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University of Maryland1Center for Advanced Life Cycle Engineering
INTRODUCTION TO
MACHINE LEARNING – VI
Dr. Gustavo Sánchez
University of Maryland2Center for Advanced Life Cycle Engineering
⦿Exploring basic concepts about
Evolutionary Computing
Goal for today
University of Maryland3Center for Advanced Life Cycle Engineering
Evolutionary Computing
⦿“This book offers a
thorough
introduction to
Evolutionary
Computing (EC),
including the basics
of all traditional
variants”University of Maryland4Center for Advanced Life Cycle Engineering
Evolutionary Computing
⦿ In 1948, Alan
Turing proposed
to use an
algorithm that
today would be
called
“evolutionary”Turing, A. (1948) “Intelligent Machinery”, in
Collected Works of A.M. Turing:
Mechanical Intelligence, Elsevier Science, 1992
2
University of Maryland5Center for Advanced Life Cycle Engineering
Evolutionary Computing
⦿Evolutionary Computing (EC) is a research
area within Computer Science which draws
inspiration from the process of natural
evolution to solve computing problems
University of Maryland6Center for Advanced Life Cycle Engineering
What is Evolution?
⦿ A population of individuals
exists in an environment
with limited resources
⦿ Competition causes
selection of fit individuals
as seeds (Parents) for the
next generation through
Recombination and
MutationEvolution naive model
University of Maryland7Center for Advanced Life Cycle Engineering
What is Evolution?
⦿ The new individuals
(Offspring) compete
again for survival
⦿Over time this natural
selection causes a rise
in the fitness of the
population
University of Maryland8Center for Advanced Life Cycle Engineering
Genotype and Phenotype
⦿ The information required to build a living organism
is coded in its Genotype (DNA)
⦿ Phenotype are those features, physical and/or
behavioral, that determine its fitness
⦿Genotype ⇒ Phenotype is a very complex mapping
3
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⦿ Each individual represents a unique combination of
phenotypic traits that will be evaluated by the
environment
⦿ If it evaluates favorably, its genes are propagated via
offspring, otherwise they are discarded
Genotype and Phenotype
University of Maryland10Center for Advanced Life Cycle Engineering
Recombination
Parent 1 Parent 2
Offspring
University of Maryland11Center for Advanced Life Cycle Engineering
Mutation
⦿ Darwin's insight was that
random mutations occur
during recombination
⦿ These mutations can be:
⦿ Catastrophic: offspring is
not viable (most likely)
⦿ Neutral: new feature
does not influence
fitness
⦿ Advantageous: useful
new feature occurs England, 1809 - 1882
University of Maryland12Center for Advanced Life Cycle Engineering
The voyage of the Beagle, 1831–1836
Ecuador
Venezuela
4
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Recombination/Mutation and Selection
Recombination and mutation
create diversity and thereby
facilitate novelty
Selection reduces diversity and acts as a force pushing
adaptation
University of Maryland15Center for Advanced Life Cycle Engineering
Fitness Function
⦿Represents the requirements that the
population should adapt to: objective function
⦿A single fitness value is assigned to each
phenotype, which will be the basis for
selection
⦿The more discrimination (different values) the
better
University of Maryland16Center for Advanced Life Cycle Engineering
Population
⦿Set of possible solutions (genotypes)
⦿Usually has a fixed size
⦿Some sophisticated algorithms assert a spatial
structure on the population e.g., a grid.
⦿Selection operators usually take whole
population into account
5
University of Maryland17Center for Advanced Life Cycle Engineering
Parent Selection
⦿ Selection probabilities are assigned to individuals
depending on their fitness
⦿ High fitness individuals are more likely to become
parents than low fitness individuals
⦿ However, even the worst individual usually has
non-zero probability of becoming a parent
University of Maryland18Center for Advanced Life Cycle Engineering
Survivor Selection
⦿Often deterministic
⦿ Fitness based : e.g., rank parents + offspring and
take best
⦿ Age based: make as many offspring as parents and
delete all parents
University of Maryland19Center for Advanced Life Cycle Engineering
Initialization / Termination
⦿ Initialization: usually random. Need to ensure even
spread. Can include previous solutions, or use
problem-specific heuristics
⦿ Termination condition is checked every generation
⦿ Reaching some (known/hoped for) fitness
⦿ Reaching some number of generations
⦿ Reaching some minimum level of diversity
⦿ Reaching some specified number of generations without fitness
improvement
University of Maryland20Center for Advanced Life Cycle Engineering
Landscape Metaphor
⦿ Population with n traits exists in a n+1-dimensional
space (landscape) with height corresponding to
fitness
⦿ Each different individual represents a single point
on this landscape
⦿ Population is therefore a cloud of points, moving on
the landscape over time as it evolves
6
University of Maryland21Center for Advanced Life Cycle Engineering
Landscape Metaphor
University of Maryland22Center for Advanced Life Cycle Engineering
Landscape Metaphor
University of Maryland23Center for Advanced Life Cycle Engineering
Landscape Metaphor
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Landscape Metaphor
Early phase:
random population distribution
Mid-phase:
population arranged around/on hills
Late phase:
population concentrated on high hills
7
University of Maryland25Center for Advanced Life Cycle Engineering
Typical RunB
est
fit
ne
ss in
po
pu
lati
on
Number of generations
Progress in 1st half
Progress in 2nd half
University of Maryland26Center for Advanced Life Cycle Engineering
Evolution and Optimization
EVOLUTION
Environment
Individual
Fitness Function
OPTIMIZATION
Problem
Decision Vector
Objective Function
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Evolutionary vs Mathematical
Optimization
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� Exploration: Discovering promising areas in
the search space, i.e. gaining information
on the problem
� Exploitation: Optimizing within a promising
area, i.e. using previous information
Exploration vs Explotation
8
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Exploration
We want to find
this treasure
Our budget is
limited
University of Maryland30Center for Advanced Life Cycle Engineering
Explotation
We will not find the
treasure!
