Basics of Genetic Algorithms and some possibilities

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Basics of Genetic Algorithmsand some
possibilities

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• Peter Spijker
• Technische Universiteit Eindhoven
• Department of Biomedical Engineering
• Division of Biomedical Imaging and Modeling
• California Institute of Technology
• Materials Process and Simulation Center
• Biochemistry Molecular Biophysics
• November 25, 2003

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Presentation Overview

• Purpose of presentation
• General introduction to Genetic Algorithms
  (GAs)
• Biological background
• Origin of species
• Natural selection
• Genetic Algorithm
• Search space
• Basic algorithm
• Coding
• Methods
• Examples
• Possibilities

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Purpose of presentation

• Optimising parameters of force fields is a
  difficult and time consuming task
• Use of optimising methods might be of use
• Methods
• steepest descent
• simulated annealing (Monte Carlo)
• genetic algorithms
• Brief introduction to genetic algorithms in
  lecture style

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General Introduction to GAs

• Genetic algorithms (GAs) are a technique to
  solve problems which need optimization
• GAs are a subclass of Evolutionary Computing
• GAs are based on Darwins theory of
  evolution
• History of GAs
• Evolutionary computing evolved in the 1960s.
• GAs were created by John Holland in the
  mid-70s.

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Biological Background (1) The cell

• Every animal cell is a complex of many small
  factories working together
• The center of this all is the cell nucleus
• The nucleus contains the genetic information

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Biological Background (2) Chromosomes

• Genetic information is stored in the chromosomes
• Each chromosome is build of DNA
• Chromosomes in humans form pairs
• There are 23 pairs
• The chromosome is divided in parts genes
• Genes code for properties
• The posibilities of the genes for one
  property is called allele
• Every gene has an unique position on the
  chromosome locus

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Biological Background (3) Genetics

• The entire combination of genes is called
  genotype
• A genotype develops to a phenotype
• Alleles can be either dominant or recessive
• Dominant alleles will always express from the
  genotype to the fenotype
• Recessive alleles can survive in the population
  for many generations, without being expressed.

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Biological Background (4) Reproduction

• Reproduction of genetical information
• Mitosis
• Meiosis
• Mitosis is copying the same genetic
  information to new offspring there is no
  exchange of information
• Mitosis is the normal way of growing of
  multicell structures, like organs.

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Biological Background (5) Reproduction

• Meiosis is the basis of sexual reproduction
• After meiotic division 2 gametes appear in
  the process
• In reproduction two gametes conjugate to a
  zygote wich will become the new individual
• Hence genetic information is shared between
  the parents in order to create new offspring

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Biological Background (6) Reproduction

• During reproduction errors occur
• Due to these errors genetic variation exists
• Most important errors are
• Recombination (cross-over)
• Mutation

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Biological Background (7) Natural selection

• The origin of species Preservation of
  favourable variations and rejection of
  unfavourable variations.
• There are more individuals born than can
  survive, so there is a continuous struggle for
  life.
• Individuals with an advantage have a greater
  chance for survive survival of the fittest.

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Biological Background (8) Natural selection

• Important aspects in natural selection are
• adaptation to the environment
• isolation of populations in different groups
  which cannot mutually mate
• If small changes in the genotypes of individuals
  are expressed easily, especially in small
  populations, we speak of genetic drift
• Mathematical expresses as fitness success in
  life

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Presentation Overview

• Purpose of presentation
• General introduction to Genetic Algorithms
  (GAs)
• Biological background
• Origin of species
• Natural selection
• Genetic Algorithm
• Search space
• Basic algorithm
• Coding
• Methods
• Examples
• Possibilities

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Genetic Algorithm (1) Search space

• Most often one is looking for the best
  solution in a specific subset of solutions
• This subset is called the search space (or state
  space)
• Every point in the search space is a possible
  solution
• Therefore every point has a fitness value,
  depending on the problem definition
• GAs are used to search the search space
  for the best solution, e.g. a minimum
• Difficulties are the local minima and the
  starting point of the search

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Genetic Algorithm (2) Basic algorithm

• Starting with a subset of n randomly chosen
  solutions from the search space (i.e.
  chromosomes). This is the population
• This population is used to produce a next
  generation of individuals by reproduction
• Individuals with a higher fitness have more
  chance to reproduce (i.e. natural selection)

