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Artificial Evolution The Evolution Strategy Technische Universität Berlin Shanghai Institute for Advanced Studies Ingo Rechenberg.

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Presentation on theme: "Artificial Evolution The Evolution Strategy Technische Universität Berlin Shanghai Institute for Advanced Studies Ingo Rechenberg."— Presentation transcript:

1 Artificial Evolution The Evolution Strategy Technische Universität Berlin Shanghai Institute for Advanced Studies Ingo Rechenberg

2 Biological Evolution

3 Artificial Evolution Making copies with errors More and more crabs Competition Science fiction story The Crab Island errors !

4 Artificial Evolution Making copies with errors More and more crabs Competition Evolution Science fiction story The Crab Island errors ! unweld

5 The science fiction story gave rise to the design of an artificial evolution experiment

6 Island Windtunnel Crab Flexible flow body Adjustable gear instead of making a copy

7 Idea for a mechanical evolution experiment

8 D ARWIN in the windtunnel The kink plate for the key experiment with the Evolution Strategy

9 Number of possible adjustments 51 5 = 345 025 251

10 The mutation apparatus – G ALTON s pin board The kink plate Nails which vertically jut out of the wall

11 The experimentum crucis – Drag minimization of the kink plate

12 Change of the environment

13 Drag minimization of the kink plate when the environment changes

14 Zigzag after D ARWIN Story in the Magazin 18 th November 1964 Artificial Evolution

15 Six manually adjustable shafts determine the form of the 90°pipe bend Evolution of a 90° pipe bend

16 10 robot-controlled cable-drives alter the 180°pipe bend Evolution of a 180° pipe bend

17 Optimized 90° pipe bend Optimized 180° pipe bend

18 Exchangeable segments made the flow nozzle mutable

19 Evolution of a two phase flow nozzle (Hans-Paul Schwefel)

20 From Eohippus to Equus – 60 million years biological evolution

21 Evolution means climbing a fitness-hill Fitness

22 Evolution-Strategy Wright HaldaneFisher ' = Number of offspring populations   '  = Number of population generations  ' = Number of parental populations  = Number of parental individuals   = Number of offspring individuals  = Generations of isolation  ' = Mixing number for populations  = Mixing number for individuals carnation

23 Elementary Evolution-Strategic Algorithms

24 (1 + 1)-ES D ARWIN s theory at the level of maximum abstraction

25 (1, )-ES Evolution Strategy with more than one offspring = 6

26 ( , )-ES Evolution Strategy with more parents and more offspring = 7  = 2

27 (    , )-ES Evolution Strategy with mixing of variables = 8  = 2  = 2

28 New founder populations The Nested Evolution Strategy

29 will be an algebraic scheme The notation

30 An artificial evolution experiment in the windtunnel D c L c

31 Evolution of a spread wing in the windtunnel

32 Multiwinglets at a glider designed with the Evolution Strategy Photo: Michael Stache

33 Ideal function in the mathematical world Rugged hill in the experimental world The difference between mathematical optimization and optimization in the real physical world

34 Mimicry in biological evolution Bad tasting Good tasting

35 A blue jay eats a monarch But it does‘t taste Because of nausea the feathers struggle Out with the poison And the teaching isn‘t forgotten Subjective selection in nature

36 Mimicry in biological evolution Bad tasting Good tasting

37 Subjective color adaptation

38 Subjective Selection Coffee-composition using the Evolution Stratey Target coffee Mix of the offspring

39 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 Subjective evaluation E N 3 Evolution-strategic development of a coffee blend M. Herdy

40 Evolutionary Experimentation (EE) „Analog computation“ in physical systems Evolutionary Computation (EC) „Digital computation“ in mathematical models

41 Darwin was very uncertain whether his theory is correct. 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. He stated in his book „The Origin of Species“:

42 F d k q k Evolution of an eye lens Computer simulated evolution of a covergent lens Flexible glass body

43 Evolution-strategic development of a framework construction

44 Weight  Minimum

45

46

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48 Evolution-strategic optimization of a truss bridge with minimum weight

49 Arched bridge Fishbelly bridge Bridge designs Lu Pu Bridge

50 Dynamic optimization of a truss bridge

51 Melencolia, engraved in 1514 by Albrecht Dürer Magic Square Chinese

52 2 0 0 7

53 Objective function for a 3  3-square ? n n 1 4 7 2 5 8 3 6 9 n n n n n n

54 Theory of the Evolution Strategy

55 Search for a document (Search)Strategies are of no use in an disordered world (Search)Strategies need a predictable order of the world

56 Strategy in military operation A military strategy is of no use, if the enemy behaves randomly General

57 An evolution strategy is of no use, if nature (opponent) behaves randomly Evolution Strategist

58 Causality Weak Causality Strong Causality A predictable world order is Equal cause, equal effect Similar cause, not similar effect Similar cause, similar effect !

