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)

3

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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6

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: