One fitness function that ties distant indices is the sum of the xor (or the complement of the xor) of the index's value and the value of the index that is its inverse mod p in the field mod p where p is prime (p is also the number of bits in the vector btw). Hopefully some indices will have inverses that are close to themselves and some that are distant. If I include 0 it will trivially be its own inverse.
The cool thing about this is that the indices are tied to each other in a predictable way that is well known. This way someone (possibly me) could conduct an experiment to see if this property of GEP that I've talked about in other posts is true (its ability to encode knowledge about distantly related bits in a bit vector). Obviously it can do some encoding of knowledge, but I've come across this one a couple of times in papers and I think that GEP may have some luck with it.
I could possibly prove something about GEP this way. I have an interest in formalizing GEP and studying its dynamics, and if nothing else that would be a really cool paper. More likely it will be just one small part of my masters thesis if I include it (because it is related to the types of problems I think BPGEP can solve well), maybe as part of the justification.
To clarify (slightly) I am talking about the multiplicative inverse not the additive one (which is a more boring relationship for this situation). Also, it is 1 that is its own inverse, as obviously 0 doesn't have a multiplicative inverse in a field as it is the additive identity.
ReplyDeleteSo how fit is my function for a long distance relationship with Tyler?
ReplyDeleteHehehe...thanks for sharing your blog!
I can only suggest that you explore the solution space created by the fitness function, and if the solutions are not good enough, change the function.
ReplyDelete