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

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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

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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”

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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

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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)