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Evolutionary Design Evolutionary Design Optimisation Optimisation
of of Self-Organised Self-Organised
and and Self-Assembly Self-Assembly
SystemsSystems
Germán Terrazas - gzt@cs.nott.ac.ukGermán Terrazas - gzt@cs.nott.ac.uk
Research Away Day 2008Research Away Day 2008
OutlineOutline
Self-Organisation and Self-AssemblySelf-Organisation and Self-Assembly Characterisation of the ProblemsCharacterisation of the Problems Evolutionary design of CAsEvolutionary design of CAs
MethodologyMethodology ModelsModels ResultsResults
Evolutionary design of Wang tilesEvolutionary design of Wang tiles MethodologyMethodology ModelsModels ResultsResults
Genotype – Phenotype – Fitness AnalysisGenotype – Phenotype – Fitness Analysis General ConclusionsGeneral Conclusions
Silicon elements self-assemblySean Stauth et al.,
Systems Self-Assembly: Multidisciplinary snapshots, page 117
Self-organisationSelf-organisation
Self-assemblySelf-assembly
Pigmentation of shells Flocks of birds
Army ants bridge
Characterisation of the Characterisation of the ProblemsProblems
Phenotype
Fitness
Genotype 3
Genotype 3
Genotype
Non-Linear
Non-Linear
F = 0.82412F = 0.82412
Genotype_1 Genotype_1
Phenotype_A
Genotype 2
Genotype 2
F = 0.98273 F = 0.98273
Phenotype_T
F = 0.22124 F = 0.22124
Phenotype_TPhenotype_Z
INTR
ICA
TE
RELA
TIO
N
StochasticMapping
Genotype 4
Genotype 4
Evolutionary design of CAsEvolutionary design of CAs
Q1: Q1:
Is it possible to make an evolutionary-driven spec. Is it possible to make an evolutionary-driven spec. of the laws (rules, parameter values) governing the CA of the laws (rules, parameter values) governing the CA dynamics ?dynamics ?
CACA
Which is the correct input ?Which is the correct input ?
Observed OutputObserved Output
v1
v2
v3
v4v5
r1r3s2
Turbulence CATurbulence CA
INSTANCE 1 :INSTANCE 1 :Continuous design optimisationContinuous design optimisation
Genotype
Phenotype(images)
Genotype
Phenotype(images)
OUTPUT
K-TIMES = k
RULES = r
INPUT
Meta-automaton CAMeta-automaton CA
r= [123]
r= [129, 46]
r= [41, 183, 195, 110]
INSTANCE 2 :INSTANCE 2 :Discrete design optimisationDiscrete design optimisation
k= 50
k= 100
k= 25
i =50.5c = 0.0r =0.0
i =100.0c=1.0r =0.0250
i =50.5c=0.5r =0.0125
Universal Similarity Metric
0 < USM(FT, Fi) < 1
Phenotype - Fitness
Mapping
Universal Similarity Metric
0 < USM(FT, Fi) < 1
Phenotype - Fitness
Mapping
Individuals (Genotype)Individuals (Genotype)
PhenotypePhenotype
Genotype – PhenotypeMapping
Genotype – PhenotypeMapping
Evolutionary design with fixed length individualsEvolutionary design with fixed length individuals
Dark triangles
Large structures
Pink triangles
Upper plain area
TargetTarget EvolvedEvolvedDesignDesign
Turbulence Results:Turbulence Results:
Mirrors
3/9
Target Evolved
r = [68, 122] r = [122, 100]
Captured
2/9
Target Evolved
r = [129, 46] r = [126, 16]
Correct5/10
r = [122] r = [122]
EvolvedTarget
Mirrors2/10
Low Similarity
1/10
Underlying diagonal flux
Complement
Target
Target
Evolved
Evolved
1st Data set - K = 100 - 10 targets1st Data set - K = 100 - 10 targets
2nd Data set - K = 50 - 9 targets2nd Data set - K = 50 - 9 targetsMeta-automaton Results:Meta-automaton Results:
r = [120] r = [106]
Mirror
Captured
3/3
Target Evolved
r = [61, 251, 23, 165] r = [38, 140, 105, 234]
Captured Chaos
Simulated
3rd Data set - K = 25 - 3 targets3rd Data set - K = 25 - 3 targets
A self-assembly Wang tileA self-assembly Wang tile
Squared shaped tileSquared shaped tile Coloured edgesColoured edges Walks randomly in a latticeWalks randomly in a lattice
Tiles stick to or bounce from one another subject to:Tiles stick to or bounce from one another subject to: the the strengthstrength colour-colour at the colliding edges encoded in colour-colour at the colliding edges encoded in
(M)(M) the the temperature (T)temperature (T) in the systemin the system
A self-assembly Wang tileA self-assembly Wang tile
Squared shaped tileSquared shaped tile Coloured edgesColoured edges Walks randomly in a latticeWalks randomly in a lattice
Tiles stick to or bounce from one another subject to:Tiles stick to or bounce from one another subject to: the the strengthstrength colour-colour at the colliding edges encoded in colour-colour at the colliding edges encoded in
(M)(M) the the temperature (T)temperature (T) in the systemin the system
Evolutionary design of Wang Evolutionary design of Wang TilesTiles
if if M[ci, cj]M[ci, cj] >> TT then then StickStick
else else Bounce offBounce off
Tiles with Tiles with deterministic deterministic
assemblyassembly
Tiles with Tiles with probabilistic probabilistic
assemblyassembly
Evolutionary design of Wang TilesEvolutionary design of Wang Tiles
Tiles Tiles SystemSystem
Supra-structureSupra-structure
Q2: Q2:
Is it possible to make an automated design of set of tiles Is it possible to make an automated design of set of tiles capable to obtain a particular supra-structure by means capable to obtain a particular supra-structure by means of SA?of SA?
