A GENETIC ALGORITHM WITH A MULTI-LAYERED

GENOTYPE-PHENOTYPE MAPPING

Seamus Hill and Colm O’Riordan

Computational Intelligence Research Group, National University of Ireland, Galway, Ireland

Keywords:

Genetic algorithms, Genotype, Phenotype, Deception.

Abstract:

In this paper we investigate the introduction of a multiple-layer genotype-phenotype mapping to a Genetic

Algorithm (GA) which attempts to mimic more closely, the effects of nature. The motivation for introducing

multiple-layers into the genotype-phenotype mapping is to create a many-to-one genotype-phenotype mapping.

The paper compares a traditional GA with a GA containing a multi-layered genotype-phenotype mapping using

a number of well understood problems in an attempt to illustrate the potential beneﬁts of including the multi-

layered mapping. Initial ﬁndings suggest that the multi-layered mapping between the genotype-phenotype

used in conjunction with a binary representation outperforms existing traditional GA approaches on well

known problems, while still allowing the use well understood genetic operators.

1 INTRODUCTION

Genetic Algorithms (GAs) (Holland, 1975) are search

algorithms based on the mechanics of natural selec-

tion and natural genetics and are a often used to solve

complex optimisation problems. However in nature

there exists a intermediate layer between the genotype

and the phenotype, which differs from the mapping

found in a traditional GA. By introducing multiple-

layers, which attempts to mimic more closely the ef-

fects of nature, into the genotype-phenotype mapping

we aim to and to maintain diversity in the popula-

tion and introduce a many-to-one genotype-phenotype

mapping. The paper compares a GA with a multi-

layered genotype-phenotype mapping to a traditional

GA using a number of well understood problems us-

ing different levels of deception in an attempt to create

a proof of concept. The paper is organised as follows:

section 2, a review of a selection of previous work.

Section 3 outlines the multiple mapping GA proposed

by the authors. Section 4 describes the experiments

conduced, while section 5 discusses the ﬁndings. Fi-

nally, section 6 concludes and outlines future work.

2 BACKGROUND

The motivation for attempting to create a GA which

includes a number of biologically plausible concepts

and yet provides a framework based on a binary

string, stems from the desire to allow a GA to provide

a many-to-one representation and to test how tradi-

tional GA operators operate within this environment.

Another motivation is that for a simple GA, solving

deceptive problems can be difﬁcult because of pre-

mature convergence. By using intermediate layers in

the genotype space, it is hoped to is to overcome this

failing while still using a binary representation.

3 MULTI-LAYERED MAPPING

GENETIC ALGORITHM

(MMGA)

The mmGA operates using a binary representation

which allows the use or standard genetic operators

such as crossover and mutation. The difference be-

tween the multi-layered mapping GA (mmGA) and

the standard representation found in a GA lies in the

fact that it contains multiple layers of mappings be-

tween the genotype to the phenotype. To discuss the

mapping, consider the collections of genes 11100001,

11101100, 10110001 and 11000110. The mmGA

randomly creates the genome string and the strings

are converted to a DNA template using the follow-

ing mapping 00 → A; 01 → C; 10 → G and 11 → T.

This maps the strings 11100001 → TGAC; 11101100

→ TGTA; 10110001 → GTAC and 11000110 → TACG.

The next step in the mmGA mapping is a conversion

369

Hill S. and O’Riordan C..

A GENETIC ALGORITHM WITH A MULTI-LAYERED GENOTYPE-PHENOTYPE MAPPING.

DOI: 10.5220/0003086203690372

In Proceedings of the International Conference on Evolutionary Computation (ICEC-2010), pages 369-372

ISBN: 978-989-8425-31-7

 2010 SCITEPRESS (Science and Technology Publications, Lda.)

from the template to DNA coding using the mapping

G → C; A → T ; T → A and C → G. The templates

TGAC becomes ACTG, TGTA becomes ACAT, GTAC be-

comes CATG and TACG maps to ATGC.

The ﬁnal stage of transcription are now carried

out and the DNA coding strings are now converted

into RNA where the only change maps T → U . The

ﬁnal stage of transcription are now carried out and

the DNA coding strings are now converted into RNA.

