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What is Neutral?

What is Neutral?

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What is Neutral?

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  1. What is Neutral? Neutral Changes and Resiliency Terence Soule Department of Computer Science University of Idaho

  2. The experiments • Gene/exon selection • Introns and exon selection • Effects of operators

  3. + + 1.0 0.5 1.0 Experiment 1 • Tree based, generational GP • Functions {+} • Terminals/Genes {0.5, 1.0} • Fitness: difference from 10 Both terminals are exons. Is one selected?

  4. Gene/Exon Choice

  5. Average Fitness Average fitness improves – after crossover.

  6. Resiliency • A measure of expected fitness change as a function of genotype change. • Resilient individuals are less likely to change fitness or have a smaller average fitness change in response to genotype changes (crossover and mutation). • Similar to the idea of effective fitness, but more general.

  7. Experiment 2 • Tree based, generational GP • Functions {+} • Terminals/Genes {0, 1, 4} • Fitness: difference from 40 Now there are two exons and an intron. What is selected?

  8. 180 160 140 120 100 0s Number of 80 1s 60 4s 40 20 0 0 500 1000 1500 2000 Generation Number of Genes

  9. 1 0 -1 -2 -3 Fitness Change -4 Mutation -5 Crossover -6 0 250 500 750 Resiliency

  10. Ratio of 1s to 4s

  11. Results – Experiment 2 • Changes don’t affect current fitness – Are they Neutral? • Changes affect expected fitness of the next generation – increase (average) resiliency

  12. Experiment 3 • Variable length, linear encoding, generational • Genes {0, 1, 4} • Sample individual: 010041014 • Fitness: difference of sum of genes from 54

  13. 00 01011 04 440 104 0401 00 104 04 440 01011 0401 Experiment 3 - Crossover • Proportional crossover – select two random points per parent. • Constant crossover – length of crossed region is: 2 50% of the time 4 25% of the time 8 12.5% of the time …

  14. Genes – Constant Crossover

  15. Genes – Proportional Crossover

  16. Mutation – Constant Crossover • Probability P of changing a gene to another value: 1 to 0, etc. • More genes (including 0s) greater chance of mutations.

  17. Growth – constant crossover

  18. Conclusions • Many ‘neutral’ changes can be explained in terms of resiliency • 1.0  two 0.5s (selecting exons) • 4s  four 1s and four 1s  one 4s • Increasing 0s (increasing introns) • Operator choice significantly affects these changes • Proportional versus constant crossover • Mutations • Per node versus per individual rates are significant.

  19. Discussion • Types of changes • 1st order – affect fitness • 2nd order – affect expected fitness of offspring (resiliency) • 3rd order? - affect expected fitness of Nth generation? Affect ability to respond to ‘environmental’ changes? • Any consistent pattern of change has an evolutionary explanation(?) • It’s possible to predict some changes by using the idea of resiliency. • Do these changes affect search?

  20. Thank YouQuestions?

  21. Bibliography • “Exons and Code Growth in GP” Genetic Programming 5th European Conference, EuroGP-2002, Springer LNCS2278, 2002 . • “Solution Stability in Evolutionary Computation” Proceedings of the 17th International Symposium on Computer and Information Sciences, CRC Press, 2002. • “Operator Choice and the Evolution of Robust Solutions” Genetic Programming Theory and Practice, Kluwer, 2003.