Evolutionary Algorithms and Self-Organised Systems

www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59

An Evolutionary Algorithm Approach to Guiding the Evolution of

Self-Organised Nanostructured Systems

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Natalio KrasnogorInterdisciplinary Optimisation LaboratoryAutomated Scheduling, Optimisation & Planning Research GroupSchool of Computer Science

Centre for Integrative Systems BiologySchool of Biology

Centre for Healthcare Associated InfectionsInstitute of Infection, Immunity & Inflammation

University of Nottingham

http://www.cs.nott.ac.uk/~nxk



Overview• Motivation

• Towards “Dial a Pattern” in Complex Systems

• Methodological Overview

• Virtual Complex Systems

• Physical Complex Systems

• Nanoparticle Simulation Details

• Results

• Conclusions & Further work

Au

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This work was done in collaboration with Prof. P. Moriarty and his group at the School of Physics and Astronomy at the University of Nottingham

Based on the paper:

P.Siepmann, C.P. Martin, I. Vancea, P.J. Moriarty, and N. Krasnogor. A genetic algorithm approach to probing the evolution of self-organised nanostructured systems. Nano Letters, 7(7):1985-1990, 2007.

http://dx.doi.org/10.1021/nl070773m

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www.cs.nott.ac.uk/~nxkFaculty of Mathematics and PhysicsCharles University - December 2008 /59ACDM 200625th April 2006

- Automated design and optimisation of complex systems’ target behaviour

- cellular automata/ ODEs/ P-systems models

- physically/chemically/biologically implemented

-present a methodology to tackle this problem

-supported by experimental illustration

Motivation

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Major advances in the rational/analytical design of large and complex systems have been reported in the literature and more recently the automated design and optimisation of these systems by modern AI and Optimisation tools have been introduced.

It is unrealistic to expect every large & complex physical, chemical or biological system to be amenable to hand-made fully analytical designs/optimisations.

We anticipate that as the number of research challenges and applications in these domains (and their complexity) increase we will need to rely even more on automated design and optimisation based on sophisticated AI & machine learning

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This has happened before in other research and industrial disciplines,e.g:

•VLSI design•Space antennae design•Transport Network design/optimisation•Personnel Rostering•Scheduling and timetabling

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That is, complex systems are plagued with NP-Hardness, non-approximability, uncertainty, undecidability, etc results

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That is, complex systems are plagued with NP-Hardness, non-approximability, uncertainty, undecidability, etc results

Yet, they are routinely solved by sophisticated optimisation and design techniques, like evolutionary algorithms, machine learning, etc

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Automated Design/Optimisation is not only good because it can solve larger problems but also because this approach gives access to different regions of the space of possible designs (examples of this abound in the literature)

AnalyticalDesign

AutomatedDesign

(e.g. evolutionary)

Space of all possible designs/optimisations

A distinct view of the space of possible designs couldenhance the understanding of underlying system

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The research challenge :

For the Engineer, Chemist, Physicist, Biologist :

To come up with a relevant (MODEL) SYSTEM M*

For the Computer Scientist:

To develop adequate sophisticated algorithms -beyond exhaustive search- to automatically design or optimise existing designs on M* regardless of computationally (worst-case) unfavourable results of exact algorithms.

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Towards “Dial a Pattern” in Complex Systems

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D

iscr

ete

Lexi

cal S

truct

ures

Towards “Dial a Pattern” in Complex Systems

How do we program?

Distributed Disc

rete C.S

Continuous (simulated) CS

Discrete/Contin. (physical) CS

Discrete/Continuos (Biological)

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Dial a Pattern requires:

Parameter Learning/Evolution Technology

Structural Learning/Evolution Technology

Integrated Parameter/Structural Learning/Evolution Tech.

Methodological Overview

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Initial Attempts at a “Dial a Pattern” Methodology

Evolutionaryalgorithms

behaviouremergent vs target

Parameters/model

CA-based / Real complex system

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- infinite, regular grid of cells- each cell in one of a finite number of states- at a given time, t, the state of a cell is a function of the states of its neighbourhood at time t-1.

Example- infinite sheet of graph paper - each square is either black or white- in this case, neighbours of a cell are the eight squares touching it- for each of the 28 possible patterns, a rules table would state whether the center cell will be black or white on the next time step.

?

- Self-organising processes

- Modelled using cellular automata, gass latice, ODEs, etc

Parameter Learning/Evolution Technology Example

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CA continuous Turbulence

Gas Lattice

Gas Lattice

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CA continuous Turbulence

Gas Lattice

Gas Lattice

globals[ row ;; current row we are now calculating done? ;; flag used to allow you to press the go button multiple times]

patches-own[ value ;; some real number between 0 and 1]

to setup-general set row screen-edge-y ;; Set the current row to be the top set done? false cp ctend

;; ]end……..

Given

Evolve

d

Given

Evolve

d

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Wang Tiles Models

Glue Strength Matrix

Temperature T

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Structural Learning/Evolution Technology Example




Wang Tiles Models

Glue Strength Matrix

Temperature T Given

Evolve

d

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Structural Learning/Evolution Technology Example








mvaT-PAO1lecA-

Env.Params

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mvaT-PAO1lecA-

Env.Params

Evolve

d

Evolve

d15




Evolutionaryalgorithms

behaviouremergent vs target

parameters

Complex System

How do we measure this?

How similar is to ?

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How Do We Program These Complex Systems?




The Universal Similarity Metric (USM)

- Is the USM a good objective function for evolving target spacio-temporal behaviour in a CA system?

- methodology for answering this question

- experimental results

CA model USM

Fitness Distance Correlation

Clustering

GENOTYPE PHENOTYPE FITNESS

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Data set

For each CA system:

• Keep all but one parameter the same

• Produce 10 behaviour patterns through the variable parameter

• Repeat for other parameters

EXAMPLE

turb_c4 refers to the spacio-temporal pattern produced by the fourth variation in parameter c of a Turbulence CA system

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Produced by MODEL(p1,p2,…,pn)

p1 p2 pn

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Clustering

• does the USM detect similarity of phenotype with a target pattern?

• if yes, it should be able to correctly cluster spatio-temporal patterns that look similar together

• and, those similar patterns should be related to a specific family of images arising from the variation of a single parameter

• calculate a similarity matrix filled with the results of the application of the USM to a set of objects

• during the clustering process, similar objects should be grouped together

CA model USM


Clustering


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• correlation analyses of a given fitness function versus parametric (genotype) distance.

• larger numbers indicate the problem could be optimised by a GA

• numbers around zero [-0.15, 0.15] indicate bad correlation

• scatter plots are helpful

1 2 3

1 4 3

Fitness = USM (T,D)distance = 2

CA model USM


Clustering


Target

Designoid

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The Evolutionary Engine“we will implement an object-oriented, platform-independent, evolutionary engine (EE). The EE will have a user-friendly interface that will allow the various platform users to specify the platform with which the EE will interact”

Evolvable CHELLware grant application

generic GA resultsspecialisedGA

XML

web-based configuration

module

Java servlet

web-based executionmodule

- no data types- no evaluation module- no parameters

- data types and bounds - evaluation module (‘plug in’) - GA parameters

Evaluationmodule

problem-specific

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http://marian.cs.nott.ac.uk/~pas/cgi-bin/chell/index.php



http://marian.cs.nott.ac.uk/pas-servlets/chellware/GA




Results on CAs

.

e5

f3

Target Designoid

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Target usm(F,T) e(i) e(c) e(r) Ep 0.91980 0.26843 0.35314 0.05552 0.22569

.

Target Designoid

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Au

~3nm

Gold core

Thiol groups

Sulphur ‘head’

Alkane ‘tail’, e.g. octane

Dispersed in toluene, and spin castonto native-oxide-terminated silicon

Thiol-passivated Au nanoparticles

Self-Organised Nanostructured Systems

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AFM images taken by Matthew O. Blunt, Nottingham

Au nanoparticles: Morphology

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Solvent is represented as a two-dimensional lattice gas

Each lattice site represents 1nm2

Nanoparticles are square, and occupy nine lattice sites

Based on the simulations of Rabani et al. (Nature 2003, 426, 271-274). Includes modifications to include next-nearest neighbours to remove anisotropy.

Nanoparticle Simulations

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http://www.nottingham.ac.uk/physics/research/nano/






• The simulation proceeds by the Metropolis algorithm:

– Each solvent cell is examined and an attempt is made to convert from liquid to vapour (or vice-versa) with an acceptance probability pacc = min[1, exp(-ΔH/kBT)]

– Similarly, the particles perform a random walk on wet areas of the substrate, but cannot move into dry areas.

– The Hamiltonian from which ΔH is obtained is as follows:


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Motivation

- optimisation problems

- large search space

- inspired by Darwinian evolution

global optimum

A brief overview of Genetic Algorithms

22 0.25 1.0 4.5

phenotype

genotype

simulator fitness function1.05

fitness

- area covered?- degree of order?- similarity to target pattern?

