3. Introduction
Genetic Algorithms (GA/AG) provide a learning method based on
principles of biological evolution.
New hypotheses are generated by mutating and recombining current
hypotheses.
At each step we have a population of hypotheses from which we
select the most fit.
GA do a parallel search over different parts of the hypothesis space.
4. Introduction
La evolución puede verse como un método robusto de adaptación,
sumamente utilizado como modelo en biología.
Los AG pueden buscar en espacios de hipótesis que contienen elementos en
compleja interacción, de tal forma que la influencia de cada elemento sobre
la medida de adaptación global de la hipótesis sea difícil de modelar.
Los AG son fácilmente paralelizables por lo que pueden sacar ventaja de la
reducción de costo de procesamiento e incremento de la performance.
5. Introduction
A hypothesis is good if it has a high “fitness” value.
In Classification: The accuracy of the hypothesis on test examples
In Games: Number of games won against other hypotheses of
the same population.
6. Parameters
A genetic algorithm has the following parameters:
A fitness function that gives a score to every hypothesis.
A fitness threshold above which we stop and take the hypothesis with
best fit.
p: The number of hypothesis in the current population.
r: the fraction of hypothesis replaced by cross-over.
m: the mutation rate.
7. Algorithm
Initialize population with p hypotheses at random
For each hypothesis h compute its fitness
While max fitness < threshold do
Create a new generation Ps
Return the hypothesis with highest fitness
9. New Population
Select: (1-r)p members of P and add them to Ps.
The probability of selecting a member is as follows: P(hi) = Fitness (hi) / Σj
Fitness (hj)
Crossover:
select rp/2 pairs of hypotheses from P according to P(hi).
For each pair (h1,h2) produce two offspring by applying the crossover operator.
Add all offspring to Ps.
Mutate:
Choose m members of Ps with uniform probability.
Invert: one bit in the representation randomly.
Update: P with Ps.
Evaluate: for each h compute its fitness.
10. Representing Hypotheses
Las hipótesis en general se representan con reglas if-then codificadas
como cadenas de bits.
Por ejemplo:
cielo: soleado, nublado, lluvia = 100, 010, 001
viento: débil, fuerte = 10, 01
Jugar_tenis = si, no = 10, 01
SI (cielo=nublado v lluvia) ^ (viento=fuerte) then jugar_tenis = NO
= 011 01 01
11. Representing Hypotheses
Some combinations may be undesirable. In those cases
we can do one of the following:
Use a different encoding.
Modify the operators to avoid constructing that combination.
Assign low fitness values to those strings.
12. Genetic Operators - Crossover
The most common is called single-point crossover (sexual
recombination):
Initial Strings:
11101001000
00001010101
Crossover Mask:
11111000000
Offspring:
11101010101
00001001000
13. Genetic Operators - Mutation
The idea is to produce small changes to a string at
random.
Under a uniform distribution, we select one bit and switch its
value.
Input string: 00001010101
Output String: 01001010101
Select and change the second bit
14. Fitness Function and Selection
If we want to learn classification rules, possible functions
are accuracy or complexity.
Sometimes the system is complex and it is hard to know
the fitness value of a rule.
We may have a method to measure the overall
performance of a systems of rules.
15. Fitness Function and Selection
Selection:
The typical approach is the “fitness proportionate selection” or “roulette
wheel selection”:
P(hi) = Fitness (hi) / Σj Fitness (hj)
Other options are rank selection: Rank according to fitness but then
select based on rank only.
Fitness Function:
squared of the classification accuracy over the training data
Fitness(h) = (Correct(h))^2
Where Correct is de % of examples correctly classified by h
16. An Example - GABIL
System GAIL by Kenneth De Jong et. al. 1993, uses
genetic algorithms to learn Boolean concepts represented
as a disjunction of rules.
If condition1 then class = +
If condition2 then class = -
If condition3 then class = +
17. Representation - GABIL
We represent the set of rules as a string of bits.
Each rule contains a pre-condition and a consequent; if we assume
only two attributes, a1 and a2, then a hypothesis can be encoded
as follows:
If a1 = T and a2 = F THEN c = T
If a2 = T THEN c = F
Corresponding string: a1 a2 c
10 01 10
11 10 01
18. Genetic Operators - GABIL
Parameters:
r: 0.6 (fraction of the parent population replaced by crossover)
m: 0.001 (mutation rate)
p: 100-1000 (population size)
Mutation:
The probability of choosing a bit is 0.001
Fitness Function:
Squared of the classification accuracy over the training data
Fitness(h) = (correct(h))2
Experiments:
Compared to C4.5 accuracy was 92.1% ; the performance of other systems
ranged from 91.2% to 96.6%
19. Extensiones - GABIL
AddCondition: sobre algún atributo generaliza cambiando un bit en 0
por un 1.
