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.