Download Genetic algorithms for neural networks

Genetic algorithms for neural
networks
An introduction
Genetic algorithms
• Why use genetic algorithms?
– “What aren’t genetic algorithms?”
• What are genetic algorithms?
• What to avoid
• Using genetic algorithms with neural
networks
Why use genetic algorithms?
What aren’t genetic algorithms?
• Hill-climbing algorithms
• Enumerative algorithms
• Random searches
– Guesses
– Ask an expert
• Educated guesses
Hill-climbing
• Calculus based approach
But…
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But…
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More realistically?
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•Noisy?
•Discontinuous?
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Robust scheme
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
What are genetic algorithms?
Chromosome
Population
Circle of life
Good
Bad
Chromosome
• A collection of genes
[xi1, xi2, xi3, xi4, …]
Fitness
• Ranked by a fitness factor
• Proportional to the likelihood of breeding
• Action of the algorithm is to maximise
fitness
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]
[x11, x22, x23, x24]
[x21, x22, x23, x24]
[x21, x12, x13, x14]
Mutation
• Small (random) variation in a gene:
[xi1, xi2, xi3, xi4] --> [xi1, xi2, xi3+∂, xi4]
Circle of life
Good
Bad
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
Potential problems
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GA deceptive functions
Premature and postmature convergence
Excessive mutation
Application to constrained problems
– Neural networks, particularly
• The meaning of fitness
Deceptive functions and
premature convergence
• A function which selects for one gene when
a combination would be better
• Can eliminate “better” genes
• Avoided by
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Elitism
Multiple populations
Mutation (which reintroduces genes)
Fitness scaling
Postmature convergence
• When all of a population performs well,
selection pressures wane
• Avoided by fitness scaling (be careful!)
Excessive mutation
• Too little mutation = loss of genes
• Too much mutation = random walk
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
The meaning of fitness
• Genetic algorithms maximise fitness
• Therefore fitness must be carefully defined
• What are you actually trying to do?
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…?
Genetic algorithms for Bayesian
neural networks
• Generally want to find an optimised input
set for a particular defined output
Define “fitness”
• Need a function that includes target and
uncertainty:
Fi 
1
i
    (t  f i )
2
i
2
y
2
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
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
Run the algorithm!
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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
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