DropCondition: reemplaza todos los bits de una subcadena por 1s.
Reportó resultados ambivalentes, mejoras en algunos problemas y
baja de desempeño en otros.
Sugiere la posibilidad que el AG evolucione su propio método de
busca de hipótesis.
20. GP - Genetic Programming
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:
+
Sin sqrt
x +
^ y
x 2
F = sin(x) + sqrt( x^2 + y)
21. GP - 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.
22. GP - Cross Over
The crossover operator is performed by replacing subtrees of
one program with subtrees of another program.
+
Sin ^
x +
x y
+
Sin sqrt
x +
^ y
x 2
2
24. Blocks
Learning an algorithm for stacking blocks.
Learn an algorithm to stack the blocks so that it reads
“UNIVERSAL”
V U L A I
N
E
S
R
25. Blocks
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.
NN (next necessary) name of the block needed above TB to read
the word “UNIVERSAL”.
26. Blocks
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
27. Blocks
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.
29. Models of Evolution and Learning
Jean-Baptiste Pierre Antoine de Monet, Caballero de
Lamarck; 1744-1829.
Lamarckian Evolution:
Propuso que la evolución sobre muchas generaciones
estaba directamente influenciada por las experiencias
de los organismos individuales durante su vida. En
particular propuso que las experiencias de un
organismo afectaban directamente el marcaje genético
de su prole.
Esta conjetura es atractiva porque podría
presumiblemente permitir un progreso evolutivo más
eficiente que el proceso genera-prueba de los
algoritmos genéticos, que ignoran la experiencia
ganada durante el tiempo de vida de los individuos.
A pesar de lo atractivo la evidencia científica actual
contradice el modelo de Lamarck. El punto de vista
aceptado actualmente es que el marcaje genético de
un individuo es de hecho, inalterable por la
experiencia de vida de sus padres biológicos.
Sin embargo, y a pesar de esta contradicción,
algunos estudios computacionales han mostrado que
los procesos Lamarckianos pueden en algunos casos,
mejorar la efectividad de los algoritmos genéticos.
30. Baldwin Effect
After J. M. Baldwin (1986).
The Baldwin effect relies on the following:
Si una especie está evolucionando en un
ambiente cambiante, habrá una presión
evolutiva a favor de los individuos con la
capacidad de aprender durante su tiempo de
vida.
Aquellos individuos que son capaces de
aprender muchos rasgos, dependen menos
de su código genético. Estos individuos
pueden soportar un pool genético más
diverso, basándose en el aprendizaje
individual para resolver rasgos perdidos o no
optimizados de su código genético. Este pool
genético diverso puede a su vez, soportar
una adaptación por evolución más rápida.
31. Fitness
Better individuals are preferred
Best is not always picked
Worst is not necessarily excluded
Nothing is guaranteed
Mixture of greedy exploitation and adventurous
exploration
Similarities to simulated annealing (SA)
32. Crowding
Individuos más aptos que otros comienzan a reproducirse
rápidamente de tal forma que copias o individuos muy
parecidos ocupan una fracción importante de P afectando
la diversidad de la población y reduce la velocidad.
Algunas técnicas para evitar el crowding incluyen:
Usar un criterio de selección por torneo o por rango, en lugar de
la selección basada en adaptación.
Reducir el índice de adaptación de un individuo si se detecta la
presencia de individuos similares en la población (fitness sharing).
Restringir que individuos pueden combinarse para producir prole,
mitigando la creación de especies o grupos de individuos
similares.
33. ¿AG vs BH?
Los algoritmos genéticos emplean una búsqueda al azar
por barrido para encontrar la mejor hipótesis.
Esta forma de buscar es diferente de la BH más
tradicional debido que en este caso la búsqueda puede
moverse abruptamente en el espacio de hipótesis
posibles, por ejemplo, cuando la prole difiere totalmente
de sus padres.
Es menos probable que el algoritmo caiga en máximos
locales.
34. Parallel Genetic Agorithms
It seems very natural to produce a parallel version of genetic
algorithms.
Some approaches divide the population into groups called demes
(“local population of closely related organisms”).
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.
35. 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.