The strings ACTG, ACAT, CATG and ATGC now become

the proteins ACUG, ACAU, CAUG and AUGC respectively.

These proteins are in turn then converted into traits

i.e. 0 or 1 based upon the mapping generated by the

mmGA, which are then combined to create the pheno-

type. The mappings created by the mmGA allow for

a many-to-one relationship between the genotype and

the phenotype. The mapping can be summarised as

follows; 11100001 → T GAC → ACT G → ACUG →

0; 11101100 → T GTA → ACAT → ACAU → 1;

10110001 → GTAC → CAT G → CAU G → 0 and

11000110 → TACG → ATGC → AU GC → 1. The

pseudocode for the process is outlined in Algorithm

Algorithm 1: Pseudecode - multi-layered map-

ping Genetic Algorithm.

initialize mmGA;

r=1; (Number of runs);

for Number of runs do

Initialise Individual Genomes P(g);

Transcribe Genome to Amino Acids P(g);

Translate Amino Acids to Phenotype P(g);

Evaluate P(g); (Phenotype ﬁtness);

for Number of Generations do

g=0; (generations);

for All members of P do

Select P(g) from P(g-1);

Crossover P(g); genotype level;

Mutation P(g); genotype level;

Transcribe Genome to Amino

Acids P(g);

Translate Amino Acids to

Phenotype P(g);

Evaluate P(g); (phenotype ﬁtness);

end

g+=1;

end

r+=1;

end

end mmGA;

4 EXPERIMENTS

In this paper the authors choose four types of problem

to examine the effects of extending the representation;

a two-bit minimal deceptive problem, a three-bit fully

deceptive problem, a 100-bit One Max problem and a

fully deceptive 30 bit problem.

4.1 Minimal Deceptive Problem (MDP)

A problem which causes a GA to diverge from the

global optimum. can be viewed as a deceptive prob-

lem. By using short low-order building block to lead

the search away from the global optimal to a sub-

optimal point in the search space we are deceiving

the GA. The MDF exhibits the characteristics of a

epistatic problem and as it can be shown that one-bit

problems cannot be deceptive the MDP is the smallest

deceptive problem possible and by using a MDP one

can carry out analysis into the workings of GAs.

4.2 Three Bit Fully Deceptive Problem

A fully deceptive problem of order-N can be viewed

as being deceptive when all of the lower-order hyper-

planes lead away from the global optimum and to-

wards a deceptive attractor (Whitley, 1991). We use a

fully deceptive order-3 problem as outlined by (Gold-

berg et al., 1990) in this paper.

4.3 One-max Problem

The One-Max problem (Ackley, 1987) can

be described formally as having a string

¯x = {x

, x

, . . . , x

}, with x

∈ {0, 1}, which at-

tempts to maximise the following:

f (¯x) =

∑

i=1

In this paper the authors have deﬁned N = 100.

4.4 Thirty-bit Fully Deceptive Problem

One failing of the 3-bit fully deceptive problem is that

it is too small to really demonstrate a search strategy.

The thirty-bit problem as outlined in (Goldberg et al.,

1990) expands the three-bit problem into ten three-bit

deceptive order-three subfunctions. To increase the

level of difﬁculty we include a loose ordering, which

makes the problem fully deceptive. This is achieved

by increasing the deﬁning length to twenty, where the

deﬁning length is the maximum distance between two

deﬁning symbols in a schema.

ICEC 2010 - International Conference on Evolutionary Computation

370

5 FINDINGS

We compare both the traditional GA and the mmGA

over a suite of problems containing a two-bit minimal

deceptive problem, a three-bit fully deceptive prob-

lem, a one hundred-bit One-Max problem and a fully

deceptive thirty-bit problem. For the ﬁrst three prob-

lems, each set of experiments has a population size of

one hundred and is executed for two hundred genera-

tions. For the ﬁnal problem, the thirty-bit fully decep-

tive the population size was increased to two hundred

and the algorithm run for three thousand generations.

Each experiment is executed over one hundred runs.

