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Genetic Algorithms, Part 2

Genetic Algorithms, Part 2. Evolving (and co-evolving) one -dimensional cellular automata to perform a computation. One-dimensional cellular automata. One-dimensional cellular automata. Rule:. One-dimensional cellular automata. Rule:. One-dimensional cellular automata. Rule:.

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Genetic Algorithms, Part 2

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  1. Genetic Algorithms, Part 2

  2. Evolving (and co-evolving) one-dimensional cellular automata to perform a computation

  3. One-dimensional cellular automata

  4. One-dimensional cellular automata Rule:

  5. One-dimensional cellular automata Rule:

  6. One-dimensional cellular automata Rule:

  7. One-dimensional cellular automata Rule:

  8. One-dimensional cellular automata Rule:

  9. Can the complex dynamics be harnessed by evolution to perform collective information processing?

  10. A task requiring collective computation in cellular automata

  11. A task requiring collective computation in cellular automata • Design a cellular automata to decide whether or not the initial pattern has a majority of “on”cells.

  12. majority on initial

  13. majority on initial final

  14. majority on majority off initial final

  15. majority on majority off initial final

  16. majority on majority off initial How to design a cellular automaton that will do this? final

  17. . . . We used cellular automata with 6 neighbors for each cell: ... ... Rule:

  18. A candidate solution that does not work: Local majority voting

  19. Evolving cellular automata with genetic algorithms • Create a random population of candidate cellular automata rules • The “fitness” of each cellular automaton is how well it performs the task. (Analogous to surviving in an environment.) • The fittest cellular automata get to reproduce themselves, with mutations and crossovers. • This process continues for many generations.

  20. . . . . . . The “chromosome” of a cellular automaton is an encoding of its rule table: Chromosome Rule table: 0 0 1 0 1

  21. Create a random population of candidate cellular automata rules: rule 1:0010001100010010111100010100110111000... rule 2:0001100110101011111111000011101001010... rule 3:1111100010010101000000011100010010101... . . . rule 100:0010111010000001111100000101001011111...

  22. Calculating the Fitness of a Rule • For each rule, create the corresponding cellular automaton. Run that cellular automaton on many initial configurations. • Fitness of rule = fraction of correct classifications

  23. . . . For each cellular automaton rule in the population: rule 1:0010001100010010111100010100110111000...1 Create rule table

  24. . . . rule 1 rule table: Run corresponding cellular automaton on many random initial lattice configurations . . . . . . . . . . . . . . . . . etc. . . . . . . . . . . . . incorrect correct Fitness of rule = fraction of correct classifications

  25. GA Population: rule 1:0010001100010010111100010100110111000... Fitness = 0.5 rule 2:0001100110101011111111000011101001010... Fitness = 0.2 rule 3:1111100010010101000000011100010010101... Fitness = 0.4 . . . rule 100:0010111010000001111100000101001011111... Fitness = 0.0 Select fittest rules to reproduce themselves rule 1:0010001100010010111100010100110111000... Fitness = 0.5 rule 3:1111100010010101000000011100010010101... Fitness = 0.4 . . .

  26. rule 1:0010001 100010010111100010100110111000... rule 3:1111100 010010101000000011100010010101... Create new generation via crossover and mutation: Parents: mutate Children: 0010001010010101000000011100010010101... 1111100 100010010111100010100110111000...

  27. rule 1:0010001 100010010111100010100110111000... rule 3:1111100 010010101000000011100010010101... Create new generation via crossover and mutation: Parents: mutate Children: 0010000010010101000000011100010010101... 1111100 100010010111100010100110111000...

  28. rule 1:0010001 100010010111100010100110111000... rule 3:1111100 010010101000000011100010010101... Create new generation via crossover and mutation: Parents: Children: 0010000010010101000000011100010010101... 1111100 100010010111100010100110111000... mutate

  29. rule 1:0010001 100010010111100010100110111000... rule 3:1111100 010010101000000011100010010101... Create new generation via crossover and mutation: Parents: Children: 0010000010010101000000011100010010101... 1111100 100010010111100010100010111000... mutate

  30. rule 1:0010001 100010010111100010100110111000... rule 3:1111100 010010101000000011100010010101... Create new generation via crossover and mutation: Parents: Children: 0010000010010101000000011100010010101... 1111100 100010010111100010100010111000...

  31. rule 1:0010001 100010010111100010100110111000... rule 3:1111100 010010101000000011100010010101... Create new generation via crossover and mutation: Parents: Children: 0010000010010101000000011100010010101... 1111100 100010010111100010100010111000... Continue this process until new generation is complete. Then start over with the new generation. Keep iterating for many generations.

  32. majority on majority off A cellular automaton evolved by the genetic algorithm

  33. How does it perform the computation? majority on majority off A cellular automaton evolved by the genetic algorithm

  34. How do we describe information processing in complex systems?

  35. “simple patterns”: black, white, checkerboard

  36. Simple patterns filtered out

  37. “particles”

  38. “particles”

  39. laws of “particle physics” “particles”

  40. Level of particles can explain:

  41. Level of particles can explain: • Why one CA is fitter than another

  42. Level of particles can explain: • Why one CA is fitter than another • What mistakes are made

  43. Level of particles can explain: • Why one CA is fitter than another • What mistakes are made • How the GA produced the observed series of innovations

  44. Level of particles can explain: • Why one CA is fitter than another • What mistakes are made • How the GA produced the observed series of innovations • Particles give an “information processing” description of the collective behavior

  45. Level of particles can explain: • Why one CA is fitter than another • What mistakes are made • How the GA produced the observed series of innovations • Particles give an “information processing” description of the collective behavior ----> “Algorithmic” level

  46. How the genetic algorithm evolved cellular automata

  47. How the genetic algorithm evolved cellular automata generation 8

  48. How the genetic algorithm evolved cellular automata generation 13 generation 8

  49. How the genetic algorithm evolved cellular automata generation 17

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