Genetic algorithms for neural networks

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Genetic algorithms for neural networks

• An introduction

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Genetic algorithms

• Why use genetic algorithms?
• What arent genetic algorithms?
• What are genetic algorithms?
• What to avoid
• Using genetic algorithms with neural networks

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Why use genetic algorithms?
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What arent genetic algorithms?

• Hill-climbing algorithms
• Enumerative algorithms
• Random searches
• Guesses
• Ask an expert
• Educated guesses

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Hill-climbing

• Calculus based approach

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But
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But
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More realistically?
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• Noisy?
• Discontinuous?

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Robust scheme
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Genetic algorithms

• Cope with non-linear functions
• Cope with large numbers of variables efficiently
• Cope with modelling uncertainties
• Do not require knowledge of the function

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What are genetic algorithms?
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Circle of life
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Chromosome

• A collection of genes
• xi1, xi2, xi3, xi4,

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Fitness

• Ranked by a fitness factor
• Proportional to the likelihood of breeding
• Action of the algorithm is to maximise fitness

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Breeding and crossover

• Parents selected randomly with a probability
  proportional to fitness
• Roulette wheel algorithm
• Genes are crossed over between parents
• x11, x12, x13, x14
• x21, x22, x23, x24

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Mutation

• Small (random) variation in a gene
• xi1, xi2, xi3, xi4 --gt xi1, xi2, xi3?, xi4

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Circle of life
Good
Bad
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Genetic algorithms

• Work on populations, not single points
• Use an objective function (fitness) only, rather
  than derivatives or other information
• Use probabilistic rules rather than deterministic
  rules
• Operate on an encoded set of values (a
  chromosome) rather than the values themselves

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Potential problems

• GA deceptive functions
• Premature and postmature convergence
• Excessive mutation
• Application to constrained problems
• Neural networks, particularly
• The meaning of fitness

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Deceptive functions and premature convergence

• A function which selects for one gene when a
  combination would be better
• Can eliminate better genes
• Avoided by
• Elitism
• Multiple populations
• Mutation (which reintroduces genes)
• Fitness scaling

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Postmature convergence

• When all of a population performs well, selection
  pressures wane
• Avoided by fitness scaling (be careful!)

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Excessive mutation

• Too little mutation loss of genes
• Too much mutation random walk

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Application to constrained problems

• Neural networks and genetic algorithms are by
  nature unconstrained
• i.e they can take any value
• Must avoid unphysical values
• Restrict mutation
• Punish through fitness function

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The meaning of fitness

• Genetic algorithms maximise fitness
• Therefore fitness must be carefully defined
• What are you actually trying to do?

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When to stop?

• How long do we run the algorithm for?
• Until we find a solution
• Until a fixed number of generations has been
  produced
• Until there is no further improvement
• Until we run out of time or money?

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Genetic algorithms for Bayesian neural networks

• Generally want to find an optimised input set for
  a particular defined output

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Define fitness

• Need a function that includes target and
  uncertainty

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Define the chromosome

• Set of inputs to the network except
• Derived inputs must be removed
• e.g. if you have both t and ln(t), or T and
  exp(-1/T), only one can be included
• Prevents unphysical input sets being found

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Create the populations

• Chromosomes are randomly generated
• (avoid non-physical values)
• Population size must be considered
• 20 is a good start
• Best to use more than one population
• Trade-off between coverage and time
• Three is good

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Run the algorithm!

• Decode chromosomes to NN inputs (i.e. calculate
  any other inputs)
• Make predictions for each chromosome
• if the target is met or enough generations have
  happened, stop
• Calculate fitness for each chromosome
• Preserve the best chromosome (elitism)
• Breed 18 new chromosomes by crossbreeding
• Mutate one (non-elite) gene at random
• Create new chromosome at random
• Go back to 1