Post on 13-Jan-2016
Introduction to Evolutionary AlgorithmsSession 4
Jim Smith
University of the West of England, UK
May/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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Demo2: Es for moving targets
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
15)3(2
yx
Tree based representation
(x true) (( x y ) (z (x y)))
Tree based representation
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
Most common mutation: replace randomly chosen subtree by randomly generated tree
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
Child 2
Parent 1 Parent 2
Child 1
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: