Dissertation Deposition
I deposited my dissertation today.
Click here to see the final version (single spaced for easy reading).
Red Dots, Blue Dots
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 
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
The Fundamental Problem with the Building Block Hypothesis (new manuscript)
Abstract: Skepticism of the building block hypothesis has previously been expressed on account of the weak theoretical foundations of this hypothesis and anomalies in the empirical record of the simple genetic algorithm. In this paper we focus on a more fundamental cause for skepticism—the extraordinary strength of some of the assumptions undergirding the building block hypothesis. As many of these assumptions have been embraced by the designers of so called “competent” genetic algorithms, our critique is relevant to an appraisal of such algorithms. We argue that these assumptions are too strong to be acceptable without additional evidence. We then point out weaknesses in the arguments that have been provided in lieu of such evidence.
What Are GAs Good For?
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.
