutrality in GAs. Section 3 outlines the genotype-
phenotype map (GP-map) used in the paper, while
Section 4 describes the experiments undertaken. Sec-
tion 5 outlines and analyses the results and Section 6
concludes.
2 BACKGROUND
Previous research on the use of neutrality in evolu-
tionary search produced mixed results. Smith et al.
(Smith et al., 2001) highlighted the effect of neutral
networks on the evolutionary search and concluded
that neutrality does not provide an advantage. Ebner
et al. (Ebner et al., 2001) examined the use of mu-
tation and found that high levels of mutation could
be sustained through the presence of neutral net-
works. They also identified that neutral networks as-
sist in maintaining diversity in the population, which
could prove useful over changing landscapes. Simi-
lar results were also found in (Grefenstette and Cobb,
140
Hill, S. and O’Riordan, C.
Diversifying Techniques & Neutrality in Genetic Algorithms.
DOI: 10.5220/0006036201400147
In Proceedings of the 8th International Joint Conference on Computational Intelligence (IJCCI 2016) - Volume 1: ECTA, pages 140-147
ISBN: 978-989-758-201-1
Copyright
c
2016 by SCITEPRESS Science and Technology Publications, Lda. All rights reserved
1993). Research carried out by Yu and Miller (Yu and
Miller, 2001) illustrated that through the incorpora-
tion of neutrality, mutation may or may not be adap-
tive depending on the gene in question. They also
examined neutrality using the OneMax problem, with
results indicating that neutrality is advantageous as it
allows the absorption of destructive mutations. Other
research in the area includes (Hill and O’Riordan,
2105) which looked at the population dynamics of
neutrality using a deceptive problem over a changing
landscape. Results indicated that neutrality had a pos-
itive impact, allowing the search to escape local op-
tima following the environmental changes. Problem
difficulty also impacted on the usefulness of neutral-
ity, as shown in (Hill and O’Riordan, 2104) and (Hill
and O’Riordan, 2013).
3 GENOTYPE-PHENOTYPE
MAPPING (GP-MAP)
In relation to redundancy, Information Theory pro-
vides a measurement of information. The information
contained in a sequence, measured in Bits B, can be
defined as the number of bits b required to represent
that given information. In other words you need to
be able to distinguish between the Bits, which repre-
sent the amount of information and the bits, which are
used to represent the information (Rothlauf, 2002). If
b > B, then your representation incorporates an ele-
ment of redundancy. With regard to the multi-layered
mapping of the MGA and using the notation out-
lined in (Rothlauf, 2002), as you progress through
the layers, the level of redundancy alters. In the tran-
scription layer, which maps |φ
g
| (the genotype space)
|φ
d
| (the DNA space) |φ
r
| (the RNA space),
k = 1 (where k represents the order of the phenotypic
building block) and there is no redundancy, therefore
b = B and k
r
= 1 (where r can be defined as the num-
ber of genotypic building blocks of length kk
r
used
to represent a phenotypic building blocks of length
k). In this paper, the chromosome length, l
g
= 24 and
|φ
g
| = 2
l
g
. The DNA space |φ
d
| consists of characters
selected from a 4 character alphabet, with the DNA
string l
d
= 12 and k = 3. Therefore, |φ
d
| = 4
l
d
also
|φ
d
| = |φ
r
| and l
d
= l
r
(the RNA string) . The trans-
lation layer which maps |φ
r
| |φ
p
| (the phenotype
space), introduces redundancy into the mapping. In
the translation layer, b > B, r = 1, k
r
= 3 and k = 1.
The RNA building blocks have size kk
r
and the re-
dundancy is uniform. As k represents the order of
the phenotypic building blocks, there are 2
k
different
phenotypes, which are represented by 4
kk
r
different
RNA strings. In other words, there are 4
kk
r
differ-
ent possibilities to encode a single phenotypic bit and
|φ
p
| = 2
l
p
. In this paper, the phenotype string l
p
= 4.
Although the redundancy is uniform, the Hamming
distances are not minimal and therefore the redun-
dancy is not linear.
Figure 1: 6-bit MGA Representation Mapping.
In summary, |φ
g
| = {0,1}
l
g
where l
g
is the geno-
type length. The transcription phase maps |φ
g
|
|φ
d
| |φ
r
|. Where: |φ
d
| = {A,C, G,T}
l
g
/2
with the
following mappings: 00 A; 01 C; 10 G and
11 T. A bijective mapping maps |φ
d
| |φ
r
|,
where: |φ
r
| = {A,C, G,U}
l
g
/2
. U is biologically in-
spired and has no impact on the evolution unless we
include operators at this level. Following transcrip-
tion, the translation phase takes place, mapping the
RNA space to a phenotype space |φ
p
|, |φ
r
| |φ
p
|,
where: |φ
p
| = {0,1}
l/c
, c is the cardinality chosen at
initialisation to create a translation table, which maps
3 characters to a phenotype bit (either 0 or 1). The
level of redundancy is determined by c, in this paper
c = 6 (see Figure 1), and implies |φ
g
| > |φ
p
| as c > 1.
Missense mutation or substitution refers to a change
in one amino acid in a protein, arising from a point
mutation in a single nucleotide. Missense mutation in
nature is carried out at the RNA level. In relation to
the MGA, the Missense mutation mapping is as fol-
lows: A U, C G, G A and U C. The varia-
tion operators, one-point crossover and single-point
mutation occur at the genotype level prior to tran-
scription and missense mutation takes place before
translation. This mapping implicitly maintains related
genetic diversity within the population, thus allowing
the occupation by the population, of a greater number
of neutral networks. This is possible as adaptive mu-
tation occurs at c locations (hot zones) on the chro-
mosome. The effect of this is to allow silent muta-
tion to occur at l
g
c locations (cold zones), which
allows 2
l
g
c
genotypes represent the same phenotype.
This increases the level of diversity within the popu-
lation and allows the creation of neutral sets, which
self-organise during evolution.
Diversifying Techniques & Neutrality in Genetic Algorithms
141
4 EXPERIMENT SET UP
Solutions and sub-solutions are normally lost in a
SGA population for three reasons: selection pressure,
selection noise and operator disruption. Selection
pressure occurs as the result of the selection process,
with less fit solutions disappearing from the popula-
tion. Selection noise is the result of the variance of
the selection process due to random choices between
identically fit solutions. Operator disruption takes
place through the implementation of the crossover
and mutation operators which possess the ability to
destroy good solutions. In an attempt to avoid prema-
ture convergence, techniques for diversifying a pop-
ulation generally attempt to reduce individually or in
combination with one another, selection pressure, se-
lection noise or operator disruption (Mahfoud, 1995).
Diversity within a population can serve a number
of purposes, such as delaying convergence (note that
premature convergence can be defined as the conver-
gence to non-global optima) in order to promote ex-
ploration. Hence the maintenance of diversity within
a population is a desirable feature for GAs. Diver-
sification methods capable of reducing all three cri-
teria, selection noise, selection pressure and operator
disruption exist. The problem lies in the fact that re-
ducing all three criteria to arbitrarily low levels re-
sults in the GA carrying out little or no useful search
(Mahfoud, 1995). The maintenance of diversity for its
own sake is undesirable; what is required is diversity
that promotes good strings (Goldberg and Richard-
son, 1987).
By comparing the performance of the MGA with a
SGA containing a number of diversifying techniques,
we can evaluate the diversity maintenance mecha-
nism implicit in the MGA representation. With re-
gard to the three mechanisms for promoting diversity,
the theory would suggest that Stochastic Universal
Selection (SUS) offers the ability to minimise selec-
tion noise, fitness scaling can decrease selection pres-
sure and lower rates of crossover and mutation can
reduce operator disruption (Mahfoud, 1995). How-
ever it is worth remembering that a relationship exists
between convergence and diversity in a GA popula-
tion. If there is no operator disruption and no selection
pressure, then the GA will maintain its initial popula-
tion and won’t perform any meaningful search. Also
with regard the mutation operator, as mutation rates
increase, the diversity produces is usually not useful
as the GA is approaching random search.
In this paper a four-bit changing deceptive land-
scape as outlined in (Hill and O’Riordan, 2105) was
used. Although this landscape is relatively small in
terms of the search space, it was chosen as it allows
the dynamics of the population evolution to be stud-
ied. The parameters chosen are outlined in Table
1. Over the set of experiments designed to examine
various diversifying techniques, we altered the selec-
tion mechanisms and scaling methods of the SGA.
We also conducted a number of experiments where
we increased the SGAs variation operators. The mo-
tivation for these changes is to vary the selection
noise, selection pressure and operator disruption for
the SGA, thereby examining the impact of the inclu-
sion of well understood diversifying techniques into
the SGA, which in turn are then compared with the
performance of the MGA.
Table 1: Parameters Used.
Parameters MGA SGA
Runs 10 10
Generations 200 200
Population P 20 20
Crossover P
c
0.7 0.7
Mutation P
m
1/l 1/l
Missense Mutation 0.2 No
Selection Mechanisms Tournament Various
Scaling Methods No Various
In Section 5 we outline the results of the ex-
periments conducted. The selection noise experi-
ments explore the use of Stochastic Remainder Se-
lection (SRS) and SUS. The selection pressure exper-
iments examine Linear, Window, Sigma Truncation
and Boltzmann scaling techniques and niching tech-
niques, such as, crowding and Incest Reduction. Fi-
nally, the operator disruption experiments look at the
impact of increasing rates of crossover and mutation.
0
5
10
15
20
25
30
35
20 40 60 80 100 120 140 160 180 200
Fitness
Generations
SGA & MGA 4-bit Deceptive Problem - Online/Offline Performance Analysis
MGA Off-line Performance
MGA On-line Performance
SGA Off-line Performance
SGA On-line Performance
Figure 2: SGA & MGA On-line/Off-line.
5 RESULTS
Figure 2 illustrates the off-line (averaged best fitness)
and on-line (averaged fitness) performance for both
the SGA and the MGA. The results indicate that the
ECTA 2016 - 8th International Conference on Evolutionary Computation Theory and Applications
142
changing 4-bit deceptive landscape initially proved
equally easy for both the SGA and the MGA, as they
both located the global optimum. This is shownby the
off-line performance of both GAs up to the change
of landscape at generation 50. After the landscape
changes, the SGA becomes trapped on the local op-
timum, while the MGA succeeds in locating the new
global optimum. To analyse the results statistically,
in this paper we used a Wilcoxon signed rank test to
compare the off-line results of the SGA and MGA,
and similarly to compare the on-line performances of
both the SGA and MGA. The results indicated that
the off-line results for both GAs were statistically
significant with a p-value < 2.2e
16
. Similarly the
on-line results were also statistically significant (p-
value < 2.2e
16
).
5.1 Neutral Networks
The neutral networks representing various fitness val-
ues are shown in Figure 3. Before the landscape
changes at generation 50, the most prominent neu-
tral network represents the global optimum pheno-
type (1111). As the population evolves, the MGA,
through its M : 1 representation, allows the size of
neutral networks to adapt as the population evolves.
The next largest neutral networks represent the phe-
notypes (0111), (1110), (1101) and (1011), which
are the four genotypes closest in Hamming distance
to the optimum, indicating that the MGAs population
evolves towards neighbouring neutral sets.
0
5
10
15
20
20 40 60 80 100 120 140 160 180 200
Number of Genotypes of Similar Fitness
Generations
MGA 4-bit Deceptive Problem - Genotype Fitness Representation Per Generation
Fitness 0 (0001 & 1000)
Fitness 2 (1011 & 0100)
Fitness 4 (1101 & 0010)
Fitness 6 (1110 & 0001)
Fitness 8 (1100 & 0011)
Fitness 10 (1010 & 0101)
Fitness 12 (1001 & 0110)
Fitness 14 (0110 & 1001)
Fitness 16 (0101 & 1010)
Fitness 18 (0011 & 1100)
Fitness 20 (1000 & 0111)
Fitness 22 (0100 & 1011)
Fitness 24 (0010 & 1101)
Fitness 26 (0001 & 1110)
Fitness 28 (0000 & 1111)
Fitness 30 (1111 & 0000)
Figure 3: Neutral Networks - Number of Genotypes with
Similar Fitness.
As the landscape changes the largest neutral net-
work represents the new local optimum (1111), as
this was the global optimum at the time of the change.
As the search continues the MGAs population es-
capes the local optimum and has located the global
optimum. At this point, the most prominent neutral
network represents the phenotype (0000) (the new
global optimum). Also, the MGA population has
evolved towards a different group of neutral sets rep-
resenting the phenotypes (0001), (0010), (0100) and
(1000), all close, phenotypically, in Hamming dis-
tance to the global optimum.
Figure 4 looks at the composition of the neutral
sets, examining the number of identical genotypes in
each set. The figure indicates that there is a high de-
gree of diversity maintained within each neutral set,
with low numbers of identical genotypes present. The
number of identical genotypes representing the global
optimum varying between 2 and 4, illustrating the im-
pact of the M : 1 representation on the population.
Overall, the results indicate that the representation,
implicitly maintains useful building blocks within the
population, which promotes good strings and assist in
improving the adaptability of the MGA.
0
2
4
6
8
10
20 40 60 80 100 120 140 160 180 200
Number of Similar Genotypes
Generations
MGA 4-bit Deceptive Problem - Genotype M:1 Representation Per Generation
Fitness 0 (0001 & 1000)
Fitness 2 (1011 & 0100)
Fitness 4 (1101 & 0010)
Fitness 6 (1110 & 0001)
Fitness 8 (1100 & 0011)
Fitness 10 (1010 & 0101)
Fitness 12 (1001 & 0110)
Fitness 14 (0110 & 1001)
Fitness 16 (0101 & 1010)
Fitness 18 (0011 & 1100)
Fitness 20 (1000 & 0111)
Fitness 22 (0100 & 1011)
Fitness 24 (0010 & 1101)
Fitness 26 (0001 & 1110)
Fitness 28 (0000 & 1111)
Fitness 30 (1111 & 0000)
Figure 4: Neutral Networks - Identical Genotype.
5.2 Selection Noise
As outlined by DeJong (De Jong, 1975), the vari-
ance of selection is one of the main contributors to
the idea of convergence. In order to examine selec-
tion variance or selection noise, we compare a number
of selection mechanisms designed to reduce selection
noise, namely SRS and SUS. With SRS, the fitness of
an individual f
i
is divided by the average fitness of the
population
¯
f. For each string i where f
i
/
¯
f is greater
than 1.0, the integer part of the number defines the
number of copies of the individual are put forward for
crossover. For example an individual with a fitness
value of 1.45, places one copy forward for crossover
and then has a 0.45 chance of putting a second copy
forward.
SUS on the other hand, is optimal with respect to
efficiency, bias (that is, the distance from the RWS
in relation to expected value) and the spread (range
of possible individuals put forward for crossover)
(Baker, 1985). SUS simulates a roulette wheel sim-
ilar to RWS. However, while RWS spins the wheel n
times (n = populationsize), SUS spins the wheel once,
using n uniformly spaced pointers at the edge of the
Diversifying Techniques & Neutrality in Genetic Algorithms
143
wheel. SUS has zero bias, is very efficient and min-
imises the spread and is regarded as the lowest noise
selection scheme.
0
5
10
15
20
25
30
35
20 40 60 80 100 120 140 160 180 200
Fitness
Generations
SGA (SRS & SUS) & MGA 4-bit Deceptive Problem - Online/Offline Performance Analysis
MGA Off-line Performance
MGA On-line Performance
SGA (SRS) Off-line Performance
SGA (SRS) On-line Performance
SGA (SUS) Off-line Performance
SGA (SUS) On-line Performance
Figure 5: Selection Noise On-line/Off-line.
Figure 5 indicates that the SGA (with SRS and
SUS individually included), located the local opti-
mum in the initial population, (see the off-line per-
formances) due in part to the level of diversity (illus-
trated by the SGA on-line performance). However,
the population converges prematurely as the search
continues and diversity is quickly eliminated from
the population. Once the landscape changes, because
the population, for both the SRS and SUS SGAs,
were trapped on the deceptive local optimum, they
automatically located to new global optimum and re-
mained there for the duration of the search. The MGA
on the other hand located the global optimum both be-
fore and after the landscape change.
Table 2: Off-Line & On-Line Selection p-values.
