[Push] Opcode Propagation & Crossover

[Rud Merriam]

I did run with over 2000 generations with a maximum points of 20. There was
no mutation because I was trying to isolate a problem (which turns out to be
due to something wrong in my mutation processing). The population size is
200. 

It appeared that the set of opcodes appearing in the programs was getting
smaller. Originally the program were diverse but now there were programs
that had repetitions of opcodes. 

When I see things like this I wish I were more conversant with the
literature and not just playing with Push because I find it interesting.
Perhaps this is a known effect. But I decided to think it through.

Say you start with the two program (A B) and (C D). When crossover is
performed it is 50% whether A or B is chosen and 50% whether C or D is
chosen. So there is a 25% chance, to get specific, that B will replace C
during crossover. Assume that happens. Now perform crossover on (A B) and (B
D) in the next generation. Now there is 25% chance of D being replaced by B.
That looks to me like what is happening in my run of many generations. It is
beyond my math ability to determine how this works with much larger
programs, more diversity, etc. But it seems to suggest that larger
populations with short generational runs would be more successful. Which is
what Lee has implied recently in emails.

This makes me question how I have implemented crossover. As illustrated
above I am allowing B to replace either C or D. Similarly A can replace C or
D. Perhaps A should only be able to replace C, and B replace D? I am
thinking about the illustration of biological crossover which occurs at the
same point in both genes. Perhaps in GP or Push, at least, the crossover
point should be at a similar point? For instance, if one program is 20
points long and the crossover is at 15, a point 3/4 of the way in the other
individual should be selected? 

I've looked at some interesting GP websites but they illustrate it using
S-expressions which are not directly translatable to Push, leaving me a bit
uncertain at times on how to proceed.
 
 - 73 - 
Rud Merriam K5RUD 
http://mysticlakesoftware.com/

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