Figure 1 illustrates that the performance of the

mmGA compares with that of a traditional GA., pos-

sibly because the MDP problem is easy for both forms

of a GA to solve. Which may indicate that there is lit-

tle to be gained by adopting the more complex multi-

layered GA on easy problems. Figure 2 shows the

performance of both GAs on a three-bit fully decep-

tive problem, which is considered GA hard. Although

both GAs are successful in locating the global opti-

mum, the GA using a traditional representation con-

verges on the global optimum, while the mmGA con-

verges for a number of generations but due to the

multi-layered representation and many-to-one repre-

sentation continues to explore the search space.

When comparing the results in Figure 2 to those of

Figure 1, we see that although both forms of GA con-

verge on the global optimum, it appears that the more

difﬁcult landscapes offer the GAs a more challenging

task and that there may be an advantage in using a

multi-layered mapping particularly on difﬁcult prob-

lems. In Figure 3 we see the performance of both

GAs on the One-Max problem. However, the One-

Max problem can be viewed as a landscape that is rel-

atively easy for a GA to search. The results indicate

that both forms of a GA were successful at converg-

ing on the global optimum. The standard GA appears

to have located the global optimum in a shorter time

frame than the mmGA. The authors believe that the

reason for this is due to the difference in the genotype-

phenotype mapping and that the extra time take for

the mmGA relates to the increased search space. This

we believe should not be viewed negatively as it re-

duces the prospect of premature convergence for the

mmGA.

The thirty-bit fully deceptive problem makes the

problem far more difﬁcult to solve particularly as the

deﬁning length has increased. Figure 4 show that the

average ﬁtness level per generation for the traditional

GA is higher than that of the mmGA, as the tradi-

tional GA has converged prematurely on the decep-

tive attractor. However, ﬁgure 5 shows the average

Figure 1: Two-bit minimal deceptive problem - Average ﬁt-

ness per generation.

Figure 2: Fully deceptive problem - Average best ﬁtness per

generation.

Figure 3: One hundred bit one max problem - Average best

ﬁtness per generation.

best ﬁtness per generation and results show that the

SGA failed to locate the global optimum as it con-

verged on the deceptive attractor. The mmGA how-

ever, did manage to locate the optimum. This ap-

pears to indicate that the genotype-phenotype map-

ping contained in the mmGA exhibits the ability to

avoid premature convergence and continue the search

to locate the global optimum. Figure 6 allows us to

see the number of subfunctions discovered per gen-

A GENETIC ALGORITHM WITH A MULTI-LAYERED GENOTYPE-PHENOTYPE MAPPING

371

Figure 4: Thirty-bit fully deceptive problem - Average ﬁt-

ness per generation.

eration. We can see from the plot that mmGA out-

performs the traditional GA in locating the ten fully

deceptive subfunctions.

Figure 5: Thirty-bit fully deceptive problem - Average best

ﬁtness generation.

Figure 6: Thirty-bit fully deceptive problem - Sub functions

discovered 3000 generations.

6 CONCLUSIONS

Initial results indicate that the mmGA has the abil-

ity to solve a number of problems over varying ﬁt-

ness landscapes. By introducing a multi-layered re-

lationship between the genotype and the phenotype,

the mmGA offers the ability to introduce a many-to-

one genotype-phenotype mapping. This implies that

identical phenotypes may be created from different

genomes. From the results outlined above, it appears

that the extended genotype-phenotype representation

exhibits the ability to avoid premature convergence,

particularly on more difﬁcult problems.

REFERENCES

Ackley, D. H. (1987). A connectionist machine for genetic

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MA, USA.

Goldberg, D. E., Korb, B., and Deb, K. (1990). Messy

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sults. Complex Systems, 3(5):493–530.

Holland, J. H. (1975). Adaptation in natural artiﬁcial sys-

tems. University of Michigan Press, Ann Arbor.

Whitley, L. D. (1991). Fundamental principles of deception

in genetic search. In Rawlins, G. J., editor, Founda-

tions of genetic algorithms, pages 221–241. Morgan

Kaufmann, San Mateo, CA.

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