June 12, 2012 18:12 PSP Book - 9in x 6in 07-Junichi-Takeno-c07
122 Artificial Neural Networks and Machine Evolution
Figure 7.16. Solution space and multimodal solutions.
second peak p
2
. Peak p
1
is the local maximum and peak p
2
is the
optimum fitness. Genotype g
2
is therefore the desirable answer.
If you always selected individuals of a high fitness in this
selection process, all of them could exist around genotype g
1
. If this
were the case, you would have ended up selecting individuals near
the local maximum, and could get out of the local area, eventually
failing to select genotypes that would surpass the local maximum.
Note that a solution space like the one shown in Fig. 7.16 is totally
unknown to humans initially. Indeed, if it were known, we need not
have any trouble.
It is known that the machine evolution approach is not effective
unless the solution space is continuous and differentiable. In other
words, for the machine evolution approach to work effectively, the
fitness determined by certain genotype g
1
must not change abruptly
(should be differentiable) from the fitness of the gene adjacent to g
1
.
Conversely, for a problem involving any sort of solution space, the
machine evolution approach finds an answer somehow. This is the
great point of the machine evolution approach.
June 12, 2012 18:12 PSP Book - 9in x 6in 07-Junichi-Takeno-c07
Theory of Robot Evolution 123
Other methods for selecting individuals include elitism (to leave
behind individuals with optimum fitness values in a generation),
rank selection, and tournament selection. Rank selection refers to
the use of ranking of individuals’ fitness values, while tournament
selection picks two individuals at a time for comparison for survival.
After selection of individuals comes the process of reproduction.
We have earlier selected 10 out of 20 individuals. Genetic
operations are performed on the selected individuals to reproduce
20 individuals again.
Two popular genetic operations are crossing and mutation.
Crossing refers to the crossover of genes of the selected individuals.
Assume we pick two genes g
1
and g
2
from a selected individual.
g
1
= (0111 0001 0101 0010 0011 1000 0001 0101)
= (g
11
g
12
)
g
2
= (0011 1000 0001 0101 0111 0001 0101 0010)
= (g
21
g
22
)
Crossing occurs between the sixth and seventh characters from
left in the above gene sequences. Random numbers may be used.
Two crossed genes g
1
and g
2
are generated.
g
1
= (0111 0000 0001 0101 0111 0001 0101 0010)
= (g
11
g
22
)
g
2
= (0011 1001 0101 0010 0011 1000 0001 0101)
= (g
21
g
12
)
The original genes g
1
=
(
g
11
g
12
)
and g
2
=
(
g
21
g
22
)
turned out
two new genes g
1
=
(
g
11
g
22
)
and g
2
=
(
g
21
g
12
)
by crossing. The
phenotype of the gene has changed as follows:
g
1
=
(
w
12
, w
12
, w
21
, w
22
, w
31
, w
32
, w
41
, w
42
)
= (7, 1, 5, 2, 3, 8, 1, 5)
to
g
1
= (7, 0, 1, 5, 7, 1, 5, 2)
The above process applies to g
2
in like manner.
Mutation is described now. Mutation means that part of the
information of the genes of a selected individual is overwritten.
June 12, 2012 18:12 PSP Book - 9in x 6in 07-Junichi-Takeno-c07
124 Artificial Neural Networks and Machine Evolution
Oneelementofthegeneissubjectedtobitconversion,or1and
0 are overwritten by 0 and 1, respectively. The position of the bit
conversion can be arbitrarily determined.
g
1
= (0111 0000 0001 0101 0111 0001 0101 0010)
↑ Position of mutation
g
1
= (0111 0000 0001 0101 0011 0001 0101 0010)
= (7, 0, 1, 5, 3, 1, 5, 2)
In the above example, the value of the 18th position (underlined
1) of gene g
1
changes by mutation and a new gene g
1
is created.
These gene-operated genes are reproduced to give birth to the next
generation. The procedure is repeated until genes of a desirable
fitness are found.
It is understood that the machine evolution approach can not
only be applied to the design of the above-mentioned function unit
but also be expanded to the study of the shape of the machine
systems in which the function unit operates.
Karl Sims is a famous researcher on the evolution of shape. His
studies are very interesting, and I invite the readers to study his
work.
7.2.2 Summary and Observations
This section explained the machine evolution approach. The ma-
chine evolution approach simulates the biological evolution method
called the survival of the fittest. New generations are created by
mating, and the fittest among the individuals is selected for further
mating. This biological method is adopted in the machine evolution
approach using an engineering technique. “Fittest” means that one
is adapted to the environment. Our eventual goal is the survival
of excellent generations. I also explained that this approach is a
powerful method for complex neural networks to learn successfully.
This approach is useful in that it can find specific solutions to
problems for which humans are utterly at a loss as to how to find
solutions.
In the machine evolution approach, humans specify the geno-
types, set pairing of genotypes and their phenotypes, and stipulate
June 12, 2012 18:12 PSP Book - 9in x 6in 07-Junichi-Takeno-c07
Theory of Robot Evolution 125
the fitness function based on the survival-of-the-fittest principle.
All of the processes of evolution are then left to computers. It is
naturally possible to set genes as the object of evolution. As a result,
artificial living organisms beyond the imagination of humans could
appear. This phenomenon is called emergence.
There are problems, though.
In the machine evolution approach, evolution takes place in
interaction with the environment in principle, but it takes an
incredible amount of time to observe how and to what extent the
evolved individuals will satisfy the fitness function. The machine
evolution approach is used jointly with computer simulators and
with back propagation and other neural network learning methods
to shorten the computation time. Despite all of these efforts, no
essential solution has yet been found. Furthermore, no one has
ever clarified theoretically the reason why the machine evolution
approach identifies good answers swiftly.
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