Off-Line SRS SUS MGA
SRS 0.04131 0.09138
SUS 0.04131 0.4005
On-Line
SRS 0.2732 < 2.2e
16
SUS 0.2732 < 2.2e
16
The statistical analysis of the results between the
MGA and the SGA are shown in Table 2 and indi-
cate that the off-line and on-line performance of SRS
and SUS are quite similar to one-another. Comparing
the MGAs off-line results to those of the SRS SGA,
shows a less significant result than that of the off-line
MGA and SUS SGA. The on-line performance of the
MGA differs significantly from both of the SGAs.
Figure 6, illustrates the rate of convergence within
the population and shows both the SGA (using SRS)
and the SGA (using SUS) converging quickly. The
MGA maintains a higher degree of diversity, both at a
phenotypic and genotypic level which assists in suc-
cessfully locating the global optimum, both before
and after the landscape change, as the level of diver-
sity maintained allows the search to escape from the
local optimum.
0
500
1000
1500
2000
2500
0 50 100 150 200
Hamming Distance
Generations
Selection Noise SGA & MGA - Genotype & Phenotype Convergence
MGA Genotype Hamming Distance
MGA Phenotype Hamming Distance
SGA (SRS) Genotype Hamming Distance
SGA (SUS) Genotype Hamming Distance
Figure 6: Selection Noise Convergence Rate.
5.3 Selection Pressure
With selection, the extraordinary individuals within
a population will begin to dominate the population
quite quickly and premature convergence will be-
gin to take hold. Even if there is significant di-
versity within a population, late in a run, the pop-
ulation’s average fitness (on-line) may be close to
the population’s best fitness (off-line). This leads
to a situation where the search for improvement be-
comes a random-walk among the mediocre (Gold-
berg, 1989).
5.3.1 Scaling Techniques
Fitness scaling has been used to overcome this prob-
lem. We now examine fitness scaling diversifying
techniques aimed at reducing the selection pressure
within the population:
Linear scaling adjusts the fitness values of all
individuals within the population, such that the
fittest individual receives a fixed number of ex-
pected offspring and therefore prevents it from
reproducing too frequently. The fitness function
f
i
= axf
i
+ b is used where a and b are normally
selected so to allow the average individual receive,
on average, one offspring copy, and the best re-
ceives the specified number of copies (normally
two). This method may return a negative fitness
value.
Window scaling, fitness is scaled by subtracting
from the raw fitness, the lowest fitness of any in-
dividual in the past number of scaling window
generations. The fitness function is f
i
= f
i
f
w
,
where w is the window size and is typically some-
ECTA 2016 - 8th International Conference on Evolutionary Computation Theory and Applications
144
where between 2 and 10 and f
w
is the worst value
observed in the w most recent generations.
Sigma Truncation avoids returning negative fit-
ness values for individuals within the population
and incorporates problem dependant information
into the scaling mechanism. The fitness of an indi-
vidual fi
i
is calculated as follows: f
i
= f
i
(
¯
f
cxσ), where c is a small integer value between 1
and 5,
¯
f is the average rawfitness and σ is the pop-
ulation standard deviation. Negative values for f
are avoided as any result f < 0 is set to zero. Indi-
viduals where f
i
< c standard deviation from the
average fitness value are not selected.
Boltzmann tournament selection procedure is de-
rived and implemented to give stable distribu-
tions within a population. It also creates another
niching mechanism for forming and sizing stable
subpopulations of individuals according to differ-
ences among them, if the cooling process is not
taken to the limit. Boltzmann scaling is expressed
as f
= e
f
k
/T
and selection pressure is low when
the control parameter T is high.
The results of the scaling experiments are illustrated
in Figure 7 and Table 3. These results indicate that
the SGA using various scaling techniques, fails to
maintain enough diversity within the population to
avoid premature convergence. The statistical results
indicate that differences between the various scaling
methods, for these experiments, are minimal. The
most significant results are between the MGA and the
SGA using each of the scaling mechanisms. Figure
8, gives an overview of the rate of convergence as-
sociated with the SGA (incorporating scaling mecha-
nisms) and the MGA. The graph illustrates that Lin-
ear, Window, Sigma Truncation and Boltzmann SGA
loose diversity very quickly in the search, which re-
sults in the failure of the SGA to adapt after the land-
scape changes. The MGA implicitly maintains a level
of diversity within the population which assists in
adapting and locating the global optimum before and
after the landscape change.
Table 3: Off-Line & On-Line Scaling p-values.
