Genetic Algorithms GAs Genetic Programming GP

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Genetic Algorithms (GAs)Genetic Programming (GP)

• Winter 2005

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Intro

• Genetic Algorithm
• Developed by John H. Holland mid-70s
• Evolutionary search algorithm
• Evolves bit-strings (1s and 0s)
• Genetic Programming
• Developed by John Koza early 90s
• Algorithm based on the GA
• Evolves program trees

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GA Chromosomes

• Usually bit-strings
• e.g. 1100101010
• Distinct mapping between genotype and phenotype
• e.g. 1100101010 blue eyes

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Basic GA
population
crossover
1100101010 1011101110 0011011001 1100110001
1100101010 1011101110 1100101110 1011101010
selection
fitness evaluation
mutation
0011011001 0011001001
decoding
new population
1100101110 1011101010 0011001001
insert / replace
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GA Algorithm

• Generate initial population of n individuals
• P c1, , cn
• Evaluate all individuals to calculate fitness
  using a fitness function
• Repeat until termination criteria met
• Select individuals from P (mating pool)
• Apply genetic operators (crossover, mutation)
• Generate offspring population
• Evaluate offspring population

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Fitness

• Driving force in evolution
• Usually explicit fitness for GAs
• Can be calculated at any time with a function
• Calculated using a fitness (or objective)
  function
• Usually non-trivial to find a good fitness
  function

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Selection

• Most important part of the algorithm
• Selects the best individuals for
  mating/reproduction purposes
• Few common selection schemes
• Fitness-Proportional
• Roulette wheel
• Rank
• Tournament

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Roulette Wheel Selection

• Parents are selected according to their fitness.
  The better the chromosomes are, the more chances
  to be selected they have. Imagine a roulette
  wheel where all the chromosomes in the population
  are placed. The size of the section in the
  roulete wheel is proportional to the value of the
  fitness function of every chromosome - the bigger
  the value is, the larger the section is. See the
  following picture for an example.

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Ranking Selection

• Hides absolute fitness differences
• Reduces selection pressure under high fitness
  variance
• Maintains selection pressure under low fitness
  variance
• Cons
• Requires sorting of individuals

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Ranking Cont..
Rank selection ranks the population first and
then every chromosome receives fitness value
determined by this ranking. The worst will have
the fitness 1, the second worst 2 etc. and the
best will have fitness N (number of chromosomes
in population).
Before Using Rank Selection
After Using Rank Selection
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Tournament Selection

• In general tournament selection n individuals are
  selected at random and the fittest is selected.
  The most common type of tournament selection is
  binary tournament selection, where just two
  individuals are selected.

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Genetic Operators

• Crossover
• The most important operator in GAs
• Choose 1 (single-point crossover) or more
  crossover points and swap corresponding sections
  of 2 parents to form children
• Usually high probability 90
• Mutation
• Secondary genetic operator
• Most common is point mutation where a bit is
  flipped with a given probability (other types
  proposed)
• Usually low probability 5 per chrom

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Genetic Programming

• Program discovery with GA
• Works directly with programs (no genotype
  encoding) usually rooted-tree representation
• Chromosome Generation
• Internal nodes from Function Set
• Leaf nodes from Terminal Set

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GP Chromosomes

• Usually trees (i.e. parse trees)
• e.g. parse tree for LISP program
• ( (- 6 1) ( x ( 1 7)))

-
x
6
1

1
7
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Genetic Operators
Parents

• Crossover

A
B
Children
A
B
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Genetic Operators

• Mutation (point-mutation)
• Replace subtree at randomly chosen node with
  another subtree
• Other types proposed

Parent
Child
Mutation point
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Sufficiency and Closure

• Terminal/Function sets and genetic operators must
  guarantee sufficiency closure
• Sufficiency TF sets must be sufficient in order
  to compute a solution to the problem
• Closure every function in F must accept as
  argument any return value from any function and
  any terminal value

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• http//cs.felk.cvut.cz/xobitko/ga/