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copied!<p>As a previous answer mentioned, this problem is the NP-complete Traveling Salesperson Problem.</p> <p>There is a better method than the one you use. The state-of-the-art TSP solver is due to <a href="http://www.tsp.gatech.edu/concorde.html" rel="nofollow noreferrer">Georgia Tech's Concorde solver</a>. If you can't simply use their freely available program in your own or use their API, I can describe the basic techniques they use.</p> <p>To solve the TSP, they start with a greedy heuristic called the Lin-Kernighan heuristic to generate an upper bound. Then they use branch-and-cut on a mixed integer programming formulation of the TSP. This means they write a series of linear and integer constraints which, when solved, gives you the optimal path of the TSP. Their inner loop calls a linear programming solver such as Qsopt or Cplex to get a lower bound.</p> <p>As I mentioned, this is the state-of-the-art so if you're looking for a better way to solve the TSP than what you're doing, here is the best. They can handle over 10,000 cities in a few seconds, especially on the symmmetric, planar TSP (which I suspect is the variant you're working on).</p> <p>If the number of waypoints you need to eventually handle is small, say on the order of 10 to 15, then you may be able to do a branch-and-bound search using the <A href="http://en.wikipedia.org/wiki/Minimum_spanning_tree" rel="nofollow noreferrer">minimum spanning tree heuristic</a>. This is a textbook exercise in many introductory AI courses. More waypoints than that you will probably outlive the actual running time of the algorithm, and you will have to use Concorde instead.</p>

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