The Traveling Salesperson Problem is one of the most well-studied problems in applied mathematics and theoretical computer science. The goal is to choose a shortest round trip visiting a given set of sights. It is very challenging to find an optimal or near-optimal solution, since the number of possible routes grow quickly with the number of sights.
The problem has many applications in different areas besides route planning problems, e.g. genome mapping or the design of computer chips. Many algorithms in the field of combinatorial optimization have been developed to find better solutions to the Traveling Salesperson Problem.
Try it yourself! How good is the best tour that you can find?