This classic optimization problem can be very simply stated --- a salesman has to visit N cities, and wants to take the shortest possible route. Here, the cost function is the length of the tour.
The change a configuration (a particular tour) is not as simple as a single spin flip in the spin glass problem, or moving an element from one side to the other in the graph partitioning problem.
Each tour can be presented as a permutation of the numbers 1 to N, which represent the cities. The simplest change to the tour is to swap pairs of cities, and measure the change in the tour path.