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

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

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

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.

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.