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?