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 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 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*. Continue reading “Red Dots, Blue Dots”