1. Kalyanmoy Deb David E. Goldberg
10/13/10
An Investigation of Niching and Species Formation in Genetic Function Optimization
Kalyanmoy Deb
David E. Goldberg
Genetic Algorithms

2. What is the paper about? Multimodal function optimization
10/13/10
What is the paper about?
Multimodal function optimization
What behavior would be like?
Find and climb the highest peak?
Have members of the population on every peak? How many?
How do we get the behavior we want:
Niching
Fitness sharing
Conclusions
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3. Where are we now? DeJong used crowding in 1975
10/13/10
Where are we now?
DeJong used crowding in 1975
Create niches by replacing existing strings according to their similarity with other strings in the population
When selecting an individual to replace: C_f (crowding factor) individuals are randomly picked from the population and the most genotypically similar to the new individual is replaced
Note that only a proportion G (generation gap) of the population reproduces every gen
Goldberg and Richardson: Fitness sharing schemes. Share according to similarity in
Genotypic space - bit string space
Phenotypic space – decoded parameter space
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4. Phenotypic Sharing Sharing function Sh(d): = 1 – (d/s)^a if d < s
10/13/10
Phenotypic Sharing
Sharing function
Sh(d):
= 1 – (d/s)^a if d < s
= if d >= s
Good results on a couple of functions
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5. How do we get s in phenotypic space?
10/13/10
How do we get s in phenotypic space?
D can simply be euclidean distance
We want s to divide the search space in such a way as to be half the distance between peaks
S = (Xmax – Xmin)/2q where q is the number of peaks
Genetic Algorithms

6. How do we get s in genotypic space?
10/13/10
How do we get s in genotypic space?
D can simply be hamming distance
We want s to divide the search space in such a way as to be half the distance between peaks
S = 0.5 (L + z * sqrt(L))
z* is the normalized bit difference corresponding to 1/q of the space
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7. 10/13/10
Results (F1)
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8. 10/13/10
Results (F1)
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9. 10/13/10
Results (F2)
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10. Mating restrictions Crossover produces individuals between peaks
10/13/10
Mating restrictions
Crossover produces individuals between peaks
Restricting mating
Find a mate for individual i
Choose random individual, j, from population
If distance (i, j) < sigma  crossover
Else
Choose another individual j, at random
Distance can be phenotypic or genotypic
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11. 10/13/10
Results
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12. Conclusions
We can maintain proportional populations on multi-peak functions through fitness sharing
We can improve performance meaning reduce the number of population members in-between peaks by using mating restrictions
To do this on a specific application, we would need to
Know the number of peaks
The distance between peaks
This may not be possible, so we would have to guess at the value of the s parameter (sigma share) in the formula
Fitness sharing to move members away from an area of the search space will be useful in other ways (Co-evolution, for example)
Genetic Algorithms