Transcript Genetic Algorithms

COMP305. Part II.
Genetic Algorithms.
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Topic 2.
Computational appeal of the
Genetic Algorithms.
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Darwinian theory of Evolution (macroscopic).
Species adapt to the environment via
natural selection.
The selection favors those species for survival
and further evolution that are best adapted to the
environmental condition –
“survival of the fittest”.
Phenotype is the manner of response and
physical embodiment of an individual.
There occur small, apparently random and
undirected variations between the phenotypes of
parents and their offspring.
These mutations prevail through selection, if
they prove their worth in light of the current
environment; otherwise they perish.
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NeoDarwinism - synthetic theory of Evolution
(microscopic).
Genes are transfer units of heredity, and genotype is the total
genetic information of an individual.
Selection acts on an individual, thus
an individual is a selection unit.
Population is the evolving unit. It confines a common gene pool
including genotypes of all individuals.
Modern biochemistry
and genetics explain
microscopic
mechanisms of
heredity.
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Natural Evolution. What is the Fitness ?
Individual fitness is measured indirectly
as the individual growth rate in
comparison to others.
The fitness is the individual
propensity to survive and reproduce in
a particular environment.
Thus, Natural Selection according to the
individual fitness
is NOT an active driving force,
IS differential survival and
reproduction within a population.
SO, what is the fitness?
I mean, can we
1. map a given genotype into the
corresponding phenotype and
2. map the phenotype into the
individual fitness to survive and
reproduce?
Not, actually…
But the idea is so beautiful...
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Natural Evolution. Computational appeal.
SO, what is the fitness?
I mean, can
we
1.
map a given genotype into the
corresponding phenotype and
2.
map the phenotype into its fitness ?
Question:
How does Nature
solve the problem?
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Natural Evolution. Computational appeal.
SO, what is the fitness?
I mean, can
we
1.
map a given genotype
into the corresponding
phenotype and
2.
map the phenotype
into its fitness ?
…
Question:
How does Nature
solve the
problem?
…
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Natural Evolution. Computational appeal.
SO, what is the fitness?
I mean, can
1.
2.
we
…
map a given genotype
into the corresponding
phenotype and
The
Nature
does it in
parallel !!!
map the phenotype
into its fitness ?
Question:
How does Nature
solve the
problem?
…
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Natural Evolution. Computational appeal.
SO, what is the fitness?
I mean,
…
can we
1.
map a given genotype
into a corresponding
phenotype and
2.
map the phenotype
into the fitness ?
The
Nature
does it in
parallel !!!
…
Coming up with better
fitted population:
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Natural Evolution. Computational appeal.
1. Parallelism.
…
2. Adaptation
to a changing
environment.
The Nature does it
in parallel and
comes up with
better fitted
population.
3. Optimisation.
…
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Natural Evolution. Computational appeal.
1. Parallelism.
…
Every individual
in the population is
tested independently in
parallel with the
others, and that speeds
up evolution of the
population.
The Nature does it
in parallel and
comes up with
better fitted
population.
2. Adaptation to a
changing
environment.
…
3. Optimisation.
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Natural Evolution. Computational appeal.
1. Parallelism.
…
2. Adaptation to a
changing
environment.
The Nature does it
in parallel and
comes up with
better fitted
population.
Due to the natural
selection, only those
individuals best fitted for
the current environment
do survive. The selection
results in the population
as a whole best adapted
to the environment.
…
3. Optimisation.
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Natural Evolution. Computational appeal.
1.
2.
Parallelism.
Adaptation to a
changing
environment.
…
The Nature does it
in parallel and
comes up with
better fitted
population.
3. Optimisation.
Due to the natural
selection, only
individuals best fitted
or “optimal” for the
current environment do
survive and reproduce.
Thus, the selection
also performs
optimisation on an
individual level.
…
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Natural Evolution. Computational appeal.
1. Parallelism.
2. Adaptation
to a changing
environment.
3. Optimisation.
The listed features of the natural
selection are very attractive for many
problems in computer science.
As these parallelism, adaptation,
and optimisation are achieved in nature by
very simple manipulation of individual
DNA sequences, it is tempting to use the
algorithm for non-bio problem solving in
engineering, computer science, etc.
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Genetic Algorithms. Historical Introduction.
By 1950s, it became clear that
if a solution of a computational problem might be
formulated, i.e. coded, in a form of string of “characters”,
then the optimal solution to the problem might be
searched for using the natural selection technique among a
“population”, i.e. set of candidate solutions.
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Genetic Algorithms. Historical Introduction.
1950s-1960s - several computer scientists independently
studied evolutionary systems with the idea to use the
algorithm to solve optimisation problems in engineering.
1960s – Rechenberg introduced “evolutionary strategies” as a
method to optimise real-valued parameters for airfoils
1966 – Fogel, Owens, and Walsh developed “evolutionary
programming”. They represented candidate solutions to
a problem as a finite-state machines evolving by
randomly mutating their state-transition diagrams and
selecting the fittest.
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Genetic Algorithms. Historical Introduction.
1960s – Genetic Algorithms (GAs) were invented by
John Holland of Michigan University and further
developed by his students, colleagues, and himself in
the 1960s and 1970s.
In contrast with “evolutionary strategies” and “evolutionary programming”,
Holland was not interested in finding solutions to particular problems, but
rather formally studied the phenomenon of adaptation as it occurs in nature
and how the algorithm might be used in the computer systems.
1975 – Holland’s book “Adaptation in Natural and
Artificial
Systems” presented the genetic algorithm as an
abstraction of natural evolution and gave a theoretical
framework for adaptation under GA.
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GAs by John Holland.
Holland introduced
a “population” of binary strings which he called “chromosomes”.
The “population” evolves using kind of “natural selection” together with the
genetics-inspired operators of crossover, mutation, and inversion.
Bits in a “chromosome” represent genes, and each “gene” is an instance of a
particular “allele”, 0 or 1.
The selection operator chooses those chromosomes in the population that will
be allowed to reproduce, and on average the fitter chromosomes produce
more offspring than the less fit ones.
Crossover exchange subparts of two chromosomes
Mutation randomly changes the allele values at some locations in the
chromosome.
Inversion reverses the order of a contiguous section of the chromosome
rearranging the genes order.
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Coding for Genetic Algorithms.
In contrast with Nature,
 there is no universal code in GAs,
 every coding is problem dependent.
The art of coding, though left beyond the scope, is very
important in Genetic Algorithms, as from the very
beginning the approach depends on whether or not the
problem can be coded as a string of characters at all.
The above implies serious restrictions on the class of
problems capable of solving by GAs.
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