>>11554538First off, cool idea, ignore all the pseuds disparaging you. Physical computation and purpose-built computation devices are very cool and it's nice that you're trying to approach a problem like TSP with them.
However, right off the bat you should be more specific about your approach. Give examples, give details, etc. I'm going to assume your idea is to just wire a bunch of resistances together, where nodes = cities, and have a current source connected to two of those nodes.
If my assumption is correct, then your idea doesn't seem to make a lot of sense, because the voltage measured at two points (A and B in my picture) will be influenced by all the "paths" the electrons can take there. If instead your idea is to measure the voltage before and after each resistance, then it should be intuitive that you're not really gaining any information VS simply plotting out the circuit on a piece of paper (because all you're doing is configuring some resistances and measuring a quantity that scales linearly with it, as per Ohm's law).
Assume that the circuit you plan to build (or simply draw) is the one in the picture. I have omitted the labels for all cities except A and B. Notice how if you start at A, your approach will tell you to take the 1 -> 2 -> 3 path to B. Since the point of TSP is to have a closed loop, and since you can't repeat edges, this then forced you to go back from B to A via 1000 -> 1000. The total cost of this is 2006.
But it should be easy to convince yourself that the 2006 closed path isn't the best one: why not simply go from A to B and back to A through 1 -> 10 -> 3 -> 10, for a total cost of 24?
