The Mona Lisa TSP challenge

Find a tour of the 100,000-city Mona Lisa instance shorter than 5,757,191, unbeaten since 2009, or prove that tour optimal.

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1	# The Mona Lisa TSP challenge
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3	Robert Bosch's 100,000-city traveling salesman instance draws Leonardo's Mona Lisa as one continuous line. The best tour has stood since March 2009, it is only 107 units above a proven lower bound, and a 1,000-dollar prize awaits the first person to find a shorter one.
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5	## Problem
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7	The instance `mona-lisa100K.tsp` lists 100,000 points with integer coordinates in TSPLIB format. The distance between two points is their Euclidean distance rounded to the nearest integer (TSPLIB `EUC_2D`). Find a tour that visits every point exactly once and returns to the start with total length below 5,757,191, or prove that no tour is shorter than 5,757,191, which would make the current tour optimal.
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9	## Background
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11	Bosch created the point set in February 2009 with techniques for continuous-line drawings that he and Craig Kaplan developed over several years (see also Bosch and Herman, 2004). The Waterloo TSP pages note that an optimal tour for this instance would set a new world record for the TSP; for comparison, the 85,900-city instance `pla85900` was solved with a certified optimal tour (Applegate et al., 2009). To revive interest after three years without a better tour, the pages offered a 1,000-dollar prize for the first tour shorter than 5,757,191.
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13	## What is known
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15	- Best tour: 5,757,191, found on 17 March 2009 by Yuichi Nagata with his genetic algorithm. Before it, Keld Helsgaun, Changxing Dong and coauthors traded improvements with LKH in February and March 2009.
16	- Best lower bound: 5,757,084, established on 27 July 2012 with Concorde, so the gap is 107 units (0.0019%).
17	- The bound came from a long series of Concorde runs: truncated branch-and-cut searches with artificial upper bounds, each adding cutting planes and pushing the bound up by a few units, the largest totalling about 30 CPU-years. As early as January 2011 the log concluded that new techniques would be needed to finish the job.
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19	## What would count as progress
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21	- A tour in TSPLIB tour format of length at most 5,757,190, which would win the prize. A script checks that it is a permutation of the 100,000 points and recomputes its rounded length in well under a second.
22	- A lower bound above 5,757,084, backed by a certificate that others can check, such as the cuts and branching tree that produce it. Raising the bound to 5,757,191 would prove Nagata's tour optimal; this is a separate and much harder kind of progress than a better tour.
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24	## References
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26	1. R. Bosch and A. Herman (2004). Continuous line drawings via the traveling salesman problem. Operations Research Letters 32, 302–303. https://doi.org/10.1016/j.orl.2003.10.001
27	2. D. L. Applegate, R. E. Bixby, V. Chvátal, W. Cook, D. G. Espinoza, M. Goycoolea and K. Helsgaun (2009). Certification of an optimal TSP tour through 85,900 cities. Operations Research Letters 37, 11–15. https://doi.org/10.1016/j.orl.2008.09.006
28	3. Y. Nagata and S. Kobayashi (2013). A powerful genetic algorithm using edge assembly crossover for the traveling salesman problem. INFORMS Journal on Computing 25, 346–363. https://doi.org/10.1287/ijoc.1120.0506
29	4. D. L. Applegate, R. E. Bixby, V. Chvátal and W. J. Cook (2006). The Traveling Salesman Problem: A Computational Study. Princeton University Press. https://press.princeton.edu/books/hardcover/9780691129938/the-traveling-salesman-problem
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31	## Source
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33	Imported from [Waterloo TSP pages, Mona Lisa TSP Challenge](https://www.math.uwaterloo.ca/tsp/data/ml/monalisa.html), curated by William Cook. Open according to the source as of 2026-10-20. The statement above is written in our own words; see the source for the original wording, history and discussion.