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An Overview of Evolutionary Cellular Automata Computation

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One-Dimensional Cellular Automata (Mitchell, Crutchfield, and Das, 1998) ... Results of Selected Rules (Crutchfield and Mitchell, 1995) ... – PowerPoint PPT presentation

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Title: An Overview of Evolutionary Cellular Automata Computation


1
An Overview of Evolutionary Cellular Automata
Computation
  • Scott McQuade
  • January 24, 2008

2
A2 Papers
  • J.P.Crutchfield and M.Mitchell. The evolution of
    emergent computation. PNAS, 92 (23) 10742, 1995.
  • M.Mitchell, J.P.Crutchfield and R.Das. Evolving
    cellular automata to perform computations. In T.
    Back, D. Fogel, and Z. Michalewicz (editors),
    Handbook of Evolutionary Computation. Oxford
    Oxford University Press, 1998.

3
Outline
  • Objectives
  • Methodology
  • Results
  • Interpretation of Results

4
Objectives
  • Study the evolution and emergence of spatially
    extended, decentralized computing
  • Occurs naturally (insect nests, aggregation of
    slime mold, parallel processing by sensory
    neurons, economical markets/pricing) (Crutchfield
    and Mitchell, 1995)
  • Applications to computations systems
  • Parallel Processing
  • Lack of Central Processor
  • More Efficient Communications

5
One-Dimensional Cellular Automata (Mitchell,
Crutchfield, and Das, 1998)
6
Example Results (Mitchell, Crutchfield, and Das,
1998)
7
The Task
  • Density Classification
  • If the initial configuration contains more 1s
    than 0s, all cells should eventually switch to
    1s
  • If the initial configuration contains more 0s
    than 1s, all cells should eventually switch to
    0s
  • This is referred to as the ?c(1/2) Task
  • ?0 refers to the density of 1s in the initial
    configuration

8
The Task
  • No Cellular Automata can perform the ?c(1/2)
    task perfectly across for all N
  • Even for fixed N, a single cell, or a linear
    combination of cells, does not have the
    computation power to perform the ?c(1/2) task
    well

9
Task Parameters
  • N 149
  • r 3
  • 27 128 bit rule string 2128 possible rules
  • ?0 was uniformly distributed between 0 and 1 for
    the test cases
  • NOT the unbiased distribution as it was too
    difficult
  • Maximum Time of 2N to produce the correct
    behavior

10
Basics of Genetic Algorithms
  • Initial pool of algorithms or strategies
  • Run all algorithms Obtain results
  • Fitness Function to evaluate the results of
    each existing algorithm
  • Reproduction using the top performing algorithms
    recombination (crossover) and mutation
  • Repeat for multiple generations

11
GA Parameters
  • The rules of the automaton will evolve, not the
    board itself
  • 100 initial random rules (generated with some
    initial biases)
  • Each rule evaluated on 100 uniformly distributed
    initial configurations (per generation)
  • Fitness was the fraction of the 100 where correct
    behavior was produced
  • For each generation
  • Top 20 rules were retained
  • Crossover of random pairings of the top 20 rules
    to produce the new 80 rules
  • 2 random mutations per crossover
  • 100 Generations

12
Results of Selected Rules (Crutchfield and
Mitchell, 1995)
13
Block Expanding Rules (Mitchell, Crutchfield, and
Das, 1998)
14
Block Expanding Rules
  • Simpler Strategy
  • Works well with small or large ?0
  • Does not exhibit coordinated communication flow
    processing done locally
  • Does not scale well

15
Particle Based Rules (Mitchell, Crutchfield, and
Das, 1998)
16
Particle Based Rules
  • Complex patterns evolve
  • Each pattern region (domain) can be classified
    and recognized be a DFA
  • The constant patterns can be filtered out,
    leaving only the boundaries between domains
  • These domain boundaries act like particles,
    travelling at constant velocities and interacting
    with each other

17
Particle Based Rules (Crutchfield and Mitchell,
1995)
18
Particle Based Rules(Crutchfield and Mitchell,
1995)
19
Synchronization Task (Mitchell, Crutchfield, and
Das, 1998)
20
Conclusions
  • Complex particle-based rules evolved infrequently
    but consistently (7 out of 300 runs)
  • The evolution consisted of distinct epochs with
    distinct innovations

21
Conclusions
  • Using an unbiased initial configuration (?0 ½),
    was too difficult for initial generations
  • A uniform 0, 1 ?0 distribution was used, but
    this proved to be too easy in later generations
  • The authors mentioned the possibility of a
    co-evolution sheme
  • Breaking of symmetries proved to be a problem

22
Conclusions
  • Possible applications to more complex real-world
    problems (image processing)
  • Insight into natural evolutionary behavior

23
References
  • 1. J.P.Crutchfield and M.Mitchell. The evolution
    of emergent computation. PNAS, 92 (23) 10742,
    1995.
  • 2. M.Mitchell, J.P.Crutchfield and R.Das.
    Evolving cellular automata to perform
    computations. In T. Back, D. Fogel, and Z.
    Michalewicz (editors), Handbook of Evolutionary
    Computation. Oxford Oxford University Press,
    1998.
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