An Evolutionary Algorithm Approach
            to Guiding the Evolution of
     Self-Organised Nanostructured Systems
    ...
Overview
                                             •    Motivation


                                             •    ...
     This work was done in collaboration with Prof. P.
          Moriarty and his group at the School of Physics and
    ...
Motivation
           - Automated design and optimisation of complex
           systems’ target behaviour
                ...
Major advances in the rational/analytical design of large and
 complex systems have been reported in the literature and mo...
Major advances in the rational/analytical design of large and
 complex systems have been reported in the literature and mo...
Major advances in the rational/analytical design of large and
 complex systems have been reported in the literature and mo...
Major advances in the rational/analytical design of large and
 complex systems have been reported in the literature and mo...
Automated Design/Optimisation is not only good because it can
     solve larger problems but also because this approach gi...
The research challenge :

               For the Engineer, Chemist, Physicist, Biologist :

                      To com...
Towards “Dial a Pattern” in Complex Systems




www.cs.nott.ac.uk/~nxk
Faculty of Mathematics and Physics
Charles Universi...
Towards “Dial a Pattern” in Complex Systems




                                            es
                           ...
Methodological Overview

   Dial a Pattern requires:

              Parameter Learning/Evolution Technology

           ...
Initial Attempts at a “Dial a Pattern” Methodology

                              behaviour        CA-based / Real
       ...
Parameter Learning/Evolution Technology Example
     - Self-organising processes
     - Modelled using cellular automata, ...
CA continuous                      Turbulence      Gas Lattice




www.cs.nott.ac.uk/~nxk
Faculty of Mathematics and Physi...
CA continuous                                      Turbulence                   Gas Lattice




                          ...
Structural Learning/Evolution Technology Example
     Wang Tiles Models
                                              Temp...
Structural Learning/Evolution Technology Example
     Wang Tiles Models




                                              ...
www.cs.nott.ac.uk/~nxk
Faculty of Mathematics and Physics
Charles University - December 2008   14 /59
Parameter Learning/Evolution Technology Example




                          lecA-               PAO1            mvaT-


...
Parameter Learning/Evolution Technology Example




                          lecA-               PAO1                 mva...
How Do We Program These Complex
  Systems?
                                                 behaviour         Complex Syst...
The Universal Similarity Metric (USM)

          - Is the USM a good objective function for evolving target spacio-tempora...
Data set
          For each CA system:
          • Keep all but one parameter the same
          • Produce 10 behaviour pa...
Produced by   MODEL(p1,p2,…,pn)




                                              p1         p2          pn




www.cs.not...
Clustering
  • does the USM detect similarity of phenotype with a target pattern?
         • if yes, it should be able to ...
www.cs.nott.ac.uk/~nxk
Faculty of Mathematics and Physics
Charles University - December 2008   21 /59
www.cs.nott.ac.uk/~nxk
Faculty of Mathematics and Physics
Charles University - December 2008   22 /59
Fitness Distance Correlation
          • correlation analyses of a given fitness function versus parametric
          (gen...
www.cs.nott.ac.uk/~nxk
Faculty of Mathematics and Physics
Charles University - December 2008   24 /59
The Evolutionary Engine
                                                  “we will implement an object-oriented, platform-...
Results on CAs

                                                Target   Designoid




                             e5



...
Target                       Designoid




                   Target              usm(F,T)      e(i)      e(c)           e...
Self-Organised Nanostructured Systems
   Thiol-passivated Au nanoparticles



                                            ...
Au nanoparticles: Morphology




                                 AFM images taken by Matthew O. Blunt, Nottingham

www.cs...
Nanoparticle Simulations

                                              Solvent is represented as a two-
                 ...
Nanoparticle Simulations


     •     The simulation proceeds by the Metropolis algorithm:
             –    Each solvent ...
Nanoparticle Simulations




www.cs.nott.ac.uk/~nxk
Faculty of Mathematics and Physics
Charles University - December 2008 ...
Nanoparticle Simulations




www.cs.nott.ac.uk/~nxk
Faculty of Mathematics and Physics
Charles University - December 2008 ...
Nanoparticle Simulations




www.cs.nott.ac.uk/~nxk
Faculty of Mathematics and Physics
Charles University - December 2008 ...
Nanoparticle Simulations




www.cs.nott.ac.uk/~nxk
Faculty of Mathematics and Physics
Charles University - December 2008 ...
Nanoparticle Simulations




www.cs.nott.ac.uk/~nxk
Faculty of Mathematics and Physics
Charles University - December 2008 ...
Nanoparticle Simulations




www.cs.nott.ac.uk/~nxk
Faculty of Mathematics and Physics
Charles University - December 2008 ...
A brief overview of Genetic Algorithms

  Motivation
        - optimisation problems                                      ...
The Universal Similarity Metric (USM)
          is a measure of similarity between two given objects in terms of
         ...
A brief overview of Genetic Algorithms

     Evolution
     - Recombination (mating)
       e.g. exchanging parameters
   ...
A brief overview of Genetic Algorithms

     Evolution
     - Recombination (mating)
       e.g. exchanging parameters
   ...
A brief overview of Genetic Algorithms

     Evolution
     - Recombination (mating)
       e.g. exchanging parameters
   ...
A brief overview of Genetic Algorithms

     Evolution
     - Recombination (mating)
       e.g. exchanging parameters
   ...
A brief overview of Genetic Algorithms

     Evolution
     - Recombination (mating)
       e.g. exchanging parameters
   ...
A brief overview of Genetic Algorithms

     Evolution
     - Recombination (mating)
       e.g. exchanging parameters
   ...
A brief overview of Genetic Algorithms

     Evolution
     - Recombination (mating)
       e.g. exchanging parameters
   ...
A brief overview of Genetic Algorithms

     Evolution
     - Recombination (mating)
       e.g. exchanging parameters
   ...
A brief overview of Genetic Algorithms

     Evolution
     - Recombination (mating)
       e.g. exchanging parameters
   ...
Evolving towards a target pattern (simulated)

      • Selected a target image from simulated data set
      • Initialised...
Evolving towards a target pattern (simulated)

                                                                      Evolv...
Evolving towards a target pattern (experimental)
                                                         Evolving to a ex...
     Using only the same fitness function as for
            the CAs was not sufficient for matching
            simulati...
Self-organising nanostructures
  Minkowski Functionals




www.cs.nott.ac.uk/~nxk
Faculty of Mathematics and Physics
Charl...
Self-organising nanostructures
  Evolved design: Minkowski functionals




www.cs.nott.ac.uk/~nxk
Faculty of Mathematics a...
Self-organising nanostructures
  Evolved design: Minkowski functionals
  Robustness checking




www.cs.nott.ac.uk/~nxk
Fa...
Self-organising nanostructures
  Evolved design: Minkowski functionals Robustness checking: i) Clustering




www.cs.nott....
Self-organising nanostructures
  Evolved design: Minkowski functionals
  Robustness checking: ii) Fitness Distance Correla...
Self-organising nanostructures
  Evolved design: Minkowski functionals
  Robustness checking: ii) Fitness Distance Correla...
Self-organising nanostructures
  Evolved design: Minkowski functionals
  Robustness checking: ii) Fitness Distance Correla...
Self-organising nanostructures
  Experimental target set
           Cell                               Island           La...
Self-organising nanostructures
  Experimental target set
           Cell                               Island           La...
Self-organising nanostructures
  Experimental target set
           Cell                               Island           La...
Self-organising
  nanostructures
  Experimental target
  set: Results

  P.Siepmann, C.P. Martin,
  I. Vancea, P.J. Moriar...
Conclusions
    • We can evolve target simulated behaviour using a GA with
    the USM but the USM is not enough
    •For ...
Future Work (I)

             use of more problem-specific fitness functions
              open ended (multiobjective) e...
Future Work (II)

                                              Collect Data                                 Evolve models...
Applications (in design and manufacture) and further work
   - Many, many systems can be modelled using CAs/Monte Carlos
 ...
Acknowledgements
       My colleagues in Physics, specially Prof.
        P. Moriarty
       EPSRC, BBSRC for funding


...
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Evolutionary Algorithms and Self-Organised Systems

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This talk presents the results from one of our papers on the use of an evolutionary algorithm for an "inverse problem" on self-organised nano particles.

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Evolutionary Algorithms and Self-Organised Systems

  1. 1. 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
  2. 2. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 2 /59
  3. 3.  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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 3 /59
  4. 4. 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 www.cs.nott.ac.uk/~nxk ACDM 2006 Faculty of Mathematics and Physics 25th April 2006 Charles University - December 2008 4 /59
  5. 5. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 5 /59
  6. 6. 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 This has happened before in other modern AI and Optimisation tools have been introduced. research and industrial disciplines,e.g: It is unrealistic to expect every large & complex physical, chemical •VLSI design or biological system to be amenable to hand-made fully analytical •Space antennae design designs/optimisations. •Transport Network design/optimisation •Personnel Rostering •Scheduling and timetabling 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 5 /59
  7. 7. Major advances in the rational/analytical design of large and complex systems have been reported in the literature and more with That is, complex systems are plagued NP-Hardness, non-approximability, recently the automated design and optimisation of these systems by modern AI and Optimisation toolsuncertainty, undecidability, etc results This has happened before in other have been introduced. research and industrial disciplines,e.g: It is unrealistic to expect every large & complex physical, chemical •VLSI design or biological system to be amenable to hand-made fully analytical •Space antennae design designs/optimisations. •Transport Network design/optimisation •Personnel Rostering •Scheduling and timetabling 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 5 /59
  8. 8. Major advances in the rational/analytical design of large and complex systems have been reported in the literature and more with That is, complex systems are plagued NP-Hardness, non-approximability, recently the automated design and optimisation of these systems by modern AI and Optimisation toolsuncertainty, undecidability, etc results This has happened before in other have been introduced. research and industrial disciplines,e.g: It is unrealistic to expect every large & complex physical, chemical •VLSI design or biological system to be amenable to hand-made fully analytical •Space antennae design designs/optimisations. •Transport Network design/optimisation •Personnel Rostering Yet, they are routinely solved by •Scheduling and timetabling We anticipate that as the number of research challenges and design sophisticated optimisation and techniques, like evolutionary applications in these domains (and their complexity) increase we algorithms, machine learning, etc will need to rely even more on automated design and optimisation based on sophisticated AI & machine learning www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 5 /59
  9. 9. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 6 /59
  10. 10. 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. www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 7 /59
  11. 11. Towards “Dial a Pattern” in Complex Systems www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 8 /59
  12. 12. Towards “Dial a Pattern” in Complex Systems es ctur Stru ical .S Lex C r ete 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) www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 8 /59
  13. 13. Methodological Overview Dial a Pattern requires:  Parameter Learning/Evolution Technology  Structural Learning/Evolution Technology  Integrated Parameter/Structural Learning/Evolution Tech. www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 9 /59
  14. 14. Initial Attempts at a “Dial a Pattern” Methodology behaviour CA-based / Real emergent vs target complex system Parameters/model Evolutionary algorithms www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 10 /59
  15. 15. 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. www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 11 /59
  16. 16. CA continuous Turbulence Gas Lattice www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 12 /59 Gas Lattice
  17. 17. 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 …….. www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 12 /59 Gas Lattice
  18. 18. Structural Learning/Evolution Technology Example Wang Tiles Models Temperature T Glue Strength Matrix www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 13 /59
  19. 19. Structural Learning/Evolution Technology Example Wang Tiles Models en iv G Temperature T Glue Strength Matrix d ve ol Ev www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 13 /59
  20. 20. www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 14 /59
  21. 21. Parameter Learning/Evolution Technology Example lecA- PAO1 mvaT- Env. Params www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 15 /59
  22. 22. Parameter Learning/Evolution Technology Example lecA- PAO1 mvaT- d d ve ve ol ol Ev Ev Env. Params www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 15 /59
  23. 23. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 16 /59
  24. 24. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 17 /59
  25. 25. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 18 /59
  26. 26. Produced by MODEL(p1,p2,…,pn) p1 p2 pn www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 19 /59
  27. 27. 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 Fitness Distance Correlation GENOTYPE PHENOTYPE FITNESS 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 20 /59
  28. 28. www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 21 /59
  29. 29. www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 22 /59
  30. 30. Fitness Distance Correlation • 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 GENOTYPE PHENOTYPE FITNESS CA model USM Target Clustering 1 2 3 distance = 2 Fitness = USM (T,D) Designoid 1 4 3 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 23 /59
