Screencast Presentation: An Introduction to the Generative Fixation Hypothesis

February 13, 2010 at 7:01 pm (Bit Frequency Visualization, generative fixation, genetic algorithms, hyperclimbing, symmetry-analysis) ()

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Red Dots, Blue Dots

June 29, 2009 at 7:02 pm (Bit Frequency Visualization, epistasis, generative fixation, symmetry-analysis)

In this blog entry I’d like to showcase just one of a number of remarkable findings that comprise the basis for the generative fixation hypothesis—a new explanation for the adaptive capacity of recombinative genetic algorithms.

Consider the following stochastic function which takes a bitstring of length \ell as input and returns a real value as output.

fitness(bitstring)
  accum = 0
  for i = 1 to 4
     accum = accum + bitstring[pivotalLoci[i]]
  end
  if accum is odd
     return a random value from normal distribution N(+0.25,1)
  else
     return a random value from normal distribution N(-0.25,1)
  end

The variable pivotalLoci is an array of four distinct integers between 1and \ell which specifies the location of  four loci—let’s call them A, B, C, D—of an input bitstring that matter in the determination the bitstring’s fitness. These four loci are said to be pivotal. Read the rest of this entry »

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What Are GAs Good For?

May 23, 2008 at 7:50 pm (QTL, combinatorial optimization, epistasis, genetic algorithms, genetics, symmetry-analysis) (, , )

Researchers studying the foundations of genetic algorithms have not, to the best of my knowledge, identified a non-trivial computational problem that a simple GA can solve robustly and scaleably (I’ve previously raised this issue here) . In my opinion, this singular fact is the most clear evidence for the inadequacy of current paradigm within which we understand/study the adaptive capacity of GAs—the question of what GAs are good for is, after all, intimately related to the question of how GAs work.

In a draft of one of my dissertation chapters I identify a hard computational problem and show that a GA can solve it robustly and scalably. Remarkably, this problem is closely related to a hairy statistical problem in computational biology. How might a GA leverage this kind of computational ability to perform adaptation? I’ll be presenting my theory about this in future chapters. The idea behind this theory is delightfully simple. Presenting it formally, however, is a another story. Stay tuned.


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