Off-Line Linear Window Sigma T. Boltzmann MGA
Linear 1 0.5807 0.5716 < 2.2e
16
Window 1 0.5807 0.5716 < 2.2e
16
Sigma T. 0.5807 0.5807 1 < 2.2e
16
Boltzmann 0.5716 0.5716 1 < 2.2e
16
On-Line
Linear 0.9319 0.1071 0.6711 < 2.2e
16
Window 0.9319 0.04809 0.9433 < 2.2e
16
Sigma T. 0.1071 0.04809 0.1353 < 2.2e
16
Boltzmann 0.6711 0.9433 0.1353 < 2.2e
16
0
5
10
15
20
25
30
35
20 40 60 80 100 120 140 160 180 200
Fitness
Generations
SGA (Scaling) & MGA 4-bit Deceptive Problem - Online/Offline Performance Analysis
MGA Off-line Performance
MGA On-line Performance
SGA (Linear) Off-line Performance
SGA (Linear) On-line Performance
SGA (Window) Off-line Performance
SGA (Window) On-line Performance
SGA (Sigma Truncation) Off-line Performance
SGA (Sigma Truncation On-line Performance
SGA (Boltzmann) Off-line Performance
SGA (Boltzmann) On-line Performance
Figure 7: Selection Pressure On-line/Off-line.
0
500
1000
1500
2000
2500
0 50 100 150 200
Hamming Distance
Generations
SGA (Boltzmann) & MGA - Genotype & Phenotype Hamming Distance
MGA Genotype Hamming Distance
MGA Phenotype Hamming Distance
SGA Linear Scaling Genotype Hamming Distance
SGA Window Scaling Genotype Hamming Distance
SGA Sigma Truncation Scaling Genotype Hamming Distance
SGA Boltzmann Scaling Genotype Hamming Distance
Figure 8: Selection Pressure Convergence Rate.
5.3.2 Niching Techniques
Niching can be defined as an approach which en-
courages a number of distinct groups of genotypes to
develop and remain in the population, with reduced
pressure from the GA to converge towards a single
type of genotype. Crowding involves a form of nich-
ing of the population. With crowding, as implemented
in this paper, before crossover or mutation, normal
fitness weighted selection is used to select members
for the next generation. Crossover then takes place
on individuals selected randomly from this set. Af-
ter individuals have been selected for crossover, the
offspring are created as usual. For each offspring,
crowding factor, in this case 2, members of the sur-
vivors are selected randomly and the Hamming dis-
tance of each genotype from the offspring is calcu-
lated for 2 individuals. The offspring the replaces
whichever survivor is nearest in Hamming distance.
Incest reduction is used in conjunction with crowding
and introduces a mechanism to reduce the percent-
age of crossover between similar genotypes. After
being selected, pairs are then selected for crossover
by choosing the first parent at random from the list
of selected individuals, then choosing a pre-defined
(incest-reduction) number of possible candidates for
Diversifying Techniques & Neutrality in Genetic Algorithms
145
0
5
10
15
20
25
30
35
20 40 60 80 100 120 140 160 180 200
Fitness
Generations
SGA (Niching) & MGA 4-bit Deceptive Problem - Online/Offline Performance Analysis
MGA Off-line Performance
MGA On-line Performance
SGA (Crowding) Off-line Performance
SGA (Crowding) On-line Performance
SGA (Incest Reduction) Off-line Performance
SGA (Incest Reduction) On-line Performance
Figure 9: Niching On-line/Off-line.
the other parent randomly. The Hamming distance
of each candidate from the first parent and the one
with the greatest Hamming distance is selected for
crossover.
The results of the SGA performance with crowd-
ing and Incest reduction are shown in Figure 9. The
results indicate that the performance of the SGA with
crowding are very similar to those of the SGA incor-
porating Incest reduction (off-line p-value = 0.03351
and the on-line p-value= 0.1663). Both niching tech-
niques fail to the escape the local optimum. The MGA
results differ, in that the diversity maintained within
the population allows the search escape the deceptive
trap. Comparing the MGA off-line and on-line results
statistically against both of the niching techniques,
indicated a high statistically significant difference in
performance. In relation to the rate of convergence.
Unlike the MGA, the niching techniques outlined,
lose diversity early in the search (see Figure 10), mak-
ing it difficult for the SGA to adapt and escape the
local optimum when the environment changed.