University of Maryland31Center for Advanced Life Cycle Engineering
Exploration vs Explotation
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Genetic Algorithms
� Developed: USA in the 1970’s (Holland)
� Typically applied to:
– discrete optimization
� Attributed features:
– slow convergence
– good for combinatorial problems
– emphasizes combining information from good parents (crossover)
– many variants, e.g., reproduction models, operators
9
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Simple Genetic Algorithm (SGA)
� Holland’s original GA is now known as the
Simple Genetic Algorithm (SGA)
� Genotype representation: Binary Strings
University of Maryland34Center for Advanced Life Cycle Engineering
SGA operators: crossover
� Choose a random point on the two parents
� Split parents at this crossover point
� Create children by exchanging tails
University of Maryland35Center for Advanced Life Cycle Engineering
� Alter each gene independently with a probability pm
� pm is called the mutation rate
Typically between 1/pop_size and 1/ chromosome_length
SGA operators: mutation
University of Maryland36Center for Advanced Life Cycle Engineering
� Main idea: better individuals get higher chance
– Implementation: roulette wheel technique
� Assign to each individual a part of the roulette wheel
� Spin the wheel n times to select n individuals
fitness(A) = 3
fitness(B) = 1
fitness(C) = 2
A C
1/6 = 17%
3/6 = 50%
B
2/6 = 33%
SGA: parents selection
10
University of Maryland37Center for Advanced Life Cycle Engineering
Representation Binary strings
Recombination 1-point
Mutation Bitwise bit-flipping with
fixed probability pm
Parent selection Fitness-Proportionate
Survivor selection All children replace
parents
Simple Genetic Algorithm (SGA)
University of Maryland38Center for Advanced Life Cycle Engineering
Application to Prognostics
University of Maryland39Center for Advanced Life Cycle Engineering
Application to Prognosis
The blue solid line represents real data and the red
dotted line represents the predicted dataUniversity of Maryland40Center for Advanced Life Cycle Engineering
Evolutionary Strategy
� Developed: Germany in the 1970’s
� Early names: Rechenberg, Schwefel
� Typically applied to:
– real-valued optimization
� Attributed features:
– acceptable results
– relatively much theory
– self-adaptation of mutation parameters
11
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Evolutionary Strategy
� Basic algorithm: “two-individuals ES”
– Vectors from Rn
directly as chromosomes
– Population size 1
– Operator: only mutation creating one child
– Greedy selection
University of Maryland42Center for Advanced Life Cycle Engineering
Evolutionary Strategy
� t = 0
� Create initial point xt = ⟨ x1t,…,xn
t ⟩
� REPEAT UNTIL (TERMIN.COND satisfied)
� Draw zi from a normal distr. for all i = 1,…,n
� yt = xt + z
� IF f(xt) < f(yt) THEN xt+1 = xt
� ELSE xt+1 = yt
� Set t = t+1
University of Maryland43Center for Advanced Life Cycle Engineering
Evolutionary Strategy
� z values drawn from normal distribution N(0,σ2)
– σ is called mutation step size
� This rule resets σ after every k iterations by
– σ = σ / c if ps > 1/5
– σ = σ • c if ps < 1/5
where ps is the rate of successful mutations, 0.8 ≤ c ≤ 1
University of Maryland44Center for Advanced Life Cycle Engineering
Genetic Programming
� Developed: USA in the 1990’s (Koza)
� Typically applied to:
– machine learning tasks (prediction, classification…)
� Attributed features:
– competes with decision trees, neural nets, etc
– needs huge populations (thousands individuals)
– slow
12
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Tree-based representation
(NOC = 2) AND (S > 80000)
AND
S2NOC 80000
>=
University of Maryland46Center for Advanced Life Cycle Engineering
Tree-based representation
University of Maryland47Center for Advanced Life Cycle Engineering
Tree-based representation
� Tree shaped chromosomes are complex structures
� Trees may vary in depth and width
University of Maryland48Center for Advanced Life Cycle Engineering
Tree-based representation
� Most common mutation: replace a randomly chosen
subtree by another randomly generated subtree
13
University of Maryland49Center for Advanced Life Cycle Engineering
Tree-based representation
Child 2
Parent 1 Parent 2
Child 1 University of Maryland50Center for Advanced Life Cycle Engineering
Genetic Programming
Representation Tree structures
Recombination Exchange of subtrees
Mutation Random change in trees
Parent selection Fitness proportional
Survivor selection All children replace
parents
University of Maryland51Center for Advanced Life Cycle Engineering
Evolutionary Computing Variants
⦿Historically different variants have been
associated with individual representations
⦿ Integer strings : Genetic Algorithms
⦿ Real-valued vectors : Evolution Strategies
⦿ Trees: Genetic Programming
University of Maryland52Center for Advanced Life Cycle Engineering
Evolutionary Computing Variants
⦿These differences are today irrelevant
⦿The best practice is to choose a good
representation to suit the problem, and
variation operators to suit representation
⦿Selection operators are independent of
representation
14
University of Maryland53Center for Advanced Life Cycle Engineering
Evolutionary Computing Demo
DEMO
University of Maryland54Center for Advanced Life Cycle Engineering
Machine Learning
Applications to PHM