Haploid-Diploid Evolutionary Algorithms

1. Haploid-Diploid Evolutionary Algorithms Larry Bull UWE

2. SEX A Social Interaction in Complex Intelligent Systems Larry Bull UWE

3. Evolutionary Computing F = f(A) F’ = f(A’)

4. Nature Hug et al. (2016) A new view of the tree of life. Nature Microbiology

5. Bacteria Conjugation :

6. Eukaryotes F’ ≠ F F = f(A+B)

7. Sex as Learning • Both genomes are active (any dominance aside). • The fitness of a diploid cell/organism is a combination of the fitness contributions of the composite haploid genomes. • With reversion to a haploid state in reproduction, there is potential for a significant mismatch between the utility of the haploid passed on compared to that of the diploid selected. • Individual haploid gametes do not contain all of the genetic material through which their fitness was determined.

8. Baldwin Effect • The existence of phenotypic plasticity which enables an organism to display a different (better) fitness than its genome directly represents. • Such learning can affect (improve) the evolutionary process by altering the shape of the underlying fitness landscape. • Haploid genome combination into a diploid can be seen as a simple form of phenotypic plasticity for the individual haploid genomes before they revert to a solitary state during reproduction.

9. Simple Example Haploid-Diploid Haploid 01-11 are always paired and the others pair homogeneously shown

10. Diploid EAs • Early examples - Bagley (1967), Rosenberg (1967) • In all but one known case, a dominance scheme is utilized to reduce the diploid down to a traditional haploid solution for evaluation, eg, • Evolutionary process also dissimilar to nature.

12. Simple Haploid-Diploid Algorithm

13. NK Model: Tuneable Landscapes 1 0 1 1 • - N binary traits per individual • - Each trait depends upon K others • - Position of dependent traits randomly assigned • Trait fitness contribution (own state + K ) randomly assigned • Fitness of genome normalised sum of contributions

14. Evolution • Population size 50, steady state, binary tournament selection, replace worst, N=50. • Mutation applied deterministically at 1/N, one-point crossover. • Results presented as average over ten random populations on each of ten NK models, ie, 100 runs. • Fitness is average of two constituent genomes. • Haploid EA run for twice as many generations as diploid.

15. NK Results

16. Random Boolean Networks 1 means active/expressed 0 means inactive/unexpressed 1 0 1 1 Rgenes (R=4) Bconnections (B=2) Each gene considers Bconnections as inputs from other genes to an assigned Boolean function, transiting to the output state per discrete update cycle. B1B2St+1 0 0 0 0 1 1 1 0 1 1 1 0

17. RBNK Model K trait connections N trait nodes 1 3 5 B regulatory connections 2 4 6 An R=6, B=2, N=2, K=1 network

18. Fitness • RBN fitness ascertained by updating each node for 50 cycles from a random set of node start states. • After update cycles, the value of each of the N trait nodes is used to calculate fitness on the given NK landscape. • Final fitness is average from ten random start states for 50 updates.

19. Evolution • Population size 50, steady state, binary tournament selection, replace worst, N=50 • RBN represented as integer list - each node’s function and connections (R=100). • Mutation applied deterministically at 1/R and can therefore either (with equal probability): • alter the Boolean function of a randomly chosen node • alter a randomly chosen B connection • Results presented as average over ten random populations on each of ten RBNK models, each started 10 times, ie, 1000 runs. • Haploid EA run for twice as many generations as diploid.

20. RBNK Results

21. Findings • Whether evolving a binary string or a string of integers, HD-EA outperforms H-EA for >K. • As K increases, the number of peaks and the steepness of their sides increases. • The HD-EA is therefore seemingly better able to search more complex fitness landscapes. • It is well-established that the Baldwin effect improves performance as fitness landscape ruggedness increases.

22. A Note on Recombination • In the haploid case, variation operators generate a new genome at a point in the fitness landscape. • A diploid represents two points in the haploid fitness landscape - with one fitness value. • Evolution forms a generalization about the typical fitness of solutions found between the two haploid genomes. • The variation operators can then be seen to alter the bounds of the generalizations. • Recombination can do this more efficiently than mutation alone.

23. Search Dynamic

26. Dominance • Numerous dominance schemes have been proposed in the EA literature. • Under the Baldwin effect view, dominance is another mechanism through which to vary the amount of learning occurring. • That is, the more dominated genes there are, the more bias there is in the fitness level of the generalization represented by the diploid. • An extreme but simple case is to evaluate only one of the haploid genomes, chosen at random.

27. Performance

28. Conclusions • Diploid representations in Evolutionary Computing are not new – nor widely used. • A new theory for the evolution of the haploid-diploid process seen in nature’s diploids suggestions a rudimentary form of learning. • Evolution appears to use diploids to generate generalizations in the underlying haploid fitness landscape – not points. • Results from a simple haploid-diploid EA suggests this may be useful in artificial systems.