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Genetic Algorithm (3) Basic algorithm

• Outline of the basic algorithm

0 START Create random population of n
chromosomes 1 FITNESS Evaluate fitness f(x) of
each chromosome in the population 2 NEW
POPULATION 0 SELECTION Based on f(x) 1
RECOMBINATION Cross-over chromosomes 2
MUTATION Mutate chromosomes 3
ACCEPTATION Reject or accept new one 3
REPLACE Replace old with new population the
new generation 4 TEST Test problem
criterium 5 LOOP Continue step 1 4 until
criterium is satisfied
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Genetic Algorithm (4) Coding

• Normal cells are diploid (containing 2 complete
  sets of chromosomes)
• On the contrary gametes are haploid
• Formalizing diploid reproduction is much more
  difficult than haploid
• Diploid populations have an extra dimension
  compared to haploid populations
• For simplicity therefore only haploid genetic
  algorithms

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Genetic Algorithm (5) Coding

• Chromosomes are encoded by bitstrings
• Every bitstring therefore is a solution but not
  necisseraly the best solution
• The way bitstrings can code differs from problem
  to problem
• Either sequence of on/off or the number 9

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Genetic Algorithm (6) Coding

• Recombination (cross-over) can when using
  bitstrings schematically be represented
• Using a specific cross-over point

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Genetic Algorithm (7) Coding

• Mutation prevents the algorithm to be trapped in
  a local minimum
• In the bitstring approach mutation is simpy the
  flipping of one of the bits

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Genetic Algorithm (8) Coding

• Both recombination and mutation depend a
  lot on the exact definition of the problem and
  the choice of representing the chromosomes
  (e.g. no bitstrings)
• Different encodings can be used
• Binary encoding
• Permutation encoding
• Value encoding
• Tree encoding
• Focus in this presentation stays with binary
  encoding

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Example Minimum of Function (1)

• First example shows how to find the minimum
  of a function

Minimum f(x) at x 809
1100101001
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Example Minimum of Function (2)
Mean fitness
Best fitness
Individual
Best individual
Generations
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Example Minimum of Function (3)

• Interactive show of this algorithm with Matlab
• Using the function genalg2()
• Variables
• Population size
• Bitstringlength
• Mutation chance
• Recombination chance
• Starting population adaption

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Genetic Algorithm (9) Remarks

• It is clear from the example that the
  convergence speed of the algorithm depends on
  many factors
• Population size
• Mutation probability
• Recombination probability
• Elitism
• Selection methods
• Random selection of parents
• Roulette wheel selection of parents
• Strong point GAs mutation prevents from
  falling in a local minimum, recombination
  initiates a fast first convergence

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Example Checkboard (1)

• We are given an n by n checkboard in which
  every field can have a different colour from
  a set of four colours.
• Goal is to achieve a checkboard in a way that
  there are no neighbours with the same colour
  (not diagonal)

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Example Checkboard (2)

• Chromosomes represent the way the
  checkboard is coloured.
• Chromosomes are not represented by bitstrings
  but by bitmatrices
• The bits in the bitmatrix can have one of the
  four values 0, 1, 2 or 3, depending on the
  colour
• Crossing-over involves matrix manipulation
  instead of point wise operating. Crossing-over
  can be combining the parential matrices in a
  horizontal, vertical, triangular or square way
• Mutation remains bitwise changing bits in either
  one of the other numbers

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Example Checkboard (3)

• Fitnesscurve for the checkboard example
• This problem can be seen as a graph with n nodes
  and (n-1) edges, so the fitness f(x) is easily
  defined as f(x) 2 (n-1) n

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Example Checkboard (4)

• Fitnesscurves for different cross-over rules

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Example Checkboard (5)

• Interactive show of this algorithm with Matlab
• Using the functions
• main()
• checkers()
• bestindividual()
• mutate()
• recombine()
• select()
• showbestindividual()

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Possibilities

• Using the genetic algorithm to optimise
  parameters for a force field
• Parameters are real numbers, so adaptations of
  these algorithms is required
• Value incoding vs. bitstring encoding
• Difficulties
• Definition fitness function
• Integration algorithm with software

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Further Questions
?