1. Haploid-Diploid Evolutionary Algorithms
SEX
A Social Interaction in Complex Intelligent Systems
Haploid-Diploid Evolutionary Algorithms
Larry Bull
UWE

2. Evolutionary Computing

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

4. Bacteria
Conjugation :

5. Eukaryotes
F’ ≠ F
F = f(A+B)

6. 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.

7. 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.

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

9. 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.

11. Simple Haploid-Diploid Algorithm

12. NK Model: Tuneable Landscapes
- 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

13. 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.

14. NK Results

15. Random Boolean Networks
1 means active/expressed
0 means inactive/unexpressed
R genes (R=4)
B connections (B=2)
B1 B2 St+1
Each gene considers B connections as inputs from other genes to an assigned Boolean function, transiting to the output state per discrete update cycle.

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

17. 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.

18. 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.

19. RBNK Results

20. 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.

21. 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.

22. Search Dynamic

23. 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.

24. Performance

25. 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.