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An Overview of Evolutionary Cellular Automata Computation. Scott McQuade January 24, 2008. A2 Papers. J.P.Crutchfield and M.Mitchell. The evolution of emergent computation. PNAS, 92 (23): 10742, 1995.
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An Overview of Evolutionary Cellular Automata Computation Scott McQuade January 24, 2008
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.
Outline • Objectives • Methodology • Results • Interpretation of Results
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
One-Dimensional Cellular Automata (Mitchell, Crutchfield, and Das, 1998)
The Task • Density Classification: • If the initial configuration contains more 1’s than 0’s, all cells should eventually switch to 1’s • If the initial configuration contains more 0’s than 1’s, all cells should eventually switch to 0’s • This is referred to as the ρc=(1/2) Task • ρ0 refers to the density of 1’s in the initial configuration
The Task • No Cellular Automata can perform the ρc=(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 ρc=(1/2) task well
Task Parameters • N = 149 • r = 3 • 2^7= 128 bit rule string; 2^128 possible rules • ρ0 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
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
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
Block Expanding Rules (Mitchell, Crutchfield, and Das, 1998)
Block Expanding Rules • Simpler Strategy • Works well with small or large ρ0 • Does not exhibit coordinated communication flow– processing done locally • Does not scale well
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
Conclusions • Complex particle-based rules evolved infrequently but consistently (7 out of 300 runs) • The evolution consisted of distinct epochs with distinct innovations
Conclusions • Using an unbiased initial configuration (ρ0 ≈ ½), was too difficult for initial generations • A uniform [0, 1] ρ0 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
Conclusions • Possible applications to more complex real-world problems (image processing) • Insight into natural evolutionary behavior
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.