Random Boolean Networks

1. Random Boolean Networks

2. Random Boolean Networks

3. Random Boolean networks (RBNs) are known as NK networks or Kauffman networks (Dubrova 2005). An RBN is a system of N binary-state nodes (representing genes) with K inputs to each node representing regulatory mechanisms. The two states (on/off) represent respectively, the status of a gene being active or inactive. The variable K is typically held constant, but it can also be varied across all genes, making it a set of integers instead of a single integer. In the simplest case each gene is assigned, at random, K regulatory inputs from among the N genes, and one of the possibleBoolean functions of K inputs. This gives a random sample of the possible ensembles of the NKnetworks. The state of a network at any point in time is given by the current states of all N genes. Thus the state space of any such network is 2^N. Random Boolean Networks Attractors A Boolean network has 2^N possible states. Sooner or later it will reach a previously visited state, and thus, since the dynamics are deterministic, fall into an attractor. If the attractor has only a single state it is called a point attractor, and if the attractor consists of more than one state it is called a cycle attractor. The set of states that lead to an attractor is called the basin of the attractor. States with no incoming connections are called garden-of-Eden states and the dynamics of the network flow from these states towards attractors. The time it takes to reach an attractor is called transient time. (Gershenson 2004)

4. Genetic Algorithms • Chapter 9, Complexity: A Guided Tour

5. Evolution by Natural Selection Charles Darwin

6. Evolution by Natural Selection • Organisms inherit traits from parents Charles Darwin

7. Evolution by Natural Selection • Organisms inherit traits from parents • Traits are inherited with some variation, via mutation and sexual recombination Charles Darwin

8. Evolution by Natural Selection • Organisms inherit traits from parents • Traits are inherited with some variation, via mutation and sexual recombination • Due to competition for limited resources, the organisms best adapted to the environment tend to produce the most offspring. Charles Darwin

9. Evolution by Natural Selection • Organisms inherit traits from parents • Traits are inherited with some variation, via mutation and sexual recombination • Due to competition for limited resources, the organisms best adapted to the environment tend to produce the most offspring. • This way traits producing adapted individuals spread in the population Charles Darwin

10. Evolution by Natural Selection in computers • Organisms inherit traits from parents • Traits are inherited with some variation, via mutation and sexual recombination • Due to competition for limited resources, the organisms best adapted to the environment tend to produce the most offspring. • This way traits producing adapted individuals spread in the population Computer programs Charles Darwin

11. Evolution by Natural Selection in computers • Organisms inherit traits from parents • Traits are inherited with some variation, via mutation and sexual recombination • Due to competition for limited resources, the organisms best adapted to the environment tend to produce the most offspring. • This way traits producing adapted individuals spread in the population Computer programs Charles Darwin John Holland

12. Evolution by Natural Selection in computers • Organisms inherit traits from parents • Traits are inherited with some variation, via mutation and sexual recombination • Due to competition for limited resources, the organisms best adapted to the environment tend to produce the most offspring. • This way traits producing adapted individuals spread in the population Computer (e.g., programs) Charles Darwin Genetic Algorithms (GAs) John Holland

13. Some real-world uses of genetic algorithms

14. Some real-world uses of genetic algorithms • Used by GE to automate parts of aircraft design

15. Some real-world uses of genetic algorithms • Used by GE to automate parts of aircraft design • Used by pharmaceutical companies to discover new drugs

16. Some real-world uses of genetic algorithms • Used by GE to automate parts of aircraft design • Used by pharmaceutical companies to discover new drugs • Used by the London Stock Exchange to automatically detect fraudulent trades

17. Some real-world uses of genetic algorithms • Used by GE to automate parts of aircraft design • Used by pharmaceutical companies to discover new drugs • Used by the London Stock Exchange to automatically detect fraudulent trades • Used to generate realistic computer animation in the movies Lord of the Rings: The Return of the King and Troy

18. Some real-world uses of genetic algorithms • Used by GE to automate parts of aircraft design • Used by pharmaceutical companies to discover new drugs • Used by the London Stock Exchange to automatically detect fraudulent trades • Used to generate realistic computer animation in the movies Lord of the Rings: The Return of the King and Troy • Used to model and understand evolution in nature!

