evolutionary computation (p. koumoutsakos) 1 what is life key point : ability to reproduce. are...
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Evolutionary Computation (P. Koumoutsakos) 1
What is Life
Key point : Ability to reproduce. Are computer programs alive ? Are viruses a form of life ? Key point : Interelatedness All living organisms are related to one another - common ancestor
BUT
Organisms come to differ from one another in function, form and complexity through
EVOLUTION
Evolutionary Computation (P. Koumoutsakos) 2
Evolution - Components
Inheritance : passing of characteristics from parent to offspring
Variation/Mutation : offsprings are not exact copies of parents
Selection : Differential favoring of some organisms over others
Evolutionary Computation (P. Koumoutsakos) 3
Life & Evolution
Life : an evolutionary process on earth
Evolution : Helps our understanding of what is important in life and how living systems come to function
Case Study : Why living organisms do not have (m)any metallic parts ?
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Evolution and Scientific Inquiry
Ø There is a grandeur in this view of life, with its several powers, having been originally breathed into a few forms or into one; and that, whilst this planet has gone cycling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being, evolved…
Ø
Ø …I have called this principle, by whicheach slight variation, if useful, is
preserved, by the term Natural Selection.
Charles Darwin,- “The origin of species”
Evolutionary Computation (P. Koumoutsakos) 5
Evolution & Optimization
Evolution : Survival of the “fittest “ in a given environment.
Optimization : Identify the best possible design given a certain environment and initial conditions.
Organisms evolve via inheritance, recombinantion, mutation, selection by the
Environment.
Parameters of a design/function are evolved via inheritance, recombinantion,
mutation, selection so as to optimize a cost function.
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Evolution & Optimization
Organisms
inheritance,
recombinantion,
mutation,
Selection
Environment.
Parameters
inheritance,
recombinantion,
mutation,
Selection
Cost Function
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Why Evolutionary Computation ?
Biomimetics vs. Evolutionary Design :
Instead of imitating the final product of biological systems, imitate the process by which they are designed..
Design must be environment and initial conditions specific.
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Why Evolutionary Computation ?
Evolution, Biology and Artificial Life
By imitating evolution we may learn something about natural evolutionary principles
As we study individual behavior of members of a population we may learn something about self-organizing principles, a few things about society organizations and possibly a few things about ourselves.
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Why Evolutionary Computation ?
The No-Free Lunch Theorem (Wolpert, McReady 1996)
There cannot exist any algorithm for solving all optimization problems that is on average superior toany competitor.
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Why Evolutionary Computation ?
Optimization in an Engineering Environment
Automation - Use of commercial codes & empirical formulas
Optimizer Empiricalformulas
CommercialCodes
Cost
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Why Evolutionary Computation ?
If there is a traditional method that works do not use EA’s.
BUT
Linearisation or over-simplification is usually used so that traditional methods are applicable.
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Why Evolutionary Computation ?
Adaptivity in design
Evolutionary Computation (P. Koumoutsakos) 13
When Evolutionary Computation ?
CPU
Knowledge of the problem
Neural Networks
Experts
First Principles
EVOLUTIONARYALGORITHMS
GRADIENTALGORITHMS
HYBRIDS ???
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A Generic Evolution Algorithm
Initialise a Population.
1. Compute Fitness of the individuals.
2. Select Parents/Survivors on the basis of Fitness
3. Extend the population by : cloning, mutation, crossover
GO TO STEP 1
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The 1+1 Evolution Strategy
X* = Xn + N(0, σ )
if
F(X*) < F(Xn+1)
Xn+1 = X* , m = m + 1
else
Xn+1 = Xn
endif
σ = Q(m) → 1 / 5th
The (1+1) - ES
I. Rechenberg, 1964
……
Generation 0
Generation 1
Generation 2
Generation 200
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The 1+1 Evolution Strategy - Examples
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Function fitting by adjusting the coefficients of polynomials.
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The 1+1 Evolution Strategy - Examples
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I. EVOLUTION STRATEGIES
k
cX =PX + δ
PB kzδ → stepsize
kz → random B contains information for the evolution path - Correlations of successful mutations - PCA of paths
The environment is identified through mutation/success
Covariance MatrixAdaptation ES - (N. Hansen)