1. Genetic algorithms for neural networks An introduction

2. Genetic algorithms Why use genetic algorithms? –“What aren’t genetic algorithms?” What are genetic algorithms? What to avoid Using genetic algorithms with neural networks

3. Why use genetic algorithms?

4. What aren’t genetic algorithms? Hill-climbing algorithms Enumerative algorithms Random searches –Guesses –Ask an expert Educated guesses

5. Hill-climbing Calculus based approach

6. But… ? ?

7. ? ? ? ? ? ?

8. More realistically? ? ? ? ? ? ? ? ? ? ? ? ? Noisy? Discontinuous?

9. Robust scheme

10. 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

11. What are genetic algorithms? Chromosome Population

12. Circle of life Good Bad

13. Chromosome A collection of genes [x i1, x i2, x i3, x i4, …]

14. Fitness Ranked by a fitness factor Proportional to the likelihood of breeding Action of the algorithm is to maximise fitness

15. Breeding and crossover Parents selected randomly with a probability proportional to fitness –Roulette wheel algorithm Genes are crossed over between parents [x 11, x 12, x 13, x 14 ] [x 21, x 22, x 23, x 24 ] [x 11, x 22, x 23, x 24 ] [x 21, x 12, x 13, x 14 ]

16. Mutation Small (random) variation in a gene: [x i1, x i2, x i3, x i4 ] --> [x i1, x i2, x i3 +∂, x i4 ]

17. Circle of life Good Bad

18. 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

19. Potential problems GA deceptive functions Premature and postmature convergence Excessive mutation Application to constrained problems –Neural networks, particularly The meaning of fitness

20. Deceptive functions and premature convergence A function which selects for one gene when a combination would be better Can eliminate “better” genes Avoided by –Elitism –Multiple populations –Mutation (which reintroduces genes) –Fitness scaling

21. Postmature convergence When all of a population performs well, selection pressures wane Avoided by fitness scaling (be careful!)

22. Excessive mutation Too little mutation = loss of genes Too much mutation = random walk

23. 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

24. The meaning of fitness Genetic algorithms maximise fitness Therefore fitness must be carefully defined What are you actually trying to do?

25. 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…?

26. Genetic algorithms for Bayesian neural networks Generally want to find an optimised input set for a particular defined output

27. Define “fitness” Need a function that includes target and uncertainty:

28. 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

29. 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

30. Run the algorithm! 1.Decode chromosomes to NN inputs (i.e. calculate any other inputs) 2.Make predictions for each chromosome if the target is met or enough generations have happened, stop 3.Calculate fitness for each chromosome 4.Preserve the best chromosome (elitism) 5.Breed 18 new chromosomes by crossbreeding 6.Mutate one (non-elite) gene at random 7.Create new chromosome at random 8.Go back to 1