Computer Science Genetic Algorithms10/13/10 1 An Investigation of Niching and Species Formation in Genetic Function Optimization Kalyanmoy Deb David E. Goldberg

Computer Science Genetic Algorithms10/13/10 2 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

Computer Science Genetic Algorithms10/13/10 3 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

Computer Science Genetic Algorithms10/13/10 4 Phenotypic Sharing Sharing function Sh(d): –= 1 – (d/s)^a if d < s –= 0 if d >= s Good results on a couple of functions

Computer Science Genetic Algorithms10/13/10 5 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

Computer Science Genetic Algorithms10/13/10 6 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

Computer Science Genetic Algorithms10/13/10 7 Results (F1)

Computer Science Genetic Algorithms10/13/10 8 Results (F1)

Computer Science Genetic Algorithms10/13/10 9 Results (F2)

Computer Science Genetic Algorithms10/13/10 10 Mating restrictions Crossover produces individuals between peaks Restricting mating

Computer Science Genetic Algorithms10/13/10 11 Results