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Evolutionary Design Optimisation of Self-Organised and Self-Assembly Systems
 

Evolutionary Design Optimisation of Self-Organised and Self-Assembly Systems

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    Evolutionary Design Optimisation of Self-Organised and Self-Assembly Systems Evolutionary Design Optimisation of Self-Organised and Self-Assembly Systems Presentation Transcript

    • Evolutionary Design Optimisation of Self-Organised and Self-Assembly Systems Germán Terrazas - gzt@cs.nott.ac.uk Research Away Day 2008
    • Outline
      • Self-Organisation and Self-Assembly
      • Characterisation of the Problems
      • Evolutionary design of CAs
        • Methodology
        • Models
        • Results
      • Evolutionary design of Wang tiles
        • Methodology
        • Models
        • Results
      • Genotype – Phenotype – Fitness Analysis
      • General Conclusions
    • Silicon elements self-assembly Sean Stauth et al., Systems Self-Assembly: Multidisciplinary snapshots, page 117 Self-organisation Self-assembly Pigmentation of shells Flocks of birds Army ants bridge
    • Characterisation of the Problems Phenotype Fitness Genotype 3 Genotype Genotype 2 F = 0.98273 F = 0.22124 Phenotype_T INTRICATE RELATION Stochastic Mapping Genotype 4 Non- Linear Non- Linear F = 0.82412 Genotype_1 Phenotype_A Phenotype_T Phenotype_Z
    • Evolutionary design of CAs Q1: Is it possible to make an evolutionary-driven spec. of the laws (rules, parameter values) governing the CA dynamics ? CA Which is the correct input ? Observed Output v 1 v 2 v 3 v 4 v 5 r 1 r 3 s 2
    • Turbulence CA INSTANCE 1 : Continuous design optimisation Genotype Phenotype (images) Genotype Phenotype (images) Meta-automaton CA r= [123] r= [129, 46] r= [41, 183, 195, 110] INSTANCE 2 : Discrete design optimisation k= 50 k= 100 k= 25 i =50.5 c = 0.0 r =0.0 i =100.0 c=1.0 r =0.0250 i =50.5 c=0.5 r =0.0125
    • Evolutionary design with fixed length individuals Universal Similarity Metric 0 < USM(FT, Fi) < 1 Phenotype - Fitness Mapping Individuals (Genotype) Phenotype Genotype – Phenotype Mapping
    • Dark triangles Large structures Pink triangles Upper plain area Target Evolved Design Turbulence Results:
    • Mirrors 3/9 Target Evolved r = [68, 122] r = [122, 100] Captured 2/9 Target Evolved r = [129, 46] r = [126, 16] Correct 5/10 r = [122] r = [122] Evolved Target Mirrors 2/10 Low Similarity 1/10 Underlying diagonal flux Target Target Evolved Evolved 1st Data set - K = 100 - 10 targets 2nd Data set - K = 50 - 9 targets Meta-automaton Results: r = [120] r = [106] Captured 3/3 Target Evolved r = [61, 251, 23, 165] r = [38, 140, 105, 234] Captured Chaos Simulated 3rd Data set - K = 25 - 3 targets Complement Mirror
      • A self-assembly Wang tile
        • Squared shaped tile
        • Coloured edges
        • Walks randomly in a lattice
      • Tiles stick to or bounce from one another subject to:
        • the strength colour-colour at the colliding edges encoded in (M)
        • the temperature (T) in the system
      Evolutionary design of Wang Tiles
      • if M[ci, cj] > T then
              • Stick
            • else
              • Bounce off
    • Tiles with deterministic assembly Tiles with probabilistic assembly
    • Evolutionary design of Wang Tiles Tiles System Supra-structure Q2: Is it possible to make an automated design of set of tiles capable to obtain a particular supra-structure by means of SA? Fixed T , Fixed M Which is the correct input ?
    • Evolutionary design with variable length individuals Individuals (Genotype) Genotype – Phenotype Mapping Phenotype Minkowski (A, P, X) Phenotype - Fitness Mapping A = 9 P = 12 X = 1 A = 12 P = 24 X = 0
    • Probabilistic Assembly + No Rotation Probabilistic Assembly + Rotation Deterministic Assembly + Rotation Deterministic Assembly + No Rotation
    • Genotype-Phenotype-Fitness Analysis Q3: Is the genotype - fitness of an individual well correlated ? i =50.5 c = 0.0 r =0.0 i =50.5 c=0.5 r =0.0125 i =100.0 c=1.0 r =0.0250 F = 0.82412 F = 0.98273 F = 0.22124 Fitness Genotype
    • Fitness Distance Correlation on CA Fitness Distance Correlation on Wang Tiles Low correlation – Fitness function is not effective in some regions of search space High correlation FDC does not give too much positive feedback Only 5 % of the analyses indicated high correlation
    • Genotype-Phenotype-Fitness Analysis Phenotype Model 3 Model 2 Model 1 Q4: Are the fitness functions properly distinguishing phenotypes ?
    • CA Clustering Wang Tiles Clustering
    • General Conclusions
      • Evolutionary design optimisation on problems:
        • genotype – phenotype – fitness is a complex, stochastic and non-linear relationship
        • continuous/discrete domain with variable/fixed length individuals
        • individuals are computationally expensive to evaluate  mapping genotype – phenotype
        • individual gives different fitness values  noisy fitness functions
      • Complementary dual assessment of GA effectiveness
        • FDC for genotype – fitness analysis. Low and high correlation values  some opt. are more difficult than others.
        • Clustering for phenotype – fitness analysis. The fitness functions did make distinction among phenotypes.
      • Meta-automaton as an innovation: spatio-temporal partitions.
      • High level of abstraction comparison method (USM). Drawbacks: confusing complementary images and mirrors.