I have to write a program that uses the shortest path that starts at a "home" city and goes to 3 other cities and back "home" again. I have been reading for a few hours about a good way to solve this problem. It seems to be a variation of the traveling salesman problem. I have read about using the dijkstra algorithm but that seems too complicated for this problem. I am using the cities Atlanta, New York, Chicago, and Los Angeles (Atlanta being "home") and want to use the actual miles between the cities in the program. My question is what would be the best way to tackle this problem? I am not asking for the code just how to get started. I am new to Java but am ok with C++.
I have made an undirectional graph with the miles between cities but I am unsure about where to go from here.