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Ingo Rechenberg
Artificial Evolution The Evolution
Strategy
Technische Universität Berlin
Shanghai Institute for Advanced Studies
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Biological Evolution
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Artificial Evolution
Competition
!
More and more crabs
errors
Making copies with errors
Science fiction story The Crab Island
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Artificial Evolution
Evolution
Competition
!
More and more crabs
errors
Making copies with errors
Science fiction story The Crab Island
unweld
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The science fiction story gave rise to the design
of an artificial evolution experiment
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Island
Windtunnel
Flexible flow body
Crab
Adjustable gear instead of making a copy
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Idea for a mechanical evolution experiment
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DARWIN in the windtunnel
The kink plate for the key experiment with the
Evolution Strategy
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Number of possible adjustments
515
345 025 251
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The kink plate
Nails which vertically jut out of the wall
The mutation apparatus GALTONs pin board
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The experimentum crucis Drag minimization of
the kink plate
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Change of the environment
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Drag minimization of the kink plate when the
environment changes
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Artificial Evolution
Zigzag after DARWIN
Story in the Magazin
18 th November 1964
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Evolution of a 90 pipe bend
Six manually adjustable shafts determine the form
of the 90pipe bend
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Evolution of a 180 pipe bend
10 robot-controlled cable-drives alter the
180pipe bend
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Optimized 90 pipe bend
Optimized 180 pipe bend
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Exchangeable segments made the flow nozzle mutable
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Evolution of a two phase flow nozzle (Hans-Paul
Schwefel)
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From Eohippus to Equus
60 million years
biological evolution
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Fitness
Evolution means climbing a
fitness-hill
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Evolution-Strategy
carnation
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Elementary Evolution-Strategic Algorithms
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(1 1)-ES
DARWINs theory at the level of maximum abstraction
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(1 , l)-ES
l 6
Evolution Strategy with more than one offspring
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(m , l)-ES
m 2
l 7
Evolution Strategy with more parents and more
offspring
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(m /r , l)-ES
m 2
r 2
l 8
Evolution Strategy with mixing of variables
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New founder populations
The Nested Evolution Strategy
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The notation
will be an algebraic scheme
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An artificial evolution experiment in the
windtunnel
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Evolution of a spread wing in the windtunnel
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Photo Michael Stache
Multiwinglets at a glider designed with the
Evolution Strategy
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The difference between mathematical optimization
and optimization in the real physical world
Ideal function in the mathematical world
Rugged hill in the experimental world
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Mimicry in biological evolution
Good tasting
Bad tasting
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A blue jay eats a monarch
But it doest taste
Because of nausea the feathers struggle
Out with the poison
And the teaching isnt forgotten
Subjective selection in nature
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Mimicry in biological evolution
Good tasting
Bad tasting
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Subjective color adaptation
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Subjective Selection
Coffee-composition using the Evolution Stratey
Mix of the offspring
Target coffee
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Parent 25 Columbia 40 Sumatra 13 Java
5 Bahia 17 Jamaica
Offspring 1 20 Columbia 34 Sumatra 23
Java 5 Bahia 18 Jamaica
Offspring 2 23 Columbia 37 Sumatra 12
Java 10 Bahia 18 Jamaica
Offspring 3 25 Columbia 32 Sumatra 15
Java 8 Bahia 20 Jamaica
Offspring 4 30 Columbia 38 Sumatra 8
Java 2 Bahia 22 Jamaica
Offspring 5 33 Columbia 38 Sumatra 9
Java 8 Bahia 12 Jamaica


