Robert Bosch has created a fascinating series of instances of the traveling salesman problem (TSP) that provide continuous-line drawings of well-known pieces of art. Techniques for developing such point sets have evolved over the past several years through work of Bosch and Craig Kaplan.

One of Bosch's instances is the 100,000-point set for the Mona Lisa TSP Challenge. Additional instances range in size up to 200,000 cities, providing a difficult test for TSP solution methods. The data sets are specified in TSPLIB format. We thank Bob for making these beautiful problems available to the research community.

Original Art Data Set Cities da Vinci's Mona Lisa mona-lisa100K.tsp 100,000 van Gogh's Self Portrait 1889 vangogh120K.tsp 120,000 Botticelli's The Birth of Venus venus140K.tsp 140,000 Velazquez's Juan de Pareja pareja160K.tsp 160,000 Courbet's The Desperate Man courbet180K.tsp 180,000 Vermeer's Girl with a Pearl Earring earring200K.tsp 200,000

The following papers discuss the mathematics behind the selection of city locations for these TSP Art instances.

Robert Bosch, Opt Art, Math Horizons , February 2006, pages 6--9.

, February 2006, pages 6--9. Craig Kaplan and Robert Bosch, TSP Art, Renaissance Banff: Bridges 2005: Mathematical Connections in Art, Music and Science , pages 301-308.

, pages 301-308. Robert Bosch and Adrianne Herman, Continuous Line Drawings via the Traveling Salesman Problem, Operations Research Letters , 2004, Volume 32, pages 302--303.

, 2004, Volume 32, pages 302--303. Ivars Peterson, Artful Routes, Mathematical Association of America Online, January 3, 2005.

Pretty examples of other TSP drawings can be found on Robert Bosch's TSP Art page and on the page of Craig Kaplan.

The best known results for the TSP Art instances are given in the table below. The tour length, given in the Best Tour column, is a link to the tour in TSPLIB format. I would be happy to post any improvements you find.