Dr Sanchez - Slides - 6.PDF

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University of Maryland1Center for Advanced Life Cycle Engineering

INTRODUCTION TO

MACHINE LEARNING – VI

[email protected]

Dr. Gustavo Sánchez


⦿Exploring basic concepts about

Evolutionary Computing

Goal for today



⦿“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


⦿ 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

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⦿Evolutionary Computing (EC) is a research

area within Computer Science which draws

inspiration from the process of natural

evolution to solve computing problems


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


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


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

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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


Recombination

Parent 1 Parent 2

Offspring


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


The voyage of the Beagle, 1831–1836

Ecuador

Venezuela

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University of Maryland13Center for Advanced Life Cycle Engineering University of Maryland14Center for Advanced Life Cycle Engineering

Recombination/Mutation and Selection

Recombination and mutation

create diversity and thereby

facilitate novelty

Selection reduces diversity and acts as a force pushing

adaptation


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


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

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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


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


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


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

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Landscape Metaphor


Landscape Metaphor


Landscape Metaphor


Landscape Metaphor

Early phase:

random population distribution

Mid-phase:

population arranged around/on hills

Late phase:

population concentrated on high hills

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Typical RunB

est

fit

ne

ss in

po

pu

lati

on

Number of generations

Progress in 1st half

Progress in 2nd half


Evolution and Optimization

EVOLUTION

Environment

Individual

Fitness Function

OPTIMIZATION

Problem

Decision Vector

Objective Function


Evolutionary vs Mathematical

Optimization


� 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

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Exploration

We want to find

this treasure

Our budget is

limited


Explotation

We will not find the

treasure!


Exploration vs Explotation


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


Simple Genetic Algorithm (SGA)

� Holland’s original GA is now known as the


� Genotype representation: Binary Strings


SGA operators: crossover

� Choose a random point on the two parents

� Split parents at this crossover point

� Create children by exchanging tails


� 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


� 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

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Representation Binary strings

Recombination 1-point

Mutation Bitwise bit-flipping with

fixed probability pm

Parent selection Fitness-Proportionate

Survivor selection All children replace

parents



Application to Prognostics


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


– real-valued optimization


– acceptable results

– relatively much theory

– self-adaptation of mutation parameters

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� Basic algorithm: “two-individuals ES”

– Vectors from Rn

directly as chromosomes

– Population size 1

– Operator: only mutation creating one child

– Greedy selection



� 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



� 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


Genetic Programming

� Developed: USA in the 1990’s (Koza)


– machine learning tasks (prediction, classification…)


– competes with decision trees, neural nets, etc

– needs huge populations (thousands individuals)

– slow

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Tree-based representation

(NOC = 2) AND (S > 80000)

AND

S2NOC 80000

>=





� Tree shaped chromosomes are complex structures

� Trees may vary in depth and width



� Most common mutation: replace a randomly chosen

subtree by another randomly generated subtree

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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


Evolutionary Computing Variants

⦿Historically different variants have been

associated with individual representations

⦿ Integer strings : Genetic Algorithms

⦿ Real-valued vectors : Evolution Strategies

⦿ Trees: Genetic Programming


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

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Evolutionary Computing Demo

DEMO


Machine Learning

Applications to PHM

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