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Basics of Genetic Algorithms and some possibilities

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Origin of species. Natural selection. Genetic Algorithm. Search space. Basic algorithm ... GA's are based on Darwin's theory of evolution. History of GA's ... – PowerPoint PPT presentation

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Title: Basics of Genetic Algorithms and some possibilities


1
Basics of Genetic Algorithmsand some
possibilities

12
  • 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

2
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

3
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

4
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.

5
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

6
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

7
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.

8
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.

9
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

10
Biological Background (6) Reproduction
  • During reproduction errors occur
  • Due to these errors genetic variation exists
  • Most important errors are
  • Recombination (cross-over)
  • Mutation

11
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.

12
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

13
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

14
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

15
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)

16
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
17
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

18
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

19
Genetic Algorithm (6) Coding
  • Recombination (cross-over) can when using
    bitstrings schematically be represented
  • Using a specific cross-over point

20
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

21

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

22
Example Minimum of Function (1)
  • First example shows how to find the minimum
    of a function

Minimum f(x) at x 809
1100101001
23
Example Minimum of Function (2)
Mean fitness
Best fitness
Individual
Best individual
Generations
24
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

25
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

26
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)

27
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

28
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

29
Example Checkboard (4)
  • Fitnesscurves for different cross-over rules

30
Example Checkboard (5)
  • Interactive show of this algorithm with Matlab
  • Using the functions
  • main()
  • checkers()
  • bestindividual()
  • mutate()
  • recombine()
  • select()
  • showbestindividual()

31
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

32
Further Questions
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