I'm trying to find an app that will automate the arduous task of finding the most efficient way to visit multiple destinations in a single trip. I know that's a little vague, so I'll elaborate with an example.

I'm currently in the early stages of planning a trip (ex-US) to China, Mongolia, Russia (Siberia), Laos, Myanmar, Bhutan and Nepal. The key is to figure out the ideal order to visit the countries to minimize the total number of flights (and minimize backtracking).

I recently did the same thing for another ASEAN trip and determining the order of countries took a lot of time to figure out.

Does such a tool exist? Any suggestions about how to automate this task?