New directions in TSP research (website hosted by Georgia Tech). The first picture shows a TSP tour on a set of points resembling "Mona Lisa". The second picture (map of the United States) is representative of a more typical TSP problem (very large set size).
 The TSP is an NP-hard graph optimization problem, which requires innovative algorithmic solutions such as the Christofides algorithm or ant colony optimization (ACO). An example from the ACO literature:
Dorigo, M. and Stutzle, T. Ant Colony Optimization: Overview and Recent Advances. In "Handbook of Metaheuristics", M. Gendreau and J.-Y. Potvin eds, International Series in Operations Research and Management Science, Springer, Berlin (2010) Chapter 8.
In a response to this post, I received this response from Minus-Five:
"Interesting article, but Christofides’ algorithm (or its analysis) is not a novelty: What’s actually new here is the discovery that it can be improved, if only by an epsilon (so far)". Klarreich, E. Computer Scientists Find New Shortcuts for Infamous Traveling Salesman Problem. Wired Science, January 30 (2013).