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I recently ran across the following problem:

There is a complete graph with edge lengths and vertex weights. The edge lengths obey the triangle inequality. There is a source node S. Find the lowest cost tour in the graph where the cost of tour is the total energy expended, that is, when a node is visited on the tour we pick up the weight from there and add to the objective that weight times the sum of the edge lengths until we get back to S.

I wonder if this TSP variant has a name, and I wonder how would you go about solving it?

LaszloLadanyi
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  • TSP burteforce in O(n!) or TSP DP solution in O(n^2*2^n) can work here with minimal modification on cost calculation – Photon Dec 04 '21 at 07:01
  • Yeah, but I'd like to solve the problem somewhat sooner than the end of the universe :-). I'm not even sure if a variant of the Christofides algorithm would work. The cumulative cost is really nasty. – LaszloLadanyi Dec 04 '21 at 22:35

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