Since we have a perfect ANN for path length of 3 & 4 steps, but longer path 
lengths always topped out in the high 80's or low 90 percentages, my conclusion 
is that evolution is the bottleneck.  It is now proven that the ANN 
configuration is capable of performing this task.  I think it is worth some 
effort to see if the evolution process can be improved.

Currently, we have no genetic operations that move sequences of floats to 
alternate locations.  We have one and two point crossover, but a sequence of 
floats can be substituted for another, it cannot be shifted to a different 
place in the chromosome.

Instead of the clumsy phrase "sequence of floats", let me call that a "gene". 
This is the definition of "gene" used by Richard Dawkins.  A biological 
chromosome is very long, hence a group of 100 or even 1000 units tends to stay 
together.  Even though the chromosome may break in 100 places as a result of 
mating, since the length of a chromosome is in the millions, the breakpoints 
are quite far apart.  When applies to our software, a "gene" can be defined as 
any group of consecutive floats which is much shorter than the total chromosome 
length.

In nature, these genes can shift position.  This results from several different 
genetic "operations" that occur.  Sometimes a gene is splice erroneously far 
from where it belongs.  Sometime a gene is reversed.   Sometimes a gene is 
removed, and not replaced, thereby shifting the rest of the chromosome.  Those 
  operations are much less common than crossover, but they do occur.

Hence, I think that it's worth the effort to add one or two additional genetic 
operators to the code to enable genes to move to other parts of the chromosome.
Perhaps I will pick a gene at random and move it to another (random) position.

m

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