Travelling Salesman with multiple salesmen?

Question

I have a problem that has been effectively reduced to a Travelling Salesman Problem with multiple salesmen. I have a list of cities to visit from an initial location, and ha

Answer 1

Have a look at this question (562904) - while not identical to yours there should be some good food for thought and references for further study.

Answer 2

As mentioned in the answer above the hierarchical clustering solution will work very well for your problem. Instead of continuing to dissolve clusters until you have a single path, however, stop when you have n, where n is the number of salesmen you have. You can probably improve it some by adding in some "fake" stops to improve the likelihood that your clusters end up evenly spaced from the initial destination if the initial clusters are too disparate. It's not optimal - but you're not going to get an optimal solution for a problem like this. I'd create an app that visualizes the problem and then test many variants of the solution to get a feel for whether your heuristic is optimal enough.

In any case I would not randomize the clusters, that would cause the majority of the clusters to be sub-optimal.