Which is the correct input ?Which is the correct input ? Fixed Fixed TT, Fixed , Fixed MM
Individuals (Genotype)Individuals (Genotype)
Genotype – PhenotypeMapping
Genotype – PhenotypeMapping
PhenotypePhenotype
Minkowski (A, P, X)
Phenotype - FitnessMapping
Minkowski (A, P, X)
Phenotype - FitnessMapping
A = 9P = 12X = 1
A = 12P = 24X = 0
Evolutionary design with variable length individualsEvolutionary design with variable length individuals
Probabilistic Assembly +
No Rotation
Probabilistic Assembly +
No Rotation
Probabilistic Assembly +
Rotation
Probabilistic Assembly +
Rotation
Deterministic Assembly +
Rotation
Deterministic Assembly +
Rotation
Deterministic Assembly +No Rotation
Deterministic Assembly +No Rotation
Genotype-Phenotype-Fitness Genotype-Phenotype-Fitness AnalysisAnalysis
Q3: Is the genotype - fitness of an individual well correlated ?
i =50.5c = 0.0r =0.0
i =50.5c = 0.0r =0.0
i =50.5c=0.5r =0.0125
i =50.5c=0.5r =0.0125
i =100.0c=1.0r =0.0250
i =100.0c=1.0r =0.0250
F = 0.82412F = 0.82412
F = 0.98273 F = 0.98273
F = 0.22124 F = 0.22124
Fitness
Genotype
Fitness Distance Fitness Distance Correlation on CACorrelation on CA
Fitness Distance Fitness Distance Correlation on Wang Correlation on Wang
TilesTiles
Low correlation – Fitness function is not effective in some regions of search
space
High correlationFDC does not give too FDC does not give too
much positive feedbackmuch positive feedback
Only 5 % of the analyses
indicated high correlation
Genotype-Phenotype-Fitness Genotype-Phenotype-Fitness AnalysisAnalysis
Phenotype
Model 3Model 3
Model 2Model 2
Model 1Model 1
Q4: Are the fitness functions properly distinguishing Q4: Are the fitness functions properly distinguishing phenotypes ?phenotypes ?
CA ClusteringCA ClusteringWang Tiles Wang Tiles ClusteringClustering
General ConclusionsGeneral Conclusions Evolutionary design optimisation on problems:Evolutionary design optimisation on problems:
genotype – phenotype – fitness is a complex, stochastic and non-linear relationshipgenotype – phenotype – fitness is a complex, stochastic and non-linear relationship
continuous/discrete domain with variable/fixed length individualscontinuous/discrete domain with variable/fixed length individuals
individuals are computationally expensive to evaluate individuals are computationally expensive to evaluate mapping genotype – mapping genotype – phenotype phenotype
individual gives different fitness values individual gives different fitness values noisy fitness functions noisy fitness functions
Complementary dual assessment of GA effectivenessComplementary dual assessment of GA effectiveness
FDC for genotype – fitness analysis. Low and high correlation values FDC for genotype – fitness analysis. Low and high correlation values some opt. are some opt. are more difficult than others.more difficult than others.
Clustering for phenotype – fitness analysis. The fitness functions did make distinction Clustering for phenotype – fitness analysis. The fitness functions did make distinction among phenotypes.among phenotypes.
Meta-automaton as an innovation: spatio-temporal partitions.Meta-automaton as an innovation: spatio-temporal partitions.
High level of abstraction comparison method (USM). Drawbacks: confusing High level of abstraction comparison method (USM). Drawbacks: confusing complementary images and mirrors.complementary images and mirrors.
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