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An Investigation of Niching and Species Formation in Genetic Function Optimization

Kalyanmoy Deb David E. Goldberg. An Investigation of Niching and Species Formation in Genetic Function Optimization. What is the paper about?. Multimodal function optimization What behavior would be like? Find and climb the highest peak?

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An Investigation of Niching and Species Formation in Genetic Function Optimization

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

  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 Genetic Algorithms

  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 Genetic Algorithms

  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 Genetic Algorithms

  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 Genetic Algorithms

  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 Genetic Algorithms

  7. Results (F1) Genetic Algorithms

  8. Results (F1) Genetic Algorithms

  9. Results (F2) Genetic Algorithms

  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 Genetic Algorithms

  11. Results Genetic Algorithms

  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

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