How does Google Maps´ "optimizeWaypoints" solve Travelling Salesmen?

Question

I want to solve a Travelling Salesman Problem like Google Maps does in its DirectionsRequest with request.setOptimizeWaypoints(true);. It orders some Waypoints in a route so that the travelling-costs are minimal.

My question: Does anybody know which algorithm stands behind it? Any heuristic? Could not find any information by google, so far.

I informed myself and found a lot of insertion-heuristics, nearest neighbour, and so on... Or is it an exact solution procedure?

Answer 1

The Wikipedia page on the Travelling Salesman Problem references a number of algorithms for finding solutions. (But unless N is small, avoid the "exact" algorithms!)

According to this post from a Google employee, the source code for the Googles route calculation algorithms is available here:

• http://code.google.com/p/or-tools/source/browse/trunk/examples/cpp/tsp.cc
• http://code.google.com/p/or-tools/source/browse/trunk/src/constraint_solver/routing.h

... but it is not entirely clear if this is the "production" code for Google Maps.

From a comment in the source code:

// Solving the vehicle routing problems is mainly done using approximate methods
// (namely local search,
// cf. http://en.wikipedia.org/wiki/Local_search_(optimization)), potentially
// combined with exact techniques based on dynamic programming and exhaustive
// tree search.

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This general issue (Google Maps vs TSP) is also discussed in various other SO questions.

References:

• Optimal map routing with Google Maps
• Travelling Salesman with Google Maps API or any other
• What is a practical solution to the Travelling Salesman prblem, using Google Maps?