Introduction to Evolutionary Algorithms Session 4

1. Introduction to Evolutionary AlgorithmsSession 4 Jim Smith University of the West of England, UK May/June 2012

2. Overview • Example of learning models from data • Continuous Representations • Tree-based Representations • Practical session with Genetic Programming

3. 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)

4. Floating point mutations • 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].

5. 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

6. Demo2: Es for moving targets

7. Tree based representation • Trees are a universal form, e.g. consider • Arithmetic formula • Logical formula • Program (x  true)  (( x  y )  (z  (x  y))) i =1; while (i < 20) { i = i +1 }

8. Tree based representation

9. Tree based representation (x  true)  (( x  y )  (z  (x  y)))

10. Tree based representation i =1; while (i < 20) { i = i +1 }

11. 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

12. Mutation • Most common mutation: replace randomly chosen subtree by randomly generated tree

13. 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

14. 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

15. Parent 1 Parent 2 Child 1 Child 2

16. 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

17. Summary • 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

18. Practical Activity: • 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, …