1. Contribution of second order evolution to evolutionary algorithms Virginie LEFORT July 11 th

2. 2 My motivation BiologyComputer Science Second order evolutionEvolutionary algorithms

3. 3 Genotype Phenotype Evolution : general principles Heredity Variation Selection

4. 4 From genotype to phenotype Genotype Proteome Phenotype DNA polymerase Exonuclease SOS System Transposase Pigmentation Mutation

5. 5 Second order evolution Evolutionary processes can vary further to mutations Theses modifications don’t have an impact on the phenotype… … but on the reproduction process fidelity « Evolution of the evolutionary processes by the evolution »

6. 6 Study of offspring

7. 7 Second order evolution influence Variation of mutation rates Variation of mutation effects

8. 8 Indirect selection

9. 9 Second order evolution Second order evolution is theoretically possible because: –Variability and robustness can vary –These variations are hereditary… –… and can be selected In biology, second order evolution allows the increase of neutrality and evolvability –What may be the contributions for evolutionary algorithms?

10. 10 Overview of evolutionary algorithms Genotype Phenotype Reproduction with variations Selection Offspring Survival Adults Parents

11. 11 Example of simple EA Goal: wash my dishes Individuals representation: Genotype: 1 – 2.5 Phenotype: the water Initial population (random)EvaluationParents choice Offspring 0 – 2 3.5– 4.5 3.5– 2.5 1 – 5 2.5– 3 3875838758 3.5 – 4.5 3.5 – 2.5 2.5 – 3 3.5 – 4.5 2.5 – 4.5 3.5 – 3 2.5 – 2.5 2.5 – 3.5 + +

12. 12 Components of EA Goal RepresentationOperators Operators effects must fit the representation Representation must allow the expression of the optimum Mutation rates must fit the search space Second order evolution?

13. 13 Contribution of 2 nd order evolution Second order evolution can dynamically fit the 3 components of an EA to increase evolvability. It can be inserted in a EA by: –Dynamic mutation rates –Dynamic operators –Dynamic representation

14. 14 Modifications of the representation Gene 2Gene 1Gene 3Gene 4 Non coding sequences Gene 2Gene 1Gene 3Gene 4 Variable order of genes Gene 2Gene 1Gene 3Gene 4Gene 2Gene 1Gene 3Gene 4 = Variable number of genes Gene 2Gene 1Gene 3Gene 4Gene 2Gene 1Gene 5 =

15. 15 Our model RBF-Gene: principles Genotype Proteome Phenotype

16. 16 Application: regression Goal Genotype Phenotype Proteome Σ Genotype Phenotype Proteome Σ Genotype Phenotype Proteome Σ

17. 17 Genotype-phenotype mapping Genetic code 1σH 0σG 1μF 0μE 1wD 0wC StopB StartA ValueParamterBase G1G2G3G4 FE…BEFDGGCDFGHEGA…D w : 101= 101 2 μ :1100= 0110 2 σ :10000= 00010 2 Protein G 1

18. 18 Generational loop Reproduction with variation Selection Offspring Survival Adults Parents Local Global Crossover

19. 19 Example: RBF-Gene in action 200 bases472 bases

20. 20 Impacts of 2 nd order evolution Final size of the genome: –doesn’t depend on initial size –but do depend on the local mutation rates

21. 21 Study of offspring Comparison of offspring distribution for the best individuals: –After evolution –With or without modifications of the genetic structure

22. 22 Non coding sequences Non coding sequences size: –Has an impact on evolvability –Is optimal after evolution

23. 23 Genes order Comparison of offspring: –With or without modification of the genes order –With or without crossover Without crossover, no influence on evolvability With crossover, – a random genes order decreases evolvability – the final order is a consensus between the individuals of the population

24. 24 Evolution of evolvability

25. 25 Conclusion Second order evolution –Is a biological fact –Increases the evolvability –Can have an interest for an evolutionary algorithm. Our model, RBF-Gene –Allows second order evolution –Shows that this evolution occurs In the size of non coding sequences In the order of the genes –Leads to an increase of the evolvability