I've a problem where I've a complete digraph \(G\) and edge weights \(0 \leq w_i\leq 1\) s.t. the weight of each path is the multiplication of the edge weights on that path. The objective is to select a maximum weight digraph - where the weight is the sum of the weights of all the paths in the digraph - s.t. there's only one edge between two nodes.
Is this a known problem (for instance maybe some variant of feedback arc set)? If it is not known, are there any problems that are related to it?