59 Billiards-Effect Example for weak causality

60 Strong Causality Normal behaviour of the world

61 Weak and strong causality in a graphic view Weak causality Strong causality

62 Experimenter Plumbing the depth Search area The search for the optimum

63 Plumbing the depth Experimenter Search area

64 distance moved uphill number of generations    Definition of the rate of progress 

65 Local climbing of the Evolution Strategy nonlinear

66 Table of progress coefficients between 1 and 3 n n 2  c,1   2·2·  = Complexity

67  = zero  = high  = medium r  increasing

68 - 5 - 3 - 131 0 0,2 0,1 0,3 1010101010 2,1   c ,1 cn   Central law of progress

69 not so but so

70 Evolution means climbing a fitness-hill

71 For n >> 1 the white catchment areas of the hills are neglectible small compared with the vaste black space between them Parent

72 - 5 - 3 - 131 0 0,2 0,1 0,3 1010101010   How to find the Evolution Window ?

73 Mutation Duplicator DNA Has made the dupli cator Heredity of the mutability Crucial point of the Evolution Strategy

74 N Two mountaineers, two climbing styles Fraidycat Hothead

75 In a compact notation Nested Evolution Strategy Two moutaineers, two climbing styles 2

76 M ATLAB -program of the (1,  )-ES

77 v=100; de=1; xe=ones(v,1);

78 M ATLAB -program of the (1,  )-ES v=100; de=1; xe=ones(v,1); for g=1:1000 end

79 M ATLAB -program of the (1,  )-ES v=100; de=1; xe=ones(v,1); for g=1:1000 qb=1e+20; end

80 M ATLAB -program of the (1,  )-ES v=100; de=1; xe=ones(v,1); for g=1:1000 qb=1e+20; for k=1:10 end

81 M ATLAB -program of the (1,  )-ES v=100; de=1; xe=ones(v,1); for g=1:1000 qb=1e+20; for k=1:10 if rand < 0.5 dn=de*1.3; else dn=de/1.3; end end end

82 M ATLAB -program of the (1,  )-ES v=100; de=1; xe=ones(v,1); qe=sum(xe.^2); for g=1:1000 qb=10000; for k=1:10 if rand < 0.5 dn=de*1.3; else dn=de/1.3; end xn=xe+dn*randn(v,1)/sqrt(v); end end

83 M ATLAB -programm of the (1,  )-ES v=100; de=1; xe=ones(v,1); for g=1:1000 qb=1e+20; for k=1:10 if rand < 0.5 dn=de*1.3; else dn=de/1.3; end xn=xe+dn*randn(v,1)/sqrt(v); qn=sum(xn.^2); end end

84 M ATLAB -programm of the (1,  )-ES v=100; de=1; xe=ones(v,1); for g=1:1000 qb=1e+20; for k=1:10 if rand < 0.5 dn=de*1.3; else dn=de/1.3; end xn=xe+dn*randn(v,1)/sqrt(v); qn=sum(xn.^2); if qn < qb qb=qn; db=dn; xb=xn; end end

85 M ATLAB -programm of the (1,  )-ES v=100; de=1; xe=ones(v,1); for g=1:1000 qb=1e+20; for k=1:10 if rand < 0.5 dn=de*1.3; else dn=de/1.3; end xn=xe+dn*randn(v,1)/sqrt(v); qn=sum(xn.^2); if qn < qb qb=qn; db=dn; xb=xn; end qe=qb; de=db; xe=xb; end

86 M ATLAB -programm of the (1,  )-ES v=100; de=1; xe=ones(v,1); for g=1:1000 qb=1e+20; for k=1:10 if rand < 0.5 dn=de*1.3; else dn=de/1.3; end xn=xe+dn*randn(v,1)/sqrt(v); qn=sum(xn.^2); if qn < qb qb=qn; db=dn; xb=xn; end qe=qb; de=db; xe=xb; semilogy(g,qe,'b.') hold on; drawnow; end Fitness function

87 I thank you for your attention www.bionik.tu-berlin.de


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