19. Robby the Robot

20. Example: Evolving Strategies for Robby the Robot

21. Example: Evolving Strategies for Robby the Robot • Input: • Contents of N, S, E, W, C(Current)

22. Example: Evolving Strategies for Robby the Robot • Input: • Contents of N, S, E, W, C(Current) • Possible actions: • Move N • Move S • Move E • Move W • Move random • Stay put • Try to pick up can

23. Example: Evolving Strategies for Robby the Robot • Input: • Contents of N, S, E, W, C(Current) • Possible actions: • Move N • Move S • Move E • Move W • Move random • Stay put • Try to pick up can Rewards/Penalties (points): Picks up can: 10 Tries to pick up can on empty site: -1 Crashes into wall: -5

24. Example Strategy

25. Encoding a Strategy Code: MoveNorth = 0 MoveSouth = 1 MoveEast = 2 MoveWest = 3 StayPut = 4 PickUpCan = 5 MoveRandom = 6

26. Encoding a Strategy Code: MoveNorth = 0 MoveSouth = 1 MoveEast = 2 MoveWest = 3 StayPut = 4 PickUpCan = 5 MoveRandom = 6

27. Encoding a Strategy 0 Code: MoveNorth = 0 MoveSouth = 1 MoveEast = 2 MoveWest = 3 StayPut = 4 PickUpCan = 5 MoveRandom = 6

28. Encoding a Strategy 0 2 Code: MoveNorth = 0 MoveSouth = 1 MoveEast = 2 MoveWest = 3 StayPut = 4 PickUpCan = 5 MoveRandom = 6

29. Encoding a Strategy 0 2 6 Code: MoveNorth = 0 MoveSouth = 1 MoveEast = 2 MoveWest = 3 StayPut = 4 PickUpCan = 5 MoveRandom = 6

30. Encoding a Strategy 0 2 6 5 . . . 3 . . . 4 Code: MoveNorth = 0 MoveSouth = 1 MoveEast = 2 MoveWest = 3 StayPut = 4 PickUpCan = 5 MoveRandom = 6

31. Encoding a Strategy 243 values 0 2 6 5 . . . 3 . . . 4 Code: MoveNorth = 0 MoveSouth = 1 MoveEast = 2 MoveWest = 3 StayPut = 4 PickUpCan = 5 MoveRandom = 6

32. Genetic algorithm for evolving strategies for Robby

33. Genetic algorithm for evolving strategies for Robby • Generate 200 random strategies (i.e., programs for controlling Robby)

34. Random Initial Population

35. Genetic algorithm for evolving strategies for Robby • Generate 200 random strategies (i.e., programs for controlling Robby) • For each strategy, calculate fitness (average reward minus penalties earned on random environments)

36. Genetic algorithm for evolving strategies for Robby • Generate 200 random strategies (i.e., programs for controlling Robby) • For each strategy, calculate fitness (average reward minus penalties earned on random environments) • The strategies pair up and create offspring via “sexual recombination” with random mutations ― the fitter the parents, the more offspring they create.

37. Parent 1: Parent 2:

38. Parent 1: Parent 2:

39. Parent 1: Parent 2: Child:

40. Genetic algorithm for evolving strategies for Robby • Generate 200 random strategies (i.e., programs for controlling Robby) • For each strategy, calculate fitness (average reward minus penalties earned on random environments) • The strategies pair up and create offspring via “sexual recombination” with random mutations ― the fitter the parents, the more offspring they create. • Keep going back to step 2 until a good-enough strategy is found!

41. My hand-designed strategy:

42. My hand-designed strategy: • “If there is a can in the current site, pick it up.”

43. My hand-designed strategy: • “If there is a can in the current site, pick it up.” • “Otherwise, if there is a can in one of the adjacent sites, move to that site.”

44. My hand-designed strategy: • “If there is a can in the current site, pick it up.” • “Otherwise, if there is a can in one of the adjacent sites, move to that site.” • “Otherwise, choose a random direction to move in.”

45. My hand-designed strategy: • “If there is a can in the current site, pick it up.” • “Otherwise, if there is a can in one of the adjacent sites, move to that site.” • “Otherwise, choose a random direction to move in.” Average fitness of this strategy: 346 (out of max possible ≈ 500)

46. My hand-designed strategy: • “If there is a can in the current site, pick it up.” • “Otherwise, if there is a can in one of the adjacent sites, move to that site.” • “Otherwise, choose a random direction to move in.” Average fitness of this strategy: 346 (out of max possible ≈ 500) Average fitness of GA evolved strategy: 486 (out of max possible ≈ 500)

47. My hand-designed strategy: • “If there is a can in the current site, pick it up.” • “Otherwise, if there is a can in one of the adjacent sites, move to that site.” • “Otherwise, choose a random direction to move in.” Average fitness of this strategy: 346 (out of max possible ≈ 500) Average fitness of GA evolved strategy: 486 (out of max possible ≈ 500) ???

48. One Run of the Genetic Algorithm Best fitness in population Generation number

49. Generation 1 • Best average score = −81

50. Time: 0 Score: 0 0 1 23 4 5 6 7 8 9 0 1 2 3 4 5 6 7 8 9