1. Evolution Strategy How Nature Solves Problems Ingo Rechenberg Shanghai Institute for Advanced Studies CAS-MPG Partner Institute for Computational Biology / 2006-04-11

2. 1 What Evolution Strategy does 2 How Evolution Strategy works

3. 1 Protoplasm lump in the primordial ocean What Evolution does

4. 2 From this the fish developed What Evolution does

5. 3 Life peeks out of the water and spreads over the country What Evolution does

6. 4 Our ancestors climb the treetops What Evolution does

7. 5 Finally we admire ourselves in the mirror What Evolution does

8. History of the Evolution Strategy

9. Windtunnel Flexible flow body to adjust random mutations Air flow Gear

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

11. Number of possible adjustments 51 5 = 345 025 251

12. The experimentum crucis – Drag minimization of the kink plate

13. Zigzag after D ARWIN Story in the Magazin 18 th November 1964

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

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

16. History Evolution Strategy today

17. 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

18. Elementary Evolution-Strategic Algorithms

19. (1 + 1)-ES D ARWIN s theory at the level of maximum abstraction

20. (1, )-ES Evolution Strategy with more than one offspring = 6

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

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

23. New founder populations The Nested Evolution Strategy

24. will be an algebraic scheme The notation

25. An artificial evolution experiment in the windtunnel

26. Evolution of a spread wing in the windtunnel

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

28. 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“:

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

30. Evolution-strategic development of a framework construction

31. Weight  Minimum

35. Evolution-strategic optimization of a truss bridge with minimum weight

36. Arched bridge Fishbelly bridge Bridge designs Lu Pu Bridge

37. Dynamic optimization of a truss bridge

38. Melencolia, engraved in 1514 by Albrecht Dürer Magic Square Chinese

39. 2 0 0 6

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

41. y x The min/max distance problem D D min max Minimum

42. ES-Solutions of the min/max- distance problem 7 Points 12 Points 24 Points 27 Points Maximum distance = 1 Minimum distance

43. Optimal swarm configuration of 48 individuals D max D min = 6.707

44. Elements of the optimal structure Structure of the 48 individual swarm

45. 2 How Evolution Strategy works

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

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

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

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

50. Billiards-Effect Example for weak causality

51. Strong Causality Normal behaviour of the world

52. Weak and strong causality in a graphic view Weak causality Strong causality

53. Experimenter Plumbing the depth Search area The search for the optimum

54. Plumbing the depth Experimenter Search area

55. 1. Global deterministic search 3. Local deterministic search 2. Global stochastic search 4. Local stochastic search 4 strategies to localize an optimum

56. 1. Global deterministic search Systematic scanning of the variable space

57. 2. Global stochastic search To find the target with 95% probability

58. 1. Global deterministic search 3. Local deterministic search 2. Global stochastic search 4. Local stochastic search 4 strategies to localize an optimum

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

60. Linearity radius  Progress  3. Local deterministic search Walking following the steepest ascent

61. Linearity radius  4. Local stochastic search Random drifting along the steepest ascent 1. Offspring 2. Offspring Parent

62. Plus-offspring Minus-offspring Ce n ter of gravity Statistical mean of the progress Determiation of the linear rate of progress Parent Linearity radius 2 / s  s + − Because half of the offspring are failures

63. 2 Dim. 3 Dim. n Dim. s s s Center of gravity n >> 1

64. Gradient Strategy contra Evolution Strategy For n >> 1 Evolution Strategy Gradient Strategy

65. Local climbing of the Evolution Strategy linear

66. Local climbing of the Evolution Strategy nonlinear

67. T AYLOR series expansion in n dimensions (M ACLAURIN series) Transformation to the principle axes

68. Tabel 10 20,5642 30,8463 41,0294 51,1630 61,2672 71,3522 81,4236 91,4850 101,5388 111,5864 121,6292 131,6680 141,7034 151,7359 161,7660 171,7939 181,8200 191,8445 201,8675 211,8892 221,9097 231,9292 241,9477 251,9653 261.9822 271,9983 282,0137 292,0285 302,0428 352,1066 402,1608 452,2077 502,2491 552,2860 602,3193 652,3496 702,3774 802,4268 902,4697 1002,5076 2002,7460 3002,8778 4002,9682 5003,0367 6003,0917 7003,1375 8003,1768 9003,2111 10003,2414 of the progress coefficients

69.  = zero  = high  = medium The complexity  r

70. - 5 - 3 - 131 0 0,2 0,1 0,3 1010101010 2,1   c ,1 cn   Central law of progress

71. not so but so

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

73. - 5 - 3 - 131 0 0,2 0,1 0,3 1010101010   How to find the Evolution Window ?

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

75. Assessment of the climbing style Climbing alone Climbing in a group

76. Four mountaineers, four climbing styles Fraidycat Columbus Amundsen Hothead

77. In a compact notation Nested Evolution Strategy Four moutaineers, four climbing styles

78. On the way to an evolution-strategic algebra

79. 1 + 1 ( ) - ES , +, On the way to an evolution-strategic algebra

80. ( ) - ES  +, On the way to an evolution-strategic algebra /   Example  = 2 ( ) - ES  +, / 2 Only half of the parental information builds up an offspring Multi-Recombination

81.  ( ) - ES  +, On the way to an evolution-strategic algebra Example: (1+ 6) 4 =

82.  ( ) - ES  +, On the way to an evolution-strategic algebra  +, [ ]  | Family  Genus { Species [ Variety ( Individual ) ] }  | Biological equivalent to the strategy nesting

83.  ( ) - ES  +, Nested Evolution Strategy  +, [ ]  Adaptation of the objektive variables x k Adaptation of the mutation size  to operate in the Evolution Window!

84. Reduction of the lateral component of the mutation step using intermediary variable mixing (multi-recombination) Contour line Parent Best of offspring Recombination of the  best of offspring Reduction of the lateral mutation step Lateral component Progress component

85. The wonder of sexual reproduction with multi-recombination without recombination  times faster !

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