OT: Nonlinear Approximation

[Bill Denney]

So this is a bit off topic, but I've looked for a while and I think that I 
just don't know the right way to search for this, and someone on the list 
may know a better way to do it.

I've got a device with four tips that can access points on a 2d surface 
like

1 2 3 4
.......

where by that I mean it hits the first dot then it hits the third dot then 
the fifth then the 7th.  If I want to hit the first then the second, I 
have to move one unit to the left.  If I want to hit the first then the 
first on the next row, I have to move one row down and two units left. 
After the 4th access then the first tip is used again (so it will be to 
the left by seven from wherever the 4th hit is).

Now, what I have is a matrix of spots that I need to hit and I want to 
move through the points as quickly as possible.  This is generally the 
travelling salesman problem I think, but it's nonlinear.

Essentially, I think that this is best broken up into two problems:

1) find the sets of 4 hits to do at a time then
2) connect those sets by a best path.

My first attempt was a simple greedy search, and it (predictably) didn't 
work too well.  Does anyone have any suggestions on how to best accomplish 
this or any resources to look into for it?

Thanks,

Bill

--
The decision doesn't have to be logical, it is unanimous.
  -- unknown



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