Traveling Salesman Problem

The Traveling Salesman Problem is one of the most intensively studied problems in computational mathematics. These pages are devoted to the history, applications, and current research of this challenge of finding the shortest route visiting each member of a collection of locations and returning to your starting point.

Screen shot of NL tour
Path in Gaia DR2 tour
Cycling tour to 57,912 Dutch monuments. How to visit 1.33 billion stars.

Screen shot of TSP DIY app front page
Optimal Tours
Traveling Salesman Problem DIY
Web app for learning/teaching TSP solution methods.
Optimal Tours
Math Encounters, August 4, 2021
National Musuem of Mathematics

TSP Postcards
Connecting the Dots in the TSP
TSP: Postcards from the edge of Impossiblity
IFORS Distinguished Lecture
EURO 2019, Dublin
Connecting the Dots in the TSP
MAA Invited Address
2018 Joint Math Meetings

Screen shot of UK Pubs tour
Screen shot of US50K points
Optimal crawl to 49,687 pubs in the UK. Visit 49,603 historic sites in the US.

TSP Tutorial in Python
Nice intro to the TSP by Peter Norvig
Cutting-plane method YouTube video (in Siri's voice)
Pokemon Go Tours
Shortest routes to Catch 'em All
Tour for Extra Milers
Drive to all 3100 US county seats
Queen of College Tours
Optimal road trip to visit 647 colleges
Hiking Tour of Austria
Get a view of 100 mountain peaks
50 USA Landmarks
Dicussion of wildly popular USA tour
Scientific American
Short piece on Yogi Berra and the TSP
Travelling Salesman
Thriller movie centered around a solution of the TSP
Mona Lisa TSP
$1,000 Prize for a 100,000-city challenge problem.
Solution of a 85,900-city TSP.
Iowa Tour
Optimal route for a 99-county campaign tour.

In Pursuit of the Traveling Salesman: Mathematics and the Limits of Computation, available for $14.27 @ Amazon. News items can be found on the book's Facebook Page. Concorde TSP app for the iPhone and iPad avaiable on the Apple App Store. It's free!
The Traveling Salesman Problem: A Computational Study by Applegate, Bixby, Chvatal, and Cook. Description of the techniques we use to compute lower bounds on the lengths of all TSP tours.
Optimal solution for visiting all 24,978 cities in Sweden. Tour has length approximately 72,500 kilometers. The TSP was featured in a contest run by Proctor and Gamble in 1962. The challenge problem had 33 cities.
A graphical user interface available for Concorde on Windows' platforms. The Concorde TSP solver is used in a genome sequencing package from the National Institutes of Health.
A collection of 25 TSP challenge problems consisting of cities in Argentina through Zimbabwe. Pages describing some of the history of the TSP as a mathematical and computational challenge.

The work described here is supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) and the Department of Combinatorics and Optimization at the University of Waterloo.

Contact: William Cook (