0
500
1000
1500
2000
2500
0 50 100 150 200
Hamming Distance
Generations
SGA & MGA - Genotype & Phenotype Convergence
MGA Genotype Hamming Distance
MGA Phenotype Hamming Distance
SGA Crowding Genotype Hamming Distance
SGA Incest Reduction Genotype Hamming Distance
Figure 10: Niching Techniques Convergence Rate.
5.4 Operator Disruption
For the operator disruption experiments, we increased
the rate of P
c
and P
m
(see Figures 11 and 12 respec-
tively). Examining the results of increasing the rate
of crossover to 0.90, the SGA located the global op-
timum early in the search but failed to adapt once the
landscape changed. The results of increasing the rate
of mutation to 0.50, illustrate that the search is be-
ing directed by randomness, with the SGA constantly
moving to and from the global optimum, shownby the
off-line performance. The result also shown a very
large degree of change in the on-line performance.
The increased crossover results, both off-line and on-
line were significantly different from the MGA results
(off-line p-value = 2.2e
16
and on-line p-value =
0.0003238). The results using mutation also indicated
a statistically significant difference. The mutation off-
line results indicate that increased mutation rates are
statistically closer to the MGA results, however as the
on-line results indicate, the search was driven by ran-
domness and failed to produce good strings, meaning
the diversity maintained wasn’t useful in terms of a
search algorithm.
0
5
10
15
20
25
30
35
20 40 60 80 100 120 140 160 180 200
Fitness
Generations
SGA (Increased Crossover) & MGA 4-bit Deceptive Problem - Online/Offline Performance Analysis
MGA Off-line Performance
MGA On-line Performance
SGA Off-line Performance
SGA On-line Performance
Figure 11: Operator Disruption (Crossover) On-line/Off-
line.
0
5
10
15
20
25
30
35
20 40 60 80 100 120 140 160 180 200
Fitness
Generations
SGA (Mutation 0.50) & MGA 4-bit Deceptive Problem - Online/Offline Performance Analysis
MGA Off-line Performance
MGA On-line Performance
SGA Off-line Performance
SGA On-line Performance
Figure 12: Operator Disruption (Mutation) On-line/Off-
line.
Regarding to the maintenance of diversity within
the population, Figure 13 outlines the impact of oper-
ator disruption. Increasing crossover failed to main-
tain diversity within the population, which converged
ECTA 2016 - 8th International Conference on Evolutionary Computation Theory and Applications
146
quickly. The mutation experiment increased the level
of diversity within the population, but as mentioned
above, the search was directed by randomness. This
random diversity failed to assist in the search.
0
500
1000
1500
2000
2500
0 50 100 150 200
Hamming Distance
Generations
SGA & MGA - Genotype & Phenotype Convergence
MGA Genotype Hamming Distance
MGA Phenotype Hamming Distance
SGA Increased Crossover Genotype Hamming Distance
SGA Increased Mutation Genotype Hamming Distance
Figure 13: Operator Disruption Convergence Rate.
6 CONCLUSION
The results presented, illustrate that through the
implementation of Neutral theory, as proposed by
Kimura (Kimura, 1968), the genotype-phenotype
mapping of the MGA allows for a tunable, non-trivial,
many-to-one relationship. By adopting this approach,
convergence at a phenotypic level can be achieved,
but genetic diversity is maintained at a genotypic
level. Through the MGAs multi-layered genotype-
phenotype mapping, adaptive (hot spots) and silent
(cold spots) mutations become possible. This phe-
nomenon allows neutral networks evolve within the
population. The MGA, as a result of genetic drift,
convergeson neutral sets close to one another in Ham-
ming space, which assists in relation to the adaptive-
ness of the MGA to changing environments. The
results indicate that neutrality, as introduced by the
MGA mapping, maintains a level of diversity within
the population, which assists in searching dynamic
landscapes as the diversity maintained by the MGA
promotes good strings. When compared to a SGA in-
corporating a number of diversifying techniques, the
implicit maintenance of diversity by the MGA proved
successful in searching the deceptive dynamic land-
scape. The MGA, as a result of genetic drift, con-
verges on neutral sets close to one another in Ham-
ming space.
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