E

N
3



Subjective evaluation
M. Herdy
Evolution-strategic development of a coffee blend
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Evolutionary Experimentation (EE) Analog
computation in physical systems
Evolutionary Computation (EC) Digital
computation in mathematical models
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Darwin was very uncertain whether his theory is
correct.
He stated in his book The Origin of Species
To suppose that the eye, with all its inimitable
contrivances for adjusting the focus to different
distances, for admitting different amounts of
light, and for the correction of spherical and
chromatic abberation, could have been formed by
natural selection, seems, I freely confess,
absurd in the highest possible degree.
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Evolution of an eye lens
Computer simulated evolution of a covergent lens
Flexible glass body
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Evolution-strategic development of a framework
construction
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Weight ? Minimum
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Weight ? Minimum
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Weight ? Minimum
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Weight ? Minimum
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Evolution-strategic optimization of a truss
bridge with minimum weight
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Bridge designs
Fishbelly bridge
Arched bridge
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Dynamic optimization of a truss bridge
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Melencolia, engraved in 1514 by Albrecht Dürer
Chinese
Magic Square
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2 0 0 7
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Objective function for a 3 ?3-square ?
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Theory of the Evolution Strategy
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Search for a document
(Search)Strategies are of no use in an disordered
world
(Search)Strategies need a predictable order of
the world
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Strategy in military operation
A military strategy is of no use, if the enemy
behaves randomly
General
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An evolution strategy is of no use, if nature
(opponent) behaves randomly
Evolution Strategist
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A predictable world order is
Causality
Equal cause, equal effect
Weak Causality
Similar cause, not similar effect
Strong Causality
!
Similar cause, similar effect
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Billiards-Effect
Example for weak causality
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Strong Causality
Normal behaviour of the world
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Strong causality
Weak causality
Weak and strong causality in a graphic view
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Search area
Experimenter
Plumbing the depth
The search for the optimum
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Search area
Experimenter
Plumbing the depth
The search for the optimum
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Definition of the rate of progress
j
j
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nonlinear
Local climbing of the Evolution Strategy
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d
d
2
j

W
-

2
n
n
? Complexity
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Central law of progress
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not so
but so
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Evolution means climbing a
fitness-hill
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How to find the Evolution Window ?
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Duplicator
DNA
Mutation
cator
dupli
the
made
Has
Heredity of the mutability
Crucial point of the Evolution Strategy
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Fraidycat
N
Hothead
Two mountaineers, two climbing styles
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Two moutaineers, two climbing styles
In a compact notation
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Nested Evolution Strategy
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MATLAB-program of the (1, l )-ES
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MATLAB-program of the (1, l )-ES
v100 de1 xeones(v,1)
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MATLAB-program of the (1, l )-ES
v100 de1 xeones(v,1) for
g11000 end
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MATLAB-program of the (1, l )-ES
v100 de1 xeones(v,1) for g11000
qb1e20 end
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MATLAB-program of the (1, l )-ES
v100 de1 xeones(v,1) for g11000
qb1e20 for k110 end end
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MATLAB-program of the (1, l )-ES
v100 de1 xeones(v,1) for g11000
qb1e20 for k110 if rand lt 0.5
dnde1.3 else dnde/1.3
end end end
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MATLAB-program of the (1, l )-ES
v100 de1 xeones(v,1) qesum(xe.2) for
g11000 qb10000 for k110 if
rand lt 0.5 dnde1.3 else dnde/1.3
end xnxednrandn(v,1)/sqrt(v)
end end
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MATLAB-programm of the (1, l )-ES
v100 de1 xeones(v,1) for g11000
qb1e20 for k110 if rand lt 0.5
dnde1.3 else dnde/1.3 end
xnxednrandn(v,1)/sqrt(v)
qnsum(xn.2) end end
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MATLAB-programm of the (1, l )-ES
v100 de1 xeones(v,1) for g11000
qb1e20 for k110 if rand lt 0.5
dnde1.3 else dnde/1.3 end
xnxednrandn(v,1)/sqrt(v)
qnsum(xn.2) if qn lt qb
qbqn dbdn xbxn end end
end
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MATLAB-programm of the (1, l )-ES
v100 de1 xeones(v,1) for g11000
qb1e20 for k110 if rand lt 0.5
dnde1.3 else dnde/1.3 end
xnxednrandn(v,1)/sqrt(v)
qnsum(xn.2) if qn lt qb
qbqn dbdn xbxn end end
qeqb dedb xexb end
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MATLAB-programm of the (1, l )-ES
v100 de1 xeones(v,1) for g11000
qb1e20 for k110 if rand lt 0.5
dnde1.3 else dnde/1.3 end
xnxednrandn(v,1)/sqrt(v)
qnsum(xn.2) if qn lt qb
qbqn dbdn xbxn end end
qeqb dedb xexb semilogy(g,qe,'b.')
hold on drawnow end
Fitness function
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I thank you for your attention
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