introduction to evolutionary algorithms session 4
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Introduction to Evolutionary Algorithms Session 4. Jim Smith University of the West of England, UK May/June 2012. Overview. Example of learning models from data Continuous Representations Tree-based Representations Practical session with Genetic Programming. Real valued problems. - PowerPoint PPT PresentationTRANSCRIPT
Introduction to Evolutionary AlgorithmsSession 4
Jim SmithUniversity of the West of England, UKMay/June 2012
Example of learning models from data– Continuous Representations– Tree-based Representations
Practical session with Genetic Programming
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Overview
Real valued problems
Many problems occur as real valued problems, e.g. continuous parameter optimisation f : n
Illustration: Ackley’s function (often used in EC)
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Floating point mutations
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• Each gene is changed independently: x -> x’ by adding a random number• Simple Uniform mutation: x’ = Rand[LB,UB] .
• Analogous to bit-flipping or resetting , • loses all sense of locality, no exploitation
• Most common method to use a Gaussian distribution and then restrict to range [LB,UB].
Crossover operators for real valued GAs
Discrete:– each gene in offspring comes from one of its
parents with equal probability. Intermediate
– exploits idea of creating children “between” parents (hence a.k.a. arithmetic recombination)
– ith gene of offspring = parent1i + (1 - ) parent2i where : 0 1.
– The parameter can be:• constant: uniform arithmetical crossover• variable (e.g. depend on the age of the population) • picked at random every time
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Tree based representation
Trees are a universal form, e.g. consider Arithmetic formula
Logical formula
Program
15)3(2 yx
(x true) (( x y ) (z (x y)))
i =1;while (i < 20){
i = i +1}
Tree based representation
In GA, ES, EP chromosomes are linear structures (bit strings, integer string, real-valued vectors, permutations)
Tree shaped chromosomes are non-linear structures
In GA, ES, EP the size of the chromosomes is fixed
Trees in GP may vary in depth and width
Mutation cont’d
Mutation has two parameters:– Probability pm to choose mutation vs. recombination– Probability to chose an internal point as the root of
the subtree to be replaced Remarkably pm is advised to be 0 (Koza’92) or
very small, like 0.05 (Banzhaf et al. ’98) The size of the child can exceed the size of the
parent
Recombination
Most common recombination: exchange two randomly chosen subtrees among the parents
Recombination has two parameters:– Probability pc to choose recombination vs. mutation– Probability to chose an internal point within each
parent as crossover point The size of offspring can exceed that of the
parents
Initialisation
Maximum initial depth of trees Dmax is set Full method (each branch has depth = Dmax):
– nodes at depth d < Dmax randomly chosen from function set F– nodes at depth d = Dmax randomly chosen from terminal set T
Grow method (each branch has depth Dmax):– nodes at depth d < Dmax randomly chosen from F T– nodes at depth d = Dmax randomly chosen from T
Common GP initialisation: ramped half-and-half, where grow & full method each deliver half of initial population
EAsare widely used to search sets of possible:– Designs e.g. optimisation– Sequences e.g path finding, scheduling ,…– Models – e.g. data mining / machine learning
Much of their strength comes from lack of assumptions.
Lots of free implementations mean you can focus on:– representing your problem– Giving fitness to a solution
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Summary
www.bit.uwe.ac.uk/~jsmith/UNESPcourse/EC4.html Using EAs to build a model from data:
– Given a set of labelled data (experiences, stimulus-response, cause-effect,...) task is to find a model that maps inputs onto the right outputs
– learning to recognise things, characterising opponents, diagnostic support, ...
So we can then use it to for future data– Predicting weather, stock market, …– Classifying images, fraud, …
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Practical Activity: