What is Neutral?

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What is Neutral?

• Neutral Changes and Resiliency
• Terence Soule
• Department of Computer Science
• University of Idaho

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The experiments

• Gene/exon selection
• Introns and exon selection
• Effects of operators

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Experiment 1

• Tree based, generational GP
• Functions
• Terminals/Genes 0.5, 1.0
• Fitness difference from 10
• Both terminals are exons. Is one selected?

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Gene/Exon Choice
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Average Fitness
Average fitness improves after crossover.
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Resiliency

• A measure of expected fitness change as a
  function of genotype change.
• Resilient individuals are less likely to change
  fitness or have a smaller average fitness change
  in response to genotype changes (crossover and
  mutation).
• Similar to the idea of effective fitness, but
  more general.

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Experiment 2

• Tree based, generational GP
• Functions
• Terminals/Genes 0, 1, 4
• Fitness difference from 40
• Now there are two exons and an intron. What is
  selected?

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Number of Genes
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Resiliency
10
Ratio of 1s to 4s
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Results Experiment 2

• Changes dont affect current fitness Are they
  Neutral?
• Changes affect expected fitness of the next
  generation increase (average) resiliency

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Experiment 3

• Variable length, linear encoding, generational
• Genes 0, 1, 4
• Sample individual 010041014
• Fitness difference of sum of genes from 54

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Experiment 3 - Crossover

• Proportional crossover select two random points
  per parent.
• Constant crossover length of crossed region is
• 2 50 of the time
• 4 25 of the time
• 8 12.5 of the time

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Genes Constant Crossover
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Genes Proportional Crossover
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Mutation Constant Crossover

• Probability P of changing a gene to another
  value 1 to 0, etc.
• More genes (including 0s) greater chance of
  mutations.

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Growth constant crossover
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Conclusions

• Many neutral changes can be explained in terms
  of resiliency
• 1.0 ? two 0.5s (selecting exons)
• 4s ? four 1s and four 1s ? one 4s
• Increasing 0s (increasing introns)
• Operator choice significantly affects these
  changes
• Proportional versus constant crossover
• Mutations
• Per node versus per individual rates are
  significant.

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Discussion

• Types of changes
• 1st order affect fitness
• 2nd order affect expected fitness of offspring
  (resiliency)
• 3rd order? - affect expected fitness of Nth
  generation? Affect ability to respond to
  environmental changes?
• Any consistent pattern of change has an
  evolutionary explanation(?)
• Its possible to predict some changes by using
  the idea of resiliency.
• Do these changes affect search?

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Thank YouQuestions?
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Bibliography

• Exons and Code Growth in GP Genetic Programming
  5th European Conference, EuroGP-2002, Springer
  LNCS2278, 2002 .
• Solution Stability in Evolutionary Computation
  Proceedings of the 17th International Symposium
  on Computer and Information Sciences, CRC Press,
  2002.
• Operator Choice and the Evolution of Robust
  Solutions Genetic Programming Theory and
  Practice, Kluwer, 2003.