1. Representing Hypothesis Operators Fitness Function Genetic Programming
Genetic Algorithms
Introduction
Representing Hypothesis
Operators
Fitness Function
Genetic Programming
Models of Evolution and Learning
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2. Population concentrates in a small region of the search space.
Crowding
A problem in genetic algorithms where one individual is much more fit than others. The population then begins to concentrate around this individual and variations of it. Population diversity is then reduced.
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F(X) X
Population concentrates in a small region
of the search space.

3. Fitness sharing (similar individuals see their fitness value reduced).
A Solution to Crowding
One solution is to change the selection function, using for example rank selection. In the case where an individual is better fit than others, the ranking would not show the magnitude of the difference.
Other solutions:
Fitness sharing (similar individuals see their fitness
value reduced).
b. Spatially distribute individuals and only allow nearby
individuals to recombine.
c. Restrict certain kinds of individuals to recombine.
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4. To do this let’s begin with the concept of a schema.
The Schema Theory
Can we characterize mathematically the evolution of a population over time?
To do this let’s begin with the concept of a schema.
A schema is a pattern over a sequence of bits represented using 0, 1, or * for don’t care.
Example:
0*10 is the set of all sequences with 010 in the 1st, 3rd, and 4rd positions.
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5. The theory tells us what to expect of m(s,t+1).
The Schema Theory
Schema theory tells us how each schema in the population evolves through time.
Let m(s,t) be the number of instances representing schema s at time or step t.
The theory tells us what to expect of m(s,t+1).
We start by remembering what is the probability of selecting a hypothesis h:
P(hi) = Fitness (hi) / Σj Fitness (hj)
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6. The probability can be expressed similarly as
The Schema Theory
The probability can be expressed similarly as
P(hi) = f (hi) / n f’ (ti)
Where f(hi) is the fitness of hi (for short) and f’(t) is the
mean of the fitness value for all hypotheses in the population
at time t.
Now let us define the mean of the fitness value of the members
of schema s in the following way:
u(s,t) = Σ f(h) / m(s,t)
Where the sum goes through only those hypotheses in schema s.
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7. E[ m(s, t+1) ] = ( u(s,t) / f’(t) ) m(s,t)
The Schema Theory
Then the expected value of the number of instances in schema s at time t+1 is:
E[ m(s, t+1) ] = ( u(s,t) / f’(t) ) m(s,t)
which means the value is proportional to the average fitness of those individuals in schema s at time t and inversely proportional to the average fitness of all individuals at time t.
The theory provides a more general formulation based on the effect of crossover and mutation.
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8. Genetic programming is a form of evolutionary computation in
which the individuals in the population are computer programs.
Programs are normally represented by trees. A program is executed
by parsing the tree. Example: +
F = sin(x) + sqrt( x^2 + y)
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Sin sqrt x
^ y
x 2

9. To apply genetic programming one has to define the functions
Vocabulary
To apply genetic programming one has to define the functions
that can be applied:
Example: sin, cos, sqrt, +, -, etc.
A genetic programming algorithm explores the space of
combinations of these functions.
The fitness of an individual is determined by executing
the program on a set of training data.
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10. The crossover operator is performed by replacing subtrees of
one program with subtrees of another program. + +
Sin ^
Sin sqrt 2 x
x y
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^ y x

11. Cross Over: Result + + Sin ^ Sin sqrt 2 x ^ x y x + + y x 2
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12. Learning an algorithm for stacking blocks:
An Example
Learning an algorithm for stacking blocks: N E S
What is machine learning? R
V U L A I
Learn an algorithm to stack the blocks so that it
reads “UNIVERSAL”

13. The only valid operations are
An Example
The only valid operations are
move a block from the stack to the surface of the table
move a block from the surface of table to the stack
The primitive functions are
CS (current stack) returns the name of the block on top of the stack.
TB (top current block) returns the name of the topmost block where
all blocks and itself are in correct order.
c. NN (next necessary) name of the block needed above TB to read
the word “UNIVERSAL”.
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14. Additional functions are
An Example
Additional functions are
(MS x) move block x to stack if x is on table.
(MT x) move block x to table if x is on the stack.
(EQ x y) returns true if x = y.
(NOT x) returns the complement of x.
DO( x y) do x until expression y is true
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15. What is the fitness value?
An Example
What is the fitness value?
In this experiment the author provided 166 different examples having
each different initial block configurations. The fitness of a program is
how many problem were correctly solved by the program.
Initial population = 100 programs
After 10 generations the genetic programming strategy found the
following program:
(EQ (DU (MT CS)(NOT CS)) (DU (MS NN)(NOT NN)) )
which solved all 166 programs correctly.
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16. Designing filter circuits.
Another Example
Designing filter circuits.
Programs are evolved to transform a fixed circuit into a
final circuit design. Primitive functions:
Insert circuit components
Delete circuit components
Fitness: measure how well the design meets the specifications
Population size = 640,000
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17. Models of Evolution and Learning
What is the relationship between what one individual learns during
his lifetime compared to what evolution learns as the population
evolves?
Lamarckian Evolution:
Lamarck (late 19th century) hypothesized that the experience of
an individual during its lifetime affects the characteristics of its
offspring.
But evidence points to the contrary: the genetic makeup of an
individual is unaffected by the experience of its parents.
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18. The Baldwin effect relies on the following:
After J. M. Baldwin (1986).
The Baldwin effect relies on the following:
If the environment is continually changing, those individuals
capable of learning and adapting quickly to the environment
will have greater advantage compared to other individuals.
Those individuals who can learn and adapt quickly will have
less dependence on the genetic code and will help to achieve
more rapid evolutionary adaptation.
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19. Parallel Genetic Agorithms
It seems very natural to produce a parallel version of genetic algorithms.
Some approaches divide the population into groups called demes.
Each deme resides on a computational node, and a standard search is
carried out on each node.
There is communication and combination among demes but these
are rare compared to those occurring within demes.
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20. Genetic algorithm do a parallel, hill climbing search looking
Summary
Genetic algorithm do a parallel, hill climbing search looking
to optimize a fitness function.
The search resembles the mechanism of biological evolution.
Genetic algorithms have many application outside machine
learning. In machine learning the goal is to evolve a population
of hypotheses to find the hypothesis with highest accuracy.
Genetic programming is similar to genetic algorithms but what
we evolve is computer programs.
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