Complexity as Fitness for Evolved Cellular Automata Update Rules

1
Complexity as Fitness for Evolved Cellular
Automata Update Rules

• Em Ward, Douglas S. Blank, Douglas Rolniak, and
  Dale R. Thompson
• University of Arkansas, USA

2
Cellular Automata (CAs)

• Computing Entities
• Turing Machine Equivalent
• Exhibit Wolfram Classification Behaviors
• Used in Pattern Recognition
• Our experiment binary density-classification
  task

3
One-dimensional CA

• Binary state, 0,1
• Neighborhood, r 1
• Rules, 22r 1
• 0000 0010
• 0101 0111
• 1000 1010
• 1101 1110

4
CA in Motion
Time

5
Time-Space Diagram of CA
6
Evolved Update Rules

• Genetic Algorithm
• Fitness function performance on binary
  density-classification task
• Rules divided into good and bad
• CA behavior induced by these rules analyzed

7
Complex Behavior of CA

• Propagating, localized structures
• May be long-lived
• long transients
• Required for computation

8
Long Transient During Computation
9
Capturing Complex Behavior

• Areas of low and high state change frequency
• Long structure (exists over many time steps)
• ? captures areas of low and high state change
  frequency
• jot captures long structure

10
Analysis Parameter, ?

• ? for each rule application
• Spread factor of state-change frequency, f
• ? frange / fmean
• good rules have higher ? than
• bad and random rules (plt0.001)

11
Analysis Parameter, jot

• jot -- jump out term
• jot m / M, where
• m time steps to solution
• M maximum allowed steps

12
Complexity as Fitness

• Complex behavior markers, ? and jot incorporated
  into fitness function for genetic algorithm
• Evolution (generations to good performance)
  faster with both, highly statistically
  significant with jot (p0.0017)
• ? affected by uniform distribution of CA initial
  configuration

13
Generations to High Performance
14
Conclusions

• Complex behavior during computation can be
  captured by numerical markers.
• Incorporation of markers into fitness function
  for genetic algorithm CA update rules speeds
  evolution.