![](bg2.png)
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
1.
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
1
, x
2
, . . . , x
N
}, with x
i
∈ {0, 1}, which at-
tempts to maximise the following:
f (¯x) =
N
∑
i=1
x
i
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