Travelling Salesman

Find the shortest possible route that visits each city exactly once and returns to the origin city.

Given a set of cities \( \{C_1, C_2, \dots, C_n\} \), the task is to determine the optimal tour, represented as a permutation of the cities:

\[ \sigma = (C_{\sigma(1)}, C_{\sigma(2)}, \dots, C_{\sigma(n)}, C_{\sigma(1)}) \] where \( \sigma(i) \) represents the position of city \( C_i \) in the tour, and the tour ends at the starting city \( C_{\sigma(1)} \).

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