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The Universal Similarity Metric (USM)

is a measure of similarity between two given objects in terms of information distance:

where K(o) is the Kolmogorov complexity

Prior Kolmogorov complexity K(o): The length of the shortest program for computing o by a Turing machine

Conditional Kolmogorov complexity K(o1|o2):How much (more) information is needed to produce object o1 if one already knows object o2 (as input)

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TIME


Evolution- Recombination (mating) e.g. exchanging parameters ‘combine the best bits of each parent’

- Mutation e.g. altering the value of a parameter at random with some small probability

GENERATION 0

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TIME




GENERATION 1

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TIME




GENERATION 1

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TIME




GENERATION 2

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TIME




GENERATION 2

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TIME




GENERATION 3

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TIME




GENERATION 3

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TIME




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TIME




FITN

ES

S

converges to optimum solution

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• Selected a target image from simulated data set

• Initialised GA- Roulette Wheel selection- Uniform crossover (probability 1)- Random reset mutation (probability 0.3)

- Population size: 10- Offspring: 5- µ + λ replacement

• Ran the GA for 200 iterations- on a single processor server, run time ≈ 5 days- using Nottingham’s cluster (up to 10 nodes), run time ≈ 12 hours

Target:

Evolving towards a target pattern (simulated)

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0.900

0.915

0.930

0.945

0.960

02468 11 15 19 23 27 31 35 39 43 47 51 55 59 63 67 71 75 79 83 87 91 95 99 104 110 116 122 128 134 140 146 152 158 164 170 176 182 188 194 200

Evolving to a simulated target

Fitness

Generations

Average

Best

Target:

Evolving towards a target pattern (simulated)

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0.900

0.925

0.950

0.975

1.000

0 3 6 9 13 18 23 28 33 38 43 48 53 58 63 68 73 78 83 88 93 98 104 111 118 125 132 139 146 153 160 167 174 181 188 195

Evolving to a experimental target

Fitness

Generations

AverageBest

Target:

Evolving towards a target pattern (experimental)

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Using only the same fitness function as for the CAs was not sufficient for matching simulation to experimental data

We extended the image analysis, i.e. fitness function, to Minkowsky functionals, namely, area, perimeter and euler characteristic

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Self-organising nanostructuresMinkowski Functionals

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Self-organising nanostructuresEvolved design: Minkowski functionals

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Self-organising nanostructuresEvolved design: Minkowski functionals Robustness checking

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Self-organising nanostructuresEvolved design: Minkowski functionals Robustness checking: i) Clustering

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Self-organising nanostructuresEvolved design: Minkowski functionals Robustness checking: ii) Fitness Distance Correlation

1/Fi

tnes

s

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1/Fi

tnes

s

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1/Fi

tnes

s

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Self-organising nanostructuresExperimental target set

Cell Island Labyrinth Worm

Evolved set

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Evolved set

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Evolved set

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Self-organising nanostructuresExperimental target set: Results

P.Siepmann, C.P. Martin, I. Vancea, P.J. Moriarty, and N. Krasnogor. A Genetic Algorithm for Evolving Patterns in Nanostructured systems.Nano Letters (to appear)

The analysis of the designability of specific patterns is important as some patterns are more evolvable (multiple solutions) than others and

Smart surface design

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• We can evolve target simulated behaviour using a GA with the USM but the USM is not enough

•For evolving target experimental designs we used Minkowsky functionals (e.g. Area, Perimeter, Euler Characteristics)

• Using Fitness Distance Correlation and Clustering, we can show whether a given fitness function is/isn’t an appropriate objective function for a given domain.

• Can we generate a target spatio-temporal behaviour in a CA/Real system? YES - GA generates very convincing designoid patterns

Conclusions

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use of more problem-specific fitness functions open ended (multiobjective) evolution

e.g. “evolve a pattern with as many large spots as possible in as ordered a fashion as possible”

parameter investigations larger populations full fitness landscape analysis Noisy, expensive, multiobjective fitness functions Datamining the results

Future Work (I)

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Future Work (II)

Physical, Chemical, BiologicalSystem

Expensive, noisy, Stochastic, etc

Model

EvolutionaryDesign

Evolve parameters toapproximate target behaviour of desired system

Try best estimates from model parameters

EvolutionaryDesign

Collect Data Evolve models using“reality runs (RR)” results as targetsfor the models themselves

Abstracted intoa model, e.g.,ODE, NN, “cook book”,etc

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Applications (in design and manufacture) and further work

- Many, many systems can be modelled using CAs/Monte Carlos

-Many complex physical/chemical systems need to be programmed

- Research into chemical ‘design’

and self-organising nanostructured systems

e.g. designoid patterns in the BZ reaction

We are actively working towards these practical goals in the context of the EPSRC grant CHELLnet (EP/D023343/1), which comprises Evolvable CHELLware (EP/D021847/1), vesiCHELL (EP/D022304/1), brainCHELL (EP/D023645/1) and wellCHELL (EP/D023807/1).

CHELLNethttp://www.chellnet.org

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Acknowledgements

My colleagues in Physics, specially Prof. P. Moriarty

EPSRC, BBSRC for funding

Thanks To Prof. R. Bartak for inviting me here!

Any questions?

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Evolutionary Algorithms and Self-Organised Systems

Education

systems bymodern ai

physics charles university

faculty of mathematics

motivation automated

optimisation toolsuncertainty

school of physics

othermodern ai

major advances