  31. 31. www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 24 /59
  32. 32. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 25 /59
  33. 33. Results on CAs Target Designoid e5 f3 . www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 26 /59
  34. 34. 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 Faculty of Mathematics and Physics Charles University - December 2008 27 /59
  35. 35. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 28 /59
  36. 36. Au nanoparticles: Morphology AFM images taken by Matthew O. Blunt, Nottingham www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 29 /59
  37. 37. 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/ www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 30 /59
  38. 38. Nanoparticle Simulations • 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: www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 31 /59
  39. 39. Nanoparticle Simulations www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 32 /59
  40. 40. Nanoparticle Simulations www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 32 /59
  41. 41. Nanoparticle Simulations www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 33 /59
  42. 42. Nanoparticle Simulations www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 33 /59
  43. 43. Nanoparticle Simulations www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 34 /59
  44. 44. Nanoparticle Simulations www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 34 /59
  45. 45. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 35 /59
  46. 46. 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) www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 36 /59
  47. 47. A brief overview of Genetic Algorithms 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 37 /59
  48. 48. A brief overview of Genetic Algorithms 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 1 TIME www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 38 /59
  49. 49. A brief overview of Genetic Algorithms 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 1 TIME www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 38 /59
  50. 50. A brief overview of Genetic Algorithms 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 2 TIME www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 39 /59
  51. 51. A brief overview of Genetic Algorithms 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 2 TIME www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 39 /59
  52. 52. A brief overview of Genetic Algorithms 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 3 TIME www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 40 /59
  53. 53. A brief overview of Genetic Algorithms 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 3 TIME www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 40 /59
  54. 54. A brief overview of Genetic Algorithms 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 TIME www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 41 /59
  55. 55. A brief overview of Genetic Algorithms 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 converges to optimum solution FITNESS TIME www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 41 /59
  56. 56. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 42 /59
  57. 57. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 43 /59
  58. 58. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 44 /59
  59. 59.  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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 45 /59
  60. 60. Self-organising nanostructures Minkowski Functionals www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 46 /59
  61. 61. Self-organising nanostructures Evolved design: Minkowski functionals www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 47 /59
  62. 62. Self-organising nanostructures Evolved design: Minkowski functionals Robustness checking www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 48 /59
  63. 63. Self-organising nanostructures Evolved design: Minkowski functionals Robustness checking: i) Clustering www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 49 /59
  64. 64. Self-organising nanostructures Evolved design: Minkowski functionals Robustness checking: ii) Fitness Distance Correlation 1/Fitness www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 50 /59
  65. 65. Self-organising nanostructures Evolved design: Minkowski functionals Robustness checking: ii) Fitness Distance Correlation 1/Fitness www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 51 /59
  66. 66. Self-organising nanostructures Evolved design: Minkowski functionals Robustness checking: ii) Fitness Distance Correlation 1/Fitness www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 52 /59
  67. 67. Self-organising nanostructures Experimental target set Cell Island Labyrinth Worm Evolved set www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 53 /59
  68. 68. Self-organising nanostructures Experimental target set Cell Island Labyrinth Worm Evolved set www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 53 /59
  69. 69. Self-organising nanostructures Experimental target set Cell Island Labyrinth Worm Evolved set www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 53 /59
  70. 70. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 54 /59
  71. 71. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 55 /59
  72. 72. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 56 /59
  73. 73. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 57 /59
  74. 74. 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 www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 58 /59
  75. 75. Acknowledgements  My colleagues in Physics, specially Prof. P. Moriarty  EPSRC, BBSRC for funding  Thanks To Prof. R. Bartak for inviting me here!  Any questions? www.cs.nott.ac.uk/~nxk Faculty of Mathematics and Physics Charles University - December 2008 59 /59

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