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## Genetic Algorithms

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### Chapter 14 Genetic Algorithms Chapter 14 Contents (1) Representation The Algorithm Fitness Crossover Mutation Termination Criteria Optimizing a mathematical function ... – PowerPoint PPT presentation

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Title: Genetic Algorithms

1
• Chapter 14
• Genetic Algorithms

2
Chapter 14 Contents (1)
• Representation
• The Algorithm
• Fitness
• Crossover
• Mutation
• Termination Criteria
• Optimizing a mathematical function

3
Chapter 14 Contents (2)
• Schemata
• The Effect of Reproduction on Schemata
• The Effect of Crossover and Mutation
• The Schema Theorem
• The Building Block Hypothesis
• Deception
• Messy Genetic Algorithms
• Evolving Pictures
• Co-Evolution

4
Representation
• Genetic techniques can be applied with a range of
representations.
• Usually, we have a population of chromosomes
(individuals).
• Each chromosome consists of a number of genes.
• Other representations are equally valid.

5
The Algorithm
• The algorithm used is as follows
• Generate a random population of chromosomes (the
first generation).
• If termination criteria are satisfied, stop.
Otherwise, continue with step 3.
• Determine the fitness of each chromosome.
• Apply crossover and mutation to selected
chromosomes from the current generation to
generate a new population of chromosomes (the
next generation).

6
Fitness
• Fitness is an important concept in genetic
algorithms.
• The fitness of a chromosome determines how likely
it is that it will reproduce.
• Fitness is usually measured in terms of how well
the chromosome solves some goal problem.
• E.g., if the genetic algorithm is to be used to
sort numbers, then the fitness of a chromosome
will be determined by how close to a correct
sorting it produces.
• Fitness can also be subjective (aesthetic)

7
Crossover (1)
• Crossover is applied as follows
• Select a random crossover point.
• Break each chromosome into two parts, splitting
at the crossover point.
• Recombine the broken chromosomes by combining the
front of one with the back of the other, and vice
versa, to produce two new chromosomes.

8
Crossover (2)
• Usually, crossover is applied with one crossover
point, but can be applied with more, such as in
the following case which has two crossover
points
• Uniform crossover involves using a probability to
select which genes to use from chromosome 1, and
which from chromosome 2.

9
Mutation
• A unary operator applies to one chromosome.
• Randomly selects some bits (genes) to be
flipped
• 1 gt 0 and 0 gt1
• Mutation is usually applied with a low
probability, such as 1 in 1000.

10
Termination Criteria
• A genetic algorithm is run over a number of
generations until the termination criteria are
reached.
• Typical termination criteria are
• Stop after a fixed number of generations.
• Stop when a chromosome reaches a specified
fitness level.
• Stop when a chromosome succeeds in solving the
problem, within a specified tolerance.
• Human judgement can also be used in some more
subjective cases.

11
Optimizing a mathematical function
• A genetic algorithm can be used to find the
highest value for f(x) sin (x).
• Each chromosome consists of 4 bits, to represent
the values of x from 0 to 15.
• Fitness ranges from 0 (f(x) -1) to 100 (f(x)
1).
• By applying the genetic algorithm it takes just a
few generations to find that the value x 8 gives
the optimal solution for f(x).

12
Schemata (1)
• As with the rules used in classifier systems, a
schema is a string consisting of 1s, 0s and
s. E.g.
• 10110010
• Matches the following four strings
• 1011000100
• 1011000110
• 1011100100
• 1011100110
• a schema with n s will match a total of 2n
chromosomes.
• Each chromosome of r bits will match 2r different
schemata.

13
Schemata (2)
• The defining length dL(S) of a schema, S, is
the distance between the first and last defined
bits. For example, the defining length of each of
the following schemata is 4
• 10111
• 101
• The order O(S) is number of defined bits in S.
The following schemata both have order 4
• 1011
• 1011
• A schema with a high order is more specific than
one with a lower order.

