Evolutionary Algorithms and Self-Organised Systems

An Evolutionary Algorithm Approach
to Guiding the Evolution of
Self-Organised Nanostructured Systems
Natalio Krasnogor
Interdisciplinary Optimisation Laboratory
Automated Scheduling, Optimisation & Planning Research Group
School of Computer Science

Centre for Integrative Systems Biology
School of Biology

Centre for Healthcare Associated Infections
Institute of Infection, Immunity & Inflammation

University of Nottingham
www.cs.nott.ac.uk/~nxk
Faculty of Mathematics and Physics
Charles University - December 2008 1 /59

Overview
• Motivation

• Towards “Dial a Pattern” in Complex Systems

• Methodological Overview

• Virtual Complex Systems

Au • Physical Complex Systems
• Nanoparticle Simulation Details

• Results

• Conclusions & Further work

 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

Motivation
- 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

ACDM 2006
25th April 2006

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


complex systems have been reported in the literature and more
This has happened before in other
modern AI and Optimisation tools have been introduced.
research and industrial disciplines,e.g:
•VLSI design
•Space antennae design
•Transport Network design/optimisation
•Personnel Rostering
•Scheduling and timetabling


complex systems have been reported in the literature and more with
That is, complex systems are plagued
NP-Hardness, non-approximability,
modern AI and Optimisation toolsuncertainty, undecidability, etc results
This has happened before in other have been introduced.
•VLSI design


complex systems have been reported in the literature and more with
That is, complex systems are plagued
NP-Hardness, non-approximability,
modern AI and Optimisation toolsuncertainty, undecidability, etc results
This has happened before in other have been introduced.
•VLSI design
Yet, they are routinely solved by
We anticipate that as the number of research challenges and design
sophisticated optimisation and
techniques, like evolutionary
algorithms, machine learning, etc


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)

Space of all possible designs/optimisations
Automated
Analytical
Design
Design
(e.g. evolutionary)

A distinct view of the space of possible designs could
enhance the understanding of underlying system


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.


Towards “Dial a Pattern” in Complex Systems


Towards “Dial a Pattern” in Complex Systems

es
ctur
Stru
ical .S
Lex
C
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rete

isc
dD
Disc

ute
is trib
D
Continuous (simulated) CS
How do we program?
Disc
rete
/Contin
. (ph
ysic
al) C
S

Dis
cre
te/C
ont
inu
o s (B
iolo
gic
al)


Methodological Overview

Dial a Pattern requires:

 Parameter Learning/Evolution Technology

 Structural Learning/Evolution Technology

 Integrated Parameter/Structural Learning/Evolution Tech.


Initial Attempts at a “Dial a Pattern” Methodology

behaviour CA-based / Real
emergent vs target complex system

Parameters/model

Evolutionary
algorithms


Parameter Learning/Evolution Technology Example
- Self-organising processes
- Modelled using cellular automata, gass latice, ODEs, etc

- 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.


CA continuous Turbulence Gas Lattice

Charles University - December 2008 12 /59 Gas Lattice

CA continuous Turbulence Gas Lattice

d
ve
n

ol
ive

Ev
G

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 ct
end

;; ]
end
……..

Charles University - December 2008 12 /59 Gas Lattice

Structural Learning/Evolution Technology Example
Wang Tiles Models
Temperature T

Glue Strength Matrix


Structural Learning/Evolution Technology Example
Wang Tiles Models

en
iv
G
Temperature T

Glue Strength Matrix

d
ve
ol
Ev



lecA- PAO1 mvaT-

Env.
Params



lecA- PAO1 mvaT-

d

d
ve

ve
ol

ol
Ev

Ev
Env.
Params


How Do We Program These Complex
Systems?
behaviour Complex System
emergent vs target

How do we measure this? parameters

How similar is to ?

Evolutionary
algorithms


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

Fitness Distance Correlation

GENOTYPE PHENOTYPE FITNESS
CA model USM

Clustering

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


Produced by MODEL(p1,p2,…,pn)

p1 p2 pn


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

CA model USM

• calculate a similarity matrix filled with the results Clustering

of the application of the USM to a set of objects
• during the clustering process, similar objects should be grouped together


• 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 Fitness Distance Correlation

CA model USM
Target
Clustering

1 2 3

distance = 2 Fitness = USM (T,D)
Designoid

1 4 3

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
- no data types
- no evaluation module - data types and bounds 
- no parameters - evaluation module (‘plug in’) 
- GA parameters 

specialised
generic GA results
GA

XML Evaluation
module
Java servlet
problem-specific
web-based web-based
configuration execution
module module


Results on CAs

Target Designoid

e5

f3

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

Target Designoid

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

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

Self-Organised Nanostructured Systems
Thiol-passivated Au nanoparticles

Gold core
Thiol groups

Au Sulphur ‘head’

Alkane ‘tail’, e.g. octane

~3nm Dispersed in toluene, and spin cast
onto native-oxide-terminated silicon

Au nanoparticles: Morphology

AFM images taken by Matthew O. Blunt, Nottingham


Nanoparticle Simulations

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.

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:


A brief overview of Genetic Algorithms

Motivation
- optimisation problems global optimum

- large search space
- inspired by Darwinian evolution

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

22 0.25 1.0 4.5 1.05
simulator fitness function

genotype fitness

phenotype


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)



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

TIME



Evolution
- Mutation
GENERATION 1

TIME



Evolution
- Mutation
GENERATION 2

TIME



Evolution
- Mutation
GENERATION 3

TIME



Evolution
- Mutation

TIME



Evolution
- Mutation
converges to
optimum solution
FITNESS

TIME


Evolving towards a target pattern (simulated)

• 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
Target:
- 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


Evolving towards a target pattern (simulated)

Evolving to a simulated target
Target:
0.960

0.945
Fitness

0.930

Average
Best

0.915

0.900
0 2 4 6 8 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
Generations


Evolving towards a target pattern (experimental)
Evolving to a experimental target Target:
1.000

0.975
Fitness

0.950

Average
Best

0.925

0.900
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
Generations


 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


Self-organising nanostructures
Minkowski Functionals


Evolved design: Minkowski functionals


Robustness checking


Evolved design: Minkowski functionals Robustness checking: i) Clustering


Robustness checking: ii) Fitness Distance Correlation
1/Fitness


1/Fitness


Experimental target set
Cell Island Labyrinth Worm

Evolved set

Self-organising
nanostructures
Experimental 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


Conclusions
• 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

Future Work (I)

 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 (II)

Collect Data Evolve models using
Evolutionary
“reality runs (RR)” results as targets
Expensive, noisy, Design for the models themselves
Stochastic, etc

Evolve parameters to
approximate target
behaviour of desired system
Physical, Chemical, Biological
Model
System Abstracted into
a model, e.g.,
ODE, NN, “cook book”,
etc Evolutionary
Design

Try best estimates from model parameters


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

and self-organising nanostructured systems

CHELLNet
http://www.chellnet.org

Acknowledgements
 My colleagues in Physics, specially Prof.
P. Moriarty
 EPSRC, BBSRC for funding

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

 Any questions?

Evolutionary Algorithms and Self-Organised Systems

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