Travelling Salesman (Demo)

Find the shortest possible route that visits every city exactly once and returns to where it started.

Given cities \( \{C_1, C_2, \dots, C_n\} \), a tour is a permutation \( \sigma \) of those cities:

\[ \sigma = (C_{\sigma(1)}, C_{\sigma(2)}, \dots, C_{\sigma(n)}, C_{\sigma(1)}) \]

The goal is to minimize the total travel distance \( D \), the sum of the distances between consecutive cities in the tour.