14
Schemata (3)
• The fitness of a schema is defined as the average
fitness of the chromosomes that match the schema.
• The fitness of a schema, S, in generation i is
written as follows
• f(S, i)
• The number of occurrences of S in the population
at time i is
• m(S, i)

15
The Effect of Reproduction on Schemata
• The probability that a chromosome c will
reproduce is proportional to its fitness, so the
expected number of offspring of c is
• a(i) is the average fitness of the chromosomes in
the population at time i
• If c matches schema S, we can rewrite as
• c1 to cn are the chromosomes in the population at
time i which match the schema S.

16
The Effect of Reproduction on Schemata
• Since
• We can now write
• This tells us that a schema that is fit will have
more chance of appearing in a subsequent
generation than less fit chromosomes.

17
The Effect of Crossover
• For a schema S to survive crossover, the
crossover point must be outside the defining
length of S.
• Hence, the probability that S will survive
crossover is
• This tells us that a short schema is more likely
to survive crossover than a longer schema.
• In fact, crossover is not always applied, so the
probability that crossover will be applied should
also be taken into account.

18
The Effect of Mutation
• The probability that mutation will be applied to
a bit in a chromosome is pm
• Hence, the probability that a schema S will
survive mutation is
• We can combine this with the effects of crossover
and reproduction to give

19
The Schema Theorem
• Hollands Schema Theorem, represented by the
above formula, can be written as
• Short, low order schemata which are fitter than
the average fitness of the population will appear
with exponentially increasing regularity in
subsequent generations.
• This helps to explain why genetic algorithms
work.
• It does not provide a complete answer.

20
The Building Block Hypothesis
• Genetic algorithms manipulate short, low-order,
high fitness schemata in order to find optimal
solutions to problems.
• These short, low-order, high fitness schemata are
known as building blocks.
• Hence genetic algorithms work well when small
groups of genes represent useful features in the
chromosomes.
• This tells us that it is important to choose a
correct representation.

21
Deception
• Genetic algorithms can be deceived by fit
building blocks that happen not to combine to
give the optimal solutions.
• Deception can be avoided by inversion this
involves reversing the order of a randomly
selected group of bits within a chromosome.

22
Messy Genetic Algorithms (1)
• An alternative to standard genetic algorithms
that avoid deception.
• Each bit in the chromosome is represented as a
(position, value) pair. For example
• ((1,0), (2,1), (4,0))
• In this case, the third bit is undefined, which
is allowed with MGAs. A bit can also
overspecified
• ((1,0), (2,1), (3,1), (3,0), (4,0))

23
Messy Genetic Algorithms (2)
• Underspecified bits are filled with bits taken
from a template chromosome.
• The template chromosome is usually the best
performing chromosome from the previous
generation.
• Overspecified bits are usually dealt with by
working from left to right and using the first
value specified for each bit.

24
Messy Genetic Algorithms (3)
• MGAs use splice and cut instead of crossover.
• Splicing involves simply joining two chromosomes
together
• ((1,0), (3,0), (4,1), (6,1))
• ((2,1), (3,1), (5,0), (7,0), (8,0))
• ((1,0), (3,0), (4,1), (6,1), (2,1), (3,1),
(5,0), (7,0), (8,0))
• Cutting involves splitting a chromosome into
two
• ((1,0), (3,0), (4,1))
• ((6,1), (2,1), (3,1), (5,0), (7,0), (8,0))

25
Evolving Pictures
• Dawkins used genetic algorithms with subjectives
metrics for fitness to evolve pictures of
insects, trees and other creatures.
• The human selection of fitness can be used to
produce amazing pictures that a person would
otherwise not be able to produce.

26
Co-Evolution
• In the real world, the presence of predators is
responsible for many evolutionary developments.
• Similarly, in many artificial life systems,
introducing predators produces better results.
• This process is known as co-evolution.
• For example, Ramps, which were evolved to sort
numbers parasites were introduced which
produced sets of numbers that were harder to
